LSST and the Dark Sector: Image processing challenges Tony Tyson University of California, Davis ADASS September 25, 2007

Dark Energy and Its Signatures Universe is 70% dark energy! Cosmology and General Relativity Energy and matter. Space and time. Space and time --- Hubble expansion Supernovae – d L (z). CMB and Baryon Oscillations – d A (z) and H(z). Energy and matter --- Gravitational structure Weak lensing – d A (z); growth of structure. Galaxies and clusters – d A (z) and H(z); growth of structure.

Weak Gravitational Lensing

mass structure vs cosmic time 7 billion lyr 3 billion lyr dark matter

Cosmic shear vs redshift

Shift-and-stare imaging Stars and galaxies are dis- registered between exposures. However, systematic errors in the CCD are registered in each frame.

Galaxy shape parameters: filtered second moments of intensity Signal-matched filter: g(x,y) = galaxy profile

Surface brightness profile of galaxies used for weak lensing with LSST 0.7 arcsec FWHM seeing

C Consider the average tangential component of the shear around circle C: Contribution due to mass inside the circle: But shear from a uniform sheet is zero, so: Where: r

C True in general case, even for off- centered circle and for non-circular mass distributions!

C R2R2 R1R1

3-D Mass Tomography 2x2 degree mass map from Deep Lens Survey

Comparing HST with Subaru

Statistical Weak Lensing: overcoming galaxy shape shot noise Each source galaxy is prepared differently and has its own intrinsic ellipticity, before its image is lens distorted! So the source galaxy population has an intrinsic ellipticity distribution but averages out to zero over large areas. Rms ellipticity = 0.3 But we need to get ellipticity noise down to on ten arcminute angular scales. -> average 10,000 galaxies.

WL shear power spectrum and statistical errors Signal Noise SNAP LSST gastrophysics LSST: fsky = 0.5, ng = 40 SNAP: fsky = 0.1, ng =100 Jain, Jarvis, and Bernstein 2006

Systematic error #1: PSF ellipticity Use foreground stars to define the PSF everywhere in the image. Then form the inverse transform (as a function of position in the image) which makes the stars round. i.e. convolve the image with this “rounding” matrix. Need enough unsaturated stars per square arcminute to fit a good PSF model. Star shapes before Convolution with rounding filter But what’s left over?

Residual Subaru Shear Correlation Test of shear systematics: Use faint stars as proxies for galaxies, and calculate the shear- shear correlation. Compare with expected cosmic shear signal. Conclusion: 300 exposures per sky patch will yield negligible PSF induced shear systematics.

Optimal Reconstruction of Galaxy Shapes: Stack-fit vs. Multi-fit

Dealing with Real Data Multiple observations of a given galaxy –Different PSFs, field distortions, placement with respect to pixels, placement relative to discontinuities, etc.

The Stack-fit Approach Combine exposures into a stack Compare to (convolved) galaxy model  Galaxy on stack Model x stack PSF

The Stack-fit Approach Benefits –Simple! Problems –Requires pixel interpolation  systematics –Combines different seeings  information lost –Discontinuous stack PSF  harder to model –Does not provide desired accuracy

The Multi-fit Approach Compare (convolved) model to all exposures symmetric shapelet  Original exposures Model convolved with individual exposure PSFs Model

Two flavors of co-measurement For a given galaxy/star: 1.Measure its magnitude or shape on each image, then combine the measurements 2.Fit a model to all the images simultaneously – more robust for faint objects which may have S/N~20 in the stack but ~1 in each image –we adopt this method as our baseline design –is mature for point-source photometry (used by 2MASS) –we are developing it for galaxy shapes and extended- source photometry

The Multi-fit Approach Benefits –Uses full suite of information  better accuracy –Circumvents problems with stack-fit Problems –More complicated –Slow  scales with number of exposures

Challenges for Multi-fit ~ floating point operations for fitting LSST data –Requires petascale computing resources –Competitive with transient object pipeline Improve efficiency? –Not clear how to beat linear scaling –Use stack when sufficient Including new exposures –Previous fit will provide useful starting point  quicker convergence

Multi-Fit Multi-Fit Simultaneous fit to the data cube: Advantages: –uses all information. Weights better-seeing images appropriately. –handles image boundaries. PSF on a stacked image changes abruptly at an image boundary. –each image PSF has less structure than the stacked image PSF –turns some systematics into random errors

MultiFit R&D Work to Date Implementation 1: –Author: Chris Roat (currently at Google) –C++, ROOT (particle physics) libraries –website: beta.physics.ucdavis.edu/~croat/MultiFit/MultiFit.shtml

First results from Multi-Fit Increased stability for small galaxiesIncreased sample at high redshift Chris Roat

MultiFit R&D Work to Date Candidate Implementation 2: “glFit” –Authors: Bernstein, Nakajima, Rusin –C++ –Shapelet-based, so convolutions are fast –Implemented only for the single-image case –Single-image fit takes 1 sec per galaxy with no speed optimization yet

MultiFit R&D Work to Date Implementation 3: –Author: Jim Bosch (UC Davis) –Models galaxies and PSFs as sums of Gaussians, so convolutions are fast. –Real galaxies are not Gaussian, but this makes a good testbed. –Upgrade to shapelets begun –Requires 1 s per galaxy for data cube of 20 images, with no speed optimization yet, on 2 GHz desktop –Being written in C++ and Python

R&D Work to Be Done Quantify improvement of comeasurement over stacking for various science cases Speed optimization Extensive Monte Carlo tests Extend fitting to include other quantities: magnitudes, colors, etc.

Multi-Fit Pipeline

Addressing Critical Issues WL shear reconstruction errors  Show control to better than required precision using existing new facilities Photometric redshift errors  Develop robust photo-z calibration plan  Undertake world campaign for spectroscopy Photometry errors  Develop and test precision flux calibration technique

Galaxy shape parameters: normalized filtered second moments of intensity Ellipticity components: e 1 = Ixx-Iyy / Ixx+Iyy e 2 = 2Ixy / Ixx+Iyy

Shear  from source ellipticity “Stretching factor” is the ratio of the two eigenvalues: Weak Lens limit:  Weak Lens limit:   ellipticity   0  / 2   Center on lens mass and then look at radial and tangential shear components: x,y to r,  principal axis transform I  -I rr / I  +I rr =  /   normalized projected 2-d mass density

Gauss-Laguerre Approach Model: I(r  b ij  ij  (r  Advantages –Few assumptions –  ij related to physical quantities –Gal, PSF in same framework

Computational Details What it does –Some coordinate basis (position, size, e) –Linear fit (over pixels) for b vector –Alter ebasis (non-linear) and repeat –Basis where b10, b20, b11 = 0 describes galaxy Run-time for convolved fit, single set of pixels: –~5 galaxies per second on a few GHz processor Works well (Nakajima & Bernstein 2007)

LSST Precision on Dark Energy WL+BAO and Cluster counts give separate estimates. Both require wide sky area deep survey. Zhan 2006 p/  = w 0 + w a (1- a)

Comparison of Stage-IV facilities for DE