Presentation on theme: "High-redshift 21cm and redshift distortions"— Presentation transcript:
1 High-redshift 21cm and redshift distortions Antony LewisInstitute of Astronomy, CambridgeWork with:Anthony Challinor (IoA, DAMTP); astro-ph/ Richard Shaw (IoA), arXiv:Following work by Scott, Rees, Zaldarriaga, Loeb, Barkana, Bharadwaj, Naoz, Scoccimarro + many more …
2 Evolution of the universe OpaqueEasyTransparentDark ages30<z<1000HardHu & White, Sci. Am., (2004)
4 Why the CMB temperature (and polarization) is great Probes scalar, vector and tensor mode perturbationsThe earliest possible observation (bar future neutrino anisotropy surveys etc…) - Includes super-horizon scales, probing the largest observable perturbations - Observable nowWhy 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
5 If only we could observe the CDM perturbations… - not erased by diffusion damping (if cold): power on all scales- full 3D distribution of perturbationsWhat about the baryons?fall into CDM potential wells; also power on small scalesfull 3D distributionbut baryon pressure non-zero: very small scales still erasedHow 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 % at l=106 (k Mpc ~ 100)
6 What about different redshifts? About 104 independent redshift shells at l=106- total of 1016 modes measure Pk to an error of 10-8 at 0.05 Mpc scalese.g. running of spectral index:If ns = 0.96 maybe expect running ~ (1-ns)2 ~ 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?
7 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 transitiontripletsingletCredit: SigurdsonDefine spin temperature Ts
8 What can we observe?Spontaneous emission: n1 A10 photons per unit volume per unit proper time1h v = E21Rate: A10 = 2.869x10-15 /sStimulated emission: net photons (n1 B10 – n0 B01)IvTotal 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
9 What determines the spin temperature? Interaction with CMB photons: drives Ts towards TCMBCollisions between atoms: drives Ts towards gas temperature TgTCMB = 2.726K/aAt recombination, Compton scattering makes Tg=TCMB Later, once few free electrons, gas cools: Tg ~ mv2/kB ~ 1/a2Spin temperature driven below TCMB by collisions:- atoms have net absorption of 21cm CMB photons(+Interaction with Lyman-alpha photons - not important during dark ages)
11 What’s the power spectrum? Use Boltzmann equation for change in CMB due to 21cm absorption:Background:Perturbation:l >1 anisotropies in TCMBFluctuation in density of H atoms, + fluctuations in spin temperatureDoppler shift to gas rest frameCMB dipole seen by H atoms: more absorption in direction of gas motion relative to CMB+ reionization re-scattering terms
12 Solve Boltzmann equation in Newtonian gauge: Redshift distortionsMain monopole sourceEffect of local CMB anisotropySachs-Wolfe, Doppler and ISW change to redshiftTiny Reionization sourcesFor k >> aH good approximation is(+re-scattering effects)
13 21cm does indeed track baryons when Ts < TCMB z=50Kleban et al. hep-th/So can indirectly observe baryon power spectrum at 30< z < via 21cm
14 Observable angular power spectrum: Integrate over window in frequencySmall scales:1/√N suppression within window‘White noise’ from smaller scalesBaryon pressure supportbaryon oscillationsz=50
15 What about large scales (Ha >~ k)? Narrow redshift window<~ 1% effect at l<50Extra terms largely negligible
16 New large scale information? - potentials etc correlated with CMB Dark ages ~2500Mpcl ~ 10Mpcz=30Opaque ages ~ 300MpcComoving distancez~1000
17 Non-linear evolutionSmall scales see build up of power from many larger scale modes - importantBut probably accurately modelled by 3rd order perturbation theory:On small scales non-linear effects many percent even at z ~ 50+ redshift distortions, see later.
18 Also lensing Modified Bessel function Unlensed Lensed Wigner functions Lensing potential power spectrumLewis, Challinor: astro-ph/c.f. Madel & Zaldarriaga: astro-ph/
19 like convolution with deflection angle power spectrum; generally small effect as 21cm spectrum quite smoothCl(z=50,z=50)Cl(z=50,z=52)Lots of information in 3-D (Zahn & Zaldarriaga 2006)
20 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 frequencyBut: large wavelength -> crude reflectors OKSee e.g. Carilli et al: astro-ph/ , Peterson et al: astro-ph/Current 21cm:LOFAR, PAST, MWA: study reionization at z <20 SKA: still being planned, z< 25
22 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/ , Kleban et al. hep-th/Varying alpha: A10 ~ α13 (21cm frequency changed: different background and perturbations) Khatri & Wandelt: astro-ph/Isocurvature modes (direct signature of baryons; distinguish CDM/baryon isocurvature) Barkana & Loeb: astro-ph/CDM particle decays and annihilations (changes temperature evolution) Shchekinov & Vasiliev: astro-ph/ , Valdes et al: astro-ph/Primordial non-Gaussianity (measure bispectrum etc of 21cm: limited by non-linear evolution) Cooray: astro-ph/ , Pillepich et al: astro-ph/Lots of other things: e.g. cosmic strings, warm dark matter, neutrino masses, early dark energy/modified gravity….
23 Back to reality – after the dark ages? First stars and other objects formLyman-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 physicsLower 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.
24 How do we get cosmology from this mess? Would like to measure dark-matter power on nearly-linear scales.Want to observe potentials not baryons1. 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 gradientsRedshift distortions
25 A closer look at redshift distortions Real spaceRedshift spaceyy(z)xx
26 + Density perturbed too. In redshift-space see Both linear (+higher) effects – same order of magnitude. Note correlated.More power in line-of-sight direction -> distinguish velocity effect
27 Linear-theory n Redshift-space distance: Actual distance: Define 3D redshift-space co-ordinateTransform using Jacobian: Redshift-space perturbationFourier transformed:
28 Linear power spectrum: Messy astrophysicsDepends only on velocities > potentials(n.k)4 component can be used for cosmologyBarkana & Loeb astro-ph/
29 Is linear-theory good enough? RMS velocityRadial displacement ~ MPcMegaparsecscaleReal SpaceRedshift spaceLooks like big non-linear effect!M(x + dx) ≠ M(x) + M’(x) dxBUT: bulk displacements unobservable. Need more detailed calculation.
30 Non-linear redshift distortions Assume all fields Gaussian.Shaw & Lewis, 2008 also Scoccimarro 2004Power spectrum from:Exact non-linear result (for Gaussian fields on flat sky):
31 Significant effect Depending on angle Small scale power boostedby superposition of lots of large-scale modesz=10
32 More important at lower redshift. Not negligible even at high z. Comparable to non-linear evolutionz=10
33 Similar effect on angular power spectrum: (A ~ velocity covariance), u= (x-z,y-z’)(sharp z=z’ window, z=10)
34 What does this mean for component separation? Angular dependence now more complicated – all μ powers, and not clean.Assuminggives wrong answer…z=10Need more sophisticated separation methods to measure small scales.
35 Also complicates non-Gaussianity detection Redshift-distortion bispectrum Mapping redshift space -> real space nonlinear, so non-GaussianLinear-theory sourceJust 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 1995Not attempted numerics as yet
36 ConclusionsHuge amount of information in dark age perturbation spectrum - could constrain early universe parameters to many significant figuresDark 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 astrophysicsRedshift-distortions probe matter density – ideally measure cosmology separately from astrophysics by using angular dependenceBUT: non-linear effects important on small scales - more sophisticated non-linear separation methods may be required