Joint Analysis of Weak Lensing and SZE data from the Arcminute Microkelvin Imager Natasha Hurley-Walker in collaboration with Farhan Feroz, Jonathan Zwart, and the AMI Team 17 th March 2008 Rencontres de Moriond: Cosmology

Talk Outline AMI Science Goals with AMI Cluster Samples pointed sample weak lensing sample Lensing Analysis Bayesian Analysis Results Prospects

AMI Small Array

AMI Large Array

Science Goals Cluster Survey Evolution of cluster population: N(m,z)‏ → σ 8 CMB power spectrum at high angular scales (ℓ > 3000)‏ Other non-Gaussian features, e.g. cosmic strings, ionization regions Pointed cluster observations (Zwart et al 2008, in prep)‏ Known clusters → H 0, q 0, f g Cluster scaling relations, L x –T, M, z, etc Galactic Objects (see Anna Scaife’s talk on Thursday) Source Counts ( → Planck etc) Joint Lensing Analysis

AMI Pointed Cluster Sample Ryle Telescope source survey (2004–6)‏ 4 days for each of ~ 80 ‘lucky’ targets Refined sample of 31 clusters Favourable 15-GHz source environments Sub-sample of 8 (Zwart et al, in prep.)‏ Range of L X, z 6 SA maps:

SA Cluster Maps

Lensing Sample 22 clusters observed with MegaCam on CFHT Selection above 10º declination leaves 16 Currently can only subtract point sources of less than 20mJy some distance from pointing centre: leaves 8 clusters: A115, A611, A851, A1914, A2111, A2218, Zw , A2259

MegaCam Images 2 hour exposures seeing of 0.7” r magnitude limit 25.9 in AB 1º x 1º field of view 2.2' square section of r-band map of A115

Lensing Analysis SExtract sources Select stars from FWHM - magnitude diagram Run im2shape (Bridle et al 2002)‏ Discard outliers Interpolate e 1, e 2 at each galaxy position to create PSF over map

Point-Spread Function Ellipticity varies over the map Amplitude by about 5% Lensing signal 2-3 orders of magnitude smaller Careful interpolation and deconvolution needed

Lensing Analysis (2)‏ Run im2shape on background galaxies, deconvolving with the interpolated PSF Extract catalogue of positions, ellipticities, position angles

Bayesian Analysis of Galaxy Clusters Parameter estimation Model comparison (evidence) MCADAM See Marshall et al 2003, Lancaster et al 2005 Improved MCMC engine: nested sampler Faster; copes well with multimodal distributions and degeneracies Parametric SZ & strong/weak lensing analysis

Cluster Models Geometry: Spherical/elliptical Temperature: Isothermal/Polytropic Mass: Singular Isothermal Sphere, NFW, Cored Power-Law Gas: Beta Model, Hydrostatic Equilibrium All model parameters including point source positions, fluxes and spectra have priors Different number of parameters for each model; evidence values allow you to compare models

SZ Data Generate mock visibilities given model parameters and compare with χ 2 Likelihood function gives you probability of model, given the data Covariance matrices C model other contributions

Noise Modelling Noise on the SZ observation can be described by the covariance matrix C = C system + C CMB + C confusion C system : diagonal matrix with elements C CMB : contains significant off diagonal elements and can be calculated from a given CMB power spectrum following Hobson & Maisinger (2002). C confusion : Scheuer expression for confusion

SZ Posteriors

Combining SZ & Lensing Data Covariance matrix for lensing is diagonal for Gaussian distribution of ellipticities Generate reduced shear given the model at each galaxy position and compare to data using χ 2 Add likelihoods from SZ and lensing for joint analysis

Results so far Images are lensing-quality: Decrements ~5-10 σ in radio data

Prospects SZ/Lensing reduction pipeline in place SA observing programme in progress Papers in preparation on Galactic objects, pointed cluster observations, source counts LA in final calibration stages  SZ survey begins soon LA map of A1914:

References Scheuer, P. A. G. “A statistical method for analysing observations of faint radio stars” 1957; Proceedings of the Cambridge Philisophical Society, vol. 53, pp Bridle, S.; Kneib, J.-P.; Bardeau, S.; Gull, S. “Bayesian galaxy shape estimation” 2002; Proceedings of the Yale Cosmology Workshop "The Shapes of Galaxies and Their Dark Matter Halos" Hobson, M. P.; Maisinger, Klaus “Maximum-likelihood estimation of the cosmic microwave background power spectrum from interferometer observations” 2002; MNRAS 334, 3, 569 Marshall, P.J.; Hobson, M. P.; Slosar, A. “Bayesian joint analysis of cluster weak lensing and Sunyaev-Zel'dovich effect data” 2003; MNRAS 346, 489 Lancaster et al “Very Small Array observations of the Sunyaev-Zel'dovich effect in nearby galaxy clusters” 2005; MNRAS 359, 16L Scaife, A. M. M.; Hurley-Walker, N.; Green, D.; “AMI limits on 15 GHz excess emission in northern HII regions” 2007; MNRAS (accepted)‏