Radiative Transfer Effects in Hydrogen Recombination: Two-Photon Transitions and Lyα Diffusion
This presentation explores the impact of radiative transfer on hydrogen recombination, focusing on two-photon transitions and the diffusion of Lyman-alpha photons. It delves into the significance of the Cosmic Microwave Background (CMB), the standard picture of recombination, and how helium and hydrogen recombination processes are affected by different decay mechanisms. Special attention is given to the role of two-photon decays in hydrogen, their calculation methods, and implications for cosmological models. Discover how these factors influence key parameters and the understanding of our universe.
Radiative Transfer Effects in Hydrogen Recombination: Two-Photon Transitions and Lyα Diffusion
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Presentation Transcript
Radiative Transfer Effects in Hydrogen Recombination: 2γ Transitions and Lyα Diffusion Christopher Hirata Orsay – July 2009 With special thanks to: E. Switzer (Chicago) D. Grin, J. Forbes, Y. Ali-Haïmoud (Caltech)
Outline • Motivation, CMB • Standard picture • He recombination • Two-photon decays in H • Lyman-α diffusion
1. Motivation, CMB Cosmic microwave background The CMB has revolutionized cosmology:- Tight parameter constraints (in combination with other data sets)- Stringent test of standard assumptions: Gaussianity, adiabatic initial conditions- Physically robust: understood from first principles. (Linear perturbation theory.) WMAP Science Team (2008)
1. Motivation, CMB CMB and inflation • Primordial scalar power spectrum: ns, s measured by broad-band shape of CMB power spectrum the damping tail will play a key role in the future (Planck, ACT, SPT, …) probe of inflationary slow-roll parameters: (for single field inflation; but measurements key for all models)
1. Motivation, CMB This is the CMB theory!
1. Motivation, CMB This is the CMB theory! ne = electron density (depends on recombination)
2. Standard picture Recombination history He2+ + e- He+ no effect He+ + e- He z: damping tail degenerate with ns H+ + e- H z: acoustic peak positions degenerate with DA z: polarization amplitude z … as computed by RECFAST1.3 (Seager, Sasselov, Scott 2000) The “standard” recombination code until Feb. 2008.
H+ + e- radiative recombination + photoionization 3s 3p 3d 2s 2p Lyman- resonance escape 2 1s 2. Standard picture Standard theory of H recombination(Peebles 1968, Zel’dovich et al 1968) = 2-photon decay rate from 2s Pesc = escape probability from Lyman- line ALy = Lyman- decay rate e = recombination rate to excited states gi = degeneracy of level i i = photoionization rate from level i R = Rydberg
H+ + e- radiative recombination + photoionization 3s 3p 3d 2s 2p Lyman- resonance escape 2 1s 2. Standard picture Standard theory of H recombination(Peebles 1968, Zel’dovich et al 1968) = 2-photon decay rate from 2s Pesc = escape probability from Lyman- line = probability that Lyman- photon will not re-excite another H atom. Higher or Pesc faster recombination. If or Pesc is large we have approximate Saha recombination.
3. He recombination Helium level diagram TRIPLETS (S=1) SINGLETS (S=0) 1s3p 31P1 1s3d 31D2 1s3d 33D1,2,3 1s3p 33P0,1,2 1s3s 31S0 1s3s 33S1 1s2p 21P1 1s2p 23P0,1,2 1s2s 21S0 1, 584Å 1.8x109/s 1s2s 23S1 1, 591Å 170/s from 23P1 only 2 52/s 1, 626Å 1.3x10-4/s 1s2 11S0
3. He recombination Issues in He recombination • Mostly similar to H recombination except: • Two line escape processesHe(21P1) He(11S0) + 584ÅHe(23P1) He(11S0) + 591Å • These are of comparable importance (Dubrovich & Grachev 2005). • Feedback: redshifted radiation from blue line absorbed in redder line. • Enhancement of escape probability by H opacity:He(21P1) He(11S0) + 584ÅH(1s) + 584Å H+ + e-(Hu et al 1995)
3. He recombination He III recombination history Accel. fromH opacity Accel. from23P1 decay Seager et al 2000 Switzer & Hirata 2007 thermal equilibrium
3. He recombination Current He recombination histories
4. Two-photon decays in H Two-photon decays • H(2s) H(1s) + + (8.2 s-1) included in all codes. • But what about 2 decays from other states? • Selection rules: ns,nd only. • Negligible under ordinary circumstances:H(3s,3d) H(2p) + 6563Å, depopulates n3 levels. • In cosmology:so 3s,3d 2 decays might compete with 2s(Dubrovich & Grachev 2005). • Obvious solution: compute 2 decay coefficients 3s,3d, add to multilevel atom code.
4. Two-photon decays in H Calculation p. 1 • Easy! This is tree-level QED. • Feynman rules (in atomic basis set): electron propagator photon propagator vertex (electric dipole) • Ignore positrons and electron spin – okay in nonrelativistic limit.
4. Two-photon decays in H Calculation p. 2 • Two diagrams for 2 decay:M= + • Total decay rate: (=k for on-shell photon) • Problem: infinite because Mcontains a pole ifn1=2 … n-1 (n1p intermediate state is on-shell).
4. Two-photon decays in H ∞ • The resolution to this problem in the cosmological context has provided some controversy. (See Dubrovich & Grachev 2005; Wong & Scott 2007; Hirata & Switzer 2007; Chluba & Sunyaev 2007; Hirata 2008). Lots more this afternoon! • Pole displacement: rate still large, e.g. Λ3d = 6.5×107 s-1. This includes sequential 1 decays, 3d2p1s. • Re-absorption of 2 radiation.No large rates or double-counting in optically thick limit.
4. Two-photon decays in H Radiative transfer calculation • A radiative transfer calculation is the only way to solve the problem. • Must consistently include: Stimulated 2 emission (Chluba & Sunyaev 2006) Absorption of spectral distortion (Kholupenko & Ivanchik 2006) Decays from n3 levels. Raman scattering – similar physics to 2 decay, except one photon in initial state:H(2s) + H(1s) + Two-photon recombination/photoionization. • 2008 code did not have Lyman- diffusion(now included – thanks to J. Forbes).
4. Two-photon decays in H Radiative transfer calculation • The Boltzmann equation: • f = photon phase space density • = number of decays / H nucleus / Hz / second • Ill-conditioned at Lyman lines: coefficients (or large). But solution is convergent:
4. Two-photon decays in H Numerical approach • Key is to discretize the 2γ continuum. • Each frequency bin (ν,Δν) is treated as a virtual level. Included in multi-level atom code. • In the steady-state limit, thevirtual level can be treatedjust like a real level: • 2γ decay • 2γ excitation • Feedback • But it’s just a mathematicaldevice! nl ν’ virtual ν 1s
4. Two-photon decays in H Physical effects 1 • Definitions: a 2 decay is “sub-Ly” if both photons have E<E(Ly). a 2 decay is “super-Ly” if one photon has E>E(Ly). • Sub-Ly decays: Accelerate recombination by providing additional path to the ground state. Delay recombination by absorbing thermal + redshifted Ly photons.The acceleration always wins, i.e. reaction: H(nl) H(1s) + + proceeds forward.
4. Two-photon decays in H Physical effects 2 • Super-Ly decays are trickier! Also provide additional path to ground state. But for every super-Ly decay there will later be a Ly excitation, e.g.: H(3d) H(1s) + <1216Å + >6563Å H(1s) + 1216Å H(2p) • The net number of decays to the ground state is zero. • But there is an effect: Early, z>1260: accelerated recombination. Later, z<1260: delayed recombination. • Same situation for Raman scattering.
4. Two-photon decays in H Phase space density Ly Ly Ly Full resultWithout 2 decaysBlackbody
4. Two-photon decays in H Correction:0.19 ACBAR 0.27 WMAP5 7 Planck L
5. Lyman-α diffusion Doppler shifts & Lyman-α diffusion • So far we’ve neglected thermal motions of atoms. • Main effect is in Lyman-α where resonant scatteringleads to diffusion in frequency space due to Doppler shift of H atoms. Diffusion coefficient is • Rapid diffusion near line center, very slow in wings.
5. Lyman-α diffusion Doppler shifts & Lyman-α diffusion • Can construct Fokker-Planck equation from two physical conditions (e.g. Rybicki 2006): Exactly conserve photons in scattering Respect the second law of thermodynamics: must preserve blackbody with μ-distortion, fν~e-hν/T. • hfν/T term can be physically interpreted as due to recoil (e.g. Krolik 1990; Grachev & Dubrovich 2008). Effect is to push photons to red side of Lyman-α, speeding up recombination. • With J. Forbes, diffusion now patched on to 2γ radiative transfer code.
5. Lyman-α diffusion Numerical details • Solve Fokker-Planck equation (FPE) in frequency region near Lyα. • Discretize FPE without Hubble term in ν direction to convert to system of stiff ODEs. (Default 2000 bins.) • No photons allowed to diffuse out of bounds. • Hubble redshift implemented by stepping all photons 1 bin to the red at each time step. • Required for solution: • fν @ blue boundary; atomic level populations. • Solve iteratively with atomic level + 2γ code.
