Cosmological Recombination and What We Can Learn From the Cosmological Recombination Spectrum?

Transcription

1 Cosmological Recombination and What We Can Learn From the Cosmological Recombination Spectrum? J. Chluba in collaboration with R.A. Sunyaev (MPA) and J.A. Rubiño-Martín (IAC) 3. Kosmologietag 8-9 May 2008, IBZ, Bielefeld, Germany Max-Planck-Institut für Astrophysik

2 Sketch of the Cosmic Ionization History Free electron (number) density Total number (density) of hydrogen nuclei

3 Cosmic Microwave Background Anisotropies Example: WMAP CMB has blackbody spectrum in every direction Variations of the CMB temperature ΔT/T~10-5

4 CMB Sky Cosmology WMAP CMB Sky a lm Gaussianity Power spectra TT TE EE BB Cosmological Parameters (Joint) analysis large scales ~1 small scales Ω tot, Ω m, Ω b, Ω Λ, h, τ, n s,... Other cosmological Dataset: small-scale CMB, Supernovae, large-scale structure, Lyman-α forest, lensing,...

5 What about the recombinational photons? Our Universe has extremely high specific entropy: N γ ~ 410 cm -3 (1+z) 3 N b ~ cm -3 (1+z) 3 N γ / N b ~ T r 3 / Ω b h 2 ~ !!! Hydrogen recombination: per recombined hydrogen atom an energy of ~ 13.6 ev in form of photons is released at z~1100 Δε/ε ~ 13.6 ev N b / N γ 2.7kT r ~ 10-8 There should be some spectral distortion due to these additional photons! (Zeldovich, Kurt & Sunyaev, 1968, ZhETF, 55, 278; Peebles, 1968, ApJ, 153, 1) In 1975 Viktor Dubrovich emphasized the possibility to observe the recombinational lines from n>3 and Δn<<n!

6 Initial Formulation of the Cosmological Recombination Problem Expanding Universe medium is isotropic and homogeneous expansion rate determined by Hubble-factor H Time evolution of particle number densities for e, p, HI, HeI, HeII and HeIII velocities according to Maxwell-Boltzmann distributions with temperature T e electrons are coupled to photon field via Compton scattering T e Time evolution of the isotropic ambient photon field spectral distortions small feedback on the recombination dynamics assumed to be negligable ambient photon field is described by a pure blackbody (T 0 =2.725K today) solution for the escape problem in the (optically thick) resonant line transitions Sobolev approximation for expanding medium escape probability Time evolution of the matter and radiation can be treated separately

7 3-level hydrogen atom and continuum continuum: e p (He) Routes to the ground state? direct recombination to 1s γ γ - Emission of photon is followed by immediate re-absorption No Hydrogen atom 2s 2γ γ γ 2p recombination to 2p followed by Lyman-α emission - medium optically thick to Ly-α phot. - many resonant scatterings - escape very hard (p z ~1100) recombination to 2s followed by 2s two-photon decay ~ 43% 1s - 2s 1s ~10 8 times slower than Ly-α - 2s two-photon decay profile maximum at ν 1/2 ν α - immediate escape ~ 57% Zeldovich, Kurt & Sunyaev, 1968, ZhETF, 55, 278 Peebles, 1968, ApJ, 153, 1

8 Our multi-level hydrogen atom and continuum Hydrogen atom continuum: ns 3s 3p 3d 2s 1s np nd nf 2p γ e p (He) collisions Cascading electrons recombination & photoionization - n small l-dependence not drastic - high shells more likely to l<<n - large n induced recombination many radiative dipole transitions - Lyman-series optically thick - Δl = ±1 restriction (electron cascade) - large n & small Δn induced emission l-changing collisions (only Δl = ±1) - help to establish full SE within the shell - only effective for n > n-changing collisions Collisional photoionization Three-body-recombination

9 Some details about the Recfast-Code Output of N e /N H Hydrogen: - up to 300 levels - Only 2s & 2p separately!!! - n>2 full SE for l-sub-states Helium: - HeI 200-levels (z ~ ) - HeII 100-levels (z ~ ) - HeIII 1 equationl In addition: - H chemistry (important 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

10 Small details in the physics of recombination Hydrogen recombination Two-photon decay from higher levels (Dubrovich & Grachev, 2005, Astr. Lett., 31, 359; Wong & Scott, 2007; JC & Sunyaev, 2007, astro-ph/ ) Induced 2s two-photon decay for hydrogen (JC & Sunyaev, 2006, A&A, 446, 39) Feedback of the Lyman-α distortion on the 2s two-photon absorption rate (Kholupenko & Ivanchik, 2006, Astr. Lett.) Non-equilibrium effects in the angular momentum sub-states (Rubiño-Martín, JC & Sunyaev, 2006, MNRAS; JC, Rubiño-Martín & Sunyaev, 2007, MNRAS) Feedback of Lyman-series photons (Ly[n] Ly[n-1]) (JC & Sunyaev, 2007, A&A) Lyman-α escape problem (JC & Sunyaev, in preparation) Helium recombination Similar list of processes as for hydrogen (Switzer & Hirata, 2007) Spin forbidden 2p-1s triplet-singlet transition (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, astro-ph/ )

11 Stimulated 2s 1s decay Transition rate in vacuum A 2s1s ~ 8.22 sec -1 Low Frequency CMB Photons CMB ambient photons field A 2s1s increased by ~1% HI - recombination slightly faster 2s-1s emission profile JC & Sunyaev, 2006, A&A

12 Feedback of the Lyman-α distortion on the 2s-1s channel - Lyman-α distortion exceeds the CMB in the Wien part by many orders of magnitude - redshifting allows them to feedback on the 2s- 1s channel - delays HI recombination - partially chancels stimulated 2s 1s Kholupenko & Ivanchik, 2006, Astr. Lett

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

14 Two-photon transitions in Hydrogen Two-photon transitions from the atomic physics point of view are in principle understood Main difficulty is connected with the radiative transfer (see discussion in JC & Sunyaev, 2007) How is the escape close to the resonance modified? Feedback due to changes on the blue side of Ly-α? Transitions involving the continuum (c 2p 1s)? List of people that are in addition working on this problem now Dubrovich & Grachev Labzowsky & Shonin Karshenboim Hirata Scott & Wong

15 Ly-α resonance scattering 3s 3p 3d - H 1s + 1γ H 2p H 1s + 1γ - No collisions (e, p) on 2p state! 2s γ 2p γ - Conserves energy of the photon in the distant damping wing (broadening due to motion of the atom is very small Δν/ν~10-5!!!) 1s Voigt - profile R II redistribution (Diffusion in frequency space) - Full redistribution (Voigt) only when electron reaches higher levels or the continuum! The probablity for this is rather small (p d ~10-4 per scattering).

16 Escape problem in the Sobolev approximation Escape == photons stop interacting with the Ly-α resonance - One of the key assumptions: every scattering leads to a complete redistribution over the line profile - τ S >> 1 even photons in the very distant red wing (-x D < ) can scatter and therefore return to the line center, where the probability to be absorpted is largest - In Sobolev approach: scattering == absorption - However, it is not important that photons scatter, but that they return to higher levels / the continuum, a process that has very small probability (p d ~10-4 per scattering) - In Sobolev approximation this probability seems overestimated - Escape probability seems underestimated

17 Line Diffusion and Escape to the Distant Red Wings - Escape fraction is very small (p esc ~10-9 per Lyman-α photon) - Line wings (below ~500 Doppler width!!!) are important!!!

18 The two-photon emission profile 3s 3p 3d 2s 1s γ γ 2p Seaton cascade (1+1 photon) No collisions two photons (mainly H-α and Ly-α) are emitted! Maria-Göppert-Mayer (1931): decription 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 ~ Doppler width) parts of the line spectra

19 3s and 3d two-photon decay spectrum Lorentzian profile Lorentzian profile Escape in optically thin regions: HI -recombination is a bit slower due to 2γ-transitions from s-states HI -recombination is a bit faster due to 2γ-transitions from d-states

20 5s two-photon decay spectrum

21 The Cosmological Recombination Spectrum and what we could learn by observing it

22 List of groups around the world Hydrogen recombination spectrum Zeldovich, Kurt & RS 1968; Peebles 1968 Dubrovich 1975; Bernshtein et al. 1977; Beigman & RS 1978 Rybicki and Dell Antonio 1993; Dubrovich & Stolyarov 1995 Burgin 2003; Dubrovich & Shakhvorostova 2004; Kholupenko et al. 2005; Wong et al. 2006; Rubino-Martin et al. 2006; JC & Sunyaev 2006; JC et al Helium recombination spectrum Dubrovich and Stolyarov 1997; Rubino-Martin et al Main difficulties for accurate predictions Early works for pre-concordance cosmologies Computational limitations (hydrogen 100 l-resolved shells ~5000 strongly coupled differential equations) Accurate & sufficiently complete atomic data for neutral helium (Drake & Morton and Beigman & Vainshtein)

23 100-shell hydrogen atom and continuum CMB spectral distortions bound-bound & 2s: - atν>1ghz: distinct features - slope ~ 0.46 JC & Sunyaev, 2006, A&A, 458, L29 (astro-ph/ )

24 100-shell hydrogen atom and continuum CMB spectral distortions bound-bound & 2s: - atν>1ghz: distinct features - slope ~ 0.46 free-bound: - only a few features distinguishable - slope ~ 0.6 JC & Sunyaev, 2006, A&A, 458, L29 (astro-ph/ )

25 100-shell hydrogen atom and continuum CMB spectral distortions bound-bound & 2s: - atν>1ghz: distinct features - slope ~ 0.46 free-bound: - only a few features distinguishable - slope ~ 0.6 JC & Sunyaev, 2006, A&A, 458, L29 (astro-ph/ ) Total: - f-b contributes ~30% and more - Balmer cont. ~90% - Balmer: 1γ per HI - in total 5γ per HI

26 100-shell hydrogen atom and continuum Relative distortions Wien-region: - L α and 2s distortions are very strong - but CIB more CMB maximum: - relative distortions extremely small - strong ν-dependence RJ-region: JC & Sunyaev, 2006, A&A, 458, L29 (astro-ph/ ) - relative distortion exceeds level of ~10-7 below ν ~ 1-2 GHz - oscillatory frequency dependence with ~1-10 percent-level amplitude: hard to mimic by known foregrounds

27 What about the contributions from helium recombination? Nuclear reactions: Y p ~0.24 N HeI / N H ~8 % expected photon number rather small BUT: (i) two epochs of He recombination HeIII HeII at z~6000 and HeII HeI at z~2500 (ii) Helium recombinations faster more narrow features with larger amplitude (iii) non-trivial superposition local amplification possible Opens a way to directly measure the primordial (pre-stellar!!!) helium abundance!

28 Grotrian diagram for helium Semi-forbidden transitions are important for HeI-recombiniation!!!

29 Bound-bound recombination spectra: high frequencies ~ 36% change HeI emissionabsorption feature (~55% drop)

30 Bound-bound recombination spectra: intermediate frequencies Shift of peak positions ~30% change Non-trivial line shapes

31 Bound-bound recombination spectra: low frequencies quasi -oscillatory template Peak-to-peak amplitude changed!!!

32 Scan over frequency instead of angular coordinate!!!

33 Experiments under construction are reaching the sensitivity on the level of 10 nk (A. Readhead, talk at NRAO Symposium)! Cosmological recombination Signal is close to ~1µK. The amplitude of the frequency modulated signal reaches ~30 nk. In both cases: No absolute measurement! In the case of the recombinational lines one can compute a Template with frequencies and amplitude of all features The lines in the CMB spectrum are the same on the whole sky

34 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 Ω b h 2 ) the CMB monopole temperature T 0 the pre-stellar abundance of helium Y p Not limited by cosmic variance (no statistical comparison with theory!) If recombination occurs as we think it does, then the lines can be predicted with very high accuracy! Current limitations: (i) HI & HeI collisional rates; (ii) HeI photoionization cross-sections and (iii) HeI bb-transition rates Is the cosmological recombination spectrum really interesting enough?

35 Energy Release in the Early Universe Full thermodynamic equilibrium (certainly valid at very high redshifts) CMB has a blackbody spectrum at every time (not affected by expansion!!!) Photon number density and energy density determined by temperature T γ Disturbance of full equilibrium for example by Energy injection (e.g. decaying or annihilating particles) Production of photons and/or particles CMB spectrum would deviate from a pure blackbody today! Early energy release (z 50000) μ-type distortion (another talk...) Late energy release (z 50000) y-type distortion Cobe/Firas spectral measurements (Mather et al., 1996; Fixsen et al. 1996) y Sunyaev& Zeldovich, 1980, Ann. Rev. Astr. Astrophy., 18, pp.537

36 Energy injection CMB Spectral Distortions How easy is it actually to learn something interesting about the thermal history? CMB distortion can be predicted for different energy injection histories and mechanisms Spectral distortions are broad and featureless Absolute (COBE-type) measurements are required Different injection histories yield very similar spectral distortion! Simplest example: pre- and post-recombinational y-type distortions - energy release at redshifts 1000 < z < SZ-effect e.g. due to unresolved clusters, y-distortion supernova remnants, shockwaves, etc. Absence of narrow spectral features makes it very hard to understand real details!!!

37 Pre-recombinational atomic transitions after possible energy release pure blackbody CMB no net emission or absorption of photons before recombination epoch! non-blackbody CMB (Lyubarsky & Sunyaev, 1983) Ly-α Ly-c atoms try to restore full equilibrium atomic loops develop (cont. bound cont.) splitting of photons loops mainly end in Lyman-continuum Balmer-cont. loops work just before recombination γ γ Lyman -c loops γ γ γ γ γ Balmer -c loops γ γ γ 2:1 2:1 3:1

38 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on y Hydrogen Helium + JC & Sunyaev, 2008, astro-ph/

39 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on y Hydrogen Helium + JC & Sunyaev, 2008, astro-ph/

40 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on y Hydrogen Helium + JC & Sunyaev, 2008, astro-ph/

41 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on y Hydrogen Helium + JC & Sunyaev, 2008, astro-ph/ Large increase in the total amplitude of the distortions with value of y! Strong emission-absorption feature in the Wien-part of CMB (absent for y=0!!!) HeII contribution to the pre-recombinational emission as strong as the one from HI!

42 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on z Hydrogen and Helium + Value allowed by Cobe/Firas JC & Sunyaev, 2008, astro-ph/

43 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on z Hydrogen and Helium + Value allowed by Cobe/Firas JC & Sunyaev, 2008, astro-ph/

44 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on z Hydrogen and Helium + Value allowed by Cobe/Firas JC & Sunyaev, 2008, astro-ph/

45 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on z Hydrogen and Helium + Value allowed by Cobe/Firas JC & Sunyaev, 2008, astro-ph/

46 CMB spectral distortions after single energy release 25 shell HI and HeII bb&fb spectra: dependence on z Hydrogen and Helium + Value allowed by Cobe/Firas JC & Sunyaev, 2008, astro-ph/ Large increase in the total amplitude of the distortions with injection redshift! Number of spectral features depends on injection redshift! Emission-Absorption feature increases ~2 for energy injection z 11000

47 CMB spectral distortions after single energy release Changes in the low-frequency variability increase of the peakpeak amplitude by up to a factor of 2! non-trivial phaseshifts additional features JC & Sunyaev, 2008, astro-ph/

48 Narrow CMB spectral distortions in y-type era today z ~ z ~ 6000 z ~ 2500 z ~ 1400 z ~ 1100 z = 0 μ-era??? We are working on this now!

49 Conclusions Cosmological Recombination Spectrum opens a way to measure: the specific entropy of our universe (related to Ω b h 2 ) the CMB monopole temperature T 0 the pre-stellar abundance of helium Y p Not limited by cosmic variance (no statistical comparison with theory!) If recombination occurs as we think it does, then the lines can be predicted with very high accuracy! Current limitations: (i) collisional rates; HeI (ii) photo-ionization crosssections and (iii) bb-transition rates If something unexspected 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-recombinational y-type distortions new constraints on energy injection history

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