CMB Spectral Distortion Computations using the Green’s function package of CosmoTherm Primordial Distortions Distortion parameter estimation 5 6 temperature-shift, z h > few x 10 4 5 µ -distortion at z h ~ 3 x 10 -1 ] -1 sr 4 y -distortion, z h < 10 3 ( ∆ ⇤ ⌘ ∆ � ∆ f ) -1 Hz 2 -2 s -18 W m 1 G th ( ν , z h , 0) [ 10 0 Fiducial values: -1 ∆ f = 1 . 2 ⇥ 10 � 4 y re = 4 ⇥ 10 � 7 -2 f ann , s = 10 � 22 eV sec � 1 -3 f ann , p = 10 � 26 eV sec � 1 1 10 100 1000 ν [GHz] Jens Chluba Cosmology School in the Canary Islands Fuerteventura, Sept 21 st , 2017
Physical mechanisms that lead to spectral distortions Standard sources • Cooling by adiabatically expanding ordinary matter of distortions (JC, 2005; JC & Sunyaev 2011; Khatri, Sunyaev & JC, 2011) • Heating by decaying or annihilating relic particles (Kawasaki et al., 1987; Hu & Silk, 1993; McDonald et al., 2001; JC, 2005; JC & Sunyaev, 2011; JC, 2013; JC & Jeong, 2013) pre-recombination epoch • Evaporation of primordial black holes & superconducting strings (Carr et al. 2010; Ostriker & Thompson, 1987; Tashiro et al. 2012; Pani & Loeb, 2013) • Dissipation of primordial acoustic modes & magnetic fields (Sunyaev & Zeldovich, 1970; Daly 1991; Hu et al. 1994; JC & Sunyaev, 2011; JC et al. 2012 - Jedamzik et al. 2000; Kunze & Komatsu, 2013) • Cosmological recombination radiation (Zeldovich et al., 1968; Peebles, 1968; Dubrovich, 1977; Rubino-Martin et al., 2006; JC & Sunyaev, 2006; Sunyaev & JC, 2009) „high“ redshifts • „low“ redshifts post-recombination • Signatures due to first supernovae and their remnants (Oh, Cooray & Kamionkowski, 2003) • Shock waves arising due to large-scale structure formation (Sunyaev & Zeldovich, 1972; Cen & Ostriker, 1999) • SZ-effect from clusters; effects of reionization (Refregier et al., 2003; Zhang et al. 2004; Trac et al. 2008) • more exotic processes (Lochan et al. 2012; Bull & Kamionkowski, 2013; Brax et al., 2013; Tashiro et al. 2013)
Average CMB spectral distortions in Λ CDM 4 10 -6 low redshift y -distortion for y = 2 x 10 relativistic correction to y signal Damping signal 3 10 cooling effect CRR negative branch negative 2 10 branch -1 ] ∆ I [ Jy sr 1 10 PIXIE sensitivity 0 h 10 c n Late time a r b e absorption v i t a g e n negative branch -1 10 1 3 6 10 30 60 100 300 600 1000 3000 ν [GHz]
Set of evolution equations for distortions x = h ν θ e = kT e Photon field kT γ m e c 2 ∂ + K BR e − x e [1 − f (e x e − 1)] + K DC e − 2 x � ∂ f ∂τ ≈ θ e ∂ ∂ xf + T γ [1 − f (e x e − 1)]+ S ( τ , x ) ∂ xx 4 f (1 + f ) x 2 x 3 x 3 T e e λ 3 K DC = 4 α K BR = α X e Z 2 3 π θ 2 i N i ¯ g ff ( Z i , T e , T γ , x e ) , γ I dc g dc ( T e , T γ , x ) √ 6 π θ 7 / 2 2 π e i ( √ ⇣ ⌘ 24 x 2 + 11 16 x 3 + 5 3 2 . 25 g dc ≈ 1 + 3 2 x + 29 12 x 4 π ln for x e ≤ 0 . 37 x e g ff ( x e ) ≈ ¯ , . 1 + 19 . 739 θ γ − 5 . 5797 θ e 1 otherwise Z x 4 f (1 + f ) d x ≈ 4 π 4 / 15 I dc = Ordinary matter temperature = t T ˙ d ρ e d τ = d( T e /T γ ) Q + 4˜ e − ρ e ] − 4˜ ρ γ ρ γ [ ρ eq H DC , BR ( ρ e ) − H t T ρ e . d τ α h θ γ α h α h k α h = 3 2 k [ N e + N H + N He ] = 3 ρ eq e = T eq e /T γ 2 kN H [1 + f He + X e ] R x 4 f (1 + f ) d x R ν 4 f (1 + f ) d ν ≡ h T eq ρ γ = ρ γ /m e c 2 = T γ ˜ e R R 4 x 3 f d x 4 ν 3 f d ν k
CosmoTherm: a new flexible thermalization code • Solve the thermalization problem for a wide range of energy release histories • several scenarios already implemented (decaying particles, damping of acoustic modes) • first explicit solution of time-dependent energy release scenarios • open source code • will be available at www.Chluba.de/CosmoTherm/ • Main reference: JC & Sunyaev, MNRAS, 2012 (arXiv:1109.6552) ν [GHz] 3 0.02 0.1 1 10 100 10 0 10 6 4 -8 z = 4.1 x 10 z = 4.0 x 10 no energy release 8 × 10 6 4 -1 z = 2.4 x 10 z = 1.4 x 10 10 6 6 4 z X = 3 x 10 z = 1.5 x 10 z = 2.4 x 10 End of HI recombination 5 3 z = 8.8 x 10 z = 8.7x 10 5 5 3 z X = 5 x 10 -2 z = 5.2 x 10 z = 5.2x 10 -8 10 5 3 6 × 10 z = 3.1 x 10 z = 3.1x 10 5 5 3 z X = 1 x 10 z = 1.9 x 10 z = 1.9x 10 5 3 -3 z = 1.1 x 10 z = 1.1x 10 10 4 4 z = 200 z X = 5 x 10 z = 6.7 x 10 -8 4 4 × 10 z X = 1 x 10 -4 T ( x ) / T CMB - 1 10 hotter than photons 1 - T e / T z -5 10 -8 2 × 10 -6 10 0 -7 10 -8 10 -8 -2 × 10 -9 10 strong low frequency evolution at low redshifts -8 -10 -4 × 10 10 -11 -4 -3 -2 -1 1 10 20 50 10 2 x 10 10 10 10 3 4 5 6 7 10 10 10 10 10 x z Electron temperature evolution Evolution of distortion
Quasi-Exact Treatment of the Thermalization Problem • For real forecasts of future prospects a precise & fast method for computing the spectral distortion is needed! • Case-by-case computation of the distortion ( e.g., with CosmoTherm, JC & Sunyaev, 2012, ArXiv:1109.6552 ) still rather time-consuming • But: distortions are small ⇒ thermalization problem becomes linear! • Simple solution: compute “response function” of the thermalization problem ⇒ Green’s function approach ( JC, 2013, ArXiv:1304.6120 ) • Final distortion for fixed energy-release history given by Z 1 G th ( ν , z 0 )d( Q/ ρ γ ) d z 0 ∆ I ν ≈ d z 0 0 Thermalization Green’s function • Fast and quasi-exact! No additional approximations! CosmoTherm available at: www.Chluba.de/CosmoTherm
What does the spectrum look like after energy injection? Intensity signal for different heating redshifts 5 6 temperature-shift, z h > few x 10 4 high-z SZ effect 5 µ -distortion at z h ~ 3 x 10 -1 ] 4 y -distortion, z h < 10 3 -1 sr n o i t -2 Hz a z i Response function : l a 2 m r -18 W m e energy injection ⇒ distortion h t l l u f 1 G th ( ν , z h , 0) [ 10 0 -1 hybrid distortion probes -2 time-dependence of energy-release history -3 1 10 100 1000 ν [GHz] JC & Sunyaev, 2012, ArXiv:1109.6552 JC, 2013, ArXiv:1304.6120
µ +y + residual distortion µ -distortion 5 6 temperature-shift, z h > few x 10 4 5 µ -distortion at z h ~ 3 x 10 -1 ] 4 3 y -distortion, z h < 10 -1 sr -2 Hz 2 -18 W m 1 G th ( ν , z h , 0) [ 10 0 -1 -2 -3 y-distortion 1 10 100 1000 ν [GHz] pre- post-recombination epoch µ-y-era HI&He µ-era T-era y-distortion era extra time-slicing at recombination New hybrid era
Simplest spectral shapes ν [ GHz ] 10 100 1000 1 1.8 1.6 Blackbody spectrum 400 1.4 Temperature shift x 1/4 1.2 full thermalization 300 1 x 3 Intensity in units of I 0 ( T ) x 3 n bb ( x ) = 0.8 -1 ] 200 e x − 1 Intensity [ MJy sr 0.6 0.4 100 0.2 0 0 -0.2 -100 -0.4 x 4 e x x 3 G ( x ) = -0.6 (e x − 1) 2 -200 -0.8 -1 -300 -1.2 0.01 0.1 1 10 30 50 x = h ν / kT I 0 = (2 h/c 2 )( kT 0 /h ) 3 ≈ 270 MJy sr − 1
Simplest spectral shapes ν [ GHz ] 10 100 1000 1 1.8 1.6 Blackbody spectrum 400 1.4 Temperature shift x 1/4 y -distortion x 1/4 1.2 equivalent of th-SZ full thermalization 300 1 Intensity in units of I 0 ( T ) 0.8 -1 ] 200 Intensity [ MJy sr 0.6 0.4 100 0.2 0 0 -0.2 y → ν c ≈ 217 GHz -100 -0.4 -0.6 x e x + 1 � -200 x 3 Y SZ ( x ) = x 3 G ( x ) e x − 1 − 4 -0.8 -1 -300 -1.2 0.01 0.1 1 10 30 50 x = h ν / kT I 0 = (2 h/c 2 )( kT 0 /h ) 3 ≈ 270 MJy sr − 1
Simplest spectral shapes ν [ GHz ] 10 100 1000 1 1.8 1.6 Blackbody spectrum 400 1.4 Temperature shift x 1/4 y -distortion x 1/4 1.2 µ -distortion x 1.401 300 1 Intensity in units of I 0 ( T ) π 2 � 18 ζ (3) − 1 0.8 -1 ] 200 x 3 M ( x ) = x 3 G ( x ) Intensity [ MJy sr x 0.6 ≈ 0 . 4561 0.4 100 0.2 0 0 -0.2 -100 -0.4 y → ν c ≈ 217 GHz -0.6 -200 -0.8 µ → ν c ≈ 124 GHz -1 -300 -1.2 0.01 0.1 1 10 30 50 x = h ν / kT I 0 = (2 h/c 2 )( kT 0 /h ) 3 ≈ 270 MJy sr − 1
Energy release histories
Energy release histories for some cases Adiabatic cooling d( Q / ρ γ ) N tot kT γ = � 3 d z 2 ρ γ (1 + z ) #" Ω b h 2 ⇡ � 5 . 71 ⇥ 10 � 10 " (1 � Y p ) # (1 + z ) 0 . 7533 0 . 02225 � � 3 " (1 + f He + X e ) # T 0 ⇥ 2 . 246 2 . 726 K Annihilation Decay � d( Q/ ρ γ ) N H ( z )(1 + z X ) Ŵ X N H ( z )(1 + z ) 2 + λ d( Q / ρ γ ) � H ( z ) ρ γ ( z ) (1 + z ) exp ( − Ŵ X t ) ≈ ϵ X = f ann � d z d z H ( z ) ρ γ ( z ) � dec Dissipation of acoustic modes Z 1 k 4 d k d( Q / ρ γ ) 2 π 2 P ζ ( k ) e � 2 k 2 / k 2 ⇡ 4 A 2 ∂ z k � 2 D , D d z k min ton damping scale (Weinberg 1971; y A 2 ⇡ (1 + 4 R ν / 15) � 2 ⇡ 0 . 813, k D ⇡ 4 . 048 ⇥ 10 (1 + z ) 3 / 2 Mpc � 1 R ν ⇡ 0 . 409 for N e ff ciency A 2 we have a heating e k min ⇡ 0 . 12 Mpc � 1 , the recombination
Decaying particle scenarios Text y - distortion µ − y transition µ - distortion -6 10 4 f X / z X = 1 eV z X = 2 x 10 4 z X = 8 x 10 effective heating rate (1+ z ) d( Q/ ρ ) / d z 5 z X = 3 x 10 -7 10 -8 10 3 4 5 6 10 10 10 10 redshift z JC & Sunyaev, 2011, Arxiv:1109.6552 JC, 2013, Arxiv:1304.6120
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