Joint Analysis of Weak Lensing and SZE data from the Arcminute

Microkelvin Imager

Natasha Hurley-Walkerin collaboration with

Farhan Feroz, Jonathan Zwart,and the AMI Team

17th March 2008Rencontres de Moriond: Cosmology

Talk Outline

AMIScience Goals with AMICluster Samples

pointed sampleweak lensing sample

Lensing AnalysisBayesian AnalysisResultsProspects

AMI Small Array

AMI Large Array

Science Goals

Cluster SurveyEvolution of cluster population: N(m,z) → σ8

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, Lx–T, M, z, etcGalactic 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 clustersFavourable 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 CFHTSelection above 10º declination leaves 16Currently can only subtract point sources of less than 20mJy some distance from pointing centre: leaves 8 clusters:

A115, A611, A851, A1914, A2111, A2218, Zw1358+62, A2259

MegaCam Images

2 hour exposuresseeing of 0.7”r magnitude limit 25.9 in AB1º x 1º field of view

2.2' square section of r-band map of A115

Lensing Analysis

SExtract sourcesSelect stars from FWHM - magnitude diagramRun im2shape (Bridle et al 2002)Discard outliers

Interpolate e1, e

2 at each galaxy position to

create PSF over map

Point-Spread Function

Ellipticity varies 0-0.1 over the mapAmplitude by about 5%Lensing signal 2-3 orders of magnitude smallerCareful 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 estimationModel comparison (evidence)

MCADAMSee Marshall et al 2003, Lancaster et al 2005Improved MCMC engine: nested sampler

Faster; copes well with multimodal distributions and degeneracies

Parametric SZ & strong/weak lensing analysis

Cluster Models

Geometry: Spherical/ellipticalTemperature: Isothermal/PolytropicMass: Singular Isothermal Sphere, NFW, Cored Power-LawGas: 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

2/1

2

2

2e1

Cπ=Z

χ

Z=θ|DataPr=L

visNL

LSZ

Generate mock visibilities given model parameters and compare with χ2

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 = Csystem + CCMB + Cconfusion

Csystem: diagonal matrix with elements

CCMB: contains significant off diagonal elements and can be calculated from a given CMB power spectrum following Hobson & Maisinger (2002).

Cconfusion: Scheuer expression for confusion

iji δσ 2

SZ Posteriors

Combining SZ & Lensing Data

Covariance matrix for lensing is diagonal for Gaussian distribution of ellipticitiesGenerate reduced shear given the model at each galaxy position and compare to data using χ2 Add likelihoods from SZ and lensing for joint analysis

LensingSZ L+L=L logloglog

Results so farImages are lensing-quality:

Decrements ~5-10 σ in radio data

Prospects

SZ/Lensing reduction pipeline in placeSA observing programme in progressPapers in preparation on Galactic objects, pointed cluster observations, source countsLA in final calibration stagesSZ 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. 764-773Bridle, 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, 569Marshall, P.J.; Hobson, M. P.; Slosar, A. “Bayesian joint analysis of cluster weak lensing and Sunyaev-Zel'dovich effect data” 2003; MNRAS 346, 489Lancaster et al “Very Small Array observations of the Sunyaev-Zel'dovich effect in nearby galaxy clusters” 2005; MNRAS 359, 16LScaife, A. M. M.; Hurley-Walker, N.; Green, D.; “AMI limits on 15 GHz excess emission in northern HII regions” 2007; MNRAS (accepted)