Introduction to Recombination Physics and Why It Is Important for Cosmology and Early-Universe Physics

Introduction to Recombination Physics and Why it is Important for Cosmology and Early-Universe Physics

Improved Recombination History HI 2s-1s two-photon decay rate CosmoRec vs Recfast++ (Recfast++ is reference) 2 CosmoRec TT + lowP + BAO

1.5 CosmoRec TTTEEE + lowP + BAO RecFast TTTEEE + lowP + BAO 1

0.5 1.0

0 0.8 -0.5 in % e N / max 0.6 e -1 P N / Δ -1.5 P 0.4 -2

-2.5 0.2 Theory

-3 0.0 -3.5 4.5 6.0 7.5 9.0 10.5 0 500 1000 1500 2000 2500 3000 l A2s 1s !

Jens Chluba CosmoTools 2018 Aachen, Germany, April 23th - 27th, 2018 Some of the “big” questions in Cosmology: • What is the Universe made of? • How did it start? What are the initial condition? • How did all the structures form? Cosmic Microwave Background Anisotropies

6000 Planck Collaboration, XIII 2015 5000

] 4000 2 K µ [ 3000 TT `

D 2000

1000

] 600

2 60

K 300 30 µ [ 0 0 TT ` -300 -30 D

-600 -60 2 10 30 500 1000 1500 2000 2500 `

Planck all sky map • CMB has a blackbody spectrum in every direction • tiny variations of the CMB temperature ΔT/T ~ 10-5 CMB anisotropies (with SN, LSS, etc...) clearly taught us a lot about the Universe we live in!

• Standard 6 parameter concordance cosmology with parameters known to percent level precision • Gaussian-distributed adiabatic fluctuations with nearly scale- invariant power spectrum over a wide range of scales • cold dark matter (“CDM”) Planck Collaboration: Cosmological parameters • accelerated expansion today (“Λ”) Table 4. Parameter 68 % conﬁdence limits for the base ⇤CDM model from Planck CMB power spectra, in combination with lensing reconstruction (“lensing”) and external data (“ext,” BAO+JLA+H0). Nuisance parameters are not listed for brevity (they can• beStandard found in the Planck BBN Legacy scenario Archive tables), → but N theeff last and three parametersYp give a summary measure of the total foreground amplitude (in µK2) at ` = 2000 for the three high-` temperature spectra used by the likelihood. In all cases the helium mass fraction used is predicted by BBN (posterior mean YP 0.2453, with theoretical uncertainties in the BBN predictions dominating over the • Standard2 ionization history⇡ → Ne(z) Planck error on ⌦bh ).

TT+lowP TT+lowP+lensing TT+lowP+lensing+ext TT,TE,EE+lowP TT,TE,EE+lowP+lensing TT,TE,EE+lowP+lensing+ext Parameter 68 % limits 68 % limits 68 % limits 68 % limits 68 % limits 68 % limits

⌦ h2 ...... 0.02222 0.00023 0.02226 0.00023 0.02227 0.00020 0.02225 0.00016 0.02226 0.00016 0.02230 0.00014 b ± ± ± ± ± ± ⌦ h2 ...... 0.1197 0.0022 0.1186 0.0020 0.1184 0.0012 0.1198 0.0015 0.1193 0.0014 0.1188 0.0010 c ± ± ± ± ± ± 100✓ ...... 1.04085 0.00047 1.04103 0.00046 1.04106 0.00041 1.04077 0.00032 1.04087 0.00032 1.04093 0.00030 MC ± ± ± ± ± ± ⌧ ...... 0.078 0.019 0.066 0.016 0.067 0.013 0.079 0.017 0.063 0.014 0.066 0.012 ± ± ± ± ± ± ln(1010 A )...... 3.089 0.036 3.062 0.029 3.064 0.024 3.094 0.034 3.059 0.025 3.064 0.023 s ± ± ± ± ± ± n ...... 0.9655 0.0062 0.9677 0.0060 0.9681 0.0044 0.9645 0.0049 0.9653 0.0048 0.9667 0.0040 s ± ± ± ± ± ± H ...... 67.31 0.96 67.81 0.92 67.90 0.55 67.27 0.66 67.51 0.64 67.74 0.46 Planck0 Collaboration, 2015,± paper XIII ± ± ± ± ± ⌦ ...... 0.685 0.013 0.692 0.012 0.6935 0.0072 0.6844 0.0091 0.6879 0.0087 0.6911 0.0062 ⇤ ± ± ± ± ± ± ⌦ ...... 0.315 0.013 0.308 0.012 0.3065 0.0072 0.3156 0.0091 0.3121 0.0087 0.3089 0.0062 m ± ± ± ± ± ± ⌦ h2 ...... 0.1426 0.0020 0.1415 0.0019 0.1413 0.0011 0.1427 0.0014 0.1422 0.0013 0.14170 0.00097 m ± ± ± ± ± ± ⌦ h3 ...... 0.09597 0.00045 0.09591 0.00045 0.09593 0.00045 0.09601 0.00029 0.09596 0.00030 0.09598 0.00029 m ± ± ± ± ± ± ...... 0.829 0.014 0.8149 0.0093 0.8154 0.0090 0.831 0.013 0.8150 0.0087 0.8159 0.0086 8 ± ± ± ± ± ± ⌦0.5 ...... 0.466 0.013 0.4521 0.0088 0.4514 0.0066 0.4668 0.0098 0.4553 0.0068 0.4535 0.0059 8 m ± ± ± ± ± ± ⌦0.25 ...... 0.621 0.013 0.6069 0.0076 0.6066 0.0070 0.623 0.011 0.6091 0.0067 0.6083 0.0066 8 m ± ± ± ± ± ± +1.8 +1.7 +1.3 +1.7 +1.4 +1.2 zre ...... 9.9 1.6 8.8 1.4 8.9 1.2 10.0 1.5 8.5 1.2 8.8 1.1 9 +0.076 10 As ...... 2.198 0.085 2.139 0.063 2.143 0.051 2.207 0.074 2.130 0.053 2.142 0.049 ± ± ± ± ± 109 A e 2⌧ ...... 1.880 0.014 1.874 0.013 1.873 0.011 1.882 0.012 1.878 0.011 1.876 0.011 s ± ± ± ± ± ± Age/Gyr ...... 13.813 0.038 13.799 0.038 13.796 0.029 13.813 0.026 13.807 0.026 13.799 0.021 ± ± ± ± ± ± z ...... 1090.09 0.42 1089.94 0.42 1089.90 0.30 1090.06 0.30 1090.00 0.29 1089.90 0.23 ⇤ ± ± ± ± ± ± r ...... 144.61 0.49 144.89 0.44 144.93 0.30 144.57 0.32 144.71 0.31 144.81 0.24 ⇤ ± ± ± ± ± ± 100✓ ...... 1.04105 0.00046 1.04122 0.00045 1.04126 0.00041 1.04096 0.00032 1.04106 0.00031 1.04112 0.00029 ⇤ ± ± ± ± ± ± z ...... 1059.57 0.46 1059.57 0.47 1059.60 0.44 1059.65 0.31 1059.62 0.31 1059.68 0.29 drag ± ± ± ± ± ± r ...... 147.33 0.49 147.60 0.43 147.63 0.32 147.27 0.31 147.41 0.30 147.50 0.24 drag ± ± ± ± ± ± k ...... 0.14050 0.00052 0.14024 0.00047 0.14022 0.00042 0.14059 0.00032 0.14044 0.00032 0.14038 0.00029 D ± ± ± ± ± ± z ...... 3393 49 3365 44 3361 27 3395 33 3382 32 3371 23 eq ± ± ± ± ± ± k ...... 0.01035 0.00015 0.01027 0.00014 0.010258 0.000083 0.01036 0.00010 0.010322 0.000096 0.010288 0.000071 eq ± ± ± ± ± ± 100✓ ...... 0.4502 0.0047 0.4529 0.0044 0.4533 0.0026 0.4499 0.0032 0.4512 0.0031 0.4523 0.0023 s,eq ± ± ± ± ± ± f 143 ...... 29.9 2.9 30.4 2.9 30.3 2.8 29.5 2.7 30.2 2.7 30.0 2.7 2000 ± ± ± ± ± ± f 143 217 ...... 32.4 2.1 32.8 2.1 32.7 2.0 32.2 1.9 32.8 1.9 32.6 1.9 2000⇥ ± ± ± ± ± ± f 217 ...... 106.0 2.0 106.3 2.0 106.2 2.0 105.8 1.9 106.2 1.9 106.1 1.8 2000 ± ± ± ± ± ±

Table 5. Constraints on 1-parameter extensions to the base ⇤CDM model for combinations of Planck power spectra, Planck lensing, and external data (BAO+JLA+H0, denoted “ext”). Note that we quote 95 % limits here.

Parameter TT TT+lensing TT+lensing+ext TT, TE, EE TT, TE, EE+lensing TT, TE, EE+lensing+ext

+0.049 +0.016 +0.0054 +0.038 +0.015 +0.0040 ⌦K ...... 0.052 0.055 0.005 0.017 0.0001 0.0052 0.040 0.041 0.004 0.015 0.0008 0.0039 ⌃m⌫ [eV] ...... < 0.715 < 0.675 < 0.234 < 0.492 < 0.589 < 0.194 +0.64 +0.62 +0.41 +0.41 +0.38 +0.33 Ne↵ ...... 3.13 0.63 3.13 0.61 3.15 0.40 2.99 0.39 2.94 0.38 3.04 0.33 +0.041 +0.040 +0.035 +0.026 +0.026 +0.025 YP ...... 0.252 0.042 0.251 0.039 0.251 0.036 0.250 0.027 0.247 0.027 0.249 0.026 +0.016 +0.015 +0.015 +0.014 +0.013 +0.013 dns/d ln k ...... 0.008 0.016 0.003 0.015 0.003 0.014 0.006 0.014 0.002 0.013 0.002 0.013 r0.002 ...... < 0.103 < 0.114 < 0.114 < 0.0987 < 0.112 < 0.113 +0.62 +0.64 +0.085 +0.58 +0.62 +0.075 w ...... 1.54 0.50 1.41 0.56 1.006 0.091 1.55 0.48 1.42 0.56 1.019 0.080

31 Initial conditions CMB anisotropiesCMB SZ effect LensingCMB E & B-modes Large-scale Free electron Total number (density) of number (density) hydrogen nuclei Sketch of the Cosmic Ionization History Ionization Sketch of the Cosmic • • • • •

recombination at z~1000 HII → HI recombination at z~2000 HeII → HeI recombination at z~6000 HeIII → HeII ~ 8%) abundance and 2 electrons has (Helium fraction z ≥ 10 → ~10 at redshifts higher than fully ionized fully 4 Universe 4 → N

e free electron free electron /N H

~ 1.16 ~ 1.16

CMB Sky à Cosmology

Ne (z) is a crucial input

alm Power spectra WMAP CMB Sky

~1° Cosmological (Joint) analysis large scales small scales Parameters

Ωtot, Ωm, Ωb, Ω , Λ Other cosmological Dataset: h, τ, ns,... small-scale CMB, Supernovae, large-scale structure/ BAO, Lyman-α forest, lensing, ... Cosmological Time in Years 790,000 370,000 260,000 130,000 18,000

1.4 Why does the ionization CMB-Anisotropies history matter so much? 1.2 Free Electron Fraction Plasma fully ionized N /[N +N ] 1 e p H • Free electron fraction determines the shape of the Thomson visibility function / last scattering surface 0.8 (maximum at z~1100 where Ne / NH ~ 16% )

• Uncertainties in the computation of Ne(z) will affect the theoretical predictions for the CMB power spectra 0.6 • This can bias the inferred values of the cosmological parameters • Experimental goal of 0.1% - 1% requires 0.1% - 1% 0.4 understanding of Ne(z) at z~1100

Visibility Function Errors in N (z) in particular compromise our ability to Plasma neutral • e measure ns (→ inflation) 0.2 • ,Getting 1016 GeV physics right means we have to understand eV physics with high precision’ (quote D. Scott)

0 700 1100 2000 3000 4000 6000 8000 Redshift z How does cosmological recombination work? What is the recombination problem about?

• coupled system describing the interaction of matter with the

electron ambient CMB photon field

• atoms can be in different excitation states Helium lots of levels to worry about proton ⟹

Hydrogen • recombination process changes Wien tail of CMB and this affects He++ the recombination dynamics ⟹ radiative transfer problem

electron temperature Only problem in time! Have to follow evolution of: Ne,Te,Np,Ni and I⌫

number densities non-thermal photons Physical Conditions during Recombination

• Anisotropies negligible for recombination problem

• Temperature Tγ ~ 2.725 (1+z) K ~ 3000 K

-7 -3 3 -3 • Baryon number density Nb ~ 2.5x10 cm (1+z) ~ 330 cm

-3 3 9 • Photon number density Nγ ~ 410 cm (1+z) ~ 2×10 Nb ⇒ photons in very distant Wien tail of blackbody spectrum can keep

hydrogen ionized until hνα ~ 40 kTγ ⟺ Tγ ~ 0.26 eV (Ly-c 13.6 eV!)

• Collisional processes negligible (completely different in stars!!!) • Rates dominated by radiative processes (e.g. stimulated emission & stimulated recombination) • Compton interaction couples electrons very tightly to

photons until z ~ 200 ⇒ Tγ ~ Te ~ Tm (number) density Total number (density) of given species i of hydrogen nuclei Saha-Equation for ionization degree Saha-Equation ionization for George Gamov free electrons free In equilibrium with (number) density Total number (density) of given species i of hydrogen nuclei „freeze out“ „freeze Saha-Equation for ionization degree Saha-Equation ionization for in Saha case! Saha in much is Recombination slower than than slower with electrons free Out of equilibrium free electrons free In equilibrium with 3-level Hydrogen Atom and Continuum

Routes to the ground state ? continuum: e p (He) • direct recombination to 1s

γ γ - Emission of photon is followed by No immediate re-absorption

2s 2p • recombination to 2p followed by Lyman-α emission γ - medium optically thick to Ly-α phot. ~ 43% - many resonant scatterings 2γ - escape very hard (p ~10-9 @ z ~1100) γ • recombination to 2s followed by 2s two-photon decay Hydrogenatom - 2s à 1s ~108 times slower than Ly- 1s α ~ 57% - 2s two-photon decay profile à

maximum at ν ∼ 1/2 να - immediate escape

Zeldovich, Kurt & Sunyaev, 1968, ZhETF, 55, 278 Peebles, 1968, ApJ, 153, 1 ΔNe / Ne ~ 10% - 20% These first computations were completed in 1968!

Moscow

Princeton

Yakov Zeldovich

Iosif Shklovskii

Jim Peebles

Rashid Sunyaev Vladimir Kurt (UV astronomer) Let’s do the simple 3-level atom derivation? Multi-level Atom ⟺ Recfast-Code

Output of Ne/NH

Hydrogen:

Total number of shells - up to 300 levels (shells) crucial for freeze-out tail - n ≥ 2 à full SE for l-sub-states

Helium:

- HeI 200-levels (z ~ 1400-1500) - HeII 100-levels (z ~ 6000-6500) - HeIII 1 equation

Low Redshifts:

- H chemistry (only at low z) - cooling of matter (Bremsstrahlung, collisional cooling, line cooling)

Seager, Sasselov & Scott, 1999, ApJL, 523, L1 Seager, Sasselov & Scott, 2000, ApJS, 128, 407

RECFAST reproduces the result of detailed recombination calculation using fudge-functions ΔNe / Ne ~ 1% - 3% Getting the job done for Planck Hydrogen recombination • Two-photon decays from higher levels (Dubrovich & Grachev, 2005, Astr. Lett., 31, 359; Wong & Scott, 2007; JC & Sunyaev, 2007; Hirata, 2008; JC & Sunyaev 2009)

• Induced 2s two-photon decay for hydrogen (JC & Sunyaev, 2006, A&A, 446, 39; Hirata 2008) • Feedback of the Lyman-α distortion on the 1s-2s two-photon absorption rate (Kholupenko & Ivanchik, 2006, Astr. Lett.; Fendt et al. 2008; Hirata 2008) • Non-equilibrium effects in the angular momentum sub-states (Rubiño-Martín, JC & Sunyaev, 2006, MNRAS; JC, Rubiño-Martín & Sunyaev, 2007, MNRAS; Grin & Hirata, 2009; JC, Vasil & Dursi, 2010) • Feedback of Lyman-series photons (Ly[n] à Ly[n-1]) (JC & Sunyaev, 2007, A&A; Kholupenko et al. 2010; Haimoud, Grin & Hirata, 2010)

• Lyman-α escape problem (atomic recoil, time-dependence, partial redistribution) (Dubrovich & Grachev, 2008; JC & Sunyaev, 2008; Forbes & Hirata, 2009; JC & Sunyaev, 2009) • Collisions and Quadrupole lines (JC, Rubiño-Martín & Sunyaev, 2007; Grin & Hirata, 2009; JC, Vasil & Dursi, 2010; JC, Fung & Switzer, 2011) • Raman scattering (Hirata 2008; JC & Thomas , 2010; Haimoud & Hirata, 2010) Helium recombination • Similar list of processes as for hydrogen (Switzer & Hirata, 2007a&b; Hirata & Switzer, 2007) • Spin forbidden 2p-1s triplet-singlet transitions (Dubrovich & Grachev, 2005, Astr. Lett.; Wong & Scott, 2007; Switzer & Hirata, 2007; Kholupenko, Ivanchik&Varshalovich, 2007)

• Hydrogen continuum opacity during He I recombination (Switzer & Hirata, 2007; Kholupenko, Ivanchik & Varshalovich, 2007; Rubiño-Martín, JC & Sunyaev, 2007; JC, Fung & Switzer, 2011) • Detailed feedback of helium photons (Switzer & Hirata, 2007a; JC & Sunyaev, 2009, MNRAS; JC, Fung & Switzer, 2011) ΔNe / Ne ~ 0.1 % Solving the problem for the Planck Collaboration was a common effort! Recombination Physics Meeting in Orsay 2008 see: http://www.b-pol.org/RecombinationConference/ Atomic Physics Challenges

Hydrogen Atom & Hydrogenic Helium

• Rather simple and basically analytic (e.g., Karzas & Latter, 1961)

• Even 2� rates can be computed precisely (e.g., Goeppert-Mayer, 1931)

• Collisional rates less robust, but effect small (new rates became available!) 2 Bohr Atom • Biggest computational challenge is the number of levels (~ n )

Neutral Helium Two electrons! • Lower levels non-hydrogenic (perturbative approach needed) • Spectrum complicated and data (was) rather sparse (e.g., Drake & Morton, 2007) Grotrian diagram for neutral helium

Fine-structure transitions

Semi-forbidden transitions are important for HeI-recombination!!!

Electron spins anti-parallel Electron spins parallel Atomic Physics Challenges

Hydrogen Atom & Hydrogenic Helium

• Rather simple and basically analytic (e.g., Karzas & Latter, 1961)

• Even 2� rates can be computed precisely (e.g., Goeppert-Mayer, 1931)

• Collisional rates less robust, but effect small (new rates became available!) 2 Bohr Atom • Biggest computational challenge is the number of levels (~ n )

Neutral Helium Two electrons! • Lower levels non-hydrogenic (perturbative approach needed) • Spectrum complicated and data (was) rather sparse (e.g., Drake & Morton, 2007)

• Collisional rate estimates pretty rough (important for distortions...) • Computational challenge because of levels not as demanding if you only want to get the free electron fraction right (not true for spectrum…) Stimulated HI 2s à1s decay

Transition rate in vacuum -1 à A2s1s~ 8.22 sec

CMB ambient photons field Vacuum rate: d⌫ à A2s1s increased by ~1%-2% A (⌫/⌫ ) 2s1s / 0 ⌫ Z 0 à HI - recombination faster by ΔNe/Ne ~ 1.3%

With CMB blackbody: d⌫ A⇤ (⌫/⌫ )[1 + n(⌫ ⌫)][1 + n(⌫)] 2s1s / 0 0 ⌫ Z 0

Low Frequency CMB Photons

2s-1s emission profile

JC & Sunyaev, 2006, A&A Feedback of Ly-α on the HI 1s à 2s transition

Dotted line: just stimulated effect • Some Ly-α photon are re- absorbed in the 1s-2s channel • delays recombination • net effect on 2s-1s channel ΔNe/Ne ~ 0.6% around z~1100 • 2s-1s self-feedback ΔNe/Ne ~ -0.08% around Late stages: net delay z~1100 (JC & Thomas, 2010)

Figure from: Kholupenko et al. 2006

Kholupenko et al. 2006 Fendt, JC, Rubino-Martin & Wandelt, 2009 Two-photon emission process from upper levels

3s 3p 3d Seaton cascade (1+1 photon) No collisions à two photons (mainly γ H-α and Ly-α) are emitted! 2s 2p Maria-Göppert-Mayer (1931): description of two-photon emission as single process in Quantum γ Mechanics àDeviations of the two-photon line profile from the Lorentzian in the 1s damping wings àChanges in the optically thin (below ~500-5000 Doppler width) parts of the line spectra 3s and 3d two-photon decay spectrum

Lorentzian profile

Direct Escape in optically thin regions: à HI -recombination is a bit slower due à HI -recombination is a bit faster due to 2γ-transitions from s-states to 2γ-transitions from d-states

JC & Sunyaev, A&A, 2008 2s-1s Raman scattering

3s 3p 3d • Computation similar to two-photon decay profiles γ • collisions weak ⟹ process needs 2s 2p to be modeled as single quantum act

γ Ly-β

Ly-α

• Enhances blues side of Ly-α line • associated feedback delays recombination around z~900 Figure from: Hirata 2008

Hirata 2008 JC & Thomas, 2010 Deviations from Statistical Equilibrium in the upper levels

Basis for Recfast computation (Seager et al. 2000) 2l +1 Nnl = 2 Ntot,n • l -dependence of populations neglected n • Levels in a given shell assumed to be in Statistical Equilibrium (SE)

• Complexity of problem scales like ~ nmax Processes for the upper levels

continuum: e p (He) • recombination & photoionization γ - n small à l-dependence not drastic - high shells à more likely to l<

2s 2p • l-changing collisions - help to establish full SE within the shell

Hydrogenatom - only effective for n > 25-30

• n-changing collisions 1s • Collisional photoionization • Three-body-recombination Deviations from Statistical Equilibrium in the upper levels

Basis for Recfast computation (Seager et al. 2000) 2l +1 Nnl = 2 Ntot,n • l -dependence of populations neglected n • Levels in a given shell assumed to be in Statistical Equilibrium (SE)

• Complexity of problem scales like ~ nmax

Refined computation (JC, Rubino-Martin & Sunyaev, 2007) • need to treat angular momentum sub-levels separately! • include collision to understand Deviations from how close things are to SE SE are present but effect is small • Complexity of problem scales 2 like ~ n max Largest effect at low redshifts! • But problem very sparse (Grin & Hirata, 2010; JC, Vasil & Dursi, 2010)

JC, Vasil & Dursi, MNRAS, 2010 Sparsity of the problem and effect of ordering

20 shell Hydrogen + 5 shell Helium model

Hydrogen Helium

Shell-by-Shell ordering Angular momentum ordering 1s, 2s, 2p, 3s, 3p, 3d, ... 1s, 2s, 3s, . . . , ns, 2s, 3p, . . . , np, 3d, 4d, ...

Grin & Hirata, 2010 JC, Vasil & Dursi, MNRAS, 2010 The Lyman-α radiative transfer problem Sobolev approximation (developed in late 50‘s to model moving envelopes of stars)

2s 2p • To solve the coupled system of rate-equations à need to know mean intensity across the Ly-α (& Ly-n) resonance at different times γ à approximate solution using escape probability à Escape == photons stop interacting with Ly-α resonance

Hydrogenatom == photons stop supporting the 2p-level A2p1s⇤ = PS A2p1s 1s == photons reach the very distant red wing

Voigt - profile • Main assumptions of Sobolev approximation • populations of level + radiation field quasi-stationary • every ‘scattering’ leads to complete redistribution • emission & absorption profiles have the same shape

Doppler width

⌫D 2kT 5 = few 10 ⌫ m c2 r H ' ⇥ Sobolev approximation (developed in late 50‘s to model moving envelopes of stars)

Hydrogenatom == photons stop supporting the 2p-level A2p1s⇤ = PS A2p1s 1s == photons reach the very distant red wing

⌧S 1 e 8 PS = 10 ⌧S '

3 c rN1s ⌫D g2p A2121 ⌧S = = N1s H ⌫ g1s 8⇡H Problems with Sobolev approximation: Complete redistribution ⟺ partial redistribution

Sobolev-approximation: Normalized to line-center • Important variation of the photon distribution at ~1.5

Sobolev-case times the ionization energy!

• For 1% accuracy one has to integrate up to ~107

== Distortion == Sobolev approximation Doppler width! No redistribution was developed for very different conditions! • Complete redistribution bad approximation and very unlikely (p~10-4-10-3)

No redistribution case: • Much closer to the correct solution (partial redistribution)

• Avoids some of the unphysical aspect

JC & Sunyaev, 2009 Other Problems with Sobolev approximation

Time-dependence of the emission process

• Quasi-stationarity ok close to line center

• Non-stationarity important in the distant wings • Wings even at ~ 104 Doppler width (Δ�/� ~ 10%) required for <0.1% precision

‘Detuned’ Balmer-α Asymmetry of emission / absorption profiles photon

• Standard textbook equations always assume � ~ �0

• Basically wrong in distant damping wings • Detailed balance off → blackbody not conserved! • Formulation that includes profile asymmetries required ‘Detuned’ Ly-α photon

See JC & Sunyaev, 2009 for detailed physics Illustration from Switzer & Hirata 2007 (meant for Helium) Evolution of the HI Lyman-series distortion

Ly α Ly β Ly γ

Computation includes all important radiative transfer processes (e.g. photon diffusion; two-photon processes; Raman-scattering)

JC & Thomas, MNRAS, 2010 Getting the job done for Planck Hydrogen recombination • Two-photon decays from higher levels (Dubrovich & Grachev, 2005, Astr. Lett., 31, 359; Wong & Scott, 2007; JC & Sunyaev, 2007; Hirata, 2008; JC & Sunyaev 2009)

• Delayed neutral helium recombination Absorption of HeI photons by small was indeed one of the amount of HI Recfast results • Effect of HI absorption already mentioned in Hu et al. 1995 (priv. comm Peebles) • Spin-forbidden HeI transition estimated in 1977 (Lin et al.) • But neutral helium recombination not as crucial for Cl’s…

Figure from Fendt et al, 2009

Kholupenko et al, 2007 Switzer & Hirata, 2007 Evolution of the HeI high frequency distortion

CosmoRec v2.0 only!

- partially overlapping lines at n>2 - resonance scattering - electron scattering in kernel approach - HI absorpion

Triplet of intercombination, quadrupole & singlet lines

JC, Fung & Switzer, 2011 So why is all this so important? Cosmological Time in Years 790,000 370,000 260,000 130,000 18,000

1.4

CMB-Anisotropies

1.2 Free Electron Fraction Plasma fully ionized N /[N +N ] 1 e p H

0.8

For the analysis of CMB data 0.6 the ionization history has to be know to very high precision! 0.4

Visibility Function Plasma neutral

0.2

0 700 1100 2000 3000 4000 6000 8000 Redshift z Cumulative Changes to the Ionization History

ComparisonCosmoRec with vs originalRecfast++ version (Recfast++ of isRECFAST reference) 2

1.5

Detailed Lyman-series 1 transport for hydrogen

0.5 identical to Recfast

0 Change in the freeze out tail because of -0.5 high-n recombinations in % e N /

e -1 N Δ -1.5 This is where it matters most! Acceleration of HeI -2 recombination by HI continuum absorption -2.5

-3

-3.5 0 500 1000 1500 2000 2500 3000 zl

JC & Thomas, MNRAS, 2010; Shaw & JC, MNRAS, 2011 Cumulative Change in the CMB Power Spectra

1.5 Comparison with original version of RECFAST

0.5

-0.5

in % -1 l / C

l -1.5 C Δ -2 • change in ‘tilt’ of CMB power spectra ↔ width of visibility -2.5 function ↔ ns & Ωbh2 • ‘wiggles’ ↔ change in -3 position of last scattering surface ↔ Ωbh2 & H0 -3.5 TT -4 EE

-4.5 0 500 1000 1500 2000 2500 3000 l

Shaw & JC, MNRAS, 2011 Importance of recombination for Planck

2 Wbh Equivalent to original 2 Planck 143GHz channel forecast Wbh version of RECFAST CosmoRec CosmoRec - 2.1 σ | - 2.8 x 10-4 Recfast++ Recfast++ (correctionRecfast++ factor)

0.0216 0.0224 0.0232 Recfast++ (correction factor) 2 Wch 0.0216 0.0224 0.0232 2 Wch 0.116 relative | absolute • Precise recombination 0.112 0.116 -0.8 σ | - 0.5 0.108 0.112 history is crucial for

0.0216 0.02240.108 0.0232 0.108 0.112 0.116 understanding inflation! H0 0.0216 0.0224 0.0232 0.108 0.112 0.116 72 72 H0 • Correction can be captured 72 72 70 70 using fudges! 70 70 (Rubino-Martin et al. 2010; Shaw & JC, 2011) 68 68

0.0216 0.022468 0.0232 0.108 0.112 680.116 68 70 72 t 0.0216 0.0224 0.0232 0.108 0.112 0.116 68 70 72 0.10 0.10 0.10 t

0.09 0.10 0.09 0.10 0.09 0.10 -3.3 σ | - 0.012 0.08 0.09 0.08 0.09 0.08 0.09 0.07 0.07 0.07 0.0216 0.02240.08 0.0232 0.108 0.1120.080.116 68 70 0.08 72 0.07 0.08 0.09 0.10 ns 0.07 0.07 0.07 0.975 0.0216 0.02240.975 0.0232 0.108 0.1120.975 0.116 68 0.97570 72 0.07 0.08 0.09 0.10 ns 0.960 0.975 0.960 0.975 0.960 0.975 0.960 0.975 -1.1 σ | - 0.01

0.945 0.960 0.945 0.960 0.945 0.960 0.945 0.960

0.0216 0.02240.945 0.0232 0.108 0.1120.9450.116 68 700.945 72 0.07 0.08 0.090.9450.10 0.945 0.960 0.975 10 log(10 As) 0.0216 0.0224 0.0232 0.108 0.112 0.116 68 70 72 0.07 0.08 0.09 0.10 0.945 0.960 0.975 3.075 3.075 3.075 3.075 3.075 10 log(10 As) 3.050 3.050 3.050 3.050 3.050 3.075 3.075 3.075 3.075 3.075 3.025 3.025 3.025 3.025 3.025 3.050 3.050 3.050 3.050 3.050 3.000 3.000 3.000 3.000 3.000 0.0216 0.02243.025 0.0232 0.108 0.1123.0250.116 68 703.025 72 0.07 0.08 0.093.0250.10 0.945 0.9603.025 0.975 3.000 3.025 3.050 3.075

3.000 3.000 3.000 3.000 3.000 Shaw0.0216 &0.0224 JC, 2011,0.0232 and references0.108 0.112 therein0.116 68 70 72 0.07 0.08 0.09 0.10 0.945 0.960 0.975 3.000 3.025 3.050 3.075 Biases as they would have been for Planck

RECFAST (original) ⟺ CosmoRec Planck TT,TE,EE + lowP + ext - 1.8 σ | - 2.4 x 10-4

-0.5 σ | - 0.24 • Biases a little less significant with real Planck data • absolute biases very similar

-2.6 σ | - 0.010 • In particular ns would be biased significantly

10 ln(10 As)

2 2 ⌦bh ⌦ch H0 ⌧ ns Planck Collaboration, XIII 2015

Text Importance of recombination for inflation constraints

Without improved recombination modules people would be talking about different inflation models! (e.g., Shaw & JC, 2011)

Planck Collaboration, 2015, paper XX

• Analysis uses refined recombination model (CosmoRec/HyRec) CMB constraints on Neff and Yp

Planck+WP+highL

Both parameters are varied → larger uncertainties

Planck Collaboration, 2013, paper XV

• Consistent with SBBN and standard value for Neff

• Future CMB constraints (Stage-IV CMB) on Yp will reach 1% level Importance of recombination for measuring helium

2 Wbh 2 (l ≤ 2000) Wbh cosmic variance limited case CosmoRec 2.0 σ | 1.2 x 10-4 Recfast++ CosmoRec

0.0224 0.0226 0.0228 0.0230 2 Recfast++ (correctionRecfast++ factor) Wch 0.120 Recfast++ (correction factor) 0.117 0.0216 0.0224 0.0232 0.114 2 Wch 0.111 2.0 σ | 1.1 • for 8 parameter case strongest bias in Yp 0.108 0.0224 0.0226 0.0228 0.0230 0.108 0.111 0.114 0.117 0.120 0.116 H0 74 74 • different parameter combinations mimic 0.112 72 72 the effect of recombination corrections on 0.108 70 70 the CMB power spectra

68 0.0216 68 0.0224 0.0232 0.108 0.112 0.116 0.0224 0.0226 0.0228 0.0230 0.108 0.111 0.114 0.117 0.120 68 70 72 74 t H0 • combination with other cosmological data

0.096 72 0.096 0.09672 sets and foregrounds will also lead to

0.090 0.090 0.090 ‘reshuffling’ of biases 70 70 0.084 0.084 0.084

0.0224 0.0226 0.022868 0.0230 0.108 0.111 0.114 0.117 0.120 6868 70 72 74 0.084 0.090 0.096 Yp 0.28 0.28 0.28 0.28 0.0216 0.0224 0.0232 0.108 0.112 0.116 68 70 72 0.26 0.26 0.26 0.26 t

0.24 0.24 0.24 0.24 3.9 σ | 0.021 0.10 0.10 0.10 0.22 0.22 0.22 0.22 0.0224 0.0226 0.0228 0.0230 0.108 0.111 0.114 0.117 0.120 68 70 72 74 0.084 0.090 0.096 0.22 0.24 0.26 0.28 0.09 0.09 0.09 Nn

0.08 0.08 0.08 3.3 3.3 3.3 3.3 3.3 1.2 σ | 0.0033 0.07 0.07 0.07 3.0 0.0216 3.0 0.0224 0.0232 3.0 0.108 0.112 0.1163.0 68 3.070 72 0.07 0.08 0.09 0.10 2.7 2.7 2.7 2.7 2.7 ns 0.0224 0.0226 0.02280.975 0.0230 0.108 0.111 0.114 0.117 0.1200.97568 70 72 74 0.0840.9750.090 0.096 0.22 0.24 0.260.9750.28 2.7 3.0 3.3 ns

0.960 0.960 0.960 0.960 0.97 0.97 0.97 0.97 0.97 0.97

0.96 0.945 0.96 0.9450.96 0.96 0.945 0.96 0.945 0.96

0.95 0.95 0.95 0.95 0.95 0.95 0.0224 0.0226 0.02280.02160.0230 0.1080.02240.111 0.1140.02320.117 0.120 68 0.10870 0.11272 0.11674 0.084 0.090 0.09668 700.22 0.2472 0.26 0.280.07 0.082.7 0.093.0 3.30.10 0.95 0.96 0.9450.97 0.960 0.975 10 log(10 As) 10 log(10 As) 3.060 3.060 3.060 3.060 3.060 3.060 3.060 3.075 3.075 3.075 3.075 3.075 3.045 3.045 3.045 3.045 3.045 3.045 3.045

3.030 3.050 3.030 3.0303.050 3.030 3.050 3.030 3.050 3.030 3.0303.050

0.0224 0.0226 0.02283.025 0.0230 0.108 0.111 0.114 0.117 0.1203.02568 70 72 74 0.0843.0250.090 0.096 0.22 0.24 0.263.0250.28 2.7 3.0 3.3 0.953.025 0.96 0.97 3.030 3.045 3.060

3.000 3.000 3.000 3.000 3.000 Shaw0.0216 &0.0224 JC, 2011,0.0232 and references0.108 0.112 therein0.116 68 70 72 0.07 0.08 0.09 0.10 0.945 0.960 0.975 3.000 3.025 3.050 3.075 Cosmological Recombination Radiation Simple estimates for hydrogen recombination

Hydrogen recombination: • per recombined hydrogen atom an energy of ~ 13.6 eV in form of photons is released -9 -8 • at z ~ 1100 à Δε/ε ~ 13.6 eV Nb / (Nγ 2.7kTr) ~ 10 -10

à recombination occurs at redshifts z < 104 à At that time the thermalization process doesn’t work anymore! à There should be some small spectral distortion due to additional Ly-α and 2s-1s photons! (Zeldovich, Kurt & Sunyaev, 1968, ZhETF, 55, 278; Peebles, 1968, ApJ, 153, 1) à In 1975 Viktor Dubrovich emphasized the possibility to observe the recombinational lines from n > 3 and Δn << n! -26 Cosmological Recombination Spectrum 10

Hydrogen only Shifts in the line positions due to presence of Helium Hydrogen and Helium Photons released in the Universe at redshift z~1400

Changes in the line shape due to presence of Helium ]

-1 in the Universe α sr α -1 Hz α -27 Lyman- -1 10 Balmer-

s transitions among -2 highly excited states α Paschen- [J m ν I Brackett- Features due to presence of Helium in the Universe Another way to do CMB-based cosmology! Direct probe of recombination physics!

-7 -6 Spectral distortion reaches level of ~10 -10 relative to CMB

-28 10 1 10 100 1000 3000 ν [ GHz ] Rubino-Martin et al. 2006, 2008; Sunyaev & JC, 2009 Cosmological Time in Years 790,000 370,000 260,000 130,000 18,000

-27 10

He II only -26 10 Singly ionized Hydrogen only Helium Lines

1.4 ] -1 sr CMB-Anisotropies -1

Hz -28 -1 ] 10 s -1 -2 sr -1 [J m ν Hz -27 I -1 10 s -2 [J m ν I

-29 10 1.2 1 10 100 1000 3000 ν [ GHz ]

-28 10 1 10 100 1000 3000 Plasma fully ν [ GHz ] Free Electron Fraction Hydrogen Lines ionized N /[N +N ] 1 e p H

-27 10

Neutral Helium only

-28 ] 10 -1 sr

0.8 -1 Hz -1 s -2 [J m

ν -29 I 10

He II-Lines

H I-Lines He I-Lines

-30 0.6 10 1 10 100 1000 3000 ν [ GHz ] Neutral Helium Lines

0.4

Visibility Function Plasma neutral

0.2

0 700 1100 2000 3000 4000 6000 8000 Redshift z New detailed and fast computation! -26 10 HI spectrum HeI spectrum HeII spectrum Total distortion Total distortion /w feedback -27 10 High-ν distortion re-processed ] -1 sr -1 Hz -1 -28 s

-2 10 Effect of free-free [J m ν I Δ

-29 10

HeI absorption features

-30 10 0.1 1 10 100 1000 JC & Ali-Haimoud, arXiv:1510.03877 ν [GHz] CosmoSpec: fast and accurate computation of the CRR

• Like in old days of CMB anisotropies! CosmoSpec will be available here: • detailed forecasts and feasibility studies • non-standard physics (variation of α, www.Chluba.de/CosmoSpec energy injection etc.)

JC & Ali-Haimoud, arXiv:1510.03877 What would we actually learn by doing such hard job?

Cosmological Recombination Spectrum opens a way to measure:

2 à the specific entropy of our universe (related to Ωbh )

à the CMB monopole temperature T0

à the pre-stellar abundance of helium Yp

à If recombination occurs as we think it does, then the lines can be predicted with very high accuracy! What would we actually learn by doing such hard job?

Cosmological Recombination Spectrum opens a way to measure:

2 à the specific entropy of our universe (related to Ωbh )

à the CMB monopole temperature T0

à the pre-stellar abundance of helium Yp

à If recombination occurs as we think it does, then the lines can be predicted with very high accuracy!

à In principle allows us to directly check our understanding of the standard recombination physics Dark matter annihilations / decays

JC, 2009, arXiv:0910.3663 • Additional photons at all frequencies • Broadening of spectral features → More tomorrow…. • Shifts in the positions What would we actually learn by doing such hard job?

Cosmological Recombination Spectrum opens a way to measure:

2 à the specific entropy of our universe (related to Ωbh )

à the CMB monopole temperature T0

à the pre-stellar abundance of helium Yp

à If recombination occurs as we think it does, then the lines can be predicted with very high accuracy!

à In principle allows us to directly check our understanding of the standard recombination physics

If something unexpected or non-standard happened: à non-standard thermal histories should leave some measurable traces à direct way to measure/reconstruct the recombination history! à possibility to distinguish pre- and post-recombination y-type distortions à sensitive to energy release during recombination à variation of fundamental constants Summary

• The standard recombination problem has been solved to a level that is sufficient for the analysis of current and future CMB data (<0.1% precision!) • Many people helped with this problem! • Without the improvements over the original version of Recfast cosmological parameters derived from Planck would be biased significantly • In particular the discussion of inflation models would have been affected • Cosmological recombination radiation allows us to directly constrain the recombination history