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His tp ries of dark ma tu er his tp rical perspec tj ve Book, chap tf r 17 R 9 7 3 . . 9 5 1 . . . J p A 0 7 9 1 P H VSICAL l a m R E r o V n I E The W the : etters to percent. 84 percent, LETTERS TO THE EDITOR

  1. His tp ries of dark ma tu er his tp rical perspec tj ve Book, chap tf r 17 R 9 7 3 . . 9 5 1 . . . J p A 0 7 9 1 P H VSICAL l a m R E r o V n I E The W the : etters to percent. 84 percent, LETTERS TO THE EDITOR within the experi- . 0 4 , 13. + 149 2 V O 21. 9 L t 4 UBLICA TION of brief reports of important . U 1 ze M mass . 47, and at o E ' a t cross sections of the s that . 73, t i n a increased . department. p i h t N y o disappear s U w i ~ c M r o be less than one percent s 7 h H p m ~ s r i E 0 is o a 3 percent. This y R have r to T h be secured e 5 7 1 T t h c that l h e o o s t e d W i t a B a n t g ~ e ofissue. e o a d a The absorbing r a m r o d of Editors t b p e for this department a t abundance isotopes y addressing a i p y n p i o r a e . n r m 1 s e Phys. Rev. 71, discoveries n a those calcu- 2 ~ ~ r s t h l k e gas y o x u a p proof A l ¹ c t first that d r being the e d o P s t h w o s o m R n e e a o e m p t d s not hold s I . t abundances l a e 0 @ still t e t e L 1, r 5 x o this by the correspondents. i l i d Agnew, other isotopes were estimated o c l ~ m 1 e be sent to the authors. s five r e ~ u r . d r w t e 9 a s h s 6 h 1 r a t h e reappear at mass 4 0 e e 9 i e n the J. Dempster, 0 words t s 4 1 s u o r b e u mental 8 e n l e well i f responsible for k a w (The upper limit l n d s Cobas, high, i isotope at mass c o t n e u e g Hughes, s l m s d - i p u n a p i e n s have i r l n a e t t h c u p . n These values, 2 the e otherwise r A g e region of the r o e t C e c h Kore and l . o e been e m s m of the neutron s n Horn, and m e t n w u h t n n e s a e i s s c exponentially u a t t r (for neutron . r t i 2 o o T o n e ' n t h n g h h the Seyaration s , the ratio between the unshielded l e observed e and Froman„are shown in Fig. value. ) s y t l c o of that of f a o s w neutrons. a a O p y t f V Kore, and Placzek. s u f r t e R. i e r g e c m t i s e . w over J n t , energies d l i c t u e h atomic r o l r o A s e f e d s by p e m m s p E. Lapp. l C r e e A i a . e n t i 2 2 s the d h n c t h i of about e c e s n c t . u o P m n g t r h i d e c order of n in o y i n i s c U l u n i R c a s c a approximately m g . d s Laboratory, . e s s R . l Elements c i b ) r n i o t n A e o 7 g r f . 4 a e the E s 1 Mev) increase A m q t i v 9 h h halfway a ~ L s 1 e r S P o . s T i { s H e o i r ( e t l v E 1 u R f s n e c ) h 5 r + c . results. The Johns Hopkins i v a t g 4 e r S w a s o 7 m p lated r of s H u of Galaxies r t i s s constant i n o p u h ' e g o f t , d . s s o h l e s w e e E M e . i n in c i e t Professor D. C. a e n i p l u m o r c e e f y , m c , and Froman's4 n r l t x s l o a h e c F s i o The cadmium ratio, n e e r , A d n a for d Cornell N g e r 4 i t g i D i s t . 1 that one Mr. D. B. c n r t U B o m of Hg to s The Origin , H. BETHE n u a heavier s & e p o n o n e r n w t University, n e c t d c r s i o finds g s e of a i o e t y r s t i c e t , h h ~ h e m c d e relative G s u a a e a and cadmium-shielded v wishes to express his gratitude r i c b ' features f v i n r 6 e e y Ithaca, o q e r a G. The George Washington and building of a s i m w p e n t h t University, , p e assume thy integral of p„dt during the building-up i a r by the c t t o g h h n o rapidly 22. 8 x t a r %em York a g i b t " t silver. In order to fit the calculated m u i i h n 8 r n e observed a g 4 G B t d " e , 9 n s l a . y n 1 i e n a q for the c A e e m G u o , A m a c s George R'ashiegton 1 , i constant per- M l to w s n 2 elements o o s a of of the e S pointed w r u n e f n University, c n 5 d F g X s a u e r lighter A O i b a J b the depth 1 d u O r n the u 0 n a 4 for the designing f d o r with m y a ' the r process, o helpful n u the expanding t the densities u 8 g sec. /cm'. c the ele- l r s 1 o e h i t t 8 ' a explanation a u s t s g , h h ' c m corresponding 1 e f i h b i n l i a 9 r hand, o m y 4 g it is necessary f v 8 agreement t e o o n e the n , g h b o e of us, ' various i u for many v members c r D t rather as i e g . n building-up universe e author curve of i C a n p — c a . make by u c t n e o d d i r p i v d Yann Mambrini v e concerning r r i l o e n u n r s c t o responsible e g f e o g 1 4 t e o to s s a h s at 0 t o want to discuss e s a certain ' t o the relativistic N6onr- s a / the density h s T g t t e ~ p arrested c r u t = 0, it e c t p . r o t u p and r c "unfinished i h nuclear i m n b S o the abundance u have existed in s e result of an equilib- process d is e n i helped s o n Research q r e c d u E i e d relation: e the under Contract a h can n t a H information i l by a rapid c e http://www.ymambrini.com/My_World/Physics.html s m m L i e s i equipment s d & a R. matter. p p n e g e b p i of a continuous e e e n r Davis, who c c e a i g o i n e e e n t a h s t d t e u s n s e h c n r e e the early stage of matter as a highly w Research at the Ordnance a g n K e e at a certain r r o e i y c h u a e , Zeits. f. Physik r h t l y of w r A t o expansion a t o assume that the building- n c n Laboratory o o c d of f this n o stages of its expansion. n s started r Phys. Rev. 69, 155 t the balloon t s n d d i i gas i e d m a u o n n e e is t m g m i s hypothesis r s i e b t r e u (overheated a y x c e t u o l o this n , p which c h d i l f t r p d d r i n t e e m e r i s get e c n p s o s a c g e i c with s y o - o u i o u work Phys. Rev. SV, 573 n r n J r o l Research p e e g i picture, n t o f t radiative n cosmogonical g of the . , f i w Q e n e s and temperatures and l t h a s d l down as o neutral n F i . t u c o ( n E i s e h 1 o f t p p 0 y mits r r 235 {1937); o gives us to=20 sec. u ' jt')dt i a we must n t g t s n o r l &0 Naval , s e c e u h n n This report is based s w a f University. s o p s n u e have de- l t s l = the have y t h u t m r u c s 5 t e a compressed e y f r n l r u o e e c m e l of deuterium d a e r r f m be based on these informations. r m e r c e a o X a n of the still remaining s y have Phys. Rev. 2'2, u e u x a e g e l i d l e s s . 1 H t t of n c Q t i e B 0 the s t n 4 i p r u c t the primordial u o i g prior to S Korff. and G. Placzek, , r d , s m o n of Princeton N 5 Rev. V3, 1010 (1940). time must r ) e e t u s gas was so high that no aggregation t a 2 s o n C w r n Kore and n e u i w g process of these neutrons l s v o d t t when the n e e h p n r i Natu+miss. m d nuclei, and the subsequent m s c 0 i i a ~ r h e = u u l a m i s 2 n the t n d e t have led first the gas 270 with h i . to u expansion. The a n m s t 5 h t time g t ) o e Vf. C. Bright, and Darol Froman, s & density . : s b A (2) t that b Laboratory 1 e remembered {1988)", S. 0 Since the building-up u (a) for the higher densities t n 2 5 here s i i l m m d e . ~ E. Funfer, d u i 5 t g sec. /cm'. This n e n t h o g r a o o 1 e r a n ) 0 o f p the l s & t l ' g sec. /cm' f e s o u t m e n w p o the t u o h . p of deuterons r e by the A . the temperature c d f e e s r l e o e . r y t h S a m i f t e i h t c a h universe u o a M P h m r a v f r o t o e t t u , due i neutron s 10' 'K (which h e r 111, s t r m . Bethe, Cobas. e stable elements t have h i a o so s a t {1946). w f into which o — order of magnitude n i w o h d t h p t n i a r o c never s e o h h c nuclei), present c , ' the . taking place, (b) p g t h e a A n a p A can possibly be understood r s e e o s v t u formation i u c e t e c r g H. d e r r e o e that later, this radiation e o s n x d m n n a c e e w f d just p u r A. Kor8 . e a c ) d a e r l s q b a e 0 e m ( u d the protons deuterium u s t i . 4 a e i i I t h l v 9 H. M. Agnew, u t n o d e t d a i t c r n l 1 h i T i y t a y u ment of their electric charges by P-decay. n - b g { e r relativistic e l l i o I S. a c d v r distribution v s ~ n e e v e d u h a e p of heavier o o d l N h only somewhat t r u c r h t F e o t e upper S f e . cayed, we o of r e T m ) ' h be h 7 n i u 4 i f t ~ i s 9 s e w f y of various l i a e ( e o g e n t f w t o h m r r w h e observed i s t e n Absorytion e t o u n g have been n nT4/c' b e of 3 h m later as the result of adjust- t Chicago, IQinois e e related s O s ) , 2 of matter, dissociation l gas, but rather to the time period permitted a l n atomic DRIPPER a universe d h s the slope of the abundance density of radiation t o e s that the large neutron i w o t h s n process. p s e e a n c . t i o J the e e water density. If, the density m s r , e nuclear species must depend not so much on their intrinsic y p t r h e u r A. o t the isotope at mass f a e t o t a u N r A 8 r o e b 4 l s stabilities a 9 o , the L of the original 1 n o , curve must 8 i l s a 2 was n n i d c n o a e e a d i p p i t n d ( v a x t m u u i N e d J e r a e e u by the neutrons s a c s defects) as f 8' oT4 ) l t paper' it was shown x for the b c n o n e u r e with a 4-mg space, o e i a g l d s b u s b t r i u r n n y o A o density g s d t n - e h t u a c n e p t in the form: i c o e e ls due n s x p o p s n the g r . a 1 mg per n is neglected because o n of various n o c - i — e The equations i d s s s n s v e a a a s repeated p p l r l u m p s p produced x a e Aux. The isotope at x d d s of their e r u e e i n r in the expansion t l a = y a recent in a thin layer of approximately m written f ( c a a t g s ) n be written o a ( n v w ; e e ln e w u 149. Since the alteration t could not be detected. , n; r distance h h n t N i r e n o t r n c g ' e " not very large, the experiment absorption i — in the curvature t n a s CAt ClMlKO ; u b ) sections for the nuclei of atomic weight i, and where f(t) is a a ; c 1 n n h a i d n i ( ; e d ) a t h h a a ; " e t y . i a = /, we can rewrite factor characterizing f f r e r a e 1 o o h r r t , 2, m n t t h : i e relative o b r o -2 r r ten mass spectra made with one milligram t a f u with a mass spectrum e g e 2 n an c n 3 i n 8 n i S s i n stronger a u i i t m density value. n mass b o e d t / c t r a h s o e where e decrease of h s term t and o t t a p sq. cm to a much x c 149 was so reduced l e a a p the isotope e ' n t 0 h u appears approximately o sample t r i e t r o t and h c o G r e density o p s together e high o x s 8 r T' p impurity f o h y t w l e of i , s t h 1 intensity r e t . i g v m two absorbing n e i F i d . gadolinium mass s T i t in i e h / t 5 T 0 f is shown a o h form: 803 t F i o One samarium. increased so . 1. L t o n g i e o f a h t a r f e t h l a e A t t i l v p with t e abundance BO m . 4 a showed 5 Atomic weight s l 32Wo' a 1 on m the one at y exposures, r o l t l n l or, integrating: a e e of plates f r 4 g 5 1 0 was no changes and 157 missing. the masses 147, 148, 152, and e have: long h 5 1 t o of t . e s h e e t p w equal density curve indicating o measurements t on 1 temperature o density s i - 3 c 5 in any of these e showed 5 p 32M t2. 1 s t of deuterium, a four n o i e t a h isotopes i m t d Photometric a e o r when h r f t For the time t mass 150 was found a absorption formation , o t the time a normal photographic t the densities a h t e that at p s t e a a n h is conserved w o h t t r t u permit e w ) n t s a o n m s f h o o a s u r s t o s u e These formulas result t a e c n n decreasing was several minutes. Let us r a d h e d e g t n s plus t a 149 u from u o a o p m b s x n a iso a E e 7 dropped low (protons the w 4 1 ' can be estimated e 8 ~. was n 4 e 1 I h radiation, , T p ) r e t t a m o of expansion, t of Since, in contrast of p, . t density I process The value l a m ills r o N the I '~7'~t & , in absorption. altered by neutron s e p o t o s i Samarium . l VlG.

  2. General Perspective Observing the present sky Clusters of Galaxies (1933) Rotations curves (1939) Simulating the Universe (1971) The dark halo hypothesis (1973) Observing the primordial sky The genesis of nucleosynthesis and the CMB (1948) The observation (1965) Filling the Universe with particles (1967) Measuring its composition (Novembre 1984)

  3. 3 scales of study Astrophysics scale Cosmological scale Particle physics The rotation curve Measurement of the CMB Cosmic rays The bullet cluster Neutrino sector

  4. Classical introduction on DM In atrophysics Rotation curve, Zwicky, Vera Rubin..

  5. Classical introduction on DM In atrophysics Rotation curve, Zwicky, Vera Rubin.. No rotation curve but viral theorem

  6. Classical introduction on DM In atrophysics Rotation curve, Zwicky, Vera Rubin.. Not M33 but M31 (Andromeda) No rotation curve but viral theorem

  7. Classical introduction on DM In atrophysics Rotation curve, Zwicky, Vera Rubin.. Not M33 but M31 (Andromeda) Not pioneer (1970) No rotation curve but Babcock (1939) but viral theorem

  8. Global Warning In this historical section, I will retrace the scientific dark matter history. In other words, I will reconstruct step by step how the hypothesis of the existence of a dark structure in the clusters of galaxies, then in the galaxies and finally in the imprints of the Cosmological Microwave Background. It means that several numbers, observations, conclusions will be falsified during the lecture. The distances for instance are twice smaller in the early time due do the Hubble parameter which has been divided by two between its first evaluation in 1930 and now. Same for the age of the Universe, or temperature of the CMB. The aim of the lecture is indeed to make you understand the process of model building from hypothesis that can change with time due to new observations. All reasonings will be based on the original articles, the complete list of references being given at the end of the lecture. All the original historical articles discussed in this section can be found on the page: http://www.ymambrini.com/My_World/History.html

  9. Observing the present sky From the clusters to the galaxies

  10. The early times (1930-1960) The first appearance of the word « dark matter » in the literature is in a paper of the physicist Jan Oort from Netherland in 1932. While he was analyzing the radial velocities, he notice a discrepancy with Newton law. He computed that only one third of the dynamically inferred mass was present in bright visible stars. It is clear from the context that, as characterizing the remainder as « dark » («Dunkle Materie »), Oort was describing all matter not in the form of visible stars with luminosity comparable or larger than that of the Sun. Gas and dusts between the stars was his « invisible mass » that should be found (for him) soon. The main reason evoked at this time was the presence of low luminosity objects (dead stars) or large absorbing gas. Imagining a new dark component took a very long time to physicists, who even preferred to modified the law of gravity at large scale before invoking a new particle. Jan Oort, Bulletin of the Astronomical Institutes of the Netherlands, Vol. 6, p.249 Jan Oort (the original articles can be found there: http://www.ymambrini.com/My_World/History.html ) In this sense, the first real work underlining that the missing mass could be problematic is Fritz Zwicky in 1933

  11. « The Redshift of Extragalactic Nebulae » Fritz Zwicky, Helv. Phys. Acta 6, 110-127 (1933) § 5. Remarks concerning the dispersion of velocities in the Coma nebular cluster. As the data in § 3 show, there are in the Coma cluster di ff erences in velocity of at least 1500 to 2000 km/sec. In the context of this enormous variation of velocities the following considerations can be made: 1. Under the supposition that the Coma system has reached, mechani- cally, a stationary state, the Virial Theorem implies � k = − 1 2 � p , (4) where � k and � p denote average kinetic and potential energies, e.g. of the The Redshift of Extragalactic Nebulae unit of mass in the system. For the purpose of estimation we assume that the matter in the cluster is distributed uniformly in space. The cluster has a radius R of about one million light-years (equal to 10 24 cm) and contains 800 by F. Zwicky. individual nebulae with a mass of each corresponding to 10 9 solar masses. (16.II.33.) The mass M of the whole system is therefore M ∼ 800 × 10 9 × 2 × 10 33 = 1 . 6 × 10 45 g. (5) Contents . This paper gives a representation of the main characteristics of extragalactic nebulae and of the methods which served their exploration. In particular, the so called redshift of extragalactic nebulae is discussed in detail. Di ff erent theories which have been worked out in order to explain this important phenomenon will be discussed briefly. Finally it will be indi- cated to what degree the redshift promises to be important for the study of penetrating radiation. This implies for the total potential energy Ω : Ω = − 3 5 Γ M 2 (6) R Γ = Gravitational constant or ε p = Ω /M ∼ − 64 × 10 12 cm 2 s − 2 (7) The Coma Cluster of Galaxies. and then ε k = v 2 / 2 ∼ − ε p / 2 = 32 × 10 12 cm 2 s − 2 This is a highly regular gravitationally bound system of � 1 / 2 � v 2 = 80 km/s . (8) thousands of galaxies at a In order to obtain the observed value of an average Doppler e ff ect of 1000 distance of about 100 Mpc km/s or more, the average density in the Coma system would have to be at least 400 times larger than that derived on the grounds of observations of (NASA, SDSS) luminous matter. 8 If this would be confirmed we would get the surprising result that dark matter is present in much greater amount than luminous matter. 2. One could also assume that the Coma system is not in stationary

  12. The calculation Book, chap tf r 17 Statement of the virial theorem: For the n point particles, bound together into a system, the time average of the kinetic energy of the particles, P 1 2 m i v 2 i , plus one half of the time average of P ~ F i . ~ r i is equal to zero. virial H = P ~ p i . ~ r i The average of the derivative of a finite R P P function cancels for large time or periodic H P X ~ dH X ~ ✓ dH ◆ dt = F i . ~ r i + 2 K = F i . ~ r i + 2 K. dt X irial theorem. If X ~ K + 1 n ~ F i = − @ V/ @ r i F i . ~ r i = 0 2 2 α GM 2 M 2 v 2 = 1 al V = − α GM 2 R , R of the galaxies α depends on the shape of the halo (3/5 for an homogenous sphere)

  13. The calculation Book, chap tf r 17 Statement of the virial theorem: Zwicky took 7500 km/s as a mean velocity to For the n point particles, bound together into a system, the time average obtain D=50 Mpc (v=H x D) of the kinetic energy of the particles, P 1 2 m i v 2 i , plus one half of the time average of P ~ F i . ~ r i is equal to zero. Table II. 3 virial H = P ~ p i . ~ r i Number of nebulae Apparent Distance in Average 10 6 light-years Nebular cluster in the cluster diameter velocity km/s Virgo . . . . . . (500) 12 ◦ 6 890 The average of the derivative of a finite Pegasus . . . . . 100 1 ◦ 23.6 3810 R P P function cancels for large time or periodic H Pisces . . . . . . 20 0.5 22.8 4630 P Cancer . . . . . 150 1.5 29.3 4820 Perseus. . . . . 500 2.0 36 5230 X ~ Coma . . . . . . 800 1.7 45 7500 dH X ~ ✓ dH ◆ dt = F i . ~ r i + 2 K = F i . ~ r i + 2 K. Ursa Major I 300 0.7 72 11800 dt Leo . . . . . . . 400 0.6 104 19600 X Gemini . . . . . (300) — 135 23500 irial theorem. If X ~ These results are shown graphically in Fig. 2. K + 1 n ~ F i = − @ V/ @ r i F i . ~ r i = 0 2 From the apparent diameter d, Zwicky deduced the 2 α GM 2 M 2 v 2 = 1 radius of the cluster, R= d x D = 1Mpc al V = − α GM 2 R , R of the galaxies And 800 galaxies of 10 9 solar mass in the cluster α depends on the shape of the halo (3/5 for an homogenous sphere)

  14. The calculation Book, chap tf r 17 Statement of the virial theorem: Zwicky took 7500 km/s as a mean velocity to For the n point particles, bound together into a system, the time average obtain D=50 Mpc (v=H x D) of the kinetic energy of the particles, P 1 2 m i v 2 i , plus one half of the time average of P ~ F i . ~ r i is equal to zero. Table II. 3 virial H = P ~ p i . ~ r i Number of nebulae Apparent Distance in Average 10 6 light-years Nebular cluster in the cluster diameter velocity km/s Virgo . . . . . . (500) 12 ◦ 6 890 The average of the derivative of a finite Pegasus . . . . . 100 1 ◦ 23.6 3810 R P P function cancels for large time or periodic H Pisces . . . . . . 20 0.5 22.8 4630 P Cancer . . . . . 150 1.5 29.3 4820 Perseus. . . . . 500 2.0 36 5230 X ~ Coma . . . . . . 800 1.7 45 7500 dH X ~ ✓ dH ◆ dt = F i . ~ r i + 2 K = F i . ~ r i + 2 K. Ursa Major I 300 0.7 72 11800 dt Leo . . . . . . . 400 0.6 104 19600 X Gemini . . . . . (300) — 135 23500 irial theorem. If X ~ These results are shown graphically in Fig. 2. K + 1 n ~ F i = − @ V/ @ r i F i . ~ r i = 0 2 From the apparent diameter d, Zwicky deduced the 2 α GM 2 M 2 v 2 = 1 radius of the cluster, R= d x D = 1Mpc al V = − α GM 2 R , R of the galaxies And 800 galaxies of 10 9 solar mass in the cluster α depends on the shape of the halo (3/5 for an homogenous sphere) He considered that the spread in velocities (~1000km/s) correspond to a mean velocity of the galaxies inside the cluster Apparent velocities in the Coma cluster v = 8500 km/s 6900 km/s 7900 6700 7600 6600 7000 5100 (?)

  15. The calculation Book, chap tf r 17 Statement of the virial theorem: Zwicky took 7500 km/s as a mean velocity to For the n point particles, bound together into a system, the time average obtain D=50 Mpc (v=H x D) of the kinetic energy of the particles, P 1 2 m i v 2 i , plus one half of the time average of P ~ F i . ~ r i is equal to zero. Table II. 3 virial H = P ~ p i . ~ r i Number of nebulae Apparent Distance in Average 10 6 light-years Nebular cluster in the cluster diameter velocity km/s Virgo . . . . . . (500) 12 ◦ 6 890 The average of the derivative of a finite Pegasus . . . . . 100 1 ◦ 23.6 3810 R P P function cancels for large time or periodic H Pisces . . . . . . 20 0.5 22.8 4630 P Cancer . . . . . 150 1.5 29.3 4820 Perseus. . . . . 500 2.0 36 5230 X ~ Coma . . . . . . 800 1.7 45 7500 dH X ~ ✓ dH ◆ dt = F i . ~ r i + 2 K = F i . ~ r i + 2 K. Ursa Major I 300 0.7 72 11800 dt Leo . . . . . . . 400 0.6 104 19600 X Gemini . . . . . (300) — 135 23500 irial theorem. If X ~ These results are shown graphically in Fig. 2. K + 1 n ~ F i = − @ V/ @ r i F i . ~ r i = 0 2 From the apparent diameter d, Zwicky deduced the 2 α GM 2 M 2 v 2 = 1 radius of the cluster, R= d x D = 1Mpc al V = − α GM 2 R , R of the galaxies And 800 galaxies of 10 9 solar mass in the cluster α depends on the shape of the halo (3/5 for an homogenous sphere) He considered that the spread in velocities (~1000km/s) correspond to a mean velocity of the galaxies inside the cluster 5 ⇥ 6 . 67 ⇥ 10 − 11 ⇥ 1 . 6 ⇥ 10 42 v 2 = 3 GM = 3 p v 2 ' 80 km / s . Apparent velocities in the Coma cluster ) 5 R 10 22 v = 8500 km/s 6900 km/s 7900 6700 One observed velocity spread of 1000 km/s whereas one should 7600 6600 oversee 80 km/s. Mass of the Coma should then be larger by a 7000 5100 (?) factor few thousands .

  16. Conclusion of the Zwicky article « In order to obtain the observed value of an average Doppler effect of 1000 km/s or more, the average density in the Coma system would have to be at least 400 times larger than that derived on the grounds of observations of luminous matter. If this would be confirmed we would get the surprising result that dark matter is present in much greater amount than luminous matter » This result was completely forgotten and nobody took really seriously this comment of Zwicky. Indeed, the large scale astrophysics was at its beginning after the Hubble discovery and a lot of physicists believed that the « missing mass » problem will be solved once we will understand better the mechanism of absorption of light in the interstellar/internebulae medium. In fact, the « missing mass » problem was a this time considered as a « missing luminosity » problem: why we do not see the astrophysics bodies that should be responsible of the Newtonian dynamics. On the other hand, several scientists tried to modify (already in the 30’s) the 1/r 2 attraction law. Then began the galaxies analysis.

  17. At the Galactic scale In 1939 , Horace Babcock presents his PhD thesis on the subject of rotation curves of galaxies. He compute the rotation curve in Andromeda and measured a constant angular velocity and concluded :

  18. At the Galactic scale In 1939 , Horace Babcock presents his PhD thesis on the subject of rotation curves of galaxies. He compute the rotation curve in Andromeda and measured a constant angular velocity and concluded : The history of the measurements of rotation curves dates back to 1914 (!!) where Slipher at the Lowell laboratory observed that the velocities measured on the left of the bulge of the nearby galaxy (nebula) Andromeda (the nearest galaxy ~800 kpc from us, but believed to be 210 kpc at this time due to the Hubble parameter determination were approaching us at higher velocities (~ 320 km/s ) than the ones on the right part of the central bulge (~ 280 km/s ). This is what is expected in a disk turn in front of us. 280 300 320

  19. At the Galactic scale In 1939 , Horace Babcock presents his PhD thesis on the subject of rotation curves of galaxies. He compute the rotation curve in Andromeda and measured a constant angular velocity and concluded : The history of the measurements of rotation In 1918 , Pease at the Mount Wilson curves dates back to 1914 (!!) where Slipher at Observatory measured the rotation out to a the Lowell laboratory observed that the velocities radius of 600 pc (central part of Andromeda ). measured on the left of the bulge of the nearby His result were expressed by the formula galaxy (nebula) Andromeda (the nearest galaxy V c = -0.48 r - 316 ~800 kpc from us, but believed to be 210 kpc at where V c is the circular velocity measured (in this time due to the Hubble parameter km/s) at a distance r from the central bulge of determination were approaching us at higher Andromeda , showing that this central portion velocities (~ 320 km/s ) than the ones on the right appears to rotate with constant angular velocity. part of the central bulge (~ 280 km/s ). This is what is expected in a disk turn in front of us. 280 300 320

  20. At the Galactic scale In 1939 , Horace Babcock presents his PhD thesis on the subject of rotation curves of galaxies. He compute the rotation curve in Andromeda and measured a constant angular velocity and concluded : The history of the measurements of rotation In 1918 , Pease at the Mount Wilson curves dates back to 1914 (!!) where Slipher at Observatory measured the rotation out to a the Lowell laboratory observed that the velocities radius of 600 pc (central part of Andromeda ). measured on the left of the bulge of the nearby His result were expressed by the formula galaxy (nebula) Andromeda (the nearest galaxy V c = -0.48 r - 316 ~800 kpc from us, but believed to be 210 kpc at where V c is the circular velocity measured (in this time due to the Hubble parameter km/s) at a distance r from the central bulge of determination were approaching us at higher Andromeda , showing that this central portion velocities (~ 320 km/s ) than the ones on the right appears to rotate with constant angular velocity. part of the central bulge (~ 280 km/s ). This is what is expected in a disk turn in front of us. Babcock in 1939 extend the study to larger scale, up to 24 kpc from the center. 280 300 320

  21. The work of Babcock Babcock measured the rotation curve much more far away from the central bulge of Andromeda, and plotted the circular velocity and the angular velocity as function of the distance r from the center of Andromeda. V c (km/s) ω (rad/s)

  22. The work of Babcock Babcock measured the rotation curve much more far away from the central bulge of Andromeda, and plotted the circular velocity and the angular velocity as function of the distance r from the center of Andromeda. V c (km/s) ω (rad/s) Babcock supposed a concentration of spheroids of densities σ 1 , σ 2 , σ 3 , and σ 4 . He then computed the 4 densities to respect the velocities measured on the left. He obtained

  23. The work of Babcock Babcock measured the rotation curve much more far away from the central bulge of Andromeda, and plotted the circular velocity and the angular velocity as function of the distance r from the center of Andromeda. V c (km/s) ω (rad/s) Babcock supposed a concentration of spheroids of densities σ 1 , σ 2 , σ 3 , and σ 4 . He then computed the 4 densities to respect the velocities measured on the left. He obtained From the computation of the density, he deduced the total mass of Andromeda of 10 11 solar mass , equivalent to a mass to light ratio M/L=50. He then concludes:

  24. Jansky sees the invisible (1932) Karl Jansky

  25. Jansky sees the invisible (1932) Karl Jansky « An airplane wing rotating on automobile (Ford Model T) wheels in potato field » Was built to investigate and eliminate the crackling thunderstorm noise (« static ») which interfered with radio-telephone conversations over trans-Atlantic short-wave links of the Bell system .

  26. Jansky sees the invisible (1932) Karl Jansky « An airplane wing rotating on automobile (Ford Model T) wheels in potato field » Was built to investigate and eliminate the crackling thunderstorm noise (« static ») which interfered with radio-telephone conversations over trans-Atlantic short-wave links of the Bell system . Small « bumps » observed by Karl Jansky , one for each revolution of the antenna every 20 minutes (rotation time)

  27. Jansky sees the invisible (1932) However, after making an analysis on a complete year, Jansky noticed that the periodicity of the larger signal was not 24 hours, but 23h56 , which corresponds to a sidereal day and not a solar day : the signal was coming from the center of the galaxy and not from the sun (« stationary with respect to the stars »).

  28. Jansky sees the invisible (1932) However, after making an analysis on a complete year, Jansky noticed that the periodicity of the larger signal was not 24 hours, but 23h56 , which corresponds to a sidereal day and not a solar day : the signal was coming from the center of the galaxy and not from the sun (« stationary with respect to the stars »). eal observer on during epoch lie in and the direction is the the needs lies (this the as is the scale so

  29. Jansky sees the invisible (1932) However, after making an analysis on a complete year, Jansky noticed that the periodicity of the larger signal was not 24 hours, but 23h56 , which corresponds to a sidereal day and not a solar day : the signal was coming from the center of the galaxy and not from the sun (« stationary with respect to the stars »). eal observer on during epoch lie in and the direction is the the needs lies (this What observed Jansky was in fact the the synchrotron radiation of ultra high energy as electrons produced in the Galactic Center. A is GeV electron emit synchrotron photons at the radio-wave ( 1 MHz=300m, 1GHz=30cm , scale so frequencies measured by WMAP and PLANCK )

  30. Jansky sees the invisible (1932) However, after making an analysis on a complete year, Jansky noticed that the periodicity of the larger signal was not 24 hours, but 23h56 , which corresponds to a sidereal day and not a solar day : the signal was coming from the center of the galaxy and not from the sun (« stationary with respect to the stars »). eal observer on during epoch lie in and the direction is the the needs lies (this What observed Jansky was in fact the the synchrotron radiation of ultra high energy as electrons produced in the Galactic Center. A is GeV electron emit synchrotron photons at the radio-wave ( 1 MHz=300m, 1GHz=30cm , scale so frequencies measured by WMAP and PLANCK ) Jansky died in 1950 (at 44) without knowing the revolution he initiated. p.s.: he was lucky to look at a wavelength of 14 meters, which was the range not absorbed by the ionosphere while still emitted by galactic center.

  31. The 21cm tracer (1944-1951) Hendrick van de Hulst In 1944 , Jan Oort in Leiden realised that should any of the atoms or molecules in space give rise to a spectral line in the radio spectrum, it would enable much information about the interstellar medium . Jan Oort

  32. The 21cm tracer (1944-1951) Hendrick van de Hulst In 1944 , Jan Oort in Leiden realised that should any of the atoms or molecules in space give rise to a spectral line in the radio spectrum, it would enable much information about the interstellar medium . Jan Oort In a magnetic field , there is a slight difference in energy of the ground state depending wether the spin of the proton and electron are in the same or opposite sense ( Casimir , friend of Oort ). This transition between them gives rise to a line close to 1420 MHz-21 cm in wavelength

  33. The 21cm tracer (1944-1951) Hendrick van de Hulst In 1944 , Jan Oort in Leiden realised that should any of the atoms or molecules in space give rise to a spectral line in the radio spectrum, it would enable much information about the interstellar medium . Jan Oort Unfortunately, van de Hulst is scooped in 1951 for 6 weeks by Ewen and Purcell at Harvard (who heard about the line in a talk by van de Hulst they assisted in 1949) for which they received the Nobel prize of Physics in 1952 (never van de Hulst). Ewen on his horn telescope In a magnetic field , there is a slight difference in energy of the ground state depending wether the spin of the proton and electron are in the same or opposite sense ( Casimir , friend of Oort ). This transition between them gives rise to a line close to 1420 MHz-21 cm in wavelength

  34. The 21cm tracer (1944-1951) Hendrick van de Hulst In 1944 , Jan Oort in Leiden realised that should any of the atoms or molecules in space give rise to a spectral line in the radio spectrum, it would enable much information about the interstellar medium . Jan Oort Unfortunately, van de Hulst is scooped in 1951 for 6 weeks by Ewen and Purcell at Harvard (who heard about the line in a talk by van de Hulst they assisted in 1949) for which they received the Nobel prize of Physics in 1952 (never van de Hulst). Ewen on his horn telescope However, van de Hulst never stopped and gave the first 21cm map of Andromeda in In a magnetic field , there is a slight 1957, showing that the difference in energy of the ground state velocities stays constant depending wether the spin of the proton and much far away from the electron are in the same or opposite sense visible region with the ( Casimir , friend of Oort ). This transition Dwingeloo telescope between them gives rise to a line close to 1420 MHz-21 cm in wavelength Van de Hulst at Dwingeloo

  35. Babcock Van de Hulst do not insist so much in his paper about the flatness of the rotation curve. But, computing the mass of M31 he conclude that is is much larger than the Milky way. The « dark matter » hypothesis does not (yet) strikes the Galactic scale.

  36. The problem of instability at a galactic scale In the 70’s, the Moore law of exponential development describing the time evolution of computing power reached astrophysics studies: the computing power doubling every two years , it was possible in the late 60’s to apply electronic computing machines in the numerical solution of complex problems (technically, it was the replacement of vacuum tubes by transistors which gives a large leap in the field).

  37. The problem of instability at a galactic scale In the 70’s, the Moore law of exponential development describing the time evolution of computing power reached astrophysics studies: the computing power doubling every two years , it was possible in the late 60’s to apply electronic computing machines in the numerical solution of complex problems (technically, it was the replacement of vacuum tubes by transistors which gives a large leap in the field). Franck Hohl in 1971 made one of the very first « N-body » simulation (100 000 stars !!) to test the stability of the galactic structures with a disk of particles supported in equilibrium almost entirely by rotation.

  38. The problem of instability at a galactic scale In the 70’s, the Moore law of exponential development describing the time evolution of computing power reached astrophysics studies: the computing power doubling every two years , it was possible in the late 60’s to apply electronic computing machines in the numerical solution of complex problems (technically, it was the replacement of vacuum tubes by transistors which gives a large leap in the field). Franck Hohl in 1971 made one of the very first « N-body » simulation (100 000 stars !!) to test the stability of the galactic structures with a disk of particles supported in equilibrium almost entirely by rotation. He noticed that a spiral-elongated shape is formed after 2 revolutions, but rapidly the kinetic energy diffuse the particles toward a pressure dominated gas with large elongated axi- symmetric ellipses

  39. The problem of instability at a galactic scale In the 70’s, the Moore law of exponential development describing the time evolution of computing power reached astrophysics studies: the computing power doubling every two years , it was possible in the late 60’s to apply electronic computing machines in the numerical solution of complex problems (technically, it was the replacement of vacuum tubes by transistors which gives a large leap in the field). Franck Hohl in 1971 made one of the very first « N-body » simulation (100 000 stars !!) to test the stability of the galactic structures with a disk of particles supported in equilibrium almost entirely by rotation. He noticed that a spiral-elongated shape is formed after 2 revolutions, but rapidly the kinetic energy diffuse the particles toward a pressure dominated gas with large elongated axi- symmetric ellipses Miller , Pendergast and Quirk tried to stabilized the model by adding energy lost, but still, reheating of the gas destroys the structures some revolutions after. This is when a dark halo came to the rescue and is first mentioned in a paper.

  40. First hypothesis of dark halo The idea Peebles and Ostriker noticed that the random velocities in our galaxies (around 30-40 km/s ) are much smaller than the systematic circular motion (around 200 km/s ). Thus, not only the system is unstable as remarked by Hohl et al. , but it shows that galaxies seems to be dominated by a cold gravitational system and not a kinetic pressure dominated one.

  41. First hypothesis of dark halo The idea Peebles and Ostriker noticed that the random velocities in our galaxies (around 30-40 km/s ) are much smaller than the systematic circular motion (around 200 km/s ). Thus, not only the system is unstable as remarked by Hohl et al. , but it shows that galaxies seems to be dominated by a cold gravitational system and not a kinetic pressure dominated one. Indeed, the virial theorem can be decomposed as: 2 T + U = 0, or 2 T rot + 2 T ran = U , which can be written t + r =1/2 with t=T rot /(-U) and r = T ran /(-U). So, if t=1/2 (r=0) the system is completely supported against gravity by rotation , but if r=1/2 (t=0) the system is completely supported by random motion .

  42. First hypothesis of dark halo The idea Peebles and Ostriker noticed that the random velocities in our galaxies (around 30-40 km/s ) are much smaller than the systematic circular motion (around 200 km/s ). Thus, not only the system is unstable as remarked by Hohl et al. , but it shows that galaxies seems to be dominated by a cold gravitational system and not a kinetic pressure dominated one. Indeed, the virial theorem can be decomposed as: 2 T + U = 0, or 2 T rot + 2 T ran = U , which can be written t + r =1/2 with t=T rot /(-U) and r = T ran /(-U). So, if t=1/2 (r=0) the system is completely supported against gravity by rotation , but if r=1/2 (t=0) the system is completely supported by random motion . Peebles and Ostriker noticed that if t > 0.14 (28% of the kinetic energy is rotational), the system is unstable and becomes elongated very quickly. However, we just saw that in our Milky Way, the rotation velocity is around 200 km/s whereas the random one approaches 40 km/s , which gives t ~ 0.49 , far in excess of the stability limit!!

  43. First hypothesis of dark halo The idea Peebles and Ostriker noticed that the random velocities in our galaxies (around 30-40 km/s ) are much smaller than the systematic circular motion (around 200 km/s ). Thus, not only the system is unstable as remarked by Hohl et al. , but it shows that galaxies seems to be dominated by a cold gravitational system and not a kinetic pressure dominated one. Indeed, the virial theorem can be decomposed as: 2 T + U = 0, or 2 T rot + 2 T ran = U , which can be written t + r =1/2 with t=T rot /(-U) and r = T ran /(-U). So, if t=1/2 (r=0) the system is completely supported against gravity by rotation , but if r=1/2 (t=0) the system is completely supported by random motion . Peebles and Ostriker noticed that if t > 0.14 (28% of the kinetic energy is rotational), the system is unstable and becomes elongated very quickly. However, we just saw that in our Milky Way, the rotation velocity is around 200 km/s whereas the random one approaches 40 km/s , which gives t ~ 0.49 , far in excess of the stability limit!! The clever idea of Peebles and Ostriker is then to add an additional component to the galaxy, a dark halo which contributes at least 50% of the mass inside the position of the Sun U -> U + U dark Then this spheroidal system would add to the gravitational potential energy, but add nothing to the rotational energy ; t would be decreased and perhaps stability restored.

  44. The article P.J. Peebles J.P. Ostriker

  45. Combining 21cm observations with Peebles idea After the work of Van de Hulst , a lot of instrumental developments allowed to have a better understanding of the rotation curves of galaxies much above the optical limit. Vera Rubin Andromeda, M31

  46. Combining 21cm observations with Peebles idea After the work of Van de Hulst , a lot of instrumental developments allowed to have a better understanding of the rotation curves of galaxies much above the optical limit. Vera Rubin Andromeda, M31 K.G. Begeman thesis NGC2403

  47. Which profiles? The rotation curve is given by v 2 (r) = GM(r)/r A constant velocity at large radius means Z 4 π r 2 ρ ( r ) dr ∝ r ⇒ ρ ( r ) = ρ 0 M ( r ) = r 2

  48. Which profiles? The rotation curve is given by v 2 (r) = GM(r)/r A constant velocity at large radius means Z 4 π r 2 ρ ( r ) dr ∝ r ⇒ ρ ( r ) = ρ 0 M ( r ) = r 2 In 1907 , R. Emden (brother in law of K. Schwarzschild ) in a book called « Gaskugeln » demonstrates by thermodynamics argument that a gaz of constant temperature is equilibrate with a density following ρ (r) = ρ 0 /r 2 . One then call these types of profile, isothermal . However, for low radius, rotation curves clearly indicates that the density of dark matter is dominated by the gaz, and does not diverge. One then add a constant term toward the center which gives ρ 0 ρ iso ( r ) = ⌘ 2 ⇣ r 1 + r c

  49. Which profiles? The rotation curve is given by v 2 (r) = GM(r)/r A constant velocity at large radius means Z 4 π r 2 ρ ( r ) dr ∝ r ⇒ ρ ( r ) = ρ 0 M ( r ) = r 2 In 1907 , R. Emden (brother in law of K. Schwarzschild ) in a book called « Gaskugeln » demonstrates by thermodynamics argument that a gaz of constant temperature is equilibrate with a density following ρ (r) = ρ 0 /r 2 . One then call these types of profile, isothermal . However, for low radius, rotation curves clearly indicates that the density of dark matter is dominated by the gaz, and does not diverge. One then add a constant term toward the center which gives ρ 0 ρ (r) ρ iso ( r ) = s l o ⌘ 2 p e ⇣ = - r 1 1 + r c slope=0 slope=-2 slope=-3 r

  50. Which profiles? The rotation curve is given by v 2 (r) = GM(r)/r A constant velocity at large radius means Z 4 π r 2 ρ ( r ) dr ∝ r ⇒ ρ ( r ) = ρ 0 M ( r ) = r 2 In 1907 , R. Emden (brother in law of K. Schwarzschild ) in a book called « Gaskugeln » demonstrates by thermodynamics argument that a gaz of constant temperature is equilibrate with a density following ρ (r) = ρ 0 /r 2 . One then call these types of profile, isothermal . However, for low radius, rotation curves clearly indicates that the density of dark matter is dominated by the gaz, and does not diverge. One then add a constant term toward the center which gives ρ 0 ρ (r) ρ iso ( r ) = s l o ⌘ 2 p e ⇣ = - r 1 1 + r c Navarro (Arizona), Frenk (Durham) and White slope=0 slope=-2 (Munchen), in a series of papers between 1995 and 1997 extracted from precise N-body simulation that the dark matter profile observes a cusp feature near the center slope=-3 proportional to 1/r and then evolves toward a 1/r 3 shape r in the outskirt regions. This profile is called NFW ρ NF W ( r ) = ρ 0 ⌘ 2 A Universal Density Profile from Hierarchical Clustering ⇣ r 1 + r r c r c Navaro, Frenk and White 1995

  51. Two examples The first N-body simulation was made by the Toomre brothers (Alar and Juri) in 1972 (!!!) with 200 points. Aquarius simulation (2009) with 10 9 points

  52. Two examples The first N-body simulation was made by the Toomre brothers (Alar and Juri) in 1972 (!!!) with 200 points. Aquarius simulation (2009) with 10 9 points

  53. Two examples The first N-body simulation was made by the Toomre brothers (Alar and Juri) in 1972 (!!!) with 200 points. Aquarius simulation (2009) with 10 9 points

  54. Summary (present sky) Oort (1932) Zwicky (1933) Jansky (1933) Movements perpendicular to Virial theorem applied to the Measuring radio waves the MW plane Coma cluster Babcock (1939) First rotation curve van de Hulst (1957) radio waves (21cm) rotation curve Rubin (1969) radio waves, hypothesis flat velocity Hohl (1971) First N-body simulation, instability Peebles (1973) N-body: First introduction of Dark Halo NFW (1995) N-body profiles in galactic structures

  55. pre-conclusion We have seen in this first part that it was a long way from the first papers of Oort and Zwicky in the 30’s to the latest N-Body simulation in the 90’s to picture a coherent framework in the analysis of dark matter in the structures and substructures of the Universe. However, in the 60’s the discovery of the CMB will shed a completely new light on the content of the Universe and will reinforce the notion of dark matter. This is the subject of the next lecture.

  56. Historical references J. Oort , « The force exerted by the stellar system in the direction perpendicular to the galactic plane and some related problems», Bull. Astro. Inst. Neth., 6 , 289-294 (1932). F. Zwicky , « Der Rotverschiebung von extragalaktischen Neblen», Act. Helm. Phys., 6 , 110-127 (1933). K.G. Jansky , « Radio waves from outside the Solar System », Nature 132 , 66 (1933). H. Babcock , « The rotation of Andromeda Nebula», Lick Obs. Bull. 498 , 41-51 (1939). H. van de Hulst, E. Raimond and H. van Woerden , « Rotation and density distribution of the Andromeda Nebula derived from observations of the 21-cm line», Bull. Astro. Inst. Neth., 14 , 1-16 (1957). V. Rubin, W. Ford , « Rotation of the andromeda nebula from a spectroscopic survey of emission regions», Astrophys. J., 159 , 379-403 (1969). F. Hohl , « Numerical experiments with a disk of stars», Astrophys. J. 168 , 343-359 (1971). J.P Ostriker and P.J. Peebles , « A numerical study of flattened galaxies: or, can cold galaxies survive? », Astrophys. J. 186 , 467-480 (1973). J. Navarro, C. Frenk and S. White , « The structure of cold dark matter halos», Astrophys. J., 463 , 563-575 (1996).

  57. Book, chap tf r 18 PH V S I C A L REVIEW : etters to t. ze VOLUME U B L . 'a. 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Physik h , h w p t Laboratory r o gives of we must t stages of its expansion. n s newly o Phys. Rev. 69, 155 r &0 t the balloon e s n capture n i d s a u o s nuclear e u t m = the i m l hypothesis u r s t e and compressed s 5 u r c e f o t l o c h o f may which of deuterium r = t r e n m e get X 104, of the still remaining p 2 o e x e 0 c with l i d work e Phys. Rev. SV, 573 s h r o Research c Quid) e t a i sec. and t f n v t p r n cosmogonical . o g e r Q o e n and temperatures and r s d e n t s F . gas was so prior to that time the two meanings: u s o o n E e u n o w t mits r l s p 235 {1937); w t u h a e p h i t s d l n must Naval , c 0 u e h s n This report is based u h f University. n s = o c e have de- must be remembered in the s l 2 have m the r s e the gas t e i expansion. The y . , r u e 5)&105 g sec. /cm'. This c h l e f m be based on these informations. r c and the o a h a n Phys. Rev. 2'2, u v a d i g g e (2) s e H e t b . h n e B n the s u (a) i t i c neutrons 2. 5 s that no aggregation t the primordial u i S Korff. and G. Placzek, led m l , i s m d of Princeton N 5 Rev. V3, 1010 (1940). t y e time must i 2 f e allowed n C r o Kore and f e g g r of these neutrons s i 1 t process the u r o n s ) 0 n Natu+miss. b & f t the higher densities t ' i i e ~ up s r m nuclei must e to the formation u the o q d e p 270 with f u by the g m e to s e e r n o heavier and heavier Vf. C. Bright, and Darol Froman, c a that, due to the comparatively . t f A . universe s t t that Laboratory o /cm' u Since the building-up r {1988)", S. r here e s neutron m the stable elements ~ E. Funfer, d t h n o i o a s r o h w f f p the w a h the neutron s v p i a e c never e r . of deuterons s r o A . h the temperature s captures r present c ' the building e o . y taking place, (b) t proceeded just above the upper fringe of g S can m i h c a s M s P h o , s 10' 'K (which t 111, exceeded . Bethe, Cobas. p so o {1946). n into which order of magnitude s o — w frequency u s c i a b l s e l nuclei), (short-lived . i y A a A . It t formation t b a t g H. d e understood i e that h later, this radiation ment of their electric charges by P-decay. n n e e a d distribution A. Kor8 . ) short value u 0 m p the protons deuterium 4 o H. M. Agnew, of heavier u n 9 d F l 1 i T y somewhat e u { r relativistic r l I S. a c T m r ~ h n e i e o d if we u N c r h s elements), o t of various S f not be related to the . cayed, we o of e ) ' be 7 n h 4 t ~ i 9 s o l f y i a a b o g e ( t w t s e w h e r s r Absorytion e t r o u v and the have been n nT4/c' gas, 3 h m e a Chicago, IQinois e O atomic s d s 2 of matter, b the dissociation l u l slope of DRIPPER a universe t h s s rather to the time period r i density of radiation o t e h s species n e e u that the large neutron w l t p t s r e t a o h n of adjust- m . c e J the nuclear species must depend not so much on o water density. If, e p the density r s e , e abundance t y s r r h . u a A. o t t the isotope at mass f e t u a o Also, the individual N r r 8 e o 4 b stabilities a 9 L of the original 1 n o , 8 i l s curve must a 2 was n n d o a e e c i p t n d a a x p u p N e e J e t (mass e u r by the neutrons m c r f 8' oT4 ) t paper' it was shown x for the e i n o t e t e with a 4-mg space, e g d building-up cross sections. d r neutron e A o a density f e b t by c u in the form: t n s d t ls due ) h a e g n 1 mg per n is neglected because as on the n c o i e e x i d s s process apparently p n s a a e n s repeated p of various r - m p The produced x — Aux. The isotope at x d e u e i v in the expansion r a t a h l a recent in a thin layer of approximately m written e u e lsd q e i r a u s s a t intrinsic a of their neutron i w o ln e 149. Since the alteration t could not be detected. = n distance h N s f t c ' ( can be written " not very large, the experiment absorption i t the curvature t in g a ) o b ( ) v 1 a ; e w i ( , r e d n h h i a e n t y r n; —;n;) i=1, 2, " 238 g /, we can rewrite e f r e a o h n; r such a n C t t sections A i a o t ClMlKO b r o n r r in ten mass spectra made with one milligram d t a f u with a mass spectrum t e e g a;. h n an c n e i n a f form: n i f r S a o s i e stronger a c r i i t t o t the relative n h mass density value. r o e d t / c - 2 a characterizing o e where nuclei h s term t t t o a p sq. cm to a much x l e 149 was so reduced o a the isotope e f n h n appears approximately o a sample t u i t o m t r o m and b o G e p i the c r together e high o x s 8 r T' p weight i, and where f(t) is a and impurity d f e o h c y r t l e c e of a a , s 1 s p ' intensity r e t 0 e u . g v of r two absorbing e n i i d F gadolinium t mass cross s h T i e t in i density with e h t f is shown T a o h form: t One samarium. increased so t n i e a h t f a t t i h e m A t l p e with t m . . 4 a showed 5 s l 32Wo' a 1 on m y exposures, r the one at o l / 5 l n t or, integrating: a 0 l e e of plates f 803 r Fio. 1. 4 g 5 1 0 was L no changes and 157 missing. o g the masses 147, 148, 152, and e have: o long f h 5 1 relative t o of t e . s h BO e e t p w equal a density curve indicating o b measurements A u t 1 temperature on n o t density o d s m a i n i c - 3 c c 5 in any of these e e showed 5 weight p 32M t2. 1 s t of deuterium, a four n o i e t a h isotopes i m t d Photometric a e o r when h r f t For the t mass 150 was found time a absorption formation , o t the time a normal photographic t the densities a h t e that at p s t e a n a h is conserved w o h t t r t u permit e w ) n t s a o n m s f h o o a s u r t o s s u e These formulas result t a e c n n decreasing was several minutes. Let us r a d h e d e g t n s plus t a 149 u from u o a o p m b s x n a iso a E e 7 dropped low (protons the w 4 1 e ' can be estimated 8 ~. was n 4 e 1 I h radiation, , T p ) r e t t a m o of expansion, t of Since, in contrast of p, . t density I process The value l a m ills r o N the I '~7'~t , & in absorption. altered by neutron s e p o t o s i Samarium . l VlG.

  58. By 1980 , the perceived problems of the stability of rotationally supported disk galaxies and the observation of non-declining rotation curves of spiral galaxies had led most astronomers to accept the idea that galaxies are embedded in a dark halo that become dynamically more important in the outer region . Astronomers in general thought in terms of rather conventional dark matter - cold gas, very low mass stars, failed stars (or super planets), stellar remnants such as cold white dwarfs, neutron stars, or low-mass black holes - i.e. baryonic dark matter At about the same time a rather different idea was gaining credence among cosmologists and particle physicists: that the dark matter consists of subatomic particles; non-baryonic dark matter that interacts only weakly with baryons and photons. That is the story we propose to tell now..

  59. G. Gamow A. Penzias « Gamow? A man whose idea is wrong in almost every detail», Penzias in his Nobel lecture, 1978.

  60. PH VSICAL REVIEW 73, VOLUME AP RI L 1, 1948 NUM HER 7 . 'a. itor : etters to t. ze We may remark at first that the building-up process was when the temperature of the neutron apparently completed still rather was since otherwise the observed gas high, abundances would have been affected the strongly by UBLICA TION of brief reports of important ~ ~ ~ discoveries in the region of the slow neutrons. According to resonances in physics ~ ~ be secured by addressing to this may them 2 the of various Hughes, neutron capture cross sections The closing date for this department is five ueeks ~ ~ department. elements (for neutron of about 1 Mev) increase energies prior to the date ofissue. proof a@ill be sent to the authors. ¹ with atomic number exponentially up the periodic halfway The Board of Editors does not hold itself responsible for the constant system, remaining approximately for heavier opinions by the correspondents. expressed Communications The concept of nucleosynthesis elements. G. Gamow not exceed 600 words in length. should these cross sections, one Using finds integrating by Eqs. (1) as shown in Fig. 1 that the relative abundances of various nuclear decrease for the lighter species rapidly elements and remain constant for the ele- approximately Alpher, Bethe Gamow (April 1st, 1948) The Origin of Chemical Elements silver. In order to fit the calculated ments heavier than R. Alpher + thesis of Alpher it is necessary the observed abundances' to R. A. ALPHER+ curve with The Johns Hopkins Applied Physics Laboratory, Un&rersity, assume thy integral of p„dt during the building-up period is Silver Spring, Maryland equal to 5 X104 g sec. /cm'. The approach of a building-up universe was not AND On the other hand, according to the relativistic theory of H. Bethe H. BETHE obvious in 1948 , when the common thought was that the expanding the density on time is universe4 dependence Cornell University, Ithaca, %em York p — the elements were generated from decay processes , 10'/t~. Since the integral of this expression given by diverges at t = 0, it is necessary to assume that the building- G. GAMow from the heavier element to the lighter one. The at a certain time the D. C. process began to, satisfying 8'ashington, up The George Washington University, concept was proposed by Alpher in his thesis 18, 1948 February relation: supervised by Gamow (from which the famous out by one of us, ' various S pointed A nuclear species J (10' jt')dt =5 X 104, (2) Alpher, Bethe Gamow paper know as the αβγ paper not as the result of an equilib- must have originated &0 to a certain temperature rium corresponding and density, is extracted). which gives us to=20 sec. and p0=2. 5)&105 g sec. /cm'. This but rather as a consequence of a continuous building-up result may have two meanings: (a) for the higher densities by a rapid process arrested and cooling of the expansion existing prior to that time the temperature of the neutron matter. to this primordial According picture, we must gas was so high that no aggregation was taking place, (b) the early stage of matter as a highly imagine compressed the of the never exceeded the value density universe neutron (overheated neutral gas nuclear which Quid) 2. 5 )& 10' g sec. /cm' which can possibly be understood if we started into protons and electrons the gas decaying when fell down as the result of universal pressure expansion. The radiative capture of the still remaining neutrons by the newly formed protons must have led first to the formation of deuterium nuclei, and the subsequent neutron captures up of heavier and heavier nuclei. It resulted in the building that, due to the comparatively must be remembered short for this procgss, ' the building time allowed up of heavier nuclei must have proceeded just above the upper fringe of the stable elements (short-lived Fermi elements), and the present distribution of various atomic frequency species was attained later as the result of adjust- only somewhat ment of their electric charges by P-decay. Thus the observed slope of the abundance curve must not be related to the temperature of the original neutron gas, but rather to the time period permitted by the expan- CAt ClMlKO sion process. Also, the individual abundances of various nuclear species must depend not so much on their intrinsic stabilities (mass defects) as on the values of their neutron capture cross sections. The equations such a -2 governing process apparently can be written in the form: building-up — =f(t)(;, n; —;n;) i=1, 2, " 238 lsd '0 BO /50 Fio. 1. where n; and a;. are the relative numbers and capture cross sections for the nuclei of atomic weight i, and where f(t) is a Log of relative abundance factor characterizing the decrease of the density with time. Atomic weight 803

  61. PH VSICAL REVIEW 73, VOLUME AP RI L 1, 1948 NUM HER 7 . 'a. itor : etters to t. ze We may remark at first that the building-up process was when the temperature of the neutron apparently completed still rather was since otherwise the observed gas high, abundances would have been affected the strongly by UBLICA TION of brief reports of important ~ ~ ~ discoveries in the region of the slow neutrons. According to resonances in physics ~ ~ be secured by addressing to this may them 2 the of various Hughes, neutron capture cross sections The closing date for this department is five ueeks ~ ~ department. elements (for neutron of about 1 Mev) increase energies prior to the date ofissue. proof a@ill be sent to the authors. ¹ with atomic number exponentially up the periodic halfway The Board of Editors does not hold itself responsible for the constant system, remaining approximately for heavier opinions by the correspondents. expressed Communications The concept of nucleosynthesis elements. G. Gamow not exceed 600 words in length. should these cross sections, one Using finds integrating by Eqs. (1) as shown in Fig. 1 that the relative abundances of various nuclear decrease for the lighter species rapidly elements and remain constant for the ele- approximately Alpher, Bethe Gamow (April 1st, 1948) The Origin of Chemical Elements silver. In order to fit the calculated ments heavier than R. Alpher + thesis of Alpher it is necessary the observed abundances' to R. A. ALPHER+ curve with The Johns Hopkins Applied Physics Laboratory, Un&rersity, assume thy integral of p„dt during the building-up period is Silver Spring, Maryland equal to 5 X104 g sec. /cm'. The approach of a building-up universe was not AND On the other hand, according to the relativistic theory of H. Bethe H. BETHE obvious in 1948 , when the common thought was that the expanding the density on time is universe4 dependence Cornell University, Ithaca, %em York p — the elements were generated from decay processes , 10'/t~. Since the integral of this expression given by diverges at t = 0, it is necessary to assume that the building- G. GAMow from the heavier element to the lighter one. The at a certain time the D. C. process began to, satisfying 8'ashington, up The George Washington University, concept was proposed by Alpher in his thesis 18, 1948 February relation: supervised by Gamow (from which the famous out by one of us, ' various S pointed A nuclear species J (10' jt')dt =5 X 104, (2) Alpher, Bethe Gamow paper know as the αβγ paper not as the result of an equilib- must have originated &0 to a certain temperature rium corresponding and density, is extracted). which gives us to=20 sec. and p0=2. 5)&105 g sec. /cm'. This but rather as a consequence of a continuous building-up result may have two meanings: (a) for the higher densities by a rapid process arrested and cooling of the expansion existing prior to that time the temperature of the neutron The fundamental idea is that the primordial Universe is made matter. to this primordial According picture, we must gas was so high that no aggregation was taking place, (b) the early stage of matter as a highly imagine compressed of neutron only, which decay into proton . Then, their the of the never exceeded the value density universe neutron (overheated neutral gas nuclear which Quid) combination form the nucleus of deuterium which 2. 5 )& 10' g sec. /cm' which can possibly be understood if we started into protons and electrons the gas decaying when subsequently will form the heavier elements like Helium, fell down as the result of universal pressure expansion. The radiative capture of the still remaining neutrons by the Lithium.. This is the « deuterium bottleneck » process. newly formed protons must have led first to the formation of deuterium nuclei, and the subsequent neutron captures up of heavier and heavier nuclei. It resulted in the building Lifetime 1/ λ n that, due to the comparatively p must be remembered short for this procgss, ' the building time allowed up of heavier Cross section σ nuclei must have proceeded just above the upper fringe of the stable elements (short-lived Fermi elements), and the present distribution of various atomic frequency species d was attained later as the result of adjust- only somewhat ment of their electric charges by P-decay. Thus the observed slope of the abundance curve must not be related to the temperature of the original neutron n n gas, but rather to the time period permitted by the expan- CAt ClMlKO sion process. Also, the individual abundances of various nuclear species must depend not so much on their intrinsic … stabilities (mass defects) as on the values of their neutron capture cross sections. The equations such a -2 governing process apparently can be written in the form: building-up — =f(t)(;, n; —;n;) i=1, 2, " 238 lsd '0 BO /50 Fio. 1. where n; and a;. are the relative numbers and capture cross sections for the nuclei of atomic weight i, and where f(t) is a Log of relative abundance factor characterizing the decrease of the density with time. Atomic weight 803

  62. PH VSICAL REVIEW 73, VOLUME AP RI L 1, 1948 NUM HER 7 . 'a. itor : etters to t. ze We may remark at first that the building-up process was when the temperature of the neutron apparently completed still rather was since otherwise the observed gas high, abundances would have been affected the strongly by UBLICA TION of brief reports of important ~ ~ ~ discoveries in the region of the slow neutrons. According to resonances in physics ~ ~ be secured by addressing to this may them 2 the of various Hughes, neutron capture cross sections The closing date for this department is five ueeks ~ ~ department. elements (for neutron of about 1 Mev) increase energies prior to the date ofissue. proof a@ill be sent to the authors. ¹ with atomic number exponentially up the periodic halfway The Board of Editors does not hold itself responsible for the constant system, remaining approximately for heavier opinions by the correspondents. expressed Communications The concept of nucleosynthesis elements. G. Gamow not exceed 600 words in length. should these cross sections, one Using finds integrating by Eqs. (1) as shown in Fig. 1 that the relative abundances of various nuclear decrease for the lighter species rapidly elements and remain constant for the ele- approximately Alpher, Bethe Gamow (April 1st, 1948) The Origin of Chemical Elements silver. In order to fit the calculated ments heavier than R. Alpher + thesis of Alpher it is necessary the observed abundances' to R. A. ALPHER+ curve with The Johns Hopkins Applied Physics Laboratory, Un&rersity, assume thy integral of p„dt during the building-up period is Silver Spring, Maryland equal to 5 X104 g sec. /cm'. The approach of a building-up universe was not AND On the other hand, according to the relativistic theory of H. Bethe H. BETHE obvious in 1948 , when the common thought was that the expanding the density on time is universe4 dependence Cornell University, Ithaca, %em York p — the elements were generated from decay processes , 10'/t~. Since the integral of this expression given by diverges at t = 0, it is necessary to assume that the building- G. GAMow from the heavier element to the lighter one. The at a certain time the D. C. process began to, satisfying 8'ashington, up The George Washington University, concept was proposed by Alpher in his thesis 18, 1948 February relation: supervised by Gamow (from which the famous out by one of us, ' various S pointed A nuclear species To compute the time t needed for the process with a J (10' jt')dt =5 X 104, (2) Alpher, Bethe Gamow paper know as the αβγ paper not as the result of an equilib- must have originated &0 density of neutron n , Alpher and Gamow supposed to a certain temperature rium corresponding and density, is extracted). which gives us to=20 sec. and p0=2. 5)&105 g sec. /cm'. This but rather as a consequence nt σ v ~ 1. of a continuous building-up result may have two meanings: (a) for the higher densities by a rapid process arrested and cooling of the expansion It means that the exposure nt was sufficiently long to existing prior to that time the temperature of the neutron The fundamental idea is that the primordial Universe is made matter. to this primordial According picture, we must initiate one reaction. Using a tabulation by Hughes (1946) gas was so high that no aggregation was taking place, (b) the early stage of matter as a highly imagine compressed of neutron only, which decay into proton . Then, their the of the never exceeded the value density universe neutron (overheated neutral for σ *(E/1 eV) 1/2 = 10 -25 cm 2 and the approximation E gas nuclear which Quid) combination form the nucleus of deuterium which 2. 5 )& 10' g sec. /cm' which can possibly be understood if we started into protons and electrons the gas decaying when ~1/2 mv 2 to deduce subsequently will form the heavier elements like Helium, fell down as the result of universal pressure expansion. The σ v ~ 1.5 x 10 -19 cm 3 s -1 . radiative capture of the still remaining neutrons by the Lithium.. This is the « deuterium bottleneck » process. newly formed protons must have led first to the formation nt should then be equal to 7x10 18 s cm -3 to initiate the of deuterium nuclei, and the subsequent neutron captures process. However, Alpher and Gamow mistakenly up of heavier and heavier nuclei. It resulted in the building Lifetime 1/ λ n considered a matter dominated Universe to compute t: that, due to the comparatively p must be remembered short for this procgss, ' the building time allowed up of heavier Cross section σ G M /a = 1/2 v 2 => ~ ρ =nm=(3/8 π G) / t 2 . nuclei must have proceeded just above the upper fringe of giving the stable elements (short-lived Fermi elements), and the present distribution of various atomic frequency nt ~ 5 x 10 29 (s/t) s cm -3 . species d was attained later as the result of adjust- only somewhat The lifetime of the neutron being ~ 1000 seconds , nt σ v is ment of their electric charges by P-decay. equal to 10 8 (very large exposure!) which means that all Thus the observed slope of the abundance curve must not be related to the temperature of the original neutron the protons has been absorbed to form the deuterium, n n gas, but rather to the time period permitted by the expan- CAt ClMlKO leaving a Universe empty of Hydrogen. The mistake was sion process. Also, the individual abundances of various of course coming from the matter domination nuclear species must depend not so much on their intrinsic … stabilities (mass defects) as on the values of their neutron hypothesis of the Universe as Gamow will notice 2 capture cross sections. The equations such a -2 governing months later. process apparently can be written in the form: building-up — =f(t)(;, n; —;n;) i=1, 2, " 238 lsd '0 BO /50 Fio. 1. where n; and a;. are the relative numbers and capture cross sections for the nuclei of atomic weight i, and where f(t) is a Log of relative abundance factor characterizing the decrease of the density with time. Atomic weight 803

  63. LETTERS TO THE EDITOR Kore, and Placzek. ' These values, as well as those calcu- to 21. 2+0. 4 percent. tra to have increased The normal of Kore and at 150 is 7. 47, and at 149, 13. 84 percent, lated from recent results Cobas, abundance the Agnew, Bright, and Froman„are shown in Fig. 2. (The upper limit sum being 21. 3 percent. This shows that within the experi- value. ) that at of q cannot exceed twice the calcuhted mental error the 149 isotopes disappear mass The cadmium ratio, i. e. , the ratio between the unshielded reappear at mass 150. The absorbing cross sections of the is of the order of 2. 2 over to be less than one percent counters, other isotopes were estimated and cadmium-shielded the depth from 22. 8 cm of Hg to 4 cm of' Hg. This is in of that of the isotope at mass 149. Bright, and Froman's4 results. with Agnew, agreement ~ R. E. Lapp. J. R. Van Horn, and A. J. Dempster, Phys. Rev. 71, wishes to express his gratitude to Professor 745 {1947). The author to Mr. D. B. R. Ladenburg for many discussions, helpful and building of for the designing Davis, who is responsible of' the Ordnance and to members The Origin of Elements and the Seyaration the balloon equipment a to make the Research Laboratory who helped flight of Galaxies successful one. G. G~ow ~ This report is based upon work performed under Contract N6onr- D. C. George R'ashiegton 6'ashiegtos, University, Research at the Ordnance Research 270 with the CNSce of Naval June 21, 1948 Laboratory of Princeton University. ~ E. Funfer, 25, 235 {1937); E. FQnfer, Zeits. f. Physik LETTERS TO THE Natu+miss. EDITOR &HE successful of the features 111, Mi {1988)", S. A. Kore and B. Hamermesh, explanation main of Phys. Rev. 69, 155 {1946). process, "" the abundance curve of chemical elements by the g H. A. Bethe, S. A. Korff. and G. Placzek, Phys. Rev. SV, 573 Kore, and Placzek. ' These values, as well as those calcu- {1940). of the "unfinished hypothesis building-up per- to 21. 2+0. 4 percent. I S. A. Kor8 and A. Cobas. Phys. Rev. V3, 1010 (1940). tra to have increased The normal mits us to get certain information the densities ~ H. M. Agnew, concerning Vf. C. Bright, and Darol Froman, Phys. Rev. 2'2, of Kore and at 150 is 7. 47, and at 149, 13. 84 percent, lated from recent results Cobas, abundance the Agnew, 2O3 (i947'). and temperatures which must have existed in the universe sum being 21. 3 percent. This shows that within Bright, and Froman„are shown in Fig. 2. (The upper limit the experi- during the early stages of its expansion. Ke want to discuss value. ) at of q cannot exceed twice the calcuhted error the that 149 mental isotopes disappear mass here some interesting which can cosmogonical conclusions The cadmium ratio, i. e. , the ratio between the unshielded reappear at mass 150. The absorbing cross sections of the be based on these informations. in SN~arium Neutron Absorytion is of the order of 2. 2 over other isotopes were estimated to be less than one percent and cadmium-shielded counters, Since the building-up process must have started with the A. J. DRIPPER the depth from 22. 8 cm of Hg to 4 cm of' Hg. This is in of that of the isotope at mass 149. formation of deuterons from the primordial neutrons and Chicago, IQinois Argent National Laboratory, some of these neutrons have de- the protons into which Bright, and Froman's4 June 28, 1948 results. with Agnew, agreement ~ R. E. Lapp. J. R. Van Horn, and A. J. Dempster, Phys. Rev. 71, " 'N a recent paper' it was shown cayed, we conclude that the temperature at that time must 745 {1947). have been of the order To — wishes to express his gratitude to Professor The author that the large neutron 10' 'K (which corresponds to to Mr. D. B. R. Ladenburg for many helpful discussions, ls due to the isotope at mass absorption ln samarium the dissociation of deuterium so that the Universe is radiation nuclei), energy of for the designing and building Davis, who is responsible 149. Since the alteration by the neutrons produced was nT4/c' was of the order of magnitude density of radiation of' the Ordnance and to members with a 4-mg The Origin of Elements not very large, the experiment was repeated and the Seyaration the balloon equipment of water density. If, as we shall show later, this radiation sample exposed in a thin layer of approximately to make 1 mg per a Laboratory the Research who helped flight of Galaxies of matter, density exceeded the density the relativistic sq. cm to a much Aux. The isotope at stronger neutron successful one. for the of the expression expansion universe must be G. G~ow G. Gamow (June 1948) that it could not be detected. 149 was so reduced mass written in the form: ~ This report is based upon work performed D. C. under Contract N6onr- George R'ashiegton 6'ashiegtos, University, One of ten mass spectra made with one milligram of the Research at the Ordnance Research 270 with the CNSce of Naval 8' oT4 ) June 21, 1948 d in Fig. 1, together with a mass spectrum sample is shown of Princeton Laboratory University. ~ E. Funfer, 25, 235 {1937); E. FQnfer, Zeits. f. Physik Natu+miss. of the isotope at mass The intensity of normal samarium. &HE successful of the features 111, Mi {1988)", S. A. Kore and B. Hamermesh, explanation main of Phys. Rev. 69, 155 The novelty in this paper is the new approach that Gamow took in 150 was greatly increased so that it appears approximately {1946). process, "" the abundance curve of chemical elements by the / is an arbitrary distance in the expanding where space, g H. A. Bethe, S. A. Korff. and G. Placzek, Phys. Rev. SV, 573 to the one at 154. A faint the computation of the temperature at which the deuterium formation equal gadolinium impurity {1940). and the term containing of the "unfinished hypothesis the curvature building-up is neglected because per- I S. A. Kor8 and A. Cobas. Phys. Rev. V3, 1010 (1940). on the the two absorbing exposures, with showed long begins. Indeed, he understood that for large temperature, the reverse mits us to get certain information of the high density value. Since for the adiabatic expansion the densities ~ H. M. Agnew, concerning Vf. C. Bright, and Darol Froman, Phys. Rev. 2'2, isotopes at 155 and 157 missing. 2O3 (i947'). T is inversely to /, we can rewrite (1) in the proportional and temperatures dissociation process which must have existed in the universe of the plates that Photometric measurements showed form: during the early stages of its expansion. Ke want to discuss the densities at the masses 147, 148, 152, and 154 fell on γ + d -> n + p T' 8xGo d here some interesting which can cosmogonical conclusions a normal photographic density curve indicating no changes forbid the formation of the deuterium. In other words, the be based on these informations. in SN~arium as a result of neutron Neutron Absorytion absorption in any of these isotopes. nucleosynthesis process can only be initiated once T drops to or, integrating: The new abundance at mass 150 was found from four spec- Since the building-up process must have started with the A. J. DRIPPER T D = 10 9 K = 0.085 MeV. of deuterons from the primordial formation neutrons and Argent 147 149 Chicago, IQinois National Laboratory, 32Wo' t ) 148 I iso the protons into which some of these neutrons have de- Notice that Gamow took a temperature well below the binding June 28, 1948 For the radiation we have: density at that time must " 'N a recent paper' it was shown cayed, we conclude that the temperature have been of the order To — energy of the deuterium ( B D =2.1 MeV ) as he should have been that the large neutron 10' 'K (which corresponds 3 to 1 Exposed ls due to the isotope at mass aware of the Saha equation. absorption ln samarium 32M t2. of deuterium the dissociation so that the ills I nuclei), energy 149. Since the alteration by the neutrons produced was density of radiation nT4/c' was of the order of magnitude show that the time to, when the temperature These formulas with a 4-mg not very large, the experiment was repeated of water density. If, as we shall show later, this radiation dropped low enough to permit the formation of deuterium, sample exposed in a thin layer of approximately 1 mg per was several minutes. Let us assume that at that time the of matter, density exceeded the density the relativistic sq. cm to a much Aux. The isotope at Normal stronger neutron of matter density (protons of the neutrons) was expression for the expansion plus universe must be p that it could not be detected. 149 was so reduced mass to radiation, Since, in contrast the matter is conserved in the form: written of expansion, p, ~. was One of ten mass spectra made with one milligram of the as the process in decreasing of p, t. ' can be estimated 8' oT4 ) I '~7'~t d in Fig. 1, together with a mass spectrum sample is shown VlG. l. Samarium &, The value from isotopes altered by neutron absorption. of the isotope at mass The intensity of normal samarium. 150 was greatly increased so that it appears approximately / is an arbitrary in the expanding where distance space, to the one at 154. A faint gadolinium equal impurity and the term containing the curvature is neglected because on the with the two absorbing showed exposures, long of the high density value. Since for the adiabatic expansion isotopes at 155 and 157 missing. T is inversely to /, we can rewrite (1) in the proportional Photometric of the plates that measurements showed form: the densities at the masses 147, 148, 152, and 154 fell on T' 8xGo d a normal photographic density curve indicating no changes as a result of neutron in any of these isotopes. absorption or, integrating: The new abundance at mass 150 was found from four spec- 147 149 32Wo' t ) 148 I iso For the radiation we have: density 3 1 Exposed 32M t2. ills I These formulas show that the time to, when the temperature dropped low enough to permit the formation of deuterium, was several minutes. Let us assume that at that time the Normal of matter density (protons neutrons) plus was p to radiation, Since, in contrast the matter is conserved of expansion, p, ~. was the as in process decreasing of p, t. ' can be estimated I '~7'~t &, The value VlG. l. Samarium from isotopes altered by neutron absorption.

  64. LETTERS TO THE EDITOR Kore, and Placzek. ' These values, as well as those calcu- to 21. 2+0. 4 percent. tra to have increased The normal of Kore and at 150 is 7. 47, and at 149, 13. 84 percent, lated from recent results Cobas, abundance the Agnew, Bright, and Froman„are shown in Fig. 2. (The upper limit sum being 21. 3 percent. This shows that within the experi- value. ) that at of q cannot exceed twice the calcuhted mental error the 149 isotopes disappear mass The cadmium ratio, i. e. , the ratio between the unshielded reappear at mass 150. The absorbing cross sections of the is of the order of 2. 2 over to be less than one percent counters, other isotopes were estimated and cadmium-shielded the depth from 22. 8 cm of Hg to 4 cm of' Hg. This is in of that of the isotope at mass 149. Bright, and Froman's4 results. with Agnew, agreement ~ R. E. Lapp. J. R. Van Horn, and A. J. Dempster, Phys. Rev. 71, wishes to express his gratitude to Professor 745 {1947). The author to Mr. D. B. R. Ladenburg for many discussions, helpful and building of for the designing Davis, who is responsible of' the Ordnance and to members The Origin of Elements and the Seyaration the balloon equipment a to make the Research Laboratory who helped flight of Galaxies successful one. G. G~ow ~ This report is based upon work performed under Contract N6onr- D. C. George R'ashiegton 6'ashiegtos, University, Research at the Ordnance Research 270 with the CNSce of Naval June 21, 1948 Laboratory of Princeton University. ~ E. Funfer, 25, 235 {1937); E. FQnfer, Zeits. f. Physik LETTERS TO THE Natu+miss. EDITOR &HE successful of the features 111, Mi {1988)", S. A. Kore and B. Hamermesh, explanation main of Phys. Rev. 69, 155 {1946). process, "" the abundance curve of chemical elements by the g H. A. Bethe, S. A. Korff. and G. Placzek, Phys. Rev. SV, 573 Kore, and Placzek. ' These values, as well as those calcu- {1940). of the "unfinished hypothesis building-up per- to 21. 2+0. 4 percent. I S. A. Kor8 and A. Cobas. Phys. Rev. V3, 1010 (1940). tra to have increased The normal mits us to get certain information the densities ~ H. M. Agnew, concerning Vf. C. Bright, and Darol Froman, Phys. Rev. 2'2, of Kore and at 150 is 7. 47, and at 149, 13. 84 percent, lated from recent results Cobas, abundance the Agnew, 2O3 (i947'). and temperatures which must have existed in the universe sum being 21. 3 percent. This shows that within Bright, and Froman„are shown in Fig. 2. (The upper limit the experi- during the early stages of its expansion. Ke want to discuss value. ) at of q cannot exceed twice the calcuhted error the that 149 mental isotopes disappear mass here some interesting which can cosmogonical conclusions The cadmium ratio, i. e. , the ratio between the unshielded reappear at mass 150. The absorbing cross sections of the be based on these informations. in SN~arium Neutron Absorytion is of the order of 2. 2 over other isotopes were estimated to be less than one percent and cadmium-shielded counters, Since the building-up process must have started with the A. J. DRIPPER the depth from 22. 8 cm of Hg to 4 cm of' Hg. This is in of that of the isotope at mass 149. formation of deuterons from the primordial neutrons and Chicago, IQinois Argent National Laboratory, some of these neutrons have de- the protons into which Bright, and Froman's4 June 28, 1948 results. with Agnew, agreement ~ R. E. Lapp. J. R. Van Horn, and A. J. Dempster, Phys. Rev. 71, " 'N a recent paper' it was shown cayed, we conclude that the temperature at that time must 745 {1947). have been of the order To — wishes to express his gratitude to Professor The author that the large neutron 10' 'K (which corresponds to to Mr. D. B. R. Ladenburg for many helpful discussions, ls due to the isotope at mass absorption ln samarium the dissociation of deuterium so that the Universe is radiation nuclei), energy of for the designing and building Davis, who is responsible 149. Since the alteration by the neutrons produced was nT4/c' was of the order of magnitude density of radiation of' the Ordnance and to members with a 4-mg The Origin of Elements not very large, the experiment was repeated and the Seyaration the balloon equipment of water density. If, as we shall show later, this radiation sample exposed in a thin layer of approximately to make 1 mg per a Laboratory the Research who helped flight of Galaxies of matter, density exceeded the density the relativistic sq. cm to a much Aux. The isotope at stronger neutron successful one. for the of the expression expansion universe must be G. G~ow G. Gamow (June 1948) that it could not be detected. 149 was so reduced mass written in the form: ~ This report is based upon work performed D. C. under Contract N6onr- George R'ashiegton 6'ashiegtos, University, One of ten mass spectra made with one milligram of the Research at the Ordnance Research 270 with the CNSce of Naval 8' oT4 ) June 21, 1948 d in Fig. 1, together with a mass spectrum sample is shown of Princeton Laboratory University. ~ E. Funfer, 25, 235 {1937); E. FQnfer, Zeits. f. Physik Natu+miss. of the isotope at mass The intensity of normal samarium. &HE successful of the features 111, Mi {1988)", S. A. Kore and B. Hamermesh, explanation main of Phys. Rev. 69, 155 The novelty in this paper is the new approach that Gamow took in 150 was greatly increased so that it appears approximately {1946). process, "" the abundance curve of chemical elements by the / is an arbitrary distance in the expanding where space, g H. A. Bethe, S. A. Korff. and G. Placzek, Phys. Rev. SV, 573 to the one at 154. A faint the computation of the temperature at which the deuterium formation equal gadolinium impurity {1940). and the term containing of the "unfinished hypothesis the curvature building-up is neglected because per- I S. A. Kor8 and A. Cobas. Phys. Rev. V3, 1010 (1940). on the the two absorbing exposures, with showed long begins. Indeed, he understood that for large temperature, the reverse mits us to get certain information of the high density value. Since for the adiabatic expansion the densities ~ H. M. Agnew, concerning Vf. C. Bright, and Darol Froman, Phys. Rev. 2'2, isotopes at 155 and 157 missing. 2O3 (i947'). T is inversely to /, we can rewrite (1) in the proportional and temperatures dissociation process which must have existed in the universe of the plates that Photometric measurements showed form: during the early stages of its expansion. Ke want to discuss the densities at the masses 147, 148, 152, and 154 fell on γ + d -> n + p T' 8xGo d here some interesting which can cosmogonical conclusions a normal photographic density curve indicating no changes forbid the formation of the deuterium. In other words, the be based on these informations. in SN~arium as a result of neutron Neutron Absorytion absorption in any of these isotopes. nucleosynthesis process can only be initiated once T drops to or, integrating: The new abundance at mass 150 was found from four spec- Since the building-up process must have started with the A. J. DRIPPER T D = 10 9 K = 0.085 MeV. of deuterons from the primordial formation neutrons and Argent 147 149 Chicago, IQinois National Laboratory, 32Wo' t ) 148 I iso the protons into which some of these neutrons have de- Notice that Gamow took a temperature well below the binding June 28, 1948 For the radiation we have: density at that time must " 'N a recent paper' it was shown cayed, we conclude that the temperature have been of the order To — energy of the deuterium ( B D =2.1 MeV ) as he should have been that the large neutron 10' 'K (which corresponds 3 to 1 Exposed ls due to the isotope at mass aware of the Saha equation. absorption ln samarium 32M t2. of deuterium the dissociation so that the ills I nuclei), energy 149. Since the alteration by the neutrons produced was density of radiation nT4/c' was of the order of magnitude show that the time to, when the temperature These formulas with a 4-mg not very large, the experiment was repeated of water density. If, as we shall show later, this radiation From Friedmann equation , one can write dropped low enough to permit the formation of deuterium, sample exposed in a thin layer of approximately 1 mg per was several minutes. Let us assume that at that time the of matter, density exceeded the density the relativistic sq. cm to a much Aux. The isotope at Normal stronger neutron of matter density (protons of the neutrons) was expression for the expansion plus universe must be p that it could not be detected. dLog(a)/dt = (8 π G/3 ρ rad ) 1/2 149 was so reduced mass to radiation, Since, in contrast the matter is conserved in the form: written of expansion, p, ~. was One of ten mass spectra made with one milligram of the as the process in decreasing of p, t. ' can be estimated 8' oT4 ) I '~7'~t d in Fig. 1, together with a mass spectrum sample is shown VlG. l. Samarium &, The value from and a*T = cste implies dLog(a)/dt = -dLog(T)/dt , and then after isotopes altered by neutron absorption. of the isotope at mass The intensity of normal samarium. integration 150 was greatly increased so that it appears approximately / is an arbitrary in the expanding where distance space, to the one at 154. A faint gadolinium equal impurity and the term containing the curvature is neglected because ρ rad = (3/32 π G)*(1/t 2 ) = π /15 T 4 ~ 8.40 (T/10 9 K) 4 g cm -3 on the with the two absorbing showed exposures, long of the high density value. Since for the adiabatic expansion isotopes at 155 and 157 missing. T is inversely to /, we can rewrite (1) in the proportional Photometric of the plates that measurements showed form: which leads to the densities at the masses 147, 148, 152, and 154 fell on T' 8xGo d t=231 (10 9 K/T) 2 seconds a normal photographic density curve indicating no changes as a result of neutron in any of these isotopes. absorption or, integrating: The new abundance at mass 150 was found from four spec- confirming that the nucleosynthesis is initiated at about 200 seconds 147 149 32Wo' t ) 148 I iso For the radiation we have: density 3 1 Exposed 32M t2. ills I These formulas show that the time to, when the temperature dropped low enough to permit the formation of deuterium, was several minutes. Let us assume that at that time the Normal of matter density (protons neutrons) plus was p to radiation, Since, in contrast the matter is conserved of expansion, p, ~. was the as in process decreasing of p, t. ' can be estimated I '~7'~t &, The value VlG. l. Samarium from isotopes altered by neutron absorption.

  65. LETTERS TO THE EDITOR Kore, and Placzek. ' These values, as well as those calcu- to 21. 2+0. 4 percent. tra to have increased The normal of Kore and at 150 is 7. 47, and at 149, 13. 84 percent, lated from recent results Cobas, abundance the Agnew, Bright, and Froman„are shown in Fig. 2. (The upper limit sum being 21. 3 percent. This shows that within the experi- value. ) that at of q cannot exceed twice the calcuhted mental error the 149 isotopes disappear mass The cadmium ratio, i. e. , the ratio between the unshielded reappear at mass 150. The absorbing cross sections of the is of the order of 2. 2 over to be less than one percent counters, other isotopes were estimated and cadmium-shielded the depth from 22. 8 cm of Hg to 4 cm of' Hg. This is in of that of the isotope at mass 149. Bright, and Froman's4 results. with Agnew, agreement ~ R. E. Lapp. J. R. Van Horn, and A. J. Dempster, Phys. Rev. 71, wishes to express his gratitude to Professor 745 {1947). The author to Mr. D. B. R. Ladenburg for many discussions, helpful and building of for the designing Davis, who is responsible of' the Ordnance and to members The Origin of Elements and the Seyaration the balloon equipment a to make the Research Laboratory who helped flight of Galaxies successful one. G. G~ow ~ This report is based upon work performed under Contract N6onr- D. C. George R'ashiegton 6'ashiegtos, University, Research at the Ordnance Research 270 with the CNSce of Naval June 21, 1948 Laboratory of Princeton University. ~ E. Funfer, 25, 235 {1937); E. FQnfer, Zeits. f. Physik LETTERS TO THE Natu+miss. EDITOR &HE successful of the features 111, Mi {1988)", S. A. Kore and B. Hamermesh, explanation main of Phys. Rev. 69, 155 {1946). process, "" the abundance curve of chemical elements by the g H. A. Bethe, S. A. Korff. and G. Placzek, Phys. Rev. SV, 573 Kore, and Placzek. ' These values, as well as those calcu- {1940). of the "unfinished hypothesis building-up per- to 21. 2+0. 4 percent. I S. A. Kor8 and A. Cobas. Phys. Rev. V3, 1010 (1940). tra to have increased The normal mits us to get certain information the densities ~ H. M. Agnew, concerning Vf. C. Bright, and Darol Froman, Phys. Rev. 2'2, of Kore and at 150 is 7. 47, and at 149, 13. 84 percent, lated from recent results Cobas, abundance the Agnew, 2O3 (i947'). and temperatures which must have existed in the universe sum being 21. 3 percent. This shows that within Bright, and Froman„are shown in Fig. 2. (The upper limit the experi- during the early stages of its expansion. Ke want to discuss value. ) at of q cannot exceed twice the calcuhted error the that 149 mental isotopes disappear mass here some interesting which can cosmogonical conclusions The cadmium ratio, i. e. , the ratio between the unshielded reappear at mass 150. The absorbing cross sections of the be based on these informations. in SN~arium Neutron Absorytion is of the order of 2. 2 over other isotopes were estimated to be less than one percent and cadmium-shielded counters, Since the building-up process must have started with the A. J. DRIPPER the depth from 22. 8 cm of Hg to 4 cm of' Hg. This is in of that of the isotope at mass 149. formation of deuterons from the primordial neutrons and Chicago, IQinois Argent National Laboratory, some of these neutrons have de- the protons into which Bright, and Froman's4 June 28, 1948 results. with Agnew, agreement ~ R. E. Lapp. J. R. Van Horn, and A. J. Dempster, Phys. Rev. 71, " 'N a recent paper' it was shown cayed, we conclude that the temperature at that time must 745 {1947). have been of the order To — wishes to express his gratitude to Professor The author that the large neutron 10' 'K (which corresponds to to Mr. D. B. R. Ladenburg for many helpful discussions, ls due to the isotope at mass absorption ln samarium the dissociation of deuterium so that the Universe is radiation nuclei), energy of for the designing and building Davis, who is responsible 149. Since the alteration by the neutrons produced was nT4/c' was of the order of magnitude density of radiation of' the Ordnance and to members with a 4-mg The Origin of Elements not very large, the experiment was repeated and the Seyaration the balloon equipment of water density. If, as we shall show later, this radiation sample exposed in a thin layer of approximately to make 1 mg per a Laboratory the Research who helped flight of Galaxies of matter, density exceeded the density the relativistic sq. cm to a much Aux. The isotope at stronger neutron successful one. for the of the expression expansion universe must be G. G~ow G. Gamow (June 1948) that it could not be detected. 149 was so reduced mass written in the form: ~ This report is based upon work performed D. C. under Contract N6onr- George R'ashiegton 6'ashiegtos, University, One of ten mass spectra made with one milligram of the Research at the Ordnance Research 270 with the CNSce of Naval 8' oT4 ) June 21, 1948 d in Fig. 1, together with a mass spectrum sample is shown of Princeton Laboratory University. ~ E. Funfer, 25, 235 {1937); E. FQnfer, Zeits. f. Physik Natu+miss. of the isotope at mass The intensity of normal samarium. &HE successful of the features 111, Mi {1988)", S. A. Kore and B. Hamermesh, explanation main of Phys. Rev. 69, 155 The novelty in this paper is the new approach that Gamow took in 150 was greatly increased so that it appears approximately {1946). process, "" the abundance curve of chemical elements by the / is an arbitrary distance in the expanding where space, g H. A. Bethe, S. A. Korff. and G. Placzek, Phys. Rev. SV, 573 to the one at 154. A faint the computation of the temperature at which the deuterium formation equal gadolinium impurity {1940). and the term containing of the "unfinished hypothesis the curvature building-up is neglected because per- I S. A. Kor8 and A. Cobas. Phys. Rev. V3, 1010 (1940). on the the two absorbing exposures, with showed long begins. Indeed, he understood that for large temperature, the reverse mits us to get certain information of the high density value. Since for the adiabatic expansion the densities ~ H. M. Agnew, concerning Vf. C. Bright, and Darol Froman, Phys. Rev. 2'2, isotopes at 155 and 157 missing. 2O3 (i947'). T is inversely to /, we can rewrite (1) in the proportional and temperatures dissociation process which must have existed in the universe of the plates that Photometric measurements showed form: during the early stages of its expansion. Ke want to discuss the densities at the masses 147, 148, 152, and 154 fell on γ + d -> n + p T' 8xGo d here some interesting which can cosmogonical conclusions a normal photographic density curve indicating no changes forbid the formation of the deuterium. In other words, the be based on these informations. in SN~arium as a result of neutron Neutron Absorytion absorption in any of these isotopes. nucleosynthesis process can only be initiated once T drops to or, integrating: The new abundance at mass 150 was found from four spec- Since the building-up process must have started with the A. J. DRIPPER T D = 10 9 K = 0.085 MeV. of deuterons from the primordial formation neutrons and Argent 147 149 Chicago, IQinois National Laboratory, 32Wo' t ) 148 I iso the protons into which some of these neutrons have de- Notice that Gamow took a temperature well below the binding June 28, 1948 For the radiation we have: density at that time must " 'N a recent paper' it was shown cayed, we conclude that the temperature have been of the order To — energy of the deuterium ( B D =2.1 MeV ) as he should have been that the large neutron 10' 'K (which corresponds 3 to 1 Exposed ls due to the isotope at mass aware of the Saha equation. absorption ln samarium 32M t2. of deuterium the dissociation so that the ills I nuclei), energy 149. Since the alteration by the neutrons produced was density of radiation nT4/c' was of the order of magnitude show that the time to, when the temperature These formulas with a 4-mg not very large, the experiment was repeated of water density. If, as we shall show later, this radiation From Friedmann equation , one can write dropped low enough to permit the formation of deuterium, sample exposed in a thin layer of approximately 1 mg per Gamow then computed the density of matter at was several minutes. Let us assume that at that time the of matter, density exceeded the density the relativistic sq. cm to a much Aux. The isotope at Normal stronger neutron this time ( 200 seconds ) to check that it is of matter density (protons of the neutrons) was expression for the expansion plus universe must be p that it could not be detected. dLog(a)/dt = (8 π G/3 ρ rad ) 1/2 149 was so reduced mass to radiation, Since, in contrast the matter is conserved in the form: written effectively radiated dominated . of expansion, p, ~. was One of ten mass spectra made with one milligram of the as the process in decreasing of p, t. ' can be estimated 8' oT4 ) I '~7'~t From T=10 9 K, Gamow deduces d in Fig. 1, together with a mass spectrum sample is shown VlG. l. Samarium &, The value from and a*T = cste implies dLog(a)/dt = -dLog(T)/dt , and then after isotopes altered by neutron absorption. of the isotope at mass The intensity v =4.8 x 10 8 cm s -1 of normal samarium. integration 150 was greatly increased so that it appears approximately and then using nt σ v = 1 , with t~200, one can / is an arbitrary in the expanding where distance space, to the one at 154. A faint gadolinium equal impurity and the term containing compute n~10 18 cm -3 , and then the curvature is neglected because ρ rad = (3/32 π G)*(1/t 2 ) = π /15 T 4 ~ 8.40 (T/10 9 K) 4 g cm -3 on the with the two absorbing showed exposures, long of the high density value. Since for the adiabatic expansion ρ m = n m ~3.6 x 10 -6 g cm -3 isotopes at 155 and 157 missing. T is inversely to /, we can rewrite (1) in the proportional which is much less than the radiation density Photometric of the plates that measurements showed form: which leads to the densities at the masses 147, 148, 152, and 154 fell on ρ rad ~10 g cm -3 (order of the water density). T' 8xGo d t=231 (10 9 K/T) 2 seconds a normal photographic density curve indicating no changes However, Gamow 4 months later will develop a as a result of neutron in any of these isotopes. absorption more detailed analysis of the nucleosynthesis . or, integrating: The new abundance at mass 150 was found from four spec- confirming that the nucleosynthesis is initiated at about 200 seconds 147 149 32Wo' t ) 148 I iso For the radiation we have: density 3 1 Exposed 32M t2. ills I These formulas show that the time to, when the temperature dropped low enough to permit the formation of deuterium, was several minutes. Let us assume that at that time the Normal of matter density (protons neutrons) plus was p to radiation, Since, in contrast the matter is conserved of expansion, p, ~. was the as in process decreasing of p, t. ' can be estimated I '~7'~t &, The value VlG. l. Samarium from isotopes altered by neutron absorption.

  66. Computing ρ matter G. Gamow (October 1948) After having understood that the Universe is not dominated by the dust (mass) but by the radiation at the time of deuterium formation, Gamow decided to compute the density of matter ρ m at that time. N n = X ρ a 3 ; N p = Y ρ a 3 dN n = − λ N n − N n ( Y ρ m ) σ v dt ⇒ ρ a 3 dX dt = − λρ a 3 X − ρ a 3 XY ρ m σ v Which gives when combining with the equation for the proton dX dt = − λ X − XY ρ mv σ dY dt = + λ X − XY ρ mv σ

  67. Computing ρ matter G. Gamow (October 1948) After having understood that the Universe is not dominated by the dust (mass) but by the radiation at the time of deuterium formation, Gamow decided to compute the density of matter ρ m at that time. N n = X ρ a 3 ; N p = Y ρ a 3 dN n = − λ N n − N n ( Y ρ m ) σ v dt ⇒ ρ a 3 dX dt = − λρ a 3 X − ρ a 3 XY ρ m σ v Gamow supposed the limit condition Y = 0.5 when t goes to infinity : he supposed that half of the mass component of the Which gives when combining with the equation for the proton Universe is made of hydrogen. As a result he obtained dX dt = − λ X − XY ρ mv σ ρ m (10 9 K) = 7.2 x 10 -3 (1s/t) 3/2 g cm -3 . dY dt = + λ X − XY ρ mv σ However, Gamow was not interested to the present temperature of the radiation, but to the formation of galaxies. It is Alpher and Herman who will, 2 weeks later , compute it.

  68. The prediction Alpher, Herman (October 1948) The article of Alpher and Herman began by 4 corrections to the preceding article of Gamow. The relation between Gamow , Alpher (his PhD student) and Herman (his postdoc) was not so clear, but some tensions seemed to have appeared after the αβγ event . In any case, correcting the ρ m of Gamow , they computed the relic temperature nowadays. They obtained R. Alpher R. Herman ρ m = 1.7 x 10 -2 (1s/t) 3/2 g cm -3 ~ 2x10 -6 g cm -3 at 10 9 K. Noting that ρ (T)/T 3 = constant , we can deduce T now = 10 9 K [ ρ now / ρ (10 9 K)] 1/3 . Taking from galaxies observations ρ now = 10 -30 g cm -3 ( ρ c = 2 x 10 -29 h 2 g cm -3 ), one obtains T now ~5 K. This is the first prediction of the Cosmic Microwave Background

  69. The prediction Alpher, Herman (October 1948) The article of Alpher and Herman began by 4 corrections to the preceding article of Gamow. The relation between Gamow , Alpher (his PhD student) and Herman (his postdoc) was not so clear, but some tensions seemed to have appeared after the αβγ event . In any case, correcting the ρ m of Gamow , they computed the relic temperature nowadays. They obtained R. Alpher R. Herman ρ m = 1.7 x 10 -2 (1s/t) 3/2 g cm -3 ~ 2x10 -6 g cm -3 at 10 9 K. Noting that ρ (T)/T 3 = constant , we can deduce T now = 10 9 K [ ρ now / ρ (10 9 K)] 1/3 . Taking from galaxies observations ρ now = 10 -30 g cm -3 ( ρ c = 2 x 10 -29 h 2 g cm -3 ), one obtains T now ~5 K. This is the first prediction of the Cosmic Microwave And then…… the field came to sleep Background for a long 20 years period….

  70. The rediscovery « Well, boys, we’ve been scooped », Dicke after a phone call by Penzias , december 1964 The story of the « accidental » discovery of the Cosmic Microwave Background ( CMB ) in 1965, which led Penzias and Wilson to the 1978 Nobel prize (shared with Kapitsa ) can be found in many textbook/websites/forums.. To make it short, Dicke and its team ( Peebles then student, Roll and Wilkinson , the « W » of WMAP ) recomputed, independently in 1963, the prediction of Gamow , and Alpher/Herman . They were in their offices in Princeton discussing about how to build an antennae able to measure such a 5 K radiation ( 3 K in their calculation), when Dicke answer to a phone-call by Penzias . As Dicke put the phone down, he turned to his colleagues and said « Well, boys, we’ve been scooped ».

  71. The rediscovery « Well, boys, we’ve been scooped », Dicke after a phone call by Penzias , december 1964 The story of the « accidental » discovery of the Cosmic Microwave Background ( CMB ) in 1965, which led Penzias and Wilson to the 1978 Nobel prize (shared with Kapitsa ) can be found in many textbook/websites/forums.. To make it short, Dicke and its team ( Peebles then student, Roll and Wilkinson , the « W » of WMAP ) recomputed, independently in 1963, the prediction of Gamow , and Alpher/Herman . They were in their offices in Princeton discussing about how to build an antennae able to measure such a 5 K radiation ( 3 K in their calculation), when Dicke answer to a phone-call by Penzias . As Dicke put the phone down, he turned to his colleagues and said « Well, boys, we’ve been scooped ». Dicke et al. noticed that an upper bound on the Helium density in the protogalaxies lead to an upper limit of mass density at deuterium composition time ρ dmax . Leading at the end by a lower value to the present radiation : T 0 = T d ( ρ 0 / ρ d ) 1/3 > T d ( ρ 0 / ρ dmax ) A 3.5 K radiation however leads to a too small mass density nowadays, inviting Dicke et al. to propose a new scalar field inspired by General Relativity.

  72. The rediscovery « Well, boys, we’ve been scooped », Dicke after a phone call by Penzias , december 1964 The story of the « accidental » discovery of the Cosmic Microwave Background ( CMB ) in 1965, which led Penzias and Wilson to the 1978 Nobel prize (shared with Kapitsa ) can be found in many textbook/websites/forums.. To make it short, Dicke and its team ( Peebles then student, Roll and Wilkinson , the « W » of WMAP ) recomputed, independently in 1963, the prediction of Gamow , and Alpher/Herman . They were in their offices in Princeton discussing about how to build an antennae able to measure such a 5 K radiation ( 3 K in their calculation), when Dicke answer to a phone-call by Penzias . As Dicke put the phone down, he turned to his colleagues and said « Well, boys, we’ve been scooped ». Dicke et al. noticed that an upper bound on the Helium density in the protogalaxies lead to an upper limit of mass density at deuterium composition time ρ dmax . Leading at the end by a lower value to the present radiation : T 0 = T d ( ρ 0 / ρ d ) 1/3 > T d ( ρ 0 / ρ dmax ) A 3.5 K radiation however leads to a too small mass density nowadays, inviting Dicke et al. to propose a new scalar field inspired by General Relativity.

  73. The Helium abundance The novelty in the Dicke et al. article, compared to the Gamow one is the introduction of a more complete fundamental setup ( positron , electron , and the newly discovered neutrino in 1956 ) and the computation of the Helium abundance . Indeed, Gamow stopped the process to the proton abundance, computing the constraints from the hydrogen limits measured in our Universe. Peebles went much further away, solving numerically the complete set of equation governing the formation of the Helium and its isotopes in an article published just 5 months after the Dicke et al. one. P.J. Peebles

  74. The Helium abundance The novelty in the Dicke et al. article, compared to the Gamow one is the introduction of a more complete fundamental setup ( positron , electron , and the newly discovered neutrino in 1956 ) and the computation of the Helium abundance . Indeed, Gamow stopped the process to the proton abundance, computing the constraints from the hydrogen limits measured in our Universe. Peebles went much further away, solving numerically the complete set of equation governing the formation of the Helium and its isotopes in an article published just 5 months after the Dicke et al. one. P.J. Peebles

  75. The Helium abundance The novelty in the Dicke et al. article, compared to the Gamow one is the introduction of a more complete fundamental setup ( positron , electron , and the newly discovered neutrino in 1956 ) and the computation of the Helium abundance . Indeed, Gamow stopped the process to the proton abundance, computing the constraints from the hydrogen limits measured in our Universe. Peebles went much further away, solving numerically the complete set of equation governing the formation of the Helium and its isotopes in an article published just 5 months after the Dicke et al. one. P.J. Peebles

  76. The discovery R. Wilson A. Penzias Penzias and Wilson , ingeener at Bell telecom discovered in 1965 the CMB at 3.5 K ( 2.7 K now) and received the Nobel prize of physics for that ion 1978. Neither Gamow , Alpher , Herman , Dicke or Peebles received Nobel prize for their work.

  77. G. Gamow A. Penzias « Gamow? A man whose idea is wrong in almost every detail», Penzias in his Nobel lecture, 1978.

  78. Summary : how to predict a CMB temperature? 1) You suppose, as Gamow in 1948 that the Universe has been building up from the lightest elements and is not originated from the decay of a « primeval atom » of the Uranium type as Lemaitre imagined in the 20’s (you should for that have a strong sense of intuition)

  79. Summary : how to predict a CMB temperature? 1) You suppose, as Gamow in 1948 that the Universe has been building up from the lightest elements and is not originated from the decay of a « primeval atom » of the Uranium type as Lemaitre imagined in the 20’s (you should for that have a strong sense of intuition) 2) You then feel as Gamow that there was a time t D in the Universe, where its temperature T D was below the binding energy of the deuterium B D =2.2 MeV = 2.2 x 10 10 K to forbid the dissociation process γ + d -> p + n. But as you heard about the Saha equation , you know that the real temperature of dissociation is 0.1 MeV (10 9 K) due to the photon statistic distribution.

  80. Summary : how to predict a CMB temperature? 1) You suppose, as Gamow in 1948 that the Universe has been building up from the lightest elements and is not originated from the decay of a « primeval atom » of the Uranium type as Lemaitre imagined in the 20’s (you should for that have a strong sense of intuition) 2) You then feel as Gamow that there was a time t D in the Universe, where its temperature T D was below the binding energy of the deuterium B D =2.2 MeV = 2.2 x 10 10 K to forbid the dissociation process γ + d -> p + n. But as you heard about the Saha equation , you know that the real temperature of dissociation is 0.1 MeV (10 9 K) due to the photon statistic distribution. 3) Then, using Friedmann equation (especially if Friedmann was your supervisor as it was the case for Gamow ) you deduce at what time Universe was heated down to T D . ✓ ˙ ◆ 2 π 2 = 8 π G ρ rad ( T ) = 8 π G a H 2 = 15 T 4 3 3 a

  81. Summary : how to predict a CMB temperature? 1) You suppose, as Gamow in 1948 that the Universe has been building up from the lightest elements and is not originated from the decay of a « primeval atom » of the Uranium type as Lemaitre imagined in the 20’s (you should for that have a strong sense of intuition) 2) You then feel as Gamow that there was a time t D in the Universe, where its temperature T D was below the binding energy of the deuterium B D =2.2 MeV = 2.2 x 10 10 K to forbid the dissociation process γ + d -> p + n. But as you heard about the Saha equation , you know that the real temperature of dissociation is 0.1 MeV (10 9 K) due to the photon statistic distribution. 3) Then, using Friedmann equation (especially if Friedmann was your supervisor as it was the case for Gamow ) you deduce at what time Universe was heated down to T D . ✓ ˙ ◆ 2 π 2 = 8 π G ρ rad ( T ) = 8 π G a H 2 = 15 T 4 ◆ 3 3 a da a = � dT And using the principle of entropy conservation you deduce aT = cste ) T r Which gives for T=T D =10 9 K r r r 8 π 3 G 45 dT t = M P L 32 π 3 ' 0 . 2 M P L ) ' T 3 = � 45 dt 32 π ) T T T 2 T 2 t ' 3 ⇥ 10 27 GeV − 1 ⇠ 200 seconds

  82. 4) Remarking that the universe was radiation dominated, you then compute the density of mass a the time of dissociation ρ m (10 9 K) = n(10 9 K) m p , noticing that at the time t D , at least one reaction should have happened ' ⇥ ⇠ 1 n ( t D ) σ v t D ' 1 ) n ( t D ) ' σ vt D

  83. 4) Remarking that the universe was radiation dominated, you then compute the density of mass a the time of dissociation ρ m (10 9 K) = n(10 9 K) m p , noticing that at the time t D , at least one reaction should have happened ' ⇥ ⇠ 1 n ( t D ) σ v t D ' 1 ) n ( t D ) ' σ vt D Noticing that the deuterium formation required a cross section σ of 10 -29 cm 2 and that at 10 9 K, the velocity of s 3 T D ⇥ c ' 5 ⇥ 10 8 cm s − 1 the nucleons are given by v = m p You deduce n(t D ) ~ 10 18 cm -3 , implying ρ m (10 9 K) ~ 10 18 GeV/cm 3 = 1.78 x 10 -6 g/cm 3

  84. 4) Remarking that the universe was radiation dominated, you then compute the density of mass a the time of dissociation ρ m (10 9 K) = n(10 9 K) m p , noticing that at the time t D , at least one reaction should have happened ' ⇥ ⇠ 1 n ( t D ) σ v t D ' 1 ) n ( t D ) ' σ vt D Noticing that the deuterium formation required a cross section σ of 10 -29 cm 2 and that at 10 9 K, the velocity of s 3 T D ⇥ c ' 5 ⇥ 10 8 cm s − 1 the nucleons are given by v = m p You deduce n(t D ) ~ 10 18 cm -3 , implying ρ m (10 9 K) ~ 10 18 GeV/cm 3 = 1.78 x 10 -6 g/cm 3 5) Then, noticing that mass should be conserved in an expanding universe, ρ m a 3 = ρ m /T 3 = constant implies ◆ 1 / 3 ◆ 1 / 3 ρ now 10 − 30 ✓ ✓ T now = 10 9 K = 10 9 K ' 8 K m ρ m (10 9 K) 1 . 78 ⇥ 10 − 6 g / cm 3 Where you have supposed that the density of mass today , measured by experimentalists like Oort is around 10 -30 g/cm 3 (the critical density ρ c is 2x10 -29 h 2 g/cm 3 ) The last argument, correcting the mistakes of Gamow , was proposed by Alpher and Hermann in their paper which appeared 2 weeks after the Gamow one in 1948

  85. ν Temperature decoupling ν γ n(T) σ v ee-> νν < H(T) e e γ e 3 MeV T < m e electrons 3x10 10 K degrees of freedom γ 511 keV γ γ γ with = 2*7/4 5x10 9 K γ 100 keV 10 9 K T γ T e T ν 3x10 -4 eV 2.75 K 2x10 -4 eV 1.95 K time

  86. Filling the Universe with neutrino The Zeldovich-Cowsik-McClelland bound, or the birth of cosmological astroparticle Once the CMB has been discovered, and measured, a lot of particle physicists jumped on it to test their predictions through interactions on it ( GZK cutoff and cosmic ray) to astrophysical consequences. Zeldovich and Ghershtein in June 1966 (!!) were the first to obtain limits on a heavy neutrino (the muonic neutrino ν µ has been discovered by Lederman in 1962 ) from cosmological consideration, asking for a Universe respecting the deceleration parameter, obtaining m ν µ < 400 eV. Cowsik and Mac Clelland in 1972 (!!) recomputed it (without citing Zeldovich) with more accurate values of the Hubble parameter and obtained m ν µ < 8 eV (the now called « Cowsik Mac Clelland » bound).

  87. The idea of Zeldovich Y. Zeldovich Suppose a gas of electrons, neutrinos and photons in equilibrium. ν = 3 n e − + n e + = n ν + n ¯ 2 n γ where 3/2 = 3/4 (fermi gas versus boson gas) *2 (2+2 degrees of freedom for fermions vs 2 degrees of freedom for photons) whereas after decoupling of the e + e - : ν = 1 n e − + n e + = 0 ; n ν + n ¯ 2 n γ where 1/2 = 3/2 * 4/11 [(2 + 7/8*4)/2 = 11/4] corresponds to the degrees of freedom of the e + e - absorbed by the photons (and not the neutrino that already decoupled) Then, from the measurements of the CMB, Zeldovich inferred n γ = 550 cm -3 implying n ν = 300 cm -3 . Having a limit on the mass density of the Universe ρ m < 1.25 x10 -28 g cm -3 , they inferred n ν x m ν < ρ m => m ν < 7 x10 -31 g =400 eV

  88. Enrico Fermi “ Tenta tj vo di una tf oria dei raggi β", Ricerca Scien tjfi ca, 1933

  89. The limit used by Zeldovich The deceleration parameter Before the observation of the anisotropies of the CMB (and thus the determination of the cosmological parameters through the measurements of the acoustic peaks ) the only way to determine the matter content of the Universe, without the knowledge of the curvature was to use the second Friedmann equation: ¨ a = − 4 π G ρ ⇒ q ( t ) = − 1 a = 4 π G ¨ a a 3 H 2 ρ 3 H 2 = 1 = 1 with H 2 = 8 π G ρ 2 Ω , ρ c 2 3 ρ c The limit on q < 2.5 from 1966 gives Ω < 5, and ρ c = 1.8 x10 -29 h 2 g cm -3 gives for h < 1.20, ρ c < 2.5 x10 -29 g cm -3 implying ρ < 1.25 x10 -28 g cm -3 . n.b. : Nowadays, ρ < 1.8 x10 -30 g cm -3 , explaining the limit m ν < 8 eV

  90. The Cowsik-Mac Clelland bound (1972) The rediscovering of Zeldovich bound ������������������������������������������������������ ����������� Enrico Fermi �������������������������� � �������� “ Tenta tj vo di una tf oria dei raggi β", Ricerca Scien tjfi ca, 1933 ��������������������� � ��������

  91. PHYSICAL REVIEW LETTERS 4 SEPTEMBER 1972 VOLUME 29, NUMBER 10 Rest Mass* An Upper Limit on the Neutrino and J. McClelland R. Cowsikg of California, Berkeley, 94720 of Pkysics, California University Department (Received 17 Ju1y 1972) In order that the effect of graviation of the thermal neutrinos on the expan- background their mass should be less than 8 eV/ c. sion of the universe not be too severe, of inter- Recently there has been a resurgence and est in the possibility may have a that neutrinos 2s, . +1 ~" finite rest mass. These discussions have been psdp theories, ' pos- (lb) ~(& exp[E/kT(z„)] — 1 2ssks in the context of weak-interaction sible decay of solar neutrinos, ' and enumerating Here n~, . is the number decay modes of the K~' meson. ' of fermions density of the possible the ith kind, n~, is the number of bosons density out that the gravita- Elsewhere, we have pointed of the ith kind, s, . is the spin of the particle (no- of finite rest tional interactions of neutrinos tice that in writing of states of the multiplicity in the discus- mass may become very important the particles we have not discriminated against of clusters of galaxies sion of the dynamics and since we are discussing the neutrinos; neutrinos of the universe. 4 Considerations mas- involving of nonzero rest mass, we have assumed that both are not new'; sive neutrinos an excellent review E = c(p'+mscs)'~s, the helicity states are allowed), in the field is given by of the early developments Kuchowicz. ' Here we wish to point out that the and T(z„) = T„(z„) k is Boltzmann's constant, =Tz(z„)=Ts(z„)=T (z„)= is the common recent measurement' of the deceleration param- temperature of radiation, fermions, bosons, eter, an upper limit of a few tens of qo, implies etc. at the latest epoch, characterized matter, electron volts on the sum of the masses of all by the red shift z„, when they may be considered stable particles the possible light, that interact to be in thermal kT(z„) = 1 MeV. equilibrium; only weakly. Since our discussion pertains to neutrinos and stable weak bosons, ' we may as- In discussing this problem we take the custom- any hypothetical is expanding ary point of view that the universe sume that kT(z„) = 1 MeV»mcs. In this limit state as en- from an initially hot and condensed Eqs. (1a) and (1b) reduce to in the "big-bang" theories. 9 In the early visaged n~. (z„) = 0. 0913(2s, + 1)[T(z„)/kc]s, phase of such a universe, when the temperature (2a) than -1 MeV, processes of neutrino was greater ns(z„) = 0. 122(2s, . + 1)[T(z„)/Kc]s. (2b) which have also been considered production, in stellar cores, ' the context of high-temperature As the universe and cools down, expands the would lead to the generation of the various kinds par- neutrinos and such other weakly interacting PHYSICAL REVIEW LETTERS 4 SzpvxMszR 1972 VoI. UMI 29, NUMB@a 10 In fact, similar processes would of neutrinos. ticles survive without annihilation because of the A little remark generate of other fermions low cross sections'2 for these proces- populations and bosons extremely as well, ses. and conditions of thermal equilibrium density decreases Consequently, the number simply as — V(z„)/V(z) = (1+z)'/(1+z„)'. Notic- n~, . (0) = 200(2s, . +1) cm '. allow us to estimate density": their number (4b) ing that 1+z = T„(z)/T„(0), the number 2s, +1 )" Treatment of Zeldovich is ok but two little mistakes has been made by Cowsik: densities psdp are huge These numbers 2~'I' J. exp[Z/kT(z. , )]+ I ' atoms in the uni- in comparison with the mean number of hydrogen density of the various particles (1a) expected at the present (the original article can be found there: http://www.ymambrini.com/My_World/History.html ) verse; all the visible matter in the universe adds up to an average of hydrogen atoms of only epoch (z =0) are given by density -2& 10 8 cm 3. Notice that the expected density of the neutrinos and other weakly interacting particles is essentially T(z„), of decoupling, Not true. Cowsik forgot to take the mea- of the temperature and such other details; independent s s T (0) n~, (0) =n~, . (z„) =0. 0913(2s, . +1) photons fixes the density of weak particles sured temperature of the universal quite w'ell. blackbody into account the reheating of Z~ Bandage's' consider measurement of the Hubble constant H, and the decelexation parameter Now, qo the thermal bath (photons) due place a limit on p„, , the density of all possible sources of gravitational His results, 8, = 50 km sec ' Mpc ' = l. 7 x 10 " sec ' and qo =+ 0. 94 + 0. 4, imply which together potential in the to the entropy conservation PHYSICAL REVIEW LETTERS 4 SzpvxMszR 1972 VoI. UMI 29, NUMB@a 10 universe, . +1) T„(0) s ns, . (0) =0. 122(2s, once the electrons/positrons (3b) Ac p„, =3H, 'q, /4no = (10~4)&&10 "g cm '= (6~2)x 10' (eV/c') cm '&10' (ev/c') cm '. n~, . (0) = 200(2s, . +1) cm '. (4b) decoupled. Factor (4/11) 1/3 (see (5) These numbers Taking T„(0) =2. 7'K, we have are huge atoms in the uni- in comparison with the mean number density of hydrogen verse; all the visible matter in the universe adds up to an average density of hydrogen atoms of only book section 2.2.7 + Entropy -2& 10 8 cm 3. Notice that the expected density of the neutrinos and other weakly interacting particles H ere G = 6. 68 x l0 n~, . (0) = 150(2s, is the gravitation- . + 1) cm s, dyn cm is essentially of the temperature T(z„), of decoupling, the mea- independent g and such other details; (4a) slide) sured temperature photons fixes the density of weak particles of the universal blackbody quite w'ell. If m, . were to represent the mass al constant, and Space Administration under Grant No. NGB05-008- consider Bandage's' measurement of the Hubble constant H, and the decelexation parameter Now, qo place a limit on p„, , the density of all possible sources of gravitational His results, 8, = 50 km sec ' Mpc ' = l. 7 x 10 " sec ' and qo =+ 0. 94 + 0. 4, imply which together and other sta- potential in the 376. spectrum of the various neutrinos universe, Be- tOn leave from the Tata Institute of Fundamental particles, ble weakly interacting we can combine p„, =3H, 'q, /4no = (10~4)&&10 "g cm '= (6~2)x 10' (eV/c') cm '&10' (ev/c') cm '. (5) search, India. Bombay, Eqs. (4a), (4b), and (5) to obtain the limit Cowsik considered left + right and S. Pakvasa, ~K. Tennakone Phys. Rev. Lett. 27, H ere G = 6. 68 x l0 is the gravitation- dyn cm g p„„q =Qns, m, +n~, . mt' 150(2s;+1)m, &p„, If m, . were to represent the mass al constant, and Space Administration under Grant No. NGB05-008- 757 (1971), and 28, 1415 (1972). handed neutrino whereas right and other sta- 376. of the various neutrinos spectrum 2J. Be- tOn leave from the Tata Institute of Fundamental Bahcall, Cabibbo, and A. Yahil, Phys. Rev. particles, ble weakly interacting we can combine (6) ox' search, India. handed neutrino does not feel Bombay, ¹ ¹ Eqs. (4a), (4b), and (5) to obtain the limit Lett. 28, 316 (1972). ~K. Tennakone and S. Pakvasa, Phys. Rev. Lett. 27, p„„q =Qns, m, +n~, . mt' 150(2s;+1)m, &p„, 757 (1971), and 28, 1415 (1972). Q(2s, + 1)m, . 66 eV/c'. ~S. Barshay, Phys. Bev. Lett. 28, 1008 (1972). weak interaction, i.e. cannot be 2J. Bahcall, Cabibbo, and A. Yahil, Phys. Rev. ox' (6) ¹ ¹ 48, Cowsik and J. McClelland, Lett. 28, 316 (1972). "Gravity of Neutrinos is to be carried out over all Q(2s, + 1)m, . 66 eV/c'. Here the summation ~S. Barshay, Phys. Bev. Lett. 28, 1008 (1972). considered as in thermal 48, Cowsik and J. McClelland, "Gravity of Neutrinos of Non-Zero is to be carried out over all Mass in Astrophysics" (to be published), Here the summation states of both fer- the particle and antipax'ticle of Non-Zero Mass in Astrophysics" (to be published), states of both fer- the particle and antipax'ticle The ¹ utrino (Nauka, equilibrium with the left 'M. A. Markov, The ¹ utrino (Nauka, 'M. A. Markov, Moscow, Moscow, mions and bosons. Considering only the neutrinos and bosons. only the neutrinos mions Considering U. S. S. B. , 1964). U. S. S. B. , 1964). of the muon and electron kind and antineutrinos J, Bahcall and B. B. Curtis, Nuovo Cimento 21, 422 handed ones: only 2 degrees of each having a mass of m„, Eg. (6) leads to the of the muon and electron kind and antineutrinos (1961). J, Bahcall and B. B. Curtis, Nuovo Cimento 21, 422 'B. Kuchowics, result m„«8 eV/c'. of the ¹ atmno The BibLiography freedom for neutrinos should each having a mass of m„, Eg. (6) leads to the big-bang cos- This limit is obtained (Gordon and Breach, New York, 1967), and Fortschr. assuming (1961). Phys. 17, 517 (1969). mology to be correct; it depends however, only 'B. Kuchowics, result m„«8 eV/c'. of the ¹ atmno Astrophys. J. 178, 485 (1972), and to be considered ( ν L + ν L ), not 4 8A. Sandage, The BibLiography very weakly on the value of the deceleration be published. and other details of the cosmology. parameter big-bang cos- This limit is obtained 9p. J. E. peebles, (Gordon and Breach, New York, 1967), and Fortschr. assuming Physical Cosmology (princeton even when one allows for a large uncertain- Thus, N. J. , 1971). Univ. Press, Princeton, Phys. 17, 517 (1969). mology to be correct; parameters, the limits it depends ty in the cosmological however, on 'OM. A. Buderman, only on Weak In- in ToPicaL Conference Astrophys. J. 178, 485 (1972), and to the masses of neutrinos and other stable weakIy 1969 (CERN teractions, CERN, Geneva, qaoitze~land, 8A. Sandage, on the value of the deceleration very weakly interacting particles derived in this paper are Scientific Information Service, Geneva, S~itzerland, 1969), p. 111. still much lower than the di. rect expeximental be published. parameter and other details of the cosmology. ~L. D. Landau and E. M. Lifshitz, Statistic/ limits's'4 Physics 9p. J. E. peebles, of m„„&1. and m„, &60 eV/c . 5 MeV/c' Physical Cosmology (princeton Mass. , 1969), 2nd ed. , (Addison-Wesley, Beading, Our thanks are due to Professor Eugene D. Com- even when one allows for a large uncertain- Thus, N. J. , 1971). p. 824. mins, Professor J. Bahcall, Professor G. B. Univ. Press, Princeton, T. de Graff and H. A. Tolhoek, Nucl. Phys, 81, 596 ¹ and Professor P. Buford Price for many Field, ty in the cosmological parameters, the limits (1966). on 'OM. A. Buderman, on Weak In- in ToPicaL Conference discussions. ~3K. Bergkvist, Nucl. Phys, B39, 817 (1972). the masses of neutrinos and K. O. H. Ziock, Phys. I ett. 87B, and other stable weakIy ~4K. V. Shrum 1969 (CERN teractions, CERN, Geneva, qaoitze~land, 115 (1971). ~Work supported in part by the National Aeronautics particles in this paper are derived Scientific Information Service, interacting S~itzerland, Geneva, 1969), p. 111. still much lower than the di. rect expeximental and E. M. Lifshitz, ~L. D. Landau Statistic/ Physics limits's'4 of m„„&1. and m„, &60 eV/c . 5 MeV/c' Mass. , 1969), 2nd ed. , (Addison-Wesley, Beading, Our thanks are due to Professor Eugene D. Com- p. 824. Professor J. Bahcall, Professor G. B. mins, T. de Graff and H. A. Tolhoek, Nucl. Phys, 81, 596 ¹ and Professor P. Buford Price for many Field, (1966). 670 discussions. ~3K. Bergkvist, Nucl. Phys, B39, 817 (1972). and K. O. H. Ziock, Phys. I ett. 87B, ~4K. V. Shrum 115 (1971). in part by the National Aeronautics ~Work supported 670

  92. But.. luckily.. A miraculous cancelation of mistakes makes this limit still valid today. Enrico Fermi Cowsik took h=0.5, Ω =2 giving Ω h 2 = 0.5 , a factor 5 larger compensated by the fact the (11/4) [e + e - degrees of freedom] * (2) [neutrino helicity] gives also an “ Tenta tj vo di una tf oria dei raggi β", Ricerca Scien tjfi ca, 1933 overabundance of ~5-6 for the neutrinos.

  93. But.. luckily.. A miraculous cancelation of mistakes makes this limit still valid today. Enrico Fermi Cowsik took h=0.5, Ω =2 giving Ω h 2 = 0.5 , a factor 5 larger compensated by the fact the (11/4) [e + e - degrees of freedom] * (2) [neutrino helicity] gives also an “ Tenta tj vo di una tf oria dei raggi β", Ricerca Scien tjfi ca, 1933 overabundance of ~5-6 for the neutrinos. In any case, the Zeldovich/Cowsik work can be considered as the first suggestion that dark matter in gravitationally bound astronomical systems might consist of non- baryonic subatomic particles . However, it is in 1977 and 1978 in papers by Lee &Weinberg and by Gunn et al. that for the first time, physicists proposed the existence of a stable, massive neutral non-baryonic particle that can dominate the present mass density in the Universe.

  94. ������������������������������������������������������ ����������� �������������������������� � �������� The Zeldovich-Hut-Lee-Weinberg bound (1977) ��������������������� � �������� Volume 69B, number 1 PHYSICS LETTERS 18 July 1977 LIMITS ON MASSES AND NUMBER OF NEUTRAL WEAKLY INTERACTING PARTICLES P. HUT Institute for Theoretical Physics, Umversity of Utrecht, Utrecht, Netherlands Received 25 April 1977 Limits on the masses and number of neutral weakly interacting particles are derived using cosmological arguments. No such particles with a mass between 120 eV and 3 GeV can exist within the usual big band model Simdar, but much more severe, restrictions follow for parUcles that interact only gravitationally. This seems of Importance with respect to supersymmetric theories. Adding more types of neutrinos relative to the standard Following an idea, put forward by Shvartsman [1], Steigman et al. [2] presented arguments leading to an big bang model increases the value of K. This would have the following observable effect. upper limit to the number of different types of mass- The neutron/proton ratio is given by the equilibrium less neutrinos, which may be summarized as follows. value n/p = exp {-(m n - mp)/T) as long as the rate of According to the hot big bang model all forms of weak interactions, like e.g. n + e ÷ ~ p + F e, is high matter in the universe, even neutrinos, are initially in enough. But this ratio freezes in soon after the time be- thermal equilibrium. The total energy density of rela- tween successive collisions grows bigger than, say, the tivistic particles is then given at a temperature T by expansion time. The mean free time is r = (oN)-1 as 0 = Ka T4. (1) long as the electrons are relativistic. The cross section a is the radiation density constant, appearing in the o " T 2 and the number density of protons and neu- black-body radiation law, and K is given by trons N ~ R -3, where R is the scale factor of the ex- panding universe. At these early times the number of nucleons is far smaller than the number of photons, t~ = ½ (nb + ~ nf). (2) electrons, positrons and neutrinos, so the cooling pro- The quantities n b and nf are the total number of Inter- ceeds adiabatically like T ~ R -1 . Therefore N ~ T 3 nal degrees of freedom of the different types of bosons and thus and fermions respectively. For a photon gas K = 1, whde r = const. × T -5. (5) for a mixture of photons, electrons, electron and muon neutrinos, together with their antiparticles, ¢ = 9/2. Putting t = r in (4), from (5) we get an effective A second expression for the total energy density p temperature Tf at which the neutron/proton ratio is given as a function of the expansion time t by solv- freezes in, given by ing the Einstein equations in a radiation dominated Tf = const. X K 1/6. (6) homogeneous and isotropic universe, p = 3/32 rr Gt 2, When the temperature falls off further nearly all neu- (3) trons are captured to form deuterium and subsequently helium. In the standard model Tf ~ 1 MeV ~ 1010 K and where G is the gravitational coupling constant, G = 6.7 the abundance by weight ofhehum produced m this way X 10 -45 MeV -2.. Combining (1) and (3) we get is Y ~ 0.23 to 0.27, depending on thepresent density (4) T = (3/32 rr Ga) 1/4 K- 1/4 t- 1/2 of nucleons in the universe. An observational upper limit [4] Y ~ 0.29 agrees well with the standard model. * We use units such that fi = c = k = 1, and the temperature Is Increasing now the number of neutrino types would expressed in MeV. 85

  95. The Lee-Weinberg way (1977) The recipe 1) Compute the temperature of freeze out T f of χ (mass m) from the thermal bath : T 2 m = m ( T f m ) 3 / 2 e − m/T f h σ v i < f n ( T f ) h σ v i = H ( T f ) ) ) T f = ln M P l 26 M P l

  96. The Lee-Weinberg way (1977) The recipe 1) Compute the temperature of freeze out T f of χ (mass m) from the thermal bath : T 2 m = m ( T f m ) 3 / 2 e − m/T f h σ v i < f n ( T f ) h σ v i = H ( T f ) ) ) T f = ln M P l 26 M P l 2) Solve the Boltzmann equation for the Yields Y=(n χ / n γ ) from the thermal equilibrium χ χ <—> γ γ T 2 1 26 dY H ( T ) h σ v i Y 2 dT = ) Y ( T now ) = M P l T f h σ v i = M P l m h σ v i

  97. The Lee-Weinberg way (1977) The recipe 1) Compute the temperature of freeze out T f of χ (mass m) from the thermal bath : T 2 m = m ( T f m ) 3 / 2 e − m/T f h σ v i < f n ( T f ) h σ v i = H ( T f ) ) ) T f = ln M P l 26 M P l 2) Solve the Boltzmann equation for the Yields Y=(n χ / n γ ) from the thermal equilibrium χ χ <—> γ γ T 2 1 26 dY H ( T ) h σ v i Y 2 dT = ) Y ( T now ) = M P l T f h σ v i = M P l m h σ v i 3) Compute the relic abundance and compare with the experimental limits = 26 ⇥ 400 cm − 3 = n ⇥ m = Y ⇥ n γ ⇥ m Ω = ρ ) h σ v i > 10 − 9 h − 2 GeV − 2 < 1 ρ c M P l h σ v i ρ c ρ c ρ c

  98. The Lee-Weinberg way (1977) The recipe 1) Compute the temperature of freeze out T f of χ (mass m) from the thermal bath : T 2 m = m ( T f m ) 3 / 2 e − m/T f h σ v i < f n ( T f ) h σ v i = H ( T f ) ) ) T f = ln M P l 26 M P l 2) Solve the Boltzmann equation for the Yields Y=(n χ / n γ ) from the thermal equilibrium χ χ <—> γ γ T 2 1 26 dY H ( T ) h σ v i Y 2 dT = ) Y ( T now ) = M P l T f h σ v i = M P l m h σ v i 3) Compute the relic abundance and compare with the experimental limits = 26 ⇥ 400 cm − 3 = n ⇥ m = Y ⇥ n γ ⇥ m Ω = ρ ) h σ v i > 10 − 9 h − 2 GeV − 2 < 1 ρ c M P l h σ v i ρ c ρ c ρ c 4) Conclude h σ v i ' G 2 F m 2 > 10 − 9 GeV − 2 ) m > 2 GeV

  99. The Lee-Weinberg way (1977) The recipe 1) Compute the temperature of freeze out T f of χ (mass m) from the thermal bath : T 2 m = m ( T f m ) 3 / 2 e − m/T f h σ v i < f n ( T f ) h σ v i = H ( T f ) ) ) T f = ln M P l 26 M P l 2) Solve the Boltzmann equation for the Yields Y=(n χ / n γ ) from the thermal equilibrium χ χ <—> γ γ T 2 1 26 dY H ( T ) h σ v i Y 2 dT = ) Y ( T now ) = M P l T f h σ v i = M P l m h σ v i 3) Compute the relic abundance and compare with the experimental limits = 26 ⇥ 400 cm − 3 = n ⇥ m = Y ⇥ n γ ⇥ m Ω = ρ ) h σ v i > 10 − 9 h − 2 GeV − 2 < 1 ρ c M P l h σ v i ρ c ρ c ρ c 4) Conclude h σ v i ' G 2 F m 2 > 10 − 9 GeV − 2 ) m > 2 GeV 5) Wait for applauses for that first lower bound on a massive non-baryonic matter filling the Universe.

  100. Enrico Fermi “ Tenta tj vo di una tf oria dei raggi β", Ricerca Scien tjfi ca, 1933

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