POWER SPECTRUM ESTIMATION FOR J PAS DATA

CENTRO DE ESTUDIOS DE FÍSICA DEL COSMOS DE ARAGÓN (CEFCA) POWER SPECTRUM ESTIMATION FOR J PAS DATA Carlos Hernández Monteagudo, Susana Gracia (CEFCA) & Raul Abramo (Univ. de Sao Paulo) Madrid, February 29 th 2012

Outline Introduction and theoretical motivation. Some words about Redshift Space Distortions (RSDs) Strategy Status Prospects and foreseen difficulties

Some unavoidable equations. Fourier Transform (can be done very fast)

Some unavoidable equations. Fourier Transform (can be done very fast) If is is a Gaussian field, it is then completely determined by Power Spectrum

Some unavoidable equations. Fourier Transform (can be done very fast) If is is a Gaussian field, it is then completely determined by Power Spectrum Inflation predicts how are fluctuations of the potential, connected to those of matter via Poisson equation But one observes galaxies, which are a priori biased tracers of matter or one may measure projected galaxy number density

Some unavoidable equations. Fourier Transform (can be done very fast) If is is a Gaussian field, it is then completely determined by Power Spectrum At the end, both 2D and 3D power spectra are related Inflation predicts how are fluctuations of the potential, connected to those of matter via Poisson equation But one observes galaxies, which are a priori biased tracers of matter or one may measure projected galaxy number density

Error in Power Spectrum estimates are low correlated!! C l P(k) l k Thomas, Abdalla & Lahav (2010) SDSS DR5 (Percival et al. 2007)

C l Growth of perturbations (D(z)) Non Gaussianity Neutrino mass X correlations to CMB (ISW, ksz, tsz, missing baryons.) P(k) l k Thomas, Abdalla & Lahav (2010) SDSS DR5 (Percival et al. 2007)

Information of the P(k) of the peculiar velocities: REDSHIFT SPACE DISTORTIONS The theory predicts that, due to isotropy and homogeneity requirements, the power spectrum (and also the correlation function) are only dependent on distances but not on orientations: = f(k) and not f(k) However, the fact that the radial coordinate is given by redshift, and that redshift is affected, via a Doppler effect, by peculiar velocities, introduces a distortion in the effective mapping of structure (Kaiser 1987) which translates into into a dependence of the power spectrum on cos(k. r) = μ

The dependence of P(k) on cos(k. r) = μ introduces the sensitivity of the power spectrum on peculiar velocities, and these, themselves, are sensitive to Dark Energy and deviations from General Relativity (e.g., Yamamoto et al. 2005, 2010) Legendre polynomials P l=0 (k,z=0) P l=2 (k,z=0) Linear theory predictions Yamamoto et al. (2005)

COMPUTING POWER SPECTRA In 2D Not so demanding CPU requirements (easier to test for systematics) Easier handling of the mask Relatively simple handling of pixel finite size and limited sky coverage In 3D It contains all cosmological information (at least at the level of linear theory): one single analysis It lies closer to the parameters defining the theory: no projection involved

OUR 2 D POWER SPECTRUM ESTIMATOR: THE MASTER APPROACH Hivon et al. 2001 The relation between sky signal and a l,m s is defined on the entire celestial sphere MASTER accounts for incomplete sky coverage and inhomogeneous noise, and provides unbiased estimates of the angular power spectrum and theoretical predictions for their uncertainties Easy to assess impact of systematics

On the 3D P(k) estimation Need to run Monte Carlo of galaxy samples mimicking as closely as possible the real data, in order to, while testing our P(k) algorithms : 1. Account for impact of observational selection function (both in angles and in depth/redshift) 2. Account for shot/poissonian noise in the galaxy distribution 3. Observe different cosmological scenarios (produce mock galaxy catalogues under different DE/cosmo models) 4. Asses the impact of systematics (residual stars, photometry calibration uncertainties, seeing variation, sky emission, etc) 5. Compare different galaxy weight functions, P(k) estimation algorithms and covariance matrices for each of them

On the 3D P(k) estimation (II) Two different methods (so far) to estimate P(k): 1. An FFT based method in which galaxies are placed in a cubic grid. It works quickly but might be sub optimal. It allows predicting peculiar velocity fields, potential fields, etc, which has great impact on other cosmological projects (beyond P(k) estimation ISW, search for hot gas and bulk flows [kinetic and thermal Sunyaev Zel dovich effects], etc) ( it is always good to have your survey in a box ) 2. A discrete method working a particle by particle basis, scaling as ~ N gals + N random, a priori easier to implement (Yamamoto 2003, which a version of Feldman, Kaiser & Peacock aiming for P(k) rather than P(k) only). depending on the success on these methods we will consider implementing a QML method (à la Hamilton 1996), supposedly optimal but extremely CPU expensive

(1) FFT based method (notes from R.Abramo) An effective window function W(x) multiplies the whole universe galaxy field, yielding the observed galaxy field In Fourier space, this results into a convolution But how does P(k) transform?

(2) Discrete method (improved FKP method) Each of the P(k,z) momenta is computed out of a sum, for each k vector, over all mock (random) galaxies and all real galaxies

Cosmological Scenario (Ω m, Ω Λ, h, n S, w 0, w a, etc Linear ρ, v cosmological simulation Halo population, observational window function, systematics Real J PLUS/ J PAS data Galaxy Catalogue FFT/grid based P(k) algorithm Discrete P(k) algorithm P(k) estimate comparison, P(k) covariance computation

IN PLACE: Simulator of 3D cosmological linear smooth density fields following the clustering properties of any given transfer function and redshift and scale (k) dependent bias. Halo/galaxy populator of 3D above simulated fields following Poisson statistics (shot noise simulator). Tools to introduce effective sky mask, depth selection function, systematics, contaminants, etc ONGOING: Accurate and efficient correction for mask effects in FFT based P(k) estimator. Discrete P(k) estimation Overall code optimization.

PROSPECTS AND FORESEEN DIFFICULTIES Simplest (serial) f90 version of code running in 2 3 months python version will take longer Application to existing light cone mock catalogues Córdoba mocks, Millenium, Marenostrum(?) Application to ALHAMBRA data (end of the year?) Need to go beyond linear theory? Zel dovich approximation? how to reconcile using non linear input transfer functions with Gaussian + Poisson simulations? Need to parallelize the code? CPU intensive when dealing with large volumes Need to optimize interface with mask production algorithms Need to un do the linear theory prediction for the BAO evolution (Padmanabhan et al. 2012) Need to think on how stars, sky and systematics alike affect the P(k), in order to properly simulate their impact in the simulations It is time to start thinking about the 2 point spatial correlation function! ideally, it would a new module in the existing software