Replacing standard galaxy profiles with mixtures of Gaussians

David W. Hogg, Dustin Lang

    Research output: Contribution to journalArticle

    Abstract

    Exponential, de Vaucouleurs, and Sérsic profiles are simple and successful models for fitting twodimensional images of galaxies. One numerical issue encountered in this kind of fitting is the pixel rendering and convolution (or correlation) of the models with the telescope point-spread function (PSF); these operations are slow, and easy to get slightly wrong at small radii. Here we exploit the realization that these models can be approximated to arbitrary accuracy with a mixture (linear superposition) of two-dimensional Gaussians (MoGs). MoGs are fast to render and fast to affine-transform. Most importantly, if you have a MoG model for the pixel-convolved PSF, the PSF-convolved, affine-transformed galaxy models are themselves MoGs and therefore very fast to compute, integrate, and render precisely. We present worked examples that can be directly used in image fitting; we are using them ourselves. The MoG profiles we provide can be swapped in to replace the standard models in any image-fitting code; they sped up model fitting in our projects by an order of magnitude; they ought to make any code faster at essentially no cost in precision.

    Original languageEnglish (US)
    Pages (from-to)719-730
    Number of pages12
    JournalPublications of the Astronomical Society of the Pacific
    Volume125
    Issue number928
    DOIs
    StatePublished - Jun 2013

    Fingerprint

    galaxies
    point spread functions
    profiles
    pixels
    pixel
    convolution integrals
    telescopes
    transform
    costs
    radii
    cost
    code

    ASJC Scopus subject areas

    • Astronomy and Astrophysics
    • Space and Planetary Science

    Cite this

    Replacing standard galaxy profiles with mixtures of Gaussians. / Hogg, David W.; Lang, Dustin.

    In: Publications of the Astronomical Society of the Pacific, Vol. 125, No. 928, 06.2013, p. 719-730.

    Research output: Contribution to journalArticle

    Hogg, David W. ; Lang, Dustin. / Replacing standard galaxy profiles with mixtures of Gaussians. In: Publications of the Astronomical Society of the Pacific. 2013 ; Vol. 125, No. 928. pp. 719-730.
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