1. Atomic physics and the cosmological 21 cm signal Jonathan Pritchard (CfA) Collaborators: Steve Furlanetto (UCLA) Avi Loeb (CfA)

2. ITAMP APR 2008 2/26 Overview 21 cm basics Wouthysen-Field Effect Heating of the IGM 21 cm fluctuations from spin temperature variation Redshift evolution of the 21 cm signal z~12 z~30

3. ITAMP APR 2008 3/26 21 cm basics 1 0 S 1/2 1 1 S 1/2 n0n0 n1n1 n 1 /n 0 =3 exp(-h 21cm /kT s ) HI hyperfine structure =21cm Use CMB backlight to probe 21cm transition z=13 f obs =100 MHz f 21cm =1.4 GHz z=0 21 cm brightness temperature 21 cm spin temperature TSTS TbTb TT HI TKTK 3D mapping of HI possible - angles + frequency Coupling mechanisms: Radiative transitions (CMB) Collisions Wouthuysen-Field

4. ITAMP APR 2008 4/26 Wouthysen-Field effect Lyman  Effective for J  >10 -21 erg/s/cm 2 /Hz/sr T s ~T  ~T k W-Frecoils 2 0 P 1/2 2 1 P 1/2 2 2 P 1/2 1 0 S 1/2 1 1 S 1/2 Selection rules:  F= 0,1 (Not F=0  F=0) Hyperfine structure of HI Field 1959 nFLJnFLJ

5. ITAMP APR 2008 5/26 Spectral Distortion of Lya Recoil sources feature as photons diffuse in frequency Chen & Miralde-Escude 2004 frequency Colour temperature Coupling ≤1 number flux Hubble flow, scattering recoils

6. ITAMP APR 2008 6/26 Lya heating Madau, Meiksin, Rees 1997 Chen & Miralda-Escude 2004 Rybicki 2008 Lya heating much reduced over initial MMR estimates since T~T R -> possibility of WF coupled 21 cm absorption regime X-ray heating dominates over Lya heating for sensible parameters Chen & Miralda-Escude 2004 Furlanetto & Pritchard 2006 Recoils lead to heating Spectral distortion + diffusion leads to counterterm Injected photons can cool (T>10K) as well as heat (T<10K) In absence of other heat sources continuum and injection processes -> T~100K Chuzhoy & Shapiro 2006

7. ITAMP APR 2008 7/26 Detailed atomic corrections Fine structure of levels Spin diffusivity Mild heating of gas so T  eff ≠T K Corrections most important at low temperatures, but typically small Detailed calculations at z~20 will need to take these into account Hirata 2006

8. ITAMP APR 2008 8/26 Higher Lyman series Two possible contributions  Direct pumping: Analogy of the W-F effect  Cascade: Excited state decays through cascade to generate Ly  Direct pumping is suppressed by the possibility of conversion into lower energy photons  Ly  scatters ~10 6 times before redshifting through resonance  Ly n scatters ~1/P abs ~10 times before converting  Direct pumping is not significant Cascades end through generation of Ly  or through a two photon decay  Use basic atomic physics to calculate fraction recycled into Ly   Discuss this process in the next few slides… Hirata 2006Pritchard & Furlanetto 2006

9. ITAMP APR 2008 9/26 Lyman   Optically thick to Lyman series  Regenerate direct transitions to ground state Two photon decay from 2S state Decoupled from Lyman  f recycle,   A  =8.2s -1 A 3p,1s =1.64  10 8 s -1 A 3p,2s =0.22  10 8 s -1

10. ITAMP APR 2008 10/26 Lyman  Cascade via 3S and 3D levels allows production of Lyman  

11. ITAMP APR 2008 11/26 Lyman alpha flux Stellar contribution continuuminjected Cascades modify estimate that all Lyn are equal Spatial distribution of Lya photons important for 21 cm signal

12. ITAMP APR 2008 12/26 Scattering in IGM Chuzhoy & Zheng 2007 Smelin, Combes & Beck 2007 Naoz & Barkana 2007 Optical depth so large photons scatter in wings before reaching line center Steepens Lya flux profile about sources Increases inhomogeneity of Lya background source line center

13. ITAMP APR 2008 13/26 X-ray heating X-rays provide dominant heating source in early universe (shocks possibly important very early on) X-ray heating often assumed to be uniform as X-rays have long mean free path Simplistic, inhomogeneities may lead to observable 21cm signal X-ray flux -> heating rate -> temperature Weak constraints from diffuse soft x-ray background Mpc Dijikstra, Haiman, Loeb 2004

14. ITAMP APR 2008 14/26 Energy deposition Shull & van Steenberg 1985 Valdes & Ferrara 2008 X-ray HI HII e-e- e-e- HI photoionization collisional ionization excitation heating Ly  Chen & Miralda-Escude 2006 heating ionization Ly  X-ray energy partitioned other  X-rays ionize HeI mostly, but secondary electrons ionize HI Makes X-ray pre-heating without WF coupling unlikely Lya from X-ray can dominate over stellar Lya near into sources Two phase medium: ionized HII regions and partially ionized IGM outside x e <0.1

15. ITAMP APR 2008 15/26 Thermal history Furlanetto 2006

16. ITAMP APR 2008 16/26 21 cm fluctuations Baryon Density Gas Temperature W-F Coupling Neutral fraction Velocity gradient X-ray sources Ly  sources ReionizationCosmology Brightness temperature Amount of neutral hydrogen Spin temperature Velocity (Mass) b

17. ITAMP APR 2008 17/26 Temporal separation? Baryon Density Gas Temperature W-F Coupling Neutral fraction Velocity gradient X-ray sources Ly  sources ReionizationCosmology Dark Ages Twilight Brightness temperature b

18. ITAMP APR 2008 18/26 Fluctuations from the first stars  dV Fluctuations in flux from source clustering, 1/r 2 law, optical depth,… Relate Ly  fluctuations to overdensities W(k) is a weighted average Barkana & Loeb 2005

19. ITAMP APR 2008 19/26 Determining the first sources Chuzhoy, Alvarez, & Shapiro 2006 Sources Spectra J ,* vs J ,X SS Pritchard & Furlanetto 2006 bias source propertiesdensity z=20   dominates  =[k 3 P(k)/2  

20. ITAMP APR 2008 20/26 Growth of fluctuations expansionX-raysCompton Fractional heating per Hubble time at z Heating fluctuations temperature fluctuations  T /  adiabatic index -1

21. ITAMP APR 2008 21/26 Indications of T K T K <T  T K >T  Learn about source bias and spectrum in same way as Ly  Constrain heating transition  T dominates

22. ITAMP APR 2008 22/26 X-ray background? TT  xx ? X-ray background at high z is poorly constrained Extrapolating low-z X-ray:IR correlation gives: Glover & Brand 2003 1st Experiments might see T K fluctuations if heating late

23. ITAMP APR 2008 23/26 Experimental efforts LOFAR: Netherlands Freq: 120-240 MHz N a = 64 A tot = 0.042 km 2 (f 21cm =1.4 GHz) SKA: S Africa/Australia Freq: 60 MHz-35 GHz N a = 5000 A tot = 0.6 km 2 MWA: Australia Freq: 80-300 MHz N a = 500 A tot = 0.007 km 2 21CMA: China Freq: 70-200 MHz N a = 20 A tot = 0.008 km 2

24. ITAMP APR 2008 24/26 Temporal separation  x T  ? MWA SKA Pritchard & Loeb 2008

25. ITAMP APR 2008 25/26 High-z Observations Need SKA to probe these brightness fluctuations Observe scales k=0.025-2 Mpc -1 Easily distinguish two models Optimistic foreground removal B~12MHz ->  z~1.5 foregrounds poor angular resolution

26. ITAMP APR 2008 26/26 Conclusions Significant recent progress in understanding details of Wouthysen-Field effect Lya heating is weak allowing WF coupled 21 cm absorption signal X-rays probably most significant heating source 21 cm fluctuations contain information about early luminous sources and thermal history Need detailed knowledge of atomic physics to extract precise information from upcoming 21 cm observations Lots of work to be done!

27. ITAMP APR 2008 27/26

28. ITAMP APR 2008 28/26 X-ray heating To heat gas above T CMB estimate the required fraction of baryons in stars as: Compare with Lya coupling and reionization Lya coupling Reionization Expect Lya coupling > X-ray heating > Reionization

29. ITAMP APR 2008 29/26 Lya production photons/baryon required fraction of baryon in stars For stars to produce critical Lya flux

30. ITAMP APR 2008 30/26 Profile around the first stars Chen & Miralda-Escude 2006

31. ITAMP APR 2008 31/26 X-ray heating about a source Zaroubi et al. 2006

32. ITAMP APR 2008 32/26 Lya heating? Lya can heat Lyn can cool Deutrium important Effect from stellar photons usually small T_K<100K, so X-ray heating dominates. Scattering blue ward of resonance important here - makes Heating more efficient as all scatterings heat gas. Figure?

33. ITAMP APR 2008 33/26 21cm fluctuations: T K Pritchard & Furlanetto 2006 Density Gas Temperature W-F Coupling Neutral fraction Velocity gradient density + x-rays coupling saturated IGM still mostly neutral In contrast to the other coefficients  T can be negative Sign of  T constrains IGM temperature b

34. ITAMP APR 2008 34/26 21 cm fluctuations: Ly  Density Gas Temperature W-F Coupling Neutral fraction Velocity gradient -negligible heating of IGM -tracks density Ly  flux varies IGM still mostly neutral Three contributions to Ly  flux: 1.Stellar photons redshifting into Ly  resonance 2.Stellar photons redshifting into higher Lyman resonances 3.X-ray photoelectron excitation of HI Chen & Miralda-Escude 2006Chen & Miralda-Escude 2004 Ly  fluctuations unimportant after coupling saturates (x  >>1) b

35. ITAMP APR 2008 35/26 Foregrounds Many foregrounds  Galactic synchrotron (especially polarized component)  Radio Frequency Interference (RFI) e.g. radio, cell phones, digital radio  Radio recombination lines  Radio point sources Foregrounds dwarf signal: foregrounds ~1000s K vs 10s mK signal Strong frequency dependence T sky  -2.6 Foreground removal exploits smoothness in frequency and spatial symmetries Cross-correlation with galaxies also important

36. ITAMP APR 2008 36/26 Angular separation? Anisotropy of velocity gradient term allows angular separation Barkana & Loeb 2005 Bharadwaj & Ali 2004 Baryon Density Gas Temperature W-F Coupling Neutral fraction Velocity gradient In linear theory, peculiar velocities correlate with overdensities Initial observations will average over angle to improve S/N b

37. ITAMP APR 2008 37/26 Global history Heating HII regions IGM expansion Furlanetto 2006 Adiabatic expansion X-ray heating Compton heating ++ UV ionization recombination + X-ray ionization recombination + continuuminjected Ly  flux Sources: Pop. II & Pop. III stars (UV+Ly  ) Starburst galaxies, SNR, mini-quasar (X-ray) Source luminosity tracks star formation rate Many model uncertainties

38. ITAMP APR 2008 38/26 Ionization history Models differ by factor ~10 in X-ray/Ly  per ionizing photon Reionization well underway at z<12 X i >0.1 z R ~7  ~0.07 (Pop II=later generation stars, Pop. III = massive metal free stars)

39. ITAMP APR 2008 39/26 T K fluctuations Fluctuations in gas temperature can be substantial Amplitude of fluctuations contains information about IGM thermal history

40. ITAMP APR 2008 40/26 Temperature fluctuations T S ~T K <T  T b <0 (absorption) Hotter region = weaker absorption  T <0 T S ~T K ~T  T b ~0 21cm signal dominated by temperature fluctuations T S ~T K >T  T b >0 (emission) Hotter region = stronger emission  T >0

41. ITAMP APR 2008 41/26 Cosmology? Density Gas Temperature W-F Coupling Neutral fraction Velocity gradient coupling saturated IGM still mostly neutral IGM hot T K >>T  Kleban, Sigurdson & Swanson 2007 Probe smaller scales than CMB Unless pristine very difficult to improve on Planck level b

42. ITAMP APR 2008 42/26 Density power spectrum Moderate improvements - cross-check Improve n s and  most See baryonic oscillation at few sigma McQuinn et al. 2006

43. ITAMP APR 2008 43/26 Reionization Density Gas Temperature W-F Coupling Neutral fraction Velocity gradient IGM hot T K >>T  Ly  coupling saturated HII regions large Z=12.1 Z=9.2Z=8.3Z=7.6 Furlanetto, Sokasian, Hernquist 2003 b

44. ITAMP APR 2008 44/26 Growth of HII Regions 100 Mpc cube N-body + UV photon ray tracing Details of heating and coupling are neglected Trac & Cen 2006

45. ITAMP APR 2008 45/26 The first sources HII Soft X-rays Hard X-rays Ly  1000 Mpc 330 Mpc 5 Mpc0.2 Mpc z=15

46. ITAMP APR 2008 46/26 21 cm fluctuations: z ? Exact form very model dependent

47. ITAMP APR 2008 47/26 Redshift slices: Ly  Pure Ly  fluctuations z=19-20

48. ITAMP APR 2008 48/26 Redshift slices: Ly  /T z=17-18 Growing T fluctuations lead first to dip in  T b then to double peak structure Double peak requires T and Ly  fluctuations to have different scale dependence

49. ITAMP APR 2008 49/26 Redshift slices: T z=15-16 T fluctuations dominate over Ly  Clear peak-trough structure visible   2 <0 on large scales indicates T K <T 

50. ITAMP APR 2008 50/26 Redshift slices: T/  z=13-14 After T K >T , the trough disappears As heating continues T fluctuations die out

51. ITAMP APR 2008 51/26 Redshift slices:  /x z=8-12 Bubbles imprint feature on power spectra once x i >0.2 Non-linearities in density field become important (T K fluc. not included)

52. ITAMP APR 2008 52/26 Low-z Observations SKA MWA LOFAR Low k cutoff from antennae size Sensitivity of LOFAR and MWA drops off by z=12 McQuinn et al. 2006