The 21cm Signal

The 21cm Signal from 

Reionization: 

Theory & Simulations 

Garrelt Mellema 

Department of Astronomy 

& 

Oskar Klein Centre 

Collaborators: Martina Friedrich, Hannes Jensen, Kanan Datta, Kai Yan Lee, Kyungjin Ahn, 

Ilian Iliev, Paul Shapiro, Yi Mao & the LOFAR EoR Key Project team. 

26 April 2012 EoR2012, Strasbourg 1

Contents 

The 21cm signal 

21cm tomography 

Statistical analysis methods 

Example of telling scenarios apart 


The 21cm Signal 

A forbidden hyperfine transition between the two 1 2s1/2 1/2 ground 

level states of neutral hydrogen. Energy difference: λ=21cm, =21cm, 

ν=1.4GHz. 1.4GHz. 

IGM during the EoR has as measurable signal, differential 

brightness temperature, 

temperature, 

δTb ) 

Astrophysical quantities: 

– n(HI) : neutral hydrogen density = x(HI)n(H) 

– Ts: : spin or excitation temperature 

– V ||: || : line of sight velocity 


The 21cm Signal 

Scaled with WMAP7 cosmological parameters: 

Mean signal is weak (for T s » T CMB ) : 

– 22 – 33 mK between z=6 – 15 (200 – 90 MHz). 

Spatial fluctuations due to fluctuations in 

– x(HI) δ T 

Ts s V || 


Spin Temperature 

Populations of the triplet and singlet states of HI follow 

Boltzmann distribution, with an excitation temperature, 

temperature, 

a.k.a. the spin temperature. 

n1/n /n0 0 = 3 exp(0.068 K / T s). ). 

Processes affecting spin temperature: 

– Collisions (T s → T k ) 

– Radiative 

CMB photons (T s 

s → T 

TCMB CMB ) 

Ly-αphotons Ly- photons (T s → TLy-α≈ 

T k) ) (”Wouthuysen-Field effect”) 

T Ly- 

IGM @ EoR: competition between CMB and Ly-αphotons. 

Ly- photons. 


Spin Temperature Regions 

in the IGM 

Depending on T k and 

local Ly-αflux: Ly- flux: 

different regions of 

21cm signals in IGM 

(for z 0 δT b < 0 

No Ly-α 

present 

CMB, , and Ly-α Ly- present: δTb > 0 

– In this case: δTb independent of T s . 

Cosmic Dawn: T IGM

Dark 

Ages 

Cosmic 

Dawn 

EoR 

History of Temperatures 

∝ 

(1+z) 

TCMB CMB 

-1 

(1+z) 

-2 

Tkin,IGM kin,IGM ∝ 

(1+z) -2 (1+z) 

z >90: collisions couple T s to T IGM 

(< T CMB for z

425/h Mpc 

simulation 

δT b ∝ x HI δ 

The Redshifted 21cm Sky 

Just as the CMB, the redshifted 21cm signal fills the sky 

with a fluctuating signal. 

– Gas density of the IGM (δ) ( 

Count total number of 

– Appearance of ionized regions (x HI ) ionizing photons! 

– Excitation variations (T s ) 

δT b 

3’ beam 

26 April 2012 EoR2012, Strasbourg 8 

Iliev, GM, et al (2012)

The Redshifted 21cm Volume 

Unlike the CMB, 21cm signal is 

line line emission: carries spatial, 

temporal, and velocity 

information. 

Frequency Redshift 

The image cube: images 

stacked in frequency space 


z 

ν 

time θ 

425/h Mpc simulation 

θ

Flying through Time and Space 

Reionization has a 

complex geometry of 

growing and 

overlapping bubbles. 

Here illustrated 

evolving redshifted 

21cm signal: 

– High density neutral 

regions are yellow 

– Ionized regions are 

blue/black blue black. 

LOFAR-like beam: 3’ 

resolution & average 

signal is zero. 



Tomography 

Analysis of 3D data is called tomography. 

tomography 

Examples of tomographic methods: 

– Bubble size distributions (Zahn et al. 2007; Friedrich et al. 2011) 

– Topological measures, e.g. Euler characteristic (Gleser et al. 2006; 

Shin et al. 2008; Friedrich et al. 2011). 


Euler characterisitic 

Friedrich, GM et al. (2011)

Imaging for First 

Generation Experiments 

Sensitivity of the upcoming EoR experiments will be too 

low to image 21cm from reionization pixel by pixel: S/N ~ 

0.2. 

Ways around: 

End of reionization: reionization: 

Low resolution imaging 

(resolution > 20’) of large neutral patches (Zaroubi et al. 

2012) 

Middle of reionization: reionization: 

Matched filter searches for 

isolated large “bubbles” (Datta et al. 2007, 2008, 2009, 

Friedrich et al. 2012) 


Matched Filter Searches 

Friedrich, Datta, GM et al. 

(2012) 

Introduce bright QSO to 

a ’stellar’ reionization 

simulation. 

NEW version of C 2-Ray -Ray 

(helium + power law 

sources). 

Region A (QSO) and B 

(cluster) are both 

detectable with spherical 

matched filter on 

visibilities (1200 h of 

LOFAR observations). 

No QSO QSO 

Filter size 


Statistical Measurements 

Alternative & complement for imaging: Statistical 

measurements. 

– First goal: goal: 

to reliably detect signatures from reionization. 

– Second goal: goal: 

to interpret them in terms of astrophysics. 

The 21cm line signal is rich in properties: 

properties 

1. Global signals: signals: 

fluctuations. 

2. Angular properties: properties: 

power spectra 

3. Frequency properties: properties: 

cross-correlation (ν ( 1, , ν2 ) 

4. Non-Gaussianity: Non-Gaussianity: 

skewness, kurtosis 

5. Redshift space effects: effects: 

distortions, light cone effect 


Global Signals 

A single dish telescope 

(EDGES): measure the 

global signal as function 

of frequency. 

An interferometer 

(LOFAR, MWA, GMRT): 

measures the 21cm (rms) 

fluctuations. 

fluctuations 

Peak of fluctuations: 

xHII~0.6-0.7 HII~0.6-0.7 

(3’ resolution). 


3’, 0.5 MHz resolution 


Global Signals 

A single dish telescope 

(EDGES): measure the 

global signal as function 

of frequency. 

An interferometer 

(LOFAR, MWA, GMRT): 

measures the 21cm (rms) 

fluctuations. 

fluctuations 

Peak of fluctuations: 

xHII~0.6-0.7 HII~0.6-0.7 

(3’ resolution). 




Power Spectra 

Information about the size 

scales can be obtained 

from the power spectra. 

Simulations show evolution: 

– power shifting to larger 

scales. 

– flattening of the power 

spectra. 

– drop for < 0.06 h/Mpc 

(120/h cMpc). 

Different models agree on 

general evolution (see e.g. 

Lidz et al. 2007). 

3D Power Spectra 



Correlation Distance 

Correlation distance: distance: 

Δνwhere Δνwhere 

Corr(ν, Corr( , ν+Δν Δν) ) falls 

below threshold. 

Evolution during reionization: 

increases from ~200 kHz to 

~1 MHz (3’ resolution): 

formation of larger HII 

regions 

Foregrounds correlated over 

the entire frequency range! 


3’ resolution 


Correlation Distance: 

Dependence of Scale 

114/h Mpc 

simulation 


Non-Gaussianity 

Probability distribution 

functions of the 21cm 

signal are non-Gaussian, 

even when smoothed. 

Largest effect at end 

of reionization. 

Ultimate statistic of 

δTb . 

Ciardi & Madau (2003), 

Mellema et al. (2006), Oh 

et al. (2009), Ichikawa et 

al. (2010), Gluscevic & 

Barkana (2010). 

3’, 200 kHz 

intrinsic 

114/h Mpc 

simulation 


Higher Order Statistics 

The non-gaussianity of the 

signal suggests the use of 

higher order statistics: statistics 

– Skewness 

– Kurtosis 

– Bi-spectrum 

Skewness and kurtosis 

useful additional 

measurements: Wyithe & 

Morales (2007); Harker et al. 

(2009, 2010); Chapman et al. 

(2012). 

Skewness & kurtosis: 

characteristic evolution 




Higher Order Statistics 

The non-gaussianity of the 

signal suggests the use of 

higher order statistics: statistics 

– Skewness 

– Kurtosis 

– Bi-spectrum 

Skewness and kurtosis 

useful additional 

measurements: Wyithe & 

Morales (2007); Harker et al. 

(2009, 2010); Chapman et al. 

(2012). 

Skewness & kurtosis: 

characteristic evolution 




Redshift Space Effects: 

1) Distortions 

Peculiar velocity field displaces signal from cosmological 

redshift. 

`Kaiser Kaiser effect´ effect´ 

or `velocity `velocity 

compression´: compression´: 

due to infall, infall, 

signal concentrates at the high density peaks. 

This is clearly seen in the simulations and gives ~30% 

increase in fluctuations (and up to a factor of 2). 

In linear theory the velocity is an independent measure of 

the matter density field δ → Cosmology! 

– Bharadhway & Ali (2005) 

– Barkana & Loeb (2005) 

– Wang & Hu (2006) 

– Mao et al. (2012) 


Redshift Space Effects: 

2) Light Cone Effect 

3D power spectrum from 21cm observations: one axis is 

the LOS axis → Evolving signal. 

Limits the band width over which 3D power spectrum can 

be extracted. 

Barkana & Loeb (2006); Datta, GM, et al. (2011) 


Telling Different Scenarios 

Apart 

How well can 21cm observations tell different source 

scenarios apart? 

Since the amount of escaping ionizing photons depends on 

the combination of IMF, f SF and f esc, esc, 

21cm measurements 

alone alone cannot distinguish these. 

Can 21cm measurements tell different source populations 

apart? 


Identical Reionization, Different 

Sources 

h H H H 

High and low mass halos 

contribute; low mass 

halos suppressible 

Only high mass halos 

contribute. 

Iliev, GM et al. (2011) 

Only very high mass halos 

(> 10 10 M ) contribute. 


21cm Fluctuations 

Figure shows 

integrated 

fluctuation signal 

(rms noise) at LOFAR 

resolution. 

Amplitude of 

fluctuations clearly 

tells the cases apart. 

Also : simulations 

with worse mass 

resolution give very 

different results. 


H 

H 

Iliev, GM et al. (2012) 

h H

Conclusions 

Redshifted 21cm measurements (e.g. LOFAR) will shed new 

light on reionization and the galaxy population beyond z=6. 

Limited tomography possible even with LOFAR. 

Rich slew of statistical measurements available. 

Some source populations can be told apart by LOFAR. 

Be careful with mass resolution in simulations!

The 21cm Signal

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