August 23, 2007JPL WL from space meeting1 Shear measurements in simulated SNAP images with realistic PSFs Håkon Dahle, Stephanie Jouvel, Jean-Paul Kneib, Eric Prieto, Sebastien Vives, Bruno Milliard Laboratoire d’Astrophysique de Marseille (LAM), France

August 23, 2007JPL WL from space meeting2 Motivation STEP-like simulations for SNAP, with PSF (800nm) from optical design Include effects of :  jitter, charge diffusion, sky background, detector noise (no CTE or diffraction spikes)  Dithering and re-sampling KSB+ analysis: Shear recovery as function of focus, distance from optical axis

August 23, 2007JPL WL from space meeting3 Skymaker simulations 34x34 grid of galaxies in 4 simulated exposures; ditherered, re-sampled and combined 0.1’’ pixels --> 0.06’’ pixels; PSF from 49 stars  All galaxies have the same intrinsic ellipticity (e = 0.25), but random orientations  5 magnitude bins (25.0,26.0,27.0,28.0,28.5)  3 size bins (galaxies of scale 0.1’’, 0.2’’ and 0.4’’)

August 23, 2007JPL WL from space meeting4 PSF variation with focus/position

August 23, 2007JPL WL from space meeting5 Note ellipticity dependence on smoothing scale (PSF wings are more elliptical) 0.34 o off-axis 0.57 o off-axis 0.8 o off-axis 0.34 o 0.57 o 0.8 o

August 23, 2007JPL WL from space meeting6 Note that e1=e2=0 PSFs are not necessarily circularly symmetric 0.34 o off-axis 0.57 o off-axis 0.8 o off-axis 0.34 o 0.57 o 0.8 o

August 23, 2007JPL WL from space meeting o off-axis 0.57 o off-axis 0.8 o off-axis 0.34 o 0.57 o 0.8 o

August 23, 2007JPL WL from space meeting o off-axis 0.57 o off-axis 0.8 o off-axis 0.34 o 0.57 o 0.8 o

August 23, 2007JPL WL from space meeting9 Analysis Select faint galaxies (6 < S/N < 250), which tend to carry most of the shear signal in real WL analyses Note: The magnitude values have an arbitrary zeropoint and should not be taken literally. S/N values are more meaningful KSB+ analysis (measuring stellar ellipticities and polarizabilities at same scale as these quantities are measured for each galaxy)

August 23, 2007JPL WL from space meeting10 Bias of shear measurements Size: 0.1”(blue), 0.2”(red), 0.4”(green)

August 23, 2007JPL WL from space meeting11 Shear Kaiser Squires & Broadhurst Ap.J (KSB) Polarization is characterized by a vector (e1, e2)  e 1 ~ (Q xx –Q yy )/(Q xx +Q yy )  e 2 ~ 2Q xy /(Q xx +Q yy )  The Q ij are Gaussian weighted second moments of the intensity distribution  NOTE: In these simulations, all galaxies have the same intrinsic |e| = sqrt(e e 2 2 )  The simulated galaxies of different sizes have their ellipticities diluted by the PSF to a varying extent --> concentric circles in e 1 -e 2 space  Noisier (fainter) galaxies make “fuzzier” circles  Anisotropic PSFs make them slightly non-concentric & non- circular

August 23, 2007JPL WL from space meeting12 “Shear recovery”  Apply standard KSB methods (+later modifications by Luppino & Kaiser 1997 and Hoekstra et al. 1998) to recover the intrinsic values of e 1, e 2 (see fig)  From these, calculate the mean value of the modulus =  Define “bias” as the ratio of the output value to the input value of the ellipticity  Define “uncertainty” as the rms scatter around

August 23, 2007JPL WL from space meeting13 Bias of the shear measurements (ellipticity modulus after PSF correction, relative to input ellipticity) Green: 0.34 o off-axis Blue: 0.57 o off-axis Red: 0.8 o off-axis

August 23, 2007JPL WL from space meeting14 Uncertainty of the shear measurements Green: 0.34 o off-axis Blue: 0.57 o off-axis Red: 0.8 o off-axis

August 23, 2007JPL WL from space meeting15 Mean value of each shear component (should in principle be zero; circle indicates ~1 sigma uncertainty).

August 23, 2007JPL WL from space meeting16 This is work in progress… Currently probing features/limitations of KSB+ more than SNAP ? Would be useful to compare to another method for shape measurement Simulations with finer sampling of different focus values (checking how smoothly uncertainty & bias vary as function of focus).

August 23, 2007JPL WL from space meeting17