Supernova Legacy Survey 5-Years Sample Analysis : a New Diﬀerential Photometry Method

SuperNova Legacy Survey 5-years sample analysis : a new diﬀerential photometry method

N. Fourmanoit Laboratoire de Physique Nucléaire et des Hautes Énergies (UPMC Paris 6)

Determining accurate flux measurements of Type Ia supernovae with well understood uncertainty budget is a crucial point for 2nd generation Type Ia supernovae search projects like the SuperNova Legacy Survey. The differential photometry consists in fitting simultaneously a large set of images of the supernova with a model of the supernova flux and position plus a galaxy background and a sky level (see SNLS 1st year paper 1, hereafter A06). We present here an improvement of that technique that intends to offer better constraints of fluxes uncertainties. Geometrical transformations and kernel convolution that match the image position and PSF are applied to the model rather to the pixels, as previously done in A06. Without any resampling nor convolution of the image pixel grid, the pixels entering the fit remain uncorrelated and then prevent the fit uncertainties to be underestimated. This on-going analysis is applied on the SNLS survey 5-years data set, with a large statistics of 419 supernovae Ia with redshifts from 0.01 to 1.1

Data sample This study takes advantages of the large sample supplied by the 5 years SNLS survey car- ried out from summer 2003 to summer 2008. It consists in more than 400 000 science images (2048×4612 CCDs from MegaCam/CFHT) dispatched among 4 fields (D1:25%, D2:22%, D3:29%, D4:24%) and 4 filters (g’:18%, r’:24%, i’:35%, z’:23%). 419 Type Ia SNe have been spectroscopically identified and photometrically monitored within this sample.

A06 photometry The differential photometry presented in A06 (hereafter A06 photometry) and still used for SNLS 3rd year analysis 2 consisted in simultaneously fitting all images in a given filter with a model that includes (1) a spatially variable galaxy (constant with time), and (2) a time variable point source (the supernova). Previously to the fit, all images are resampled to the pixel grid defined by the image of best quality (IQ) chosen as a reference. The intensity Di,p in a pixel p of image i is modeled as :

Di,p = fluxi × PSFref (x − xsn, y − ysn) + galref (x, y) ⊗ Kernref→i + skyi (1) [( ) ]p where the fit parameters are : fluxi is the supernova flux in image i, galref the non parametric galaxy model made of independent pixels which represents the galaxy in the reference image. PSFref is the normalized Point Spread Function of the reference image centered on the supernova position, Kernref→i the convolution kernel that matches the PSF of the reference image to the PSF of image i and skyi the local background level. In A06, the kernel is a semi analytical model fit based on several hundred objects selected for their high, but unsaturated, peak flux (see Alard, 2000 3). These convolution kernels not only match the PSFs, but also contain the photometric ratios of each image to the reference through their integral values. Eventually a least squares minimization is done including all images that contains the supernova position, and all pixels in the fitted stamp of this image. We typically fit 50×50 galaxy pixels and several hundred images, thus each supernova fit as several thousands parameters.

Flux uncertainties in A06 photometry However a current problem is the minimization does not take into account the correlations between neighboring pixels introduced by image resampling. In order to derive accurate uncertainties, we used the fact that for each epoch, several images in the same night are available which measure the same object flux. We fit a common flux per night to the fluxes measured 2 on each individual image by minimizing a χnight. The covariance of the per-night fluxes is then extracted, 2 and normalized so that the minimum χnight/ndf is 1. New differential photometry Keeping the previous point in mind, we developped a new differential photometry we actually called WNR photomery for “Without aNy Resampling” since the images are not resampled anymore. The intensity Di,p in a pixel p of coordinates (x, y) of image i is now modeled as :

Di,p = fluxi × PSFi T F x x − xsn, y − ysn , T F y x − xsn, y − ysn) [ ( ) ( )] (2) + galref T F x x − xsn, y − ysn , T F y x − xsn, y − ysn) ⊗ Kernref→i + skyi , [ ( ) ( )] where the model is resampled using the pixel coordinates transformations TFx(x, y) and TFy(x, y). PSFi is the PSF of the image i centered on the supernova position. Note that PSFs are not normalized here. Kernref→i is now computed using the PSFref and the PSFi. The photometric ratio, applied on image i, is now computed using the stars PSF ﬂux measured on the image i and the reference image. We mention that SDSS-II SNe Survey uses a similar technique, based on the same principle that A06 photometry, with non-resampled images but with a diﬀerent implementations of the PSFs, the geometrical transformations and the galaxy model (see Holtzman, 2008 4).

Flux uncertainties in WNR photometry The pixels entering the least-squares photometric ﬁt minimizing (2) are now uncorrelated. As a consequence, uncertainties on ﬂuxes estimations are up to 20% larger, which is what we expected for more réalistic uncertainties.

2 Figure 1: A shown by the distribution of χnight with A06 (left) and WNR photometry (right), the correction obtained by measuring the additional scatter between measurements on a same night is reduced by 20-25% depending on ﬁlter.

Conclusion and acknowledgments

The differential photometry without any resampling nor convolution we presently exposed is a part of a more global effort for a better control of systematics budget in the the SuperNova Legacy Surve. It shows very promising features and has been check extensively with field star photometry. A posteriori scatter correction is minimised with the same photometric precision guarantéed. Next step of the analysis will be to undertake an investigation for an impact on cosmological results. I would like to express my gratitude to D. Hardin, P. Astier and J. Guy, and all other members of the SNLS team without whom this work would not have been brought to a successful conclusion.

References

1. P. Astier, J. Guy, N. Regnault, et al. (2006). The Supernova Legacy Survey: measurement of ΩM , ΩΛ and w from the ﬁrst year data set. Astronomy & Astrophysics, 447:31–48. 2. J. Guy, A. Conley, M. Sullivan, N. Regnault (2010) The Supernova Legacy Survey 3-year sample: Type Ia Supernovae photometric distances and cosmological constraints. (in prep) 3. C. Alard (2000). Image subtraction using a space-varying kernel. Astronomy & Astrophysics Supplement, 144:363–370. 4. J. A. Holtzman, J. Marriner, R. Kessler, et al. (2008). The Sloan Digital Sky Survey-II: Photometry and Supernova IA Light Curves from the 2005 Data. Astronomical Journal, 136:2306–2320.