High-redshift 21cm and redshift distortions. Antony Lewis Institute of Astronomy, Cambridge http://cosmologist.info/. Work with:. Anthony Challinor (IoA, DAMTP); astro-ph/0702600 Richard Shaw (IoA ), arXiv:0808.1724 .
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Institute of Astronomy, Cambridge
Anthony Challinor (IoA, DAMTP); astro-ph/0702600Richard Shaw (IoA), arXiv:0808.1724
Following work by Scott, Rees, Zaldarriaga, Loeb, Barkana, Bharadwaj, Naoz, Scoccimarro + many more …
Hu & White, Sci. Am., 290 44 (2004)
Why it is bad
- Only one sky, so cosmic variance limited on large scales
- Diffusion damping and line-of-sight averaging: all information on small scales destroyed! (l>~2500)- Only a 2D surface (+reionization), no 3D information
- not erased by diffusion damping (if cold): power on all scales
- full 3D distribution of perturbations
What about the baryons?
How does the information content compare with the CMB?
CMB temperature, 1<l<~2000: - about 106 modes - can measure Pk to about 0.1% at l=2000 (k Mpc~ 0.1)
Dark age baryons at one redshift, 1< l < 106: - about 1012 modes
- measure Pk to about 0.0001% at l=106 (k Mpc ~ 100)
e.g. running of spectral index:
If ns = 0.96 maybe expect running ~ (1-ns)2 ~ 10-3Expected change in Pk ~ 10-3 per log k
- measure running to 5 significant figures!?
So worth thinking about… can we observe the baryons somehow?
- after recombination, Hydrogen atoms in ground state and CMB photons have hν << Lyman-alpha frequency* high-frequency tail of CMB spectrum exponentially suppressed * essentially no Lyman-alpha interactions * atoms in ground state: no higher level transitions either
- Need transition at much lower energy* Essentially only candidate for hydrogen is the hyperfine spin-flip transition
Define spin temperature Ts
Spontaneous emission: n1 A10 photons per unit volume per unit proper time
h v = E21
Rate: A10 = 2.869x10-15 /s
Stimulated emission: net photons (n1 B10 – n0 B01)Iv
Total net number of photons:
In terms of spin temperature:
Net emission or absorption if levels not in equilibrium with photon distribution
- observe baryons in 21cm emission or absorption if Ts <> TCMB
TCMB = 2.726K/a
At recombination, Compton scattering makes Tg=TCMBLater, once few free electrons, gas cools: Tg ~ mv2/kB ~ 1/a2
Spin temperature driven below TCMB by collisions:
- atoms have net absorption of 21cm CMB photons
Use Boltzmann equation for change in CMB due to 21cm absorption:
l >1 anisotropies in TCMB
Fluctuation in density of H atoms,+ fluctuations in spin temperature
Doppler shiftto gas rest frame
CMB dipole seen by H atoms:more absorption in direction of gas motion relative to CMB
+ reionization re-scattering terms
Effect of localCMB anisotropy
Sachs-Wolfe, Doppler and ISW change to redshift
Tiny Reionization sources
For k >> aH good approximation is
Kleban et al. hep-th/0703215
So can indirectly observe baryon power spectrum at 30< z < 100-1000 via 21cm
Integrate over window in frequency
1/√N suppressionwithin window
‘White noise’from smaller scales
Narrow redshift window
<~ 1% effect at l<50
Extra terms largely negligible
l ~ 10
14 000 Mpc
Opaque ages ~ 300Mpc
Small scales see build up of power from many larger scale modes - important
But probably accurately modelled by 3rd order perturbation theory:
On small scales non-linear effects many percent even at z ~ 50
+ redshift distortions, see later.
Modified Bessel function
Lensing potential power spectrum
Lewis, Challinor: astro-ph/0601594
c.f. Madel & Zaldarriaga: astro-ph/0512218
like convolution with deflection angle power spectrum;generally small effect as 21cm spectrum quite smooth
Lots of information in 3-D (Zahn & Zaldarriaga 2006)
No time soon…
- (1+z)21cm wavelengths: ~ 10 meters for z=50- atmosphere opaque for z>~ 70: go to the moon?- fluctuations in ionosphere: phase errors: go to moon?- interferences with terrestrial radio: far side of the moon?- foregrounds: large! use signal decorrelation with frequency
But: large wavelength -> crude reflectors OK
See e.g. Carilli et al: astro-ph/0702070, Peterson et al: astro-ph/0606104
LOFAR, PAST, MWA: study reionization at z <20SKA: still being planned, z< 25
Would like to measure dark-matter power on nearly-linear scales.
Want to observe potentials not baryons
1. Do gravitational lensing: measure source shears - probes line-of-sight transverse potential gradients (independently of what the sources are)
2. Measure the velocities induced by falling into potentials - probe line-of-sight velocity, depends on line-of-sight potential gradients
Both linear (+higher) effects – same order of magnitude. Note correlated.
More power in line-of-sight direction -> distinguish velocity effect
Define 3D redshift-space co-ordinate
Transform using Jacobian: Redshift-space perturbation
Depends only on velocities -> potentials
(n.k)4 component can be used for cosmology
Barkana & Loeb astro-ph/0409572
Radial displacement ~ 0.1-1 MPc
RMS velocity 10-4-10-3
Looks like big non-linear effect!
M(x + dx) ≠ M(x) + M’(x) dx
BUT: bulk displacements unobservable. Need more detailed calculation.
Shaw & Lewis, 2008 also Scoccimarro 2004
Assume all fields Gaussian.
Power spectrum from:
Exact non-linear result (for Gaussian fields on flat sky):
Small scale power boosted
by superposition of lots oflarge-scale modes
Comparable to non-linear evolution
(A ~ velocity covariance), u= (x-z,y-z’)
(sharp z=z’ window, z=10)
Angular dependence now more complicated – all μ powers, and not clean.
gives wrong answer…
Need more sophisticated separation methods to measure small scales.
Just lots of Gaussian integrals (approximating sources as Gaussian)..
Zero if all k orthogonal to line of sight.
Can do exactly, or leading terms are:
Also Scoccimarro et al 1998, Hivon et al 1995
Not attempted numerics as yet