Joint Analysis of Weak Lensing and SZE data from the Arcminute Microkelvin Imager

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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
• 17th March 2008
• Rencontres de Moriond Cosmology

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AMI Small Array
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AMI Large Array
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Science Goals

• Cluster Survey
• Evolution of cluster population N(m,z)? ? s8
• CMB power spectrum at high angular scales (l gt
  3000)?
• Other non-Gaussian features, e.g. cosmic strings,
  ionization regions
• Pointed cluster observations (Zwart et al 2008,
  in prep)?
• Known clusters ? H0, q0, fg
• Cluster scaling relations, LxT, M, z, etc
• Galactic Objects (see Anna Scaifes talk on
  Thursday)
• Source Counts (? Planck etc)
• Joint Lensing Analysis

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AMI Pointed Cluster Sample

• Ryle Telescope source survey (20046)?
• 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 LX, z
• 6 SA maps

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SA Cluster Maps
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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, Zw135862,
  A2259

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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
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Lensing Analysis

• SExtract sources
• Select stars from FWHM - magnitude diagram
• Run im2shape (Bridle et al 2002)?
• Discard outliers

• Interpolate e1, e2 at each galaxy position to
  create PSF over map

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Point-Spread Function

• Ellipticity varies 0-0.1 over the map
• Amplitude by about 5
• Lensing signal 2-3 orders of magnitude smaller
• Careful interpolation and deconvolution needed

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Lensing Analysis (2)?

• Run im2shape on background galaxies, deconvolving
  with the interpolated PSF

• Extract catalogue of positions, ellipticities,
  position angles

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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

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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

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SZ Data

• Generate mock visibilities given model parameters
  and compare with ?2
• Likelihood function gives you probability of
  model, given the data

• Covariance matrices C model other contributions

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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

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SZ Posteriors
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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 ?2
• Add likelihoods from SZ and lensing for joint
  analysis

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Results so far

• Images are lensing-quality

• Decrements 5-10 s in radio data

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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

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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. 764-773
• 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)?