GaaP: PSF- and aperture-matched photometry using shapelets

TL;DR

The paper tackles the problem of obtaining accurate galaxy colours across bands with different seeing by introducing the Gaussian-aperture-and-PSF (GaaP) flux and a shapelet-based pipeline to estimate PSF- and pixel-scale–independent colours. It develops a formalism where both sources and PSFs are expanded in Gauss-Hermite shapelets, enabling an analytical computation of the GaaP flux and its uncertainty from observed, pixellated data. A two-pronged correction scheme addresses residuals from imperfect shapelet fits and PSF modeling, yielding percent-level accuracy in simulations across a range of morphologies and PSFs. The method offers a scalable, PSF-independent path to multi-band photometry for large imaging surveys and photometric redshift studies, with potential extensions to time-domain comparisons.

Abstract

We describe a new technique for measuring accurate galaxy colours from images taken under different seeing conditions. The method involves two ingredients. First we define the Gaussian-aperture-and-PSF flux, which is the Gaussian-weighted flux a galaxy would have if it were observed with a Gaussian PSF. This theoretical aperture flux is independent of the PSF or pixel scale that the galaxy was observed with. Second we develop a procedure to measure such a `GaaP' flux from observed, pixellated images. This involves modelling source and PSF as a superposition of orthogonal shapelets. A correction scheme is also described, which approximately corrects for any residuals to the shapelet expansions. A series of tests on simulated images shows that with this method it is possible to reduce systematic errors in the matched-aperture fluxes to a percent, which makes it useful for deriving photometric redshifts from large imaging surveys.

Figures (19)

• Figure 1: Left: The GaaP aperture flux for different Sersic profiles of effective radius 1, and total flux 1, as a function of aperture radius $q$. From steepest to flattest, Sersic index 0.5 (Gaussian), 1 (exponential), 2, 3 and 4 (de Vaucouleur) are plotted. Right: the top-hat aperture fluxes within radius $q$ for the same profiles.
• Figure 2: The ratio of the measured GaaP flux to the true value, for a series of simulated Sersic profile model galaxies convolved with Moffat PSF profiles. Models are identified in Table \ref{['tab:types']}. The horizontal axis is the aperture radius $q$, divided by the shapelet scale used to describe the observed image. See the text for details. Shapelet order 8 was used. (Colour versions of this and similar figures indicating the parameter dependence of the results are included in the on-line materials.)
• Figure 3: As fig. \ref{['fig:firstrun']}, but now including the additive correction for residual pixel flux to the observed sources' shapelet expansions.
• Figure 4: As fig. \ref{['fig:secondrun']}, but now furthermore including the multiplicative correction for residual pixel flux to the PSFs' shapelet expansions.
• Figure 5: As Fig. \ref{['fig:thirdrun']}, but for a two-armed spiral galaxy