Overview of different recombination codes

Overview of different recombination codes

CosmoRec vs Recfast++ (Recfast++ is reference)

2

2 1.5

1.5

1

1

0.5 0.5 0

ΔCl / Cl in %

ΔNe / Ne in %

0 -0.5 -1 -1.5

-0.5 -1 -1.5 -2 -2.5

-2

-3 -2.5

-3.5

-3 -3.5

TT EE

-4 0

500

1000

1500

l

2000

2500

3000

-4.5

0

500

1000

1500

l

Jens Chluba School on Cosmological Tools Madrid, Spain, Nov 12th - 15th, 2013

2000

2500

3000

Cosmological Time in Years 790,000

1.4

370,000 260,000

130,000

18,000

CMB-Anisotropies

1.2 Plasma fully ionized

Free Electron Fraction Ne/[Np+NH]

1

0.4

Function

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

Visibility

0.6

Plasma neutral

0.8

0.2

0 700

1100

2000

3000

Redshift z

4000

6000

8000

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]  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 %

Recombination code overview Code

Recfast

Recfast++

CosmoRec

Language

Fortran 77/90 & C

C++

C++

Requirements

-

-

GNU Scientific Lib (GSL)

Solves for

Xp, XHeI, Te

Xp, XHeI, Te

X1s, Xns, Xnp, Xnd, Te

Solves for

Xp, XHeI, Te

Xp, XHeI, Te

X1s, Xns, Xnp, Xnd, Te

ODE-Solver

explicit

implicit (Gears method)

implicit (Gears method)

PDE-Solver

-

-

semi-implicit (Crank-Nicolson)

Approach

derivative fudge

correction function

physics

Simplicity

simple

simpler

pretty big code

Flexibility

limited

better but limited

very flexible

Validity

close to standard cosmology

close to standard cosmology

wide range of cosmologies

Tools

-

ODE Solver

HI & He Atom, Solvers, Quadrature routines

Extras

-

DM annihilation

DM annihilation, high-𝝂 distortion

Runtime

0.01 sec

0.08 sec

1.5 - 2 sec

Recfast Equations

• Old expressions from Peebles 1969 • second shell quasistationary • recombination rates and escape probabilities fudged • spin-forbidden transition added to helium equation (Wong, Moss & Scott, 2009)

Seager et al, 1999

Recfast

recfast.readme

meaning of parameters

write into recfast.ini

Execute code like./recfast < recfast.ini

recfast.for

Recfast++

Initialization for Recfast++ uses same file as CosmoRec ./runfiles/parameters.dat

parameters for both Recfast++ & CosmoRec

main CosmoRec parameters

Execute Recfast++ like ./CosmoRec REC runfiles/parameters.dat

(equivalent to old recfast)

./CosmoRec RECcf runfiles/parameters.dat (recfast + correction function)

Correction function approach just uses full correction! CosmoRec vs Recfast++ (Recfast++ is reference)

2 1.5

Detailed Lyman-series transport for hydrogen

1 0.5

identical to Recfast

ΔNe / Ne in %

0

Change in the freeze out tail because of high-n recombinations

-0.5 -1 -1.5

Acceleration of HeI recombination by HI continuum absorption

-2 -2.5 -3 -3.5

0

500

1000

1500 zl

Introduced in Rubino-Martin et al, 2009

2000

2500

3000

CosmoRec

Extended Effective Multi-level Atom

CosmoRec & HyRec • need to treat angular momentum sub-levels separately • Complexity of problem scales like ~ n2max • Full problem pretty demanding (500 shells ≃ 130000 equations!) ⟹ effective multi-level approach

(Ali-Haimoud & Hirata, 2010)

• This allowed fast computation of the recombination problem!

CosmoRec parameters ./runfiles/parameters.dat

Execute CosmoRec like ./CosmoRec runfiles/parameters.dat

Annihilation and extra energy release

Extra Sources of Ionizations or Excitations • ,Hypothetical’ source of extra photons parametrized by εα & εi • Extra excitations

delay of Recombination

• Extra ionizations

affect ‘freeze out’ tail

• This affects the Thomson visibility function • From WMAP εα < 0.39 & εi < 0.058 at 95% confidence level (Galli et al. 2008) • Extra ionizations & excitations should also lead to additional photons in the recombination radiation!!! • This in principle should allow us to check for such sources at z~1000

Peebles, Seager & Hu, ApJ, 2000

Dark Matter Annihilation: Energy Branching Ratios

curves from Slatyer et al. 2009

• N2 - dependence

Efficiencies according to Chen & Kamionkowski, 2004 & Shull & van Steenberg 1985

dE/dt ∝(1+z)6 and dE/dz ∝(1+z)3...3.5

• only part of the energy is really deposited (fd ~ 0.1) • Branching into heating (100% at high z), ionizations and excitations (mainly during recombination) • Branching depends on considered DM model

Dark Matter Annihilation: Effect on CMB Anisotropies and the Recombination Spectrum

• ‘Delay of recombination’

• Additional photons at all frequencies

• Affects Thomson visibility function

• Broadening of spectral features

• Possibility of Sommerfeld-enhancement

• Shifts in the positions

• Clumpiness of matter at z1

JC, Rubino-Martin & Sunyaev, MNRAS, 2007

Deviations from Statistical Equilibrium in the upper levels Basis for Recfast computation (Seager et al. 2000) • l -dependence of populations neglected

Nnl

2l + 1 = Ntot,n 2 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 how close things are to SE • Complexity of problem scales like ~ n2max • But problem very sparse (Grin &

Deviations from SE are present but effect is small

Largest effect at low redshifts!

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

1s, 2s, 2p, 3s, 3p, 3d, ...

Angular momentum ordering

1s, 2s, 3s, . . . , ns, 2s, 3p, . . . , np, 3d, 4d, ... Grin & Hirata, 2010 JC, Vasil & Dursi, MNRAS, 2010

Collisions during hydrogen recombination • effective recombination cross section of the atom matters most at low z

JC, Vasil & Dursi, MNRAS, 2010

Collisions during hydrogen recombination • effective recombination cross section of the atom matters most at low z • collisions increase recombination rate l = ±1 only

JC, Vasil & Dursi, MNRAS, 2010

Collisions during hydrogen recombination • effective recombination cross section of the atom matters most at low z • collisions increase recombination rate l = ±1 only

JC, Vasil & Dursi, MNRAS, 2010

• effect on ionization history remains small

Collisions during hydrogen recombination • effective recombination cross section of the atom matters most at low z • collisions increase recombination rate l = ±1 only

• effect on ionization history remains small • uncertainties in collision rates may change this by factors of a few

JC, Vasil & Dursi, MNRAS, 2010

Collisions during hydrogen recombination • effective recombination cross section of the atom matters most at low z • collisions increase recombination rate l = ±1 only

• effect on ionization history remains small • uncertainties in collision rates may change this by factors of a few • this should be checked, even if the final result may not dramatically change things

JC, Vasil & Dursi, MNRAS, 2010

Collisions during hydrogen recombination • effective recombination cross section of the atom matters most at low z • collisions increase recombination rate l = ±1 only

• effect on ionization history remains small • uncertainties in collision rates may change this by factors of a few • this should be checked, even if the final result may not dramatically change things • updated rates (with large ∆l) available!

JC, Vasil & Dursi, MNRAS, 2010

Quadrupole lines during hydrogen recombination

l = 0 and ± 2

Overall effect is negligible! Quadrupole transitions between excited levels dominant at z~1100

effect of 3d1s Quadrupole line in agreement with result of Grin & Hirata 2009

JC, Fung & Switzer, 2011

Two-photon transitions from the upper levels and the Lyman-α escape problem

Sobolev approximation (developed in late 50‘s to model moving envelopes of stars)

Hydrogen atom

2s

2p

• To solve the coupled system of rate-equations  need to know mean intensity across the Ly-α (& Ly-n) resonance at different times

γ

1s

 solution by introducing the escape probability  Escape == photons stop interacting with Ly-α resonance == photons stop supporting the 2p-level == photons reach the very distant red wing

Sobolev approximation (developed in late 50‘s to model moving envelopes of stars)

Hydrogen atom

2s

2p

• To solve the coupled system of rate-equations  need to know mean intensity across the Ly-α (& Ly-n) resonance at different times

γ

1s

 solution by introducing the escape probability  Escape == photons stop interacting with Ly-α resonance == photons stop supporting the 2p-level == photons reach the very distant red wing

• 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

Sobolev approximation (developed in late 50‘s to model moving envelopes of stars)

Hydrogen atom

2s

2p

• To solve the coupled system of rate-equations  need to know mean intensity across the Ly-α (& Ly-n) resonance at different times

γ

 solution by introducing the escape probability  Escape == photons stop interacting with Ly-α resonance == photons stop supporting the 2p-level == photons reach the very distant red wing

1s 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 = ⌫

r

2kT ' few ⇥ 10 2 mH c

5

Sobolev approximation (developed in late 50‘s to model moving envelopes of stars)

Hydrogen atom

2s

2p

• To solve the coupled system of rate-equations  need to know mean intensity across the Ly-α (& Ly-n) resonance at different times

γ

 solution by introducing the escape probability  Escape == photons stop interacting with Ly-α resonance == photons stop supporting the 2p-level == photons reach the very distant red wing

1s 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

• Sobolev escape probability & optical depth PS = ⌧S =

c

1

r N1s

H

e ⌧S

⌧S

' 10

8

⌫D g2p A21 321 = N1s ⌫ g1s 8⇡H

Problems with Sobolev approximation: Complete redistribution ⟺ partial redistribution Sobolev-approximation:

No redistribution

Sobolev approximation was developed for very different conditions!

v-case Sobole

== Distortion

Normalized to line-center

• Important variation of the photon distribution at ~1.5 times the ionization energy! • For 1% accuracy one has to integrate up to ~107 Doppler width! • 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

Problems with Sobolev approximation: Time dependence of radiation field

Normalized to line-center at z=1000

• Evolution close to line center is indeed quasi-stationary • non-stationarity important in the wings

(emitted at z~1400)

⟹ information takes time to travel from line center to the wings • For support of 2p level even spectrum up to |xD| ~ 104 is important ⟹ time dependence has to be included

JC & Sunyaev, 2009

Problems with Sobolev approximation: Difference between emission and absorption profile • Standard textbook: 1 dN⌫ c dt

Normalized Ly-α profile



Z

(⌫) d⌫ d⌦ = 1

= A21 (⌫) N2p (1 + n⌫ ) Ly ↵

g2p N1s n⌫ g1s

photon occupation number

Problems with Sobolev approximation: Difference between emission and absorption profile • Standard textbook: 1 dN⌫ c dt

Normalized Ly-α profile



Z

(⌫) d⌫ d⌦ = 1

= A21 (⌫) N2p (1 + n⌫ ) Ly ↵

g2p N1s n⌫ g1s

photon occupation number

1 dN⌫ , c dt

Ly ↵



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

n⌫ 1 + n⌫

Problems with Sobolev approximation: Difference between emission and absorption profile • Standard textbook: 1 dN⌫ c dt

Normalized Ly-α profile



Z

(⌫) d⌫ d⌦ = 1

= A21 (⌫) N2p (1 + n⌫ ) Ly ↵

g2p N1s n⌫ g1s

photon occupation number

1 dN⌫ , c dt

Ly ↵

In equilibrium:



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

n⌫ =e 1 + n⌫

h⌫ kT

g1s N2p and =e g2p N1s

h⌫21 kTm

n⌫ 1 + n⌫

=) T ⌘ Tm and ⌫ ⌘ ⌫21

Problems with Sobolev approximation: Difference between emission and absorption profile • Standard textbook: 1 dN⌫ c dt

Normalized Ly-α profile



Z

(⌫) d⌫ d⌦ = 1

= A21 (⌫) N2p (1 + n⌫ ) Ly ↵

g2p N1s n⌫ g1s

photon occupation number

1 dN⌫ , c dt

Ly ↵

In equilibrium:



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

n⌫ =e 1 + n⌫

h⌫ kT

g1s N2p and =e g2p N1s

h⌫21 kTm

n⌫ 1 + n⌫

=) T ⌘ Tm and ⌫ ⌘ ⌫21

Only fulfilled at line center! Detailed balance not guaranteed in the line wings!

Problems with Sobolev approximation: Difference between emission and absorption profile • Standard textbook: 1 dN⌫ c dt

Normalized Ly-α profile



Z

(⌫) d⌫ d⌦ = 1

= A21 (⌫) N2p (1 + n⌫ ) Ly ↵

g2p N1s n⌫ g1s

photon occupation number

1 dN⌫ , c dt

Ly ↵

In equilibrium:



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

n⌫ =e 1 + n⌫

h⌫ kT

g1s N2p and =e g2p N1s

h⌫21 kTm

n⌫ 1 + n⌫

=) T ⌘ Tm and ⌫ ⌘ ⌫21

Only fulfilled at line center!

• Effective 1𝛾 expression 1 dN⌫ ) c dt

Ly ↵

Detailed balance not guaranteed in the line wings!



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

e

h(⌫ ⌫21 ) kT

n⌫ 1 + n⌫

Problems with Sobolev approximation: Difference between emission and absorption profile • Standard textbook: 1 dN⌫ c dt

Normalized Ly-α profile



Z

(⌫) d⌫ d⌦ = 1

= A21 (⌫) N2p (1 + n⌫ ) Ly ↵

g2p N1s n⌫ g1s

photon occupation number

1 dN⌫ , c dt

Ly ↵

In equilibrium:



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

n⌫ =e 1 + n⌫

h⌫ kT

g1s N2p and =e g2p N1s

h⌫21 kTm

n⌫ 1 + n⌫

=) T ⌘ Tm and ⌫ ⌘ ⌫21

Only fulfilled at line center!

• Effective 1𝛾 expression 1 dN⌫ ) c dt

Ly ↵

Detailed balance not guaranteed in the line wings!



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

e

h(⌫ ⌫21 ) kT

n⌫ 1 + n⌫

Asymmetry of emission and absorption profile

Problems with Sobolev approximation: Difference between emission and absorption profile • Standard textbook: 1 dN⌫ c dt

Normalized Ly-α profile



Z

(⌫) d⌫ d⌦ = 1

= A21 (⌫) N2p (1 + n⌫ ) Ly ↵

g2p N1s n⌫ g1s

photon occupation number

1 dN⌫ , c dt

Ly ↵

In equilibrium:



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

n⌫ =e 1 + n⌫

h⌫ kT

g1s N2p and =e g2p N1s

h⌫21 kTm

n⌫ 1 + n⌫

=) T ⌘ Tm and ⌫ ⌘ ⌫21

Only fulfilled at line center!

• Effective 1𝛾 expression 1 dN⌫ ) c dt

Ly ↵

Detailed balance not guaranteed in the line wings!



g2p g1s N2p = A21 N1s (⌫)(1 + n⌫ ) g1s g2p N1s

• Naturally comes out of 2𝛾 treatment (JC & Sunyaev 2009)

e

h(⌫ ⌫21 ) kT

n⌫ 1 + n⌫

Asymmetry of emission and absorption profile

Problems with Sobolev approximation: Difference between emission and absorption profile

‘Detuned’ Balmer-α photon

‘Detuned’ Ly-α photon

Illustration from Switzer & Hirata 2007 (meant for Helium)

• Real absorption & emission requires a second photon! JC & Sunyaev, 2009

Problems with Sobolev approximation: Difference between emission and absorption profile

Blackbody spectrum close to the Doppler core

‘Detuned’ Balmer-α photon

‘Detuned’ Ly-α photon

Illustration from Switzer & Hirata 2007 (meant for Helium)

• Real absorption & emission requires a second photon! JC & Sunyaev, 2009

Problems with Sobolev approximation: Difference between emission and absorption profile

Small changes in red wing Blackbody spectrum close to the Doppler core

‘Detuned’ Balmer-α photon

‘Detuned’ Ly-α photon

Illustration from Switzer & Hirata 2007 (meant for Helium)

• Real absorption & emission requires a second photon! JC & Sunyaev, 2009

Problems with Sobolev approximation: Difference between emission and absorption profile

Small changes in red wing

Reduction

Blackbody spectrum close to the Doppler core

‘Detuned’ Balmer-α photon

‘Detuned’ Ly-α photon

Illustration from Switzer & Hirata 2007 (meant for Helium)

• Real absorption & emission requires a second photon! JC & Sunyaev, 2009

Problems with Sobolev approximation: Difference between emission and absorption profile

Small changes in red wing

Blackbody spectrum also in the far Wien tail

Reduction

Blackbody spectrum close to the Doppler core

‘Detuned’ Balmer-α photon

‘Detuned’ Ly-α photon

Illustration from Switzer & Hirata 2007 (meant for Helium)

• Real absorption & emission requires a second photon! JC & Sunyaev, 2009

Problems with Sobolev approximation: Difference between emission and absorption profile

Small changes in red wing

Reduction

Blackbody spectrum close to the Doppler core

Blackbody spectrum also in the far Wien tail

‘Detuned’ Balmer-α photon

‘Detuned’ Ly-α photon

Illustration from Switzer & Hirata 2007 (meant for Helium)

Part of the two-photon profile corrections...

JC & Sunyaev, 2009

• Real absorption & emission requires a second photon!

Two-photon emission profile 3p

3s

2p

γ

1s

Seaton cascade (1+1 photon) No collisions  two photons (mainly H-α and Ly-α) are emitted!

γ 2s

3d

Maria-Göppert-Mayer (1931): description of two-photon emission as single process in Quantum Mechanics Deviations of the two-photon line profile from the Lorentzian in the damping wings Changes in the optically thin (below ~500-5000 Doppler width) parts of the line spectra

3s and 3d two-photon decay spectrum

Lorentzian profile

Lorentzian profile

Direct Escape in optically thin regions:  HI -recombination is a bit slower due to 2γ-transitions from s-states JC & Sunyaev, A&A, 2008

 HI -recombination is a bit faster due to 2γ-transitions from d-states

2s-1s Raman scattering 3p

3s

3d

γ 2p

2s

• Computation similar to two-photon decay profiles • collisions weak ⟹ process needs to be modeled as single quantum act

γ

Ly-β

1s

Ly-α

• Enhances blues side of Ly-α line • associated feedback delays recombination around z~900 Hirata 2008 JC & Thomas, 2010

Figure from: Hirata 2008

Evolution of the HI Lyman-series distortion Ly α

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

JC & Thomas, MNRAS, 2010

Ly β Ly γ

Effect of Raman scattering and 2γ decays

2s-1s Raman scattering: 2s + γ → 1s + γ’

Decreased Ly-n feedback

Increased Lyβ feedback delay HI recombination result in good agreement with Hirata 2008

JC & Thomas, MNRAS, 2010

Getting Ready 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]  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 %

Main corrections during HeI Recombination

Absorption of HeI photons by small amount of HI

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

Overall effect of detailed HeI radiative transfer

CosmoRec v2.0 only

JC, Fung & Switzer, 2011

Cumulative Changes to the Ionization History CosmoRec vs Recfast++ (Recfast++ is reference)

2 1.5

Detailed Lyman-series transport for hydrogen

1 0.5

identical to Recfast

ΔNe / Ne in %

0

Change in the freeze out tail because of high-n recombinations

-0.5 -1 -1.5

Acceleration of HeI recombination by HI continuum absorption

-2 -2.5 -3 -3.5

0

500

1000

1500 zl

JC & Thomas, MNRAS, 2010; Shaw & JC, MNRAS, 2011

2000

2500

3000

Cumulative Changes to the Ionization History CosmoRec vs Recfast++ (Recfast++ is reference)

2 1.5

Detailed Lyman-series transport for hydrogen

1 0.5

identical to Recfast

ΔNe / Ne in %

0

Change in the freeze out tail because of high-n recombinations

-0.5 -1 -1.5

This is where it matters most!

-2

Acceleration of HeI recombination by HI continuum absorption

-2.5 -3 -3.5

0

500

1000

1500 zl

JC & Thomas, MNRAS, 2010; Shaw & JC, MNRAS, 2011

2000

2500

3000

Cumulative Change in the CMB Power Spectra 2

Comparison with Recfast++

1.5 1

3 / l - Benchmark (Seljak et al. 2003)

0.5

ΔCl / Cl in %

0 -0.5 -1 -1.5 -2

•

change in ‘tilt’ of CMB power spectra ↔ width of visibility function ↔ ns & Ωbh2

•

‘wiggles’ ↔ change in position of last scattering surface ↔ Ωbh2

-2.5 -3 -3.5

TT EE

-4 -4.5

0

500

1000

1500

l Shaw & JC, MNRAS, 2011

2000

2500

3000

Importance of recombination for inflation W b h2

Planck 143GHz channel forecast

W b h2

CosmoRec CosmoRec Recfast++ Recfast++ Recfast++ (correction factor) Recfast++ (correction factor)

- 2.1 σ | - 2.8 x 10-4 0.0216

0.0224

0.0232

0.0216

0.0224

0.0232

W c h2

W c h2

0.116 0.112

0.116

0.108

0.112

0.0216

0.108 0.0224

0.0232

0.0216 72 70 68 0.0216

72

0.108

0.0224 72

0.0216 0.10

0.108

0.112

0.116

H0

H0

70 0.108

0.0224

0.116

72

68 0.0232

0.112

0.0232

70

70 0.0224 68

0.112 680.116

0.0232

0.108

0.10

68

0.112

70

72

0.116

68

0.09

0.10

0.09

0.10

0.08

0.09

0.08

0.09

0.08

0.09

0.1120.080.116

0.07

0.975

0.0232

0.07 0.0216

0.07

0.0224 0.975

72

t

t

0.10

0.08 0.0224

70

0.10

0.09

0.07 0.0216

Precise recombination history is crucial for understanding inflation!

-0.8 σ | - 0.5

0.108

0.0232

0.07

0.108

0.112 0.975

68

0.116

70 0.08

0.07

-3.2 σ | - 0.012 72

68

0.07

70 0.975

0.08

72

0.09

0.10

0.07

0.960

0.975

0.960

0.975

0.960

0.975

0.960

0.975

0.945

0.960

0.945

0.960

0.945

0.960

0.945

0.960

0.0216

3.075 3.050 3.025 3.000 0.0216

0.945 0.0224

0.0232

0.0216

0.0224 3.075

0.0232

3.000 0.0216

3.000

0.108

3.075

3.025

3.050

0.9450.116 0.112

0.0232

3.050

3.075

0.0224 3.025

0.108

3.050 0.108

0.112 3.0250.116

3.000

68

0.112 3.075

0.116

3.050

72

68

0.0232 0.108 0.112 0.116 Shaw &0.0224 JC, 2011, and references therein

703.025

3.000

70 3.075

0.08

0.090.945 0.10

72

0.07

72

68

3.000 0.07

70

0.08

0.093.025 0.10

72

3.000 0.07

0.10

0.945

0.08

0.09 3.075

ns

0.08

0.09

0.975

log(1010 As ) 0.945

0.960

0.975

log(1010 As )

3.075

3.025 3.000

0.960

0.10

3.050

3.050 0.08

0.09

-1.1 σ | - 0.01

3.075

3.025

3.050 68

0.07

3.050

3.075

3.025 3.000

700.945

ns

3.050 0.945

0.10

0.960 3.025 0.975

3.000

3.000

0.945

0.960

3.025

3.050

0.975

3.075

3.000

3.025

3.050

3.075

Importance of recombination for inflation

Without recombination corrections people would now be talking about pretty different inflation models!

Planck Collaboration, 2013, paper XXII

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 (SPTPol & ACTPol) on Yp will reach 1% level

Importance of recombination for measuring helium W b h2

cosmic variance limited case (l ≤ 2000)

W b h2

CosmoRec Recfast++ CosmoRec Recfast++ Recfast++ (correction factor) Recfast++ (correction factor)

2.0 σ | 1.2 x 10-4 W c h2

0.0224 0.0226 0.0228 0.0230

0.120 0.117 0.114

0.0216

0.0224

0.0232

W c h2

0.111 0.108 74 72 70 68 0.096 0.090 0.084

0.0224 0.0226 0.0228 0.0230 0.108 0.111 0.114 0.117 0.120

0.116

70

0.0216 68 0.0224

0.0232

0.0224 0.0226 0.0228 0.0230 0.108 0.111 0.114 0.117 0.120

70

68

0.096

0.096 72

0.090

0.090 70 0.084

0.084

0.0224 0.0226 0.0228 68 0.0230 0.108 0.111 0.114 0.117 0.120

0.28

0.0216

0.26 0.24

0.28

0.0224

0.0232

0.26

68 68 0.28

3.0 2.7

0.97 0.96 0.95

3.030

70

70

0.108

0.112 72

72

0.112

0.116 74

0.08

74

0.08 3.3

3.3

0.07 0.0216 3.0 0.0224

72

0.07 3.0

0.0232

2.7 0.0224 0.0226 0.0228 68 0.975 0.0230 0.108 0.111 0.114 0.117 0.1200.975

0.112

0.1163.0

2.7

0.960 0.945

72

0.96

0.945 0.96

0.96

0.95

0.95

70 0.108

72 0.112

0.95 74 0.116 3.060

3.045

3.060 3.075 3.045

3.030

3.050 3.030

3.030

0.0224 0.0226 0.0228 68 3.025 0.0230 0.108 0.111 0.114 0.117 0.1203.025

3.000 0.0216

3.000

3.045

70

72

74

0.0232 and references 0.108 0.112 therein 0.116 Shaw &0.0224 JC, 2011,

Yp 70

72

t

3.9 σ | 0.021 0.10 0.084 0.090 0.096

0.09 0.08 0.07

0.22

0.24

0.26

0.28

Nn

1.2 σ | 0.0033

3.3

68

3.0 70

72

0.07

0.08

0.09

0.10

2.7

3.0

3.3

2.7 0.08

3.0 0.09

3.3 0.10

ns

2.7 0.0840.975 0.090 0.096

74

0.97

3.060

3.050

70

0.960 0.97

68

68

2.7

0.97

0.0224 0.0226 0.0228 0.0230 0.108 0.111 0.1140.0232 0.117 0.120 0.0216 0.0224

3.075

0.22

3.3

0.108

•

0.084 0.090 0.096

0.28 0.116 0.26 0.24

70

H0

t

74

0.24

0.10

3.060 3.045

0.108

0.26

0.24 0.10 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 0.09 0.09 3.3

for 8 parameter case strongest bias in Yp different parameter combinations mimic the effect of recombination corrections on the CMB power spectra combination with other cosmological data sets and foregrounds will also lead to ‘reshuffling’ of biases

72

0.108

72

• •

H0

74

0.112

2.0 σ | 1.1

0.960

0.22

0.24

0.26 0.975 0.28

0.960

0.97

0.945

0.95 0.22 70

0.24 72

0.26

0.95

0.28 0.07

3.060

3.075

3.030

0.0843.025 0.090 0.096

3.000

3.060

68

0.22

70

0.24

72

0.95

0.96

0.97 0.945

0.95 3.025 0.96

0.97

3.045

3.060 3.075 3.045

3.050 3.030

3.0303.050

3.075

3.045

3.050

0.97

0.945 0.96

0.96

0.084 0.090 0.096 68

ns

0.26 3.025 0.28

3.000 0.07

2.7

3.0

0.08

0.09

3.3

0.10

3.000

0.945

0.960

0.975 log(1010 As )

log(1010 As )

3.030 3.045 3.060

0.960

0.975

3.000

3.025

3.050

3.075

What if something unexpected happened? • E.g., something standard was missed, or something non-standard happened !? • A non-parametric estimation of possible corrections to the recombination history would be very useful → Principle component analysis (PCA)

Farhang, Bond & JC, 2012

What if something unexpected happened? • E.g., something standard was missed, or something non-standard happened !? • A non-parametric estimation of possible corrections to the recombination history would be very useful → Principle component analysis (PCA)

Farhang, Bond & JC, 2012

Measured mode amplitudes for ACT & SPT

• First mode detected at ~ 2σ • Similar for current Planck data • Effect very similar to the one of helium • In the future 2-3 modes detectable • Can we break the degeneracies??? Farhang, Bond & JC, 2012

Can the Cosmological Recombination Radiation help us with this?

Shifts in the line positions due to presence of Helium in the Universe

Photons released at redshift z~1400

transitions among highly excited states

Brackett-α

-27

Paschen-α

-1 -2 -1

10

Lyman-α

Changes in the line shape due to presence of Helium in the Universe

-1

Iν [J m s Hz sr ]

Hydrogen only Hydrogen and Helium

Balmer-α

10

Cosmological Recombination Spectrum

-26

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 10

-28

1

10

100 ν [ GHz ]

1000

3000

Cosmological Time in Years 790,000

370,000 260,000 10

1.4

130,000

18,000

-2 -1

-1

-1

-2 -1

Iν [J m s Hz sr ]

-1

-1

CMB-Anisotropies

-27

He II only

Iν [J m s Hz sr ]

Hydrogen only

1.2

10

Singly ionized Helium Lines

-26

10

-27

10

10

-28

-29

1

10

100

1000

3000

ν [ GHz ]

10

1

10

100

1000

Plasma fully ionized

Free Electron Fraction Ne/[Np+NH]

-28

3000

ν [ GHz ]

Hydrogen Lines

1 10

-27

Neutral Helium only

10

-28

Function Visibility

10

-29

-30

1

10

100 ν [ GHz ]

Neutral Helium Lines

1000

3000

He II-Lines

ines He I-L

0.4

10

H I-Lines

0.6

Plasma neutral

-2 -1

-1

-1

Iν [J m s Hz sr ]

0.8

0.2

0 700

1100

2000

3000

Redshift z

4000

6000

8000

What would we actually learn by doing such hard job? Cosmological Recombination Spectrum opens a way to measure:  the

specific entropy of our universe (related to Ωbh2)

 the

CMB monopole temperature T0

 the

pre-stellar abundance of helium Yp

 If

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

computations prepared by Chad Fendt in 2009 using detailed recombination code

Large improvements!

• CMB based cosmology alone

• Spectrum helps to break some of the parameter degeneracies

• Planning to provide a module that computes the recombination spectrum in a fast way

• detailed forecasts: which lines to measure; how important is the absolute amplitude; how accurately one should measure; best frequency resolution;

What would we actually learn by doing such hard job? Cosmological Recombination Spectrum opens a way to measure:  the

specific entropy of our universe (related to Ωbh2)

 the

CMB monopole temperature T0

 the

pre-stellar abundance of helium Yp

 If

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

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

The importance of HI continuum absorption

Fine-structure absorption features

Rubino-Martin, JC & Sunyaev, A&A, 2008

Dark matter annihilations / decays

• Additional photons at all frequencies • Broadening of spectral features • Shifts in the positions

JC, 2009, arXiv:0910.3663

What would we actually learn by doing such hard job? Cosmological Recombination Spectrum opens a way to measure:  the

specific entropy of our universe (related to Ωbh2)

 the

CMB monopole temperature T0

 the

pre-stellar abundance of helium Yp

 If

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

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

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

Conclusions • The standard recombination problem has been solved to a level that is sufficient for the analysis of current and future CMB data (