Sterile neutrinos as dark matter dark matter candidate: sterile - PowerPoint PPT Presentation

Alexander Kusenko (UCLA) KIAS ’05 Sterile neutrinos as dark matter • dark matter candidate: sterile neutrino, m = 2 − 20 keV • Pulsar kicks can be explained by neutrino oscillations • Constraints and searches [ AK , Segr` e, Fuller, Pascoli, Mocioiu, D’Olivo, et al.] 1

Alexander Kusenko (UCLA) KIAS ’05 Dark matter The only data at variance with the Standard Model The evidence for dark matter is very strong: • galactic rotation curves cannot be explained by the disk alone • cosmic microwave background radiation • gravitational lensing of background galaxies by clusters is so strong that it requires a signficant dark matter component. • clusters are filled with hot X-ray emitting intergalactic gas (without dark matter, this gas would dissipate quickly). 2

Alexander Kusenko (UCLA) KIAS ’05 Dark matter: what is it? 3

Alexander Kusenko (UCLA) KIAS ’05 Dark matter: what is it? Can make guesses based on... • ...compelling theoretical ideas • ...simplicity • ...observational clues 4

Alexander Kusenko (UCLA) KIAS ’05 Dark matter: beautiful theoretical ideas SUSY is an appealing theoretical idea 5

Alexander Kusenko (UCLA) KIAS ’05 Dark matter: beautiful theoretical ideas SUSY is an appealing theoretical idea 5

Alexander Kusenko (UCLA) KIAS ’05 Dark matter: beautiful theoretical ideas SUSY is an appealing theoretical idea 6

Alexander Kusenko (UCLA) KIAS ’05 Dark matter: beautiful theoretical ideas SUSY is an appealing theoretical idea Dark matter comes as part of the package as one of the following: • Neutralino • Gravitino (produced in freeze-out, or non-thermally) • Axino • SUSY Q-balls Theoretically motivated!! By no means minimal. No experimental evidence so far. 7

Alexander Kusenko (UCLA) KIAS ’05 Dark matter: a simple (minimalist) solution Need one particle ⇒ add just one particle If a fermion, must be gauge singlet (anomalies) Interactions only through mixing with neutrinos ⇒ sterile neutrino 8

Alexander Kusenko (UCLA) KIAS ’05 Sterile neutrinos with a small mixing to active neutrinos � | ν 1 � = cos θ | ν e � − sin θ | ν s � (1) | ν 2 � = sin θ | ν e � + cos θ | ν s � The almost-sterile neutrino, | ν 2 � was never in equilibrium. Production of ν 2 could take place through oscillations. The coupling of ν 2 to weak currents is also suppressed, and σ ∝ sin 2 θ . The probability of ν e → ν s conversion in presence of matter is � 2 � − 1 � � P m � = 1 � λ osc sin 2 2 θ m , 1 + (2) 2 2 λ s where λ osc is the oscillation length, and λ s is the scattering length. 9

Alexander Kusenko (UCLA) KIAS ’05 Sterile neutrinos in cosmology: dark matter Sterile neutrinos are produced in primordial plasma through oscillations. The mixing angle is suppressed at high temperature: (∆ m 2 / 2 p ) 2 sin 2 2 θ sin 2 2 θ m = (∆ m 2 / 2 p ) 2 sin 2 2 θ + (∆ m 2 / 2 p cos 2 θ − V ( T )) 2 , (3) 10

Alexander Kusenko (UCLA) KIAS ’05 For small angles, sin 2 θ sin 2 θ m ≈ (4) 1 + 0 . 79 × 10 − 13 ( T/MeV ) 6 (keV 2 / ∆ m 2 ) Production of sterile neutrinos peaks at temperature � 1 / 6 � ∆ m 2 T max = 130 MeV keV 2 11

Alexander Kusenko (UCLA) KIAS ’05 Ω = 0.3 s Ω > 0.3 s 10 m s [keV] dark matter The resulting density of relic sterile neutrinos in conventional cosmology, in the absence of a 1 1e-11 1e-10 1e-09 1e-08 1e-07 large lepton asymmetry: 2 θ sin � � m s sin 2 2 θ � � 2 Ω ν 2 ∼ 0 . 3 10 − 8 keV [Dodelson, Widrow; Dolgov, Hansen; Fuller, Shi; Abazajian, Fuller, Patel] 12

Alexander Kusenko (UCLA) KIAS ’05 Ω = 0.3 s The resulting density of relic Ω > 0.3 s 10 m s [keV] sterile neutrinos in conventional dark matter cosmology, in the absence of a large lepton asymmetry: too warm � � m s sin 2 2 θ 1 � � 2 1e-11 1e-10 1e-09 1e-08 1e-07 2 θ sin Ω ν 2 ∼ 0 . 3 10 − 8 keV Lyman- α forest clouds show significant structure on small scales. Dark matter must be cold enough to preserve this structure. 13

Alexander Kusenko (UCLA) KIAS ’05 Observational hint: the pulsar velocities 14

Alexander Kusenko (UCLA) KIAS ’05 Observational hint: the pulsar velocities Pulsars have large velocities, � v � ≈ 250 − 450 km / s . [Cordes et al. ; Hansen, Phinney; Kulkarni et al. ; Lyne et al. ] A significant population with v > 700 km / s , about 15 % have v > 1000 km / s , up to 1600 km / s . [Arzoumanian et al. ; Thorsett et al. ] 14

Alexander Kusenko (UCLA) KIAS ’05 15

Alexander Kusenko (UCLA) KIAS ’05 Proposed explanations: • asymmetric collapse [Shklovskii] (small kick) • evolution of close binaries [Gott, Gunn, Ostriker] (not enough) • acceleration by EM radiation [Harrison, Tademaru] (kick small, predicted polarization not observed) • asymmetry in EW processes that produce neutrinos [Chugai; Dorofeev, Rodinov, Ternov] (asymmetry washed out) • “cumulative” parity violation [Lai, Qian; Janka] (it’s not cumulative ) 16

Alexander Kusenko (UCLA) KIAS ’05 Asymmetric collapse “...the most extreme asymmetric collapses do not produce final neutron star velocities above 200km/s” [Fryer ’03] 17

Alexander Kusenko (UCLA) KIAS ’05 Supernova neutrinos Nuclear reactions in stars lead to a formation of a heavy iron core. When it reaches M ≈ 1 . 4 M ⊙ , the pressure can no longer support gravity. ⇒ collapse. Energy released: ∆ E ∼ G N M 2 Fe core ∼ 10 53 erg R 99% of this energy is emitted in neutrinos 18

Alexander Kusenko (UCLA) KIAS ’05 Pulsar kicks from neutrino emission? Pulsar with v ∼ 500 km/s has momentum M ⊙ v ∼ 10 41 g cm/s 19

Alexander Kusenko (UCLA) KIAS ’05 Pulsar kicks from neutrino emission? Pulsar with v ∼ 500 km/s has momentum M ⊙ v ∼ 10 41 g cm/s SN energy released: 10 53 erg ⇒ in neutrinos. Thus, the total neutrino momentum is P ν ; total ∼ 10 43 g cm/s 19

Alexander Kusenko (UCLA) KIAS ’05 Pulsar kicks from neutrino emission? Pulsar with v ∼ 500 km/s has momentum M ⊙ v ∼ 10 41 g cm/s SN energy released: 10 53 erg ⇒ in neutrinos. Thus, the total neutrino momentum is P ν ; total ∼ 10 43 g cm/s ✓ ✏ a 1% asymmetry in the distribution of neutrinos ✒ ✑ is sufficient to explain the pulsar kick velocities But what can cause the asymmetry?? 19

Alexander Kusenko (UCLA) KIAS ’05 Magnetic field? Neutron stars have large magnetic fields. A typical pulsar has surface magnetic field B ∼ 10 12 − 10 13 G . Recent discovery of soft gamma repeaters and their identification as magnetars ⇒ some neutron stars have surface magnetic fields as high as 10 15 − 10 16 G . ⇒ magnetic fields inside can be 10 15 − 10 16 G. Neutrino magnetic moments are negligible, but the scattering of neutrinos off polarized electrons and nucleons is affected by the magnetic field. 20

Alexander Kusenko (UCLA) KIAS ’05 Core collapse supernova Onset of the collapse: t = 0 21

Alexander Kusenko (UCLA) KIAS ’05 Core collapse supernova Onset of the collapse: t = 0 core Fe 21

Alexander Kusenko (UCLA) KIAS ’05 Core collapse supernova Shock formation and “neutronization burst”: t = 1 − 10 ms shock ν PNS burst Protoneutron star formed. Neutrinos are trapped. The shock wave breaks up nuclei, and the initial neutrino come out (a few %). 22

Alexander Kusenko (UCLA) KIAS ’05 Core collapse supernova Thermal cooling: t = 10 − 15 s ν PNS thermal Most of the neutrinos emitted during the cooling stage. 23

Alexander Kusenko (UCLA) KIAS ’05 Electroweak processes producing neutrinos (urca), p + e − ⇀ ↽ n + ν e and n + e + ⇀ ↽ p + ¯ ν e have an asymmetry in the production cross section, depending on the spin orientation. σ ( ↑ e − , ↑ ν ) � = σ ( ↑ e − , ↓ ν ) The asymmetry: g 2 V − g 2 A ˜ ǫ = k 0 ≈ 0 . 4 k 0 , g 2 V + 3 g 2 A where k 0 is the fraction of electrons in the lowest Landau level. 24

Alexander Kusenko (UCLA) KIAS ’05 In a strong magnetic field, 0.7 16 B=3x10 G 0.6 0.5 0.4 K 0 16 B=10 G 0.3 0.2 15 B=3x10 G 0.1 0 20 30 40 50 60 20 30 40 50 60 µ , MeV k 0 is the fraction of electrons in the lowest Landau level. Pulsar kicks from the asymmetric production of neutrinos? [Chugai; Dorofeev, Rodionov, Ternov] 25

Alexander Kusenko (UCLA) KIAS ’05 Can the weak interactions asymmetry cause an anisotropy in the flux of neutrinos due to a large magnetic field? No ν e ν ν e e ν e ν ν ν e ν e e ν e ν ν e e e ν ν e e ν e ν e Neutrinos are trapped at high density. 26

Alexander Kusenko (UCLA) KIAS ’05 Can the weak interactions asymmetry cause an anisotropy in the flux of neutrinos due to a large magnetic field? No Rescattering washes out the asymmetry [Vilenkin ApJ 451, 700 (1995); AK,Segr` e, Vilenkin, PLB 437,359 (1998); Arras,Lai, ApJ 519, 745 (1999)]. In approximate thermal equilibrium the asymmetries in scattering amplitudes do not lead to an anisotropic emission. Only the outer regions, near neutrinospheres, contribute (a negligible amount). However, if a weaker-interacting sterile neutrino was produced in these processes, the asymmetry would, indeed, result in a pulsar kick! 27