high-redshift 21cm and redshift distortions antony lewis institute of astronomy, cambridge anthony...
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High-redshift 21cm
and redshift distortions
Antony LewisInstitute of Astronomy, Cambridge
http://cosmologist.info/
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 …
Work with:
Hu & White, Sci. Am., 290 44 (2004)
Evolution of the universe
Opaque
Transparent
Easy
Hard
Dark ages
30<z<1000
CMB temperature
Why the CMB temperature (and polarization) is great
Why it is bad
- Probes scalar, vector and tensor mode perturbations
- The earliest possible observation (bar future neutrino anisotropy surveys etc…)
- Includes super-horizon scales, probing the largest observable perturbations
- Observable now
- 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
If only we could observe the CDM perturbations…
- not erased by diffusion damping (if cold): power on all scales - full 3D distribution of perturbations
What about the baryons?
- fall into CDM potential wells; also power on small scales- full 3D distribution- but baryon pressure non-zero: very small scales still erased
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)
About 104 independent redshift shells at l=106
- total of 1016 modes - measure Pk to an error of 10-8 at 0.05 Mpc scales
What about different redshifts?
e.g. running of spectral index:
If ns = 0.96 maybe expect running ~ (1-ns)2 ~ 10-3
Expected change in Pk ~ 10-3 per log k
- measure running to 5 significant figures!?
So worth thinking about… can we observe the baryons somehow?
• How can light interact with the baryons (mostly neutral H + He)?
- 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
Credit: Sigurdson
triplet
singlet
Define spin temperature Ts
Spontaneous emission: n1 A10 photons per unit volume per unit proper time
Rate: A10 = 2.869x10-15 /s
Stimulated emission: net photons (n1 B10 – n0 B01)Iv
0
1
h v = E21
Net emission or absorption if levels not in equilibrium with photon distribution- observe baryons in 21cm emission or absorption if Ts <> TCMB
What can we observe?
In terms of spin temperature:
Total net number of photons:
What determines the spin temperature?
• Interaction with CMB photons: drives Ts towards TCMB
• Collisions between atoms: drives Ts towards gas temperature Tg
• (+Interaction with Lyman-alpha photons - not important during dark ages)
TCMB = 2.726K/a
At recombination, Compton scattering makes Tg=TCMB
Later, 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
What’s the power spectrum?
Use Boltzmann equation for change in CMB due to 21cm absorption:
Background: Perturbation:
Fluctuation in density of H atoms,+ fluctuations in spin temperature
CMB dipole seen by H atoms:more absorption in direction of gas motion relative to CMB
l >1 anisotropies in TCMB
Doppler shiftto gas rest frame
+ reionization re-scattering terms
Solve Boltzmann equation in Newtonian gauge:
Redshift distortionsMain monopolesource Effect of local
CMB anisotropy
Tiny Reionization sourcesSachs-Wolfe, Doppler and ISW change to redshift
For k >> aH good approximation is
(+re-scattering effects)
21cm does indeed track baryons when Ts < TCMB
So can indirectly observe baryon power spectrum at 30< z < 100-1000 via 21cm
z=50
Kleban et al. hep-th/0703215
Observable angular power spectrum:
‘White noise’from smaller scales
Baryonpressuresupport
1/√N suppressionwithin window
baryon oscillations
z=50
Integrate over window in frequency
Small scales:
What about large scales (Ha >~ k)?
<~ 1% effect at l<50 Extra terms largely negligible
Narrow redshift window
14 000 Mpc
Dark ages~2500Mpc
Opaque ages ~ 300MpcComoving distance
z=30
z~1000
New large scaleinformation?- potentials etccorrelated with CMB
l ~ 10
Non-linear evolution
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.
Also lensing
Lensing potential power spectrum
Lensed
Unlensed
Lewis, Challinor: astro-ph/0601594
Modified Bessel function
Wigner functions
c.f. Madel & Zaldarriaga: astro-ph/0512218
like convolution with deflection angle power spectrum;generally small effect as 21cm spectrum quite smooth
Cl(z=50,z=52)Cl(z=50,z=50)
Lots of information in 3-D (Zahn & Zaldarriaga 2006)
Observational prospects
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
See e.g. Carilli et al: astro-ph/0702070, Peterson et al: astro-ph/0606104
But: large wavelength -> crude reflectors OK
Current 21cm:
LOFAR, PAST, MWA: study reionization at z <20SKA: still being planned, z< 25
Things you could do with precision dark age 21cm
• High-precision on small-scale primordial power spectrum(ns, running, features [wide range of k], etc.)e.g. Loeb & Zaldarriaga: astro-ph/0312134, Kleban et al. hep-th/0703215
• Varying alpha: A10 ~ α13 (21cm frequency changed: different background and perturbations)Khatri & Wandelt: astro-ph/0701752
• Isocurvature modes(direct signature of baryons; distinguish CDM/baryon isocurvature)Barkana & Loeb: astro-ph/0502083
• CDM particle decays and annihilations(changes temperature evolution)Shchekinov & Vasiliev: astro-ph/0604231, Valdes et al: astro-ph/0701301
• Primordial non-Gaussianity(measure bispectrum etc of 21cm: limited by non-linear evolution)Cooray: astro-ph/0610257, Pillepich et al: astro-ph/0611126
• Lots of other things: e.g. cosmic strings, warm dark matter, neutrino masses, early dark energy/modified gravity….
Back to reality – after the dark ages?
• First stars and other objects form• Lyman-alpha and ionizing radiation present:
Wouthuysen-Field (WF) effect: - Lyman-alpha couples Ts to Tg
- Photoheating makes gas hot at late times so signal in emission
Ionizing radiation: - ionized regions have little hydrogen – regions with no 21cm signal Both highly non-linear: very complicated physics
• Lower redshift, so less long wavelengths:- much easier to observe! GMRT (z<10), MWA, LOFAR (z<20), SKA (z<25)….
• Discrete sources: lensing, galaxy counts (~109 in SKA), etc.
How do we get cosmology from this mess?
1. Do gravitational lensing: measure source shears
- probes line-of-sight transverse potential gradients (independently of what the sources are)
Would like to measure dark-matter power on nearly-linear scales.
Want to observe potentials not baryons
2. Measure the velocities induced by falling into potentials
- probe line-of-sight velocity, depends on line-of-sight potential gradients
Redshift distortions
A closer look at redshift distortions
x
y
x
y(z)
Real space Redshift space
+
Density perturbed too. In redshift-space see
More power in line-of-sight direction -> distinguish velocity effect
Both linear (+higher) effects – same order of magnitude. Note correlated.
Linear-theory
Redshift-space distance:
Actual distance:
n
Define 3D redshift-space co-ordinate
Fourier transformed:
Transform using Jacobian: Redshift-space perturbation
Linear power spectrum:
Messy astrophysics Depends only on velocities -> potentials
(n.k)4 component can be used for cosmology
Barkana & Loeb astro-ph/0409572
Is linear-theory good enough?
RMS velocity 10-4-10-3 Radial displacement ~ 0.1-1 MPc
Megaparsecscale
Looks like big non-linear effect!
Real Space Redshift space
BUT: bulk displacements unobservable. Need more detailed calculation.
M(x + dx) ≠ M(x) + M’(x) dx
Non-linear redshift distortions
Power spectrum from:
Exact non-linear result (for Gaussian fields on flat sky):
Assume all fields Gaussian. Shaw & Lewis, 2008 also Scoccimarro 2004
Significant effectDepending on angle
z=10
Small scale power boostedby superposition of lots oflarge-scale modes
More important at lower redshift.Not negligible even at high z. Comparable to non-linear evolution
z=10
Similar effect on angular power spectrum:
(sharp z=z’ window, z=10)
(A ~ velocity covariance), u= (x-z,y-z’)
What does this mean for component separation?Angular dependence now more complicated – all μ powers, and not clean.
Assuming gives wrong answer…
Need more sophisticated separation methods to measure small scales.
z=10
Also complicates non-Gaussianity detectionRedshift-distortion bispectrum
• Mapping redshift space -> real space nonlinear, so non-Gaussian
Just lots of Gaussian integrals (approximating sources as Gaussian)..
Linear-theory source
Can do exactly, or leading terms are:
Not attempted numerics as yet
Zero if all k orthogonal to line of sight.
Also Scoccimarro et al 1998, Hivon et al 1995
Conclusions• Huge amount of information in dark age perturbation spectrum
- could constrain early universe parameters to many significant figures
• Dark age baryon perturbations in principle observable at 30<z< 500 up to l<107 via observations of CMB at (1+z)21cm wavelengths.
• Dark ages very challenging to observe (e.g. far side of the moon)
• Easier to observe at lower z, but complicated astrophysics
• Redshift-distortions probe matter density – ideally measure cosmology separately from astrophysics by using angular dependence
• BUT: non-linear effects important on small scales - more sophisticated non-linear separation methods may be required
Correlation function
z=10
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