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Shapelets for shear surveys

Taking shear and faking. images. :. Shapelets for shear surveys. Shapelets. for shear surveys. Richard Massey (IoA, Cambridge) Alexandre Refregier (CEA Saclay), Richard Ellis (CalTech), Chris Conselice (CalTech), David Bacon (Edinburgh), & SNAP team:

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Shapelets for shear surveys

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  1. Taking shear and faking images : Shapelets for shear surveys Shapelets for shear surveys Richard Massey (IoA, Cambridge) Alexandre Refregier (CEA Saclay), Richard Ellis (CalTech), Chris Conselice (CalTech), David Bacon (Edinburgh), & SNAP team: Jason Rhodes (GSFC), Justin Albert (CalTech), Mike Lampton (LBL), Alex Kim (LBL), Gary Bernstein (U.Penn) & Tim McKay (Michigan)

  2. Shapelet (Gauss-Hermite) basis fns • Orthonormal basis set of 2D ‘Gauss-Hermite’ functions; AKA the eigenfunctions of the Quantum Harmonic Oscillator. • Fourier transform invariant • (easy image manipulation • e.g. convolution). • Powerful bra-ket notation • already exists. • Gaussian-weighted • multipole moments • (many astronomical uses). m=rotational oscillations (c.f. QM Lr momn) n=radial oscillations (c.f. QM energy) m=rotational oscillations (c.f. QM Lr momn) n=radial oscillations (c.f. QM energy) Refregier (2001)

  3. Modelling HDF galaxy shapes > > | | = a00 + a01 +… > | Any image I(x) can be represented as a Taylor series (like a Fourier transform): Orthogonal Basis functions Decomposition of a galaxy image into shape components: < > | Refregier (2001) Refregier & Bacon (2001)

  4. HDF galaxies in “shapelet space” < > | Real space Shapelet space (series is in practise truncated at finite nmax) Complete, 1-to-1 uniquely specified map

  5. PSF deconvolution 6-fold symmetry due to refraction around the 3 secondary support struts appears as power in the m=±6, ±12 coefficients. • Shapelets are not necesarily convenient for the physics of galaxy morphology, but the mathematics of image manipulation. • PSF convolution is trivial in shapelet space: a bra-ket multiplication. Can implement deconvolution from the WFPC2 PSF via a matrix inversion. • Dilations, translations and shears can also be represented as QM ladder operations (â, â†) in shapelet space. SNAP PSF Shapelet NB: logarithmic scale! Circular core in the m=0 coefficients. Bacon & Refregier (2001) Kim et al. (2002) Lampton et al. (2002) Rhodes et al. (2002)

  6. Shapelets for shear measurement Shapelets is a logical extension of traditional methods. We automatically deconvolve the PSF and can use extra information to form a more robust shear estimator with ~2S/N. KSB uses Gaussian-weighted quadrupole moments of a galaxy image to measure ellipticities, and octupole moments to convert into shears. Kaiser, Squires & Broadhurst (1995) Refregier & Bacon (2001)

  7. Shapelet parameter space of HDF galaxies Parameter space of galaxy morphology c.f. Hubble tuning fork! • Do combinations of shapelet parameters correlate with ‘eye-balled’ morphological Hubble types? • Quantitative galaxy morphology classification? In doing this, we’ve built up a catalogue of all HDF galaxy shapes in n parameters… -functions representing every HDF galaxy are placed into an n-dimensional parameter space, with each axis corresponding to a (polar) shapelet coefficient or size/magnitude.

  8. Galaxy morphology classification (PCA) First 10 principal components of morphology distribution in shapelet space: As before but with galaxies rotated and flipped, so that they are aligned with the x-axis and have the same chirality, before being stacked: Average HDF galaxy: First 10 principal components of morphology distribution in shapelet space.

  9. Galaxy morphology classification (estimators) Gravitational lensing shear Size Chirality (asymmetry) Concentration Invariant under flux change, rotations. Changes linearly with dilations. Invariant under dilations, rotations. Changes sign under parity flip. Invariant under rotations, shears. Slope of “shapelet power spectrum” Conselice et al. (2000) Bershady et al. (1998)

  10. SuperNova/Acceleration Probe Door Assembly • 300sq.degree optical +NIR survey is planned to R=28: yielding 150 million resolved galaxies! • Need new high precision,robust • shear measurement algorithm • (current limiting factor in • weak shear surveys). • Algorithms need calibrating: • old methods also required • this, using simulated images • and entire mock DR pipeline. Secondary Mirror Hexapod Bonnet Light Baffles Secondary Metering structure Solar Array, ‘Sun side’ Primary Mirror Optical Bench Instrument Metering Structure Tertiary Mirror Solar Array, ‘dark side’ Fold-Flat Mirror Instrument Radiator Spacecraft Instrument Bay ACS CD & H Comm Power Data CCD detectorsNIR detectorsSpectrographFocal Plane guiders Cryo/Particle shield Solid-state recorders Perlmutter et al. (2002) Lampton et al. (2002) Shutter Hi Gain Antenna

  11. Simulated SNAP images Fake Simulated Image Who needs a real • telescope now?! • HDF is deep (R=28.6), but too small to do this. Most importantly, the properties of objects in it are not known. We need deep images, containing realistic galaxies – but with known sizes, magnitudes & shears. • Calibrate future shear (astrometry) • measurement algorithms. • Optimise telescope design (SNAP, • GAIA) and survey strategy. • Estimate errors upon cosmological • parameter constraints which will • be possible with the real data. A bit like IRAF.noao.artdata, but much better!

  12. HDF galaxy morphology PDF Parameter space of galaxy morphology c.f. Hubble tuning fork! -functions representing every HDF galaxy are placed into an n-dimensional parameter space, with each axis corresponding to a (polar) shapelet coefficient or size/magnitude. • The PDF is: • kernel-smoothed (assume a smooth underlying PDF exists) • Monte-Carlo sampled, to synthesise new ‘fake’ galaxies.

  13. Morphing in shapelet space smoothing param space smoothing param space Used in sims Real HDF Used in sims Real HDF Oversmoothed galaxies become random junk… Massey et al. (2002)

  14. Simulated images Objects have known positions, magnitudes and added shear: Animation shows 0%-10% shear in 1% steps. ftp://ftp.ast.cam.ac.uk/pub/rjm/simages/

  15. Proof of the pudding I Blind test: run SExtractor on HDFs and simulated images.

  16. Proof of the pudding II Even second-order statistics match, including morphology parameters. Non-trivial that this should work: shapelet modelling is capturing something important, & simulations are realistic! Asymmetry Concentration Concentration Conselice et al. (2000)

  17. Simulating SNAP sensitivity Model HDF galaxies Morphology parameter space Simulated images SNe shear Catalogue of objects before observational noise Add SNe on top of galaxies Add varying PSF, and stars from which to measure it Try to detect them Detection efficiency Add instrumental distortions due to telescope optics Cosmological parameter constraints Gravitationally shear galaxies (by known amount)

  18. SNAP Weak Lensing sensitivity

  19. Mapping the Dark Matter CDM (Jain, Seljak & White 1997) CDM: 1’ smoothed SNAP-deep WHT Statistical errors based on realized performance

  20. Cosmological constraints with SNAP Combining constraints based on DM power spectrum with those from CMB (and SNe) breaks degeneracies between M and w and directly tests for growth of structure

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