Atomic physics and the cosmological 21 cm signal

Jonathan Pritchard (CfA)

Collaborators: Steve Furlanetto (UCLA) Avi Loeb (CfA)

2/26ITAMPAPR 2008 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

3/26ITAMPAPR 2008 21 cm basics

10S1/2

11S1/2

n0

n1

n1/n0=3 exp(-h21cm/kTs)

•HI hyperfine structure

=21cm

•Use CMB backlight to probe 21cm transition

z=13fobs=100 MHzf21cm=1.4 GHz

z=0

•21 cm brightness temperature

•21 cm spin temperature

TS TbT

HITK

•3D mapping of HI possible - angles + frequency

Coupling mechanisms: Radiative transitions (CMB) Collisions Wouthuysen-Field

4/26ITAMPAPR 2008 Wouthysen-Field effect

Lyman

Effective for J>10-21erg/s/cm2/Hz/sr

Ts~T~Tk

W-F recoils 20P1/2

21P1/2

21P1/2

22P1/2

10S1/2

11S1/2 Selection rules: F= 0,1 (Not F=0F=0)

Hyperfine structure of HI

Field 1959

nFLJ

5/26ITAMPAPR 2008 Spectral Distortion of Lya

• Recoil sources featureas photons diffuse in frequency

Chen & Miralde-Escude 2004frequency

• Colour temperature

• Coupling

≤1

numberflux

•Hubble flow, scatteringrecoils

6/26ITAMPAPR 2008 Lya heating

Madau, Meiksin, Rees 1997

Chen & Miralda-Escude 2004Rybicki 2008

• Lya heating much reduced over initial MMR estimates since T~TR

-> possibility of WF coupled 21 cm absorption regime

•X-ray heating dominates over Lya heating for sensible parameters

Chen & Miralda-Escude 2004Furlanetto & 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~100KChuzhoy & Shapiro 2006

7/26ITAMPAPR 2008

Detailed atomic corrections

• Fine structure of levels• Spin diffusivity• Mild heating of gas so T

eff≠TK

• Corrections most important at low temperatures, but typically small• Detailed calculations at z~20 will need to take these into account

Hirata 2006

8/26ITAMPAPR 2008 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 ~106 times before redshifting through

resonance Ly n scatters ~1/Pabs~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

9/26ITAMPAPR 2008 Lyman

•Optically thick to Lyman series Regenerate direct transitions to ground state

•Two photon decay from 2S state•Decoupled from Lyman •frecycle,

A=8.2s-1

A3p,1s=1.64108s-1A3p,2s=0.22108s-1

10/26ITAMPAPR 2008 Lyman

•Cascade via 3S and 3D levelsallows production of Lyman

11/26ITAMPAPR 2008 Lyman alpha flux•Stellar contribution

continuum injected

• Cascades modify estimate that all Lyn are equal• Spatial distribution of Lya photons important for 21 cm signal

12/26ITAMPAPR 2008 Scattering in IGM

Chuzhoy & Zheng 2007Smelin, Combes & Beck 2007Naoz & 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

13/26ITAMPAPR 2008 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

14/26ITAMPAPR 2008 Energy deposition

Shull & van Steenberg 1985Valdes & Ferrara 2008

X-ray

HIHII

e-

e-

HI

photoionization

collisionalionization

excitation

heating

Ly

Chen & Miralda-Escude 2006

heatingionization

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 xe<0.1

15/26ITAMPAPR 2008 Thermal history

Furlanetto 2006

16/26ITAMPAPR 2008 21 cm fluctuations

BaryonDensity

Gas Temperature

W-FCoupling

Neutralfraction

Velocitygradient

X-raysources

Lysources

ReionizationCosmology Cosmology

Brightnesstemperature

Amount ofneutral hydrogen

Spin temperature

Velocity(Mass)

b

17/26ITAMPAPR 2008 Temporal separation?

BaryonDensity

Gas Temperature

W-FCoupling

Neutralfraction

Velocitygradient

X-raysources

Lysources

ReionizationCosmology Cosmology

Dark AgesTwilight

Brightnesstemperature

b

18/26ITAMPAPR 2008

Fluctuations from the first stars

dV

•Fluctuations in flux from source clustering, 1/r2 law, optical depth,…•Relate Ly fluctuations to overdensities

•W(k) is a weighted average Barkana & Loeb 2005

19/26ITAMPAPR 2008Determining the first sources

Chuzhoy,Alvarez, & Shapiro 2006

Sources

Spectra

J,* vs J,X

S

Pritchard &Furlanetto 2006

bias source properties density

z=20

dominates

=[k3P(k)/2

20/26ITAMPAPR 2008 Growth of fluctuations

expansion X-rays Compton

Fractional heating per Hubble time at z Heating fluctuations temperature

fluctuations

T/

adiabatic index -1

21/26ITAMPAPR 2008 Indications of TK

TK<T

TK>T

• Learn about source bias and spectrum in same way as Ly • Constrain heating transition

T dominates

22/26ITAMPAPR 2008 X-ray background?

T 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 TK fluctuations if heating late

23/26ITAMPAPR 2008 Experimental effortsLOFAR: NetherlandsFreq: 120-240 MHzNa= 64 Atot= 0.042 km2

(f21cm=1.4 GHz)

SKA: S Africa/AustraliaFreq: 60 MHz-35 GHzNa= 5000 Atot= 0.6 km2

MWA: AustraliaFreq: 80-300 MHzNa= 500 Atot= 0.007 km2

21CMA: ChinaFreq: 70-200 MHzNa= 20 Atot= 0.008 km2

24/26ITAMPAPR 2008 Temporal separation

x T

?

MWA

SKA

Pritchard& Loeb 2008

25/26ITAMPAPR 2008 High-z Observations•Need SKA to probe these brightnessfluctuations

•Observe scalesk=0.025-2 Mpc-1

•Easily distinguishtwo models

•Optimistic foregroundremoval

•B~12MHz ->z~1.5

foregroundspoor angular resolution

26/26ITAMPAPR 2008 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!

27/26ITAMPAPR 2008

28/26ITAMPAPR 2008 X-ray heating

•To heat gas above TCMB 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

29/26ITAMPAPR 2008 Lya production

photons/baryon

required fraction ofbaryon in stars

• For stars to produce critical Lya flux

30/26ITAMPAPR 2008

Profile around the first stars

Chen & Miralda-Escude 2006

31/26ITAMPAPR 2008

X-ray heating about a source

Zaroubi et al. 2006

32/26ITAMPAPR 2008 Lya heating?

•Lya can heat•Lyn can cool•Deutrium important•Effect from stellar photons usually small T_K<100K, so X-rayheating dominates. •Scattering blue ward of resonance important here - makesHeating more efficient as all scatterings heat gas.•Figure?

33/26ITAMPAPR 2008 21cm fluctuations: TK

Pritchard & Furlanetto 2006

Density Gas Temperature

W-FCoupling

Neutralfraction

Velocitygradient

density + x-rays

couplingsaturated

IGM still mostlyneutral

•In contrast to the other coefficientsT can be negative

•Sign of T constrains IGM temperature

b

34/26ITAMPAPR 2008 21 cm fluctuations: Ly

Density Gas Temperature

W-FCoupling

Neutralfraction

Velocitygradient

-negligible heating of IGM-tracks density

Ly flux varies

IGM still mostlyneutral

• Three contributions to Ly flux:1. Stellar photons redshifting into Ly resonance2. Stellar photons redshifting into higher Lyman resonances3. X-ray photoelectron excitation of HI

Chen & Miralda-Escude 2006Chen & Miralda-Escude 2004

• Ly fluctuations unimportant after coupling saturates (x>>1)

b

35/26ITAMPAPR 2008 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 Tsky-2.6

• Foreground removal exploits smoothness in frequency and spatial symmetries

• Cross-correlation with galaxies also important

36/26ITAMPAPR 2008 Angular separation?

•Anisotropy of velocity gradient term allows angular separation

Barkana & Loeb 2005

Bharadwaj & Ali 2004

BaryonDensity

Gas Temperature

W-FCoupling

Neutralfraction

Velocitygradient

•In linear theory, peculiar velocities correlate with overdensities

•Initial observations will average over angle to improve S/N

b

37/26ITAMPAPR 2008 Global history

Heating

HII regions

IGM

expansion

Furlanetto 2006

Adiabaticexpansion

X-rayheating

Comptonheating

+ +

UV ionization recombination+

X-ray ionization recombination+

continuum injectedLy 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

38/26ITAMPAPR 2008 Ionization history

•Models differ by factor ~10 in X-ray/Ly per ionizing photon•Reionization well underway at z<12

Xi>0.1

zR~7~0.07

(Pop II=later generation stars, Pop. III = massive metal free stars)

39/26ITAMPAPR 2008 TK fluctuations

•Fluctuations in gas temperature can be substantial•Amplitude of fluctuations contains information about IGM thermal history

40/26ITAMPAPR 2008 Temperature fluctuations

TS~TK<T Tb<0 (absorption)Hotter region = weaker absorptionT<0

TS~TK~T

Tb~021cm signal dominated by temperature fluctuations

TS~TK>T

Tb>0 (emission)Hotter region = stronger emissionT>0

41/26ITAMPAPR 2008 Cosmology?

Density Gas Temperature

W-FCoupling

Neutralfraction

Velocitygradient

couplingsaturated

IGM still mostlyneutral

IGM hotTK>>T

Kleban, Sigurdson & Swanson 2007

• Probe smaller scales than CMB

• Unless pristine very difficult toimprove on Planck level

b

42/26ITAMPAPR 2008 Density power spectrum

• Moderate improvements - cross-check• Improve ns and most• See baryonic oscillation at few sigma

McQuinn et al. 2006

43/26ITAMPAPR 2008 Reionization

Density Gas Temperature

W-FCoupling

Neutralfraction

Velocitygradient

IGM hotTK>>T

Ly coupling saturated

HII regions large

Z=12.1 Z=9.2 Z=8.3 Z=7.6

Furlanetto, Sokasian, Hernquist 2003

b

44/26ITAMPAPR 2008 Growth of HII Regions

QuickTime™ and aGIF decompressor

are needed to see this picture.

•100 Mpc cube N-body + UV photon ray tracing•Details of heating and coupling are neglected

Trac & Cen 2006

45/26ITAMPAPR 2008 The first sources

HII

Soft X-rays

Hard X-rays

Ly

1000 Mpc

330 Mpc

5 Mpc 0.2 Mpc

z=15

46/26ITAMPAPR 2008 21 cm fluctuations: z

?

•Exact form very model dependent

47/26ITAMPAPR 2008 Redshift slices: Ly

•Pure Ly fluctuations

z=19-20

48/26ITAMPAPR 2008 Redshift slices: Ly/Tz=17-18

•Growing T fluctuationslead first to dip in Tb then to double peak structure

•Double peak requiresT and Ly fluctuationsto have different scaledependence

49/26ITAMPAPR 2008 Redshift slices: Tz=15-16

•T fluctuations dominate over Ly

•Clear peak-trough structure visible

• 2 <0 on largescales indicates TK<T

50/26ITAMPAPR 2008 Redshift slices: T/z=13-14

•After TK>T , thetrough disappears

•As heating continuesT fluctuations die out

51/26ITAMPAPR 2008 Redshift slices: /xz=8-12

•Bubbles imprint featureon power spectra once xi>0.2

•Non-linearities in density fieldbecome important

(TK fluc. not included)

52/26ITAMPAPR 2008 Low-z Observations

SKA

MWALOFAR

•Low k cutofffrom antennaesize

•Sensitivity ofLOFAR and MWA drops off by z=12

McQuinn et al. 2006