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Future 21cm surveys and non-Gaussianity

Future 21cm surveys and non-Gaussianity. Antony Lewis Institute of Astronomy, Cambridge http://cosmologist.info/. work with Anthony Challinor & Richard Shaw + (mostly) review. Evolution of the universe. Opaque. Easy. Transparent. Dark ages. 30<z<1000. Hard.

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Future 21cm surveys and non-Gaussianity

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  1. Future 21cm surveys and non-Gaussianity Antony Lewis Institute of Astronomy, Cambridge http://cosmologist.info/ work with Anthony Challinor & Richard Shaw + (mostly) review

  2. Evolution of the universe Opaque Easy Transparent Dark ages 30<z<1000 Hard Hu & White, Sci. Am., 290 44 (2004)

  3. After recombination essentially only one transition at low enough energy: - hyperfine spin-flip transition of hydrogen • CMB great way to measure perturbations down to silk damping scale • To observe small scale perturbations, need to see the CDM or baryons • How can light interact with the baryons (mostly neutral H + He)? triplet Credit: Sigurdson singlet Define spin temperature Ts to quantify occupation numbers:

  4. What can we observe? Spontaneous emission: n1 A10 photons per unit volume per unit proper time 1 h v = E21 Rate: A10 = 2.869x10-15 /s (decay time 107 years) 0 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

  5. Thermal history

  6. What’s the linear-theory power spectrum? Use Boltzmann equation for change in CMB due to 21cm absorption: Background: Perturbation: 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 + self-absorption and reionization re-scattering terms

  7. Solve Boltzmann equation in Newtonian gauge Lewis & Challinor: astro-ph/0702600 Redshift distortions Main monopolesource Effect of localCMB anisotropy Sachs-Wolfe, Doppler and ISW change to redshift Tiny Reionization sources (+ few percent self-absorption effects) For k >> aH good approximation is

  8. Observable angular power spectrum: Integrate over window in frequency 1/√N suppressionwithin window(bandwidth) ‘White noise’from smaller scales Baryonpressuresupport baryon oscillations z=50

  9. Comparison with CMB power spectrum Kleban et al. hep-th/0703215

  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: Lewis & Challinor: astro-ph/0702600 On small scales non-linear effects many percent even at z ~ 50

  11. Non-linear redshift distortions Shaw & Lewis, 2008 in prep. also Scoccimarro 2004 Exact non-linear result (for Gaussian fields on flat sky):

  12. Non-Gaussianity • Primordial non-Gaussianity, e.g. fNl • Non-linear evolution • Non-linear redshift distortions • Lensing • First sources • Foregrounds • Observational things

  13. Squeezed bispectrum for shell at z=50 (0.1MHz bandwidth) fNL=1 • need to calculate non-linear contribution accurately to subtract off • have large cosmic variance Pillepich, Porciani, Matarrese: astro-ph/0611126

  14. Cumulative S/N for one redshift shell at z=50, fNl=1 Squeezed Equilateral Pillepich, Porciani, Matarrese: astro-ph/0611126 Can do better with full redshift dependence: claims of fNL ~ 0.01 Cooray: astro-ph/0610257

  15. Redshift distortion bispectrum • Mapping redshift space -> real space nonlinear, so non-Gaussian Linear-theory source Can do exactly, or leading terms are: Not attempted numerics as yet Also Scoccimarro et al 1998, Hivon et al 1995

  16. Lensing • Generally small effect on power spectrum as 21cm spectrum quite smooth • Effect of smoothing primordial bispectrum (Cooray et al,0803.4194) • Small bispectrum, potentially important trispectrum

  17. Dark-age observational prospects No time soon… - (1+z)21cm wavelengths: ~ 10 meters for z=50- atmosphere opaque for z>~ 70: go to space?- fluctuations in ionosphere: phase errors: go to space?- 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

  18. 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 emissionIonizing radiation: - ionized regions have little hydrogen – regions with no 21cm signalOver-densities start brighter (more hot gas), but ionize first, so end off dimmer Highly non-linear 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.

  19. Non-linear implies large non-Gaussianities… Mellema, Iliev, Pen, Shapiro:astro-ph/0603518 Detect skewness ‘soon’with MWA Stuart et al: astro-ph/0703070

  20. Lots of potentially useful information:clumping of IGM, mass of ionizing sources, source bias, ionization redshift, etc…- but probably not directly about primordial fNL Wyithe & Morales: astro-ph/0703070

  21. 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. • Non-linear effects small but important even at z ~ 50 • Dark ages very challenging to observe (e.g. far side of the moon) • After dark ages physics is complicated – mostly learn about astrophysics, but also - BAO standard ruler (dark energy) - lensing - non-linear bias, etc.- SKA, LOFAR, GMRT, MWA should actually happen

  22. Non-Gaussianity? • Lots, but much the largest from non-linear evolution (+ redshift distortions). Different angular dependence from fNl • Bispectrum ultimately may in theory give fNl<1.- Calculations currently incomplete and highly idealizede.g. what happens if you filter large scales as when removing foregrounds?- Complicated modelling of high-order perturbation theory of the signal from non-linear evolution • Trispectrum (+ higher); e.g. see gNL >~ 10 Cooray, Li, Melchiorri 0801.3463 • Possibly other powerful non-Gaussianity probes, e.g. non-linear biasc.f. Dalal et al 0710.4560, Verde & Matarrese 0801.4826, Slosar & Seljak in prep.

  23. Other 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, primordial black holes(changes temperature evolution)Shchekinov & Vasiliev: astro-ph/0604231, Valdes et al: astro-ph/0701301, Mack & Wesley 0805.1531 • Lots of other things: e.g. cosmic strings, warm dark matter, neutrino masses, early dark energy/modified gravity….

  24. Why the CMB temperature (and polarization) is great • 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 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

  25. Instead try to observe the baryons… - Fall into CDM potential wells after recombination - not erased by photon diffusion power on all scales down to baryon sound horizon at recombination - full 3D distribution of perturbations 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)

  26. 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 scales 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?

  27. What determines the spin temperature? • Interaction with CMB photons (stimulated emission): drives Ts towards TCMB • Collisions between atoms: drives Ts towards gas temperature Tg 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 to Tg < TCMB by collisions: - atoms have net absorption of 21cm CMB photons

  28. New large scaleinformation?- potentials etccorrelated with CMB Dark ages~2500Mpc l ~ 10 14 000 Mpc z=30 Opaque ages ~ 300Mpc Comoving distance z~1000

  29. Non-linear redshift distortions Shaw & Lewis, 2008 in prep. also Scoccimarro 2004 Power spectrum from: Exact non-linear result (for Gaussian fields on flat sky):

  30. Idealised fNl constraint from redshift slice Cosmic variance on bispectrum z=100 Power spectrum Non-linear growth weightedbispectrumfor fNl=1 Cooray: astro-ph/0610257 …Can do better with full redshift dependence: claims fNL ~ 0.01

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