New insights into galaxy structure from GALPHAT - I. Motivation, methodology and benchmarks for Sersic models

We introduce a new galaxy image decomposition tool, GALPHAT (GALaxy PHotometric ATtributes), which is a front-end application of the Bayesian Inference Engine (BIE), a parallel Markov chain Monte Carlo package, to provide full posterior probability distributions and reliable confidence intervals for all model parameters. The BIE relies on GALPHAT to compute the likelihood function. GALPHAT generates scale-free cumulative image tables for the desired model family with precise error control. Interpolation of this table yields accurate pixellated images with any centre, scale and inclination angle. GALPHAT then rotates the image by position angle using a Fourier shift theorem, yielding high-speed, accurate likelihood computation. We benchmark this approach using an ensemble of simulated Sersic model galaxies over a wide range of observational conditions: the signal-to-noise ratio S/N, the ratio of galaxy size to the point spread function (PSF) and the image size, and errors in the assumed PSF; and a range of structural parameters: the half-light radius r(e) and the Sersic index n. We characterize the strength of parameter covariance in the Sersic model, which increases with S/N and n, and the results strongly motivate the need for the full posterior probability distribution in galaxy morphology analyses and later inferences. The test results for simulated galaxies successfully demonstrate that, with a careful choice of Markov chain Monte Carlo algorithms and fast model image generation, GALPHAT is a powerful analysis tool for reliably inferring morphological parameters from a large ensemble of galaxies over a wide range of different observational conditions.