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Luc Simard
UCO/Lick Observatory, Kerr Hall, University of California,
Santa Cruz, CA 95064, Email: simard@ucolick.org
GIM2D (Galaxy IMage 2D) is an IRAF package written to perform detailed
bulge/disk decompositions of low signal-to-noise images of distant
galaxies.
GIM2D consists of 14 tasks which can be used to fit 2D
galaxy profiles, build residual images, simulate realistic galaxies,
and determine multidimensional galaxy selection functions. This
paper gives an overview of GIM2D capabilities.
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(1) |
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(2) |
Detector undersampling (as in the HST/WFPC2 camera) is taken into account by generating the surface brightness model on an oversampled grid, convolving it with the appropriate Point-Spread-Function (PSF) and rebinning the result to the detector resolution.
The Metropolis in GIM2D starts from an initial set of parameters given
by the image moments of the object and computes the likelihood
P(w|D,M) that the parameter set w is the true one given the data
D and the model M. It then generates random perturbations
about that initial location with a given
``temperature''. When the search is ``hot'', large perturbations are
tried. After each trial perturbation, the Metropolis computes the
likelihood value P1 at the new location, and immediately accepts
the trial perturbation if P1 is greater than the old value
P0. However, if P1 < P0, then the Metropolis will
accept the trial perturbation only P1/P0 of the time.
Therefore, the Metropolis will sometime accept trial perturbations
which take it to regions of lower likelihood, and this apparently
strange behavior is very valuable. If the Metropolis finds a minimum,
it will try to get out of it, but it will only have a finite
probability (related to the depth of the minimum) of succeeding.
The step matrix for the trial perturbations is given
by the simple equation
where the vector
consists of randomly generated numbers between 0 and 1, and
the matrix Q is obtained through Choleski inversion of the local
covariance matrix. In short, the sampling of parameter space shapes
itself to the local topology.
Convergence is achieved when the difference between two likelihood
values separated by 100 iterations is less than 3- of the
likelihood fluctuations. After convergence, the Metropolis
Monte-Carlo samples the region where the likelihood is thus maximized
and stores the accepted parameter sets as it goes along to build the
distribution P(w|D,M). Once the region has been sufficiently
sampled, the Metropolis computes the median of P(w|D,M) for each
model parameter as well as the 99
confidence limits. The output
of the fitting process consists of a PSF-convolved model image O, a
residual image R, and a log file containing all Metropolis
iterations, the final parameter values and their confidence intervals,
and image asymmetry indices.
GIM2D has a simple image reduction pipeline for HST (or ground-based) images which makes GIM2D particularly suitable for the analysis of archival data:
Hubble Deep Field F814W images were analyzed with GIM2D (Marleau and
Simard 1998). The number of bulge-dominated galaxies is much lower
( 10
) than indicated by qualitative morphological studies.
Some of these studies quoted bulge-dominated galaxy fraction as high
as 30
(van den Bergh et al. 1996). It was also found that a
number of HDF galaxies have surface brightness profiles with Sérsic
index n
1. Some of them exhibit double exponential profiles
which can be easily mistaken for pure bulge systems. However, these
systems have spectra resembling those of late-type star-forming
galaxies. Other HDF objects are best-fitted with a single n <
1 component.
The rich cluster CL0024+16 at z = 0.4 was the perfect testing ground for the galaxy image deblending in GIM2D. CL0024+16 had been extensively studied for gravitational lensing effects, but a quantitative morphological analysis had never been performed. A total of 560 objects were analyzed in two colors with GIM2D, and about 260 objects were large and/or bright enough to produce reliable bulge/disk decompositions. Figure 1 shows a WFPC2/F814W image of a section of CL0024+16 and the corresponding GIM2D residual image.
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Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393
Marleau, F., & Simard, L. 1998, in preparation
Metropolis N., Rosenbluth, N., Rosenbluth, A., Teller, A., & Teller, E. 1953, Journal of Chemical Physics, 21, 1087
Sérsic, J.-L. 1968, Atlas de Galaxias Australes, Observatorio Astronomico, Cordoba
van den Bergh, S., Abraham, R., Ellis, R.S., Tanvir, N.R., Santiago, B.X., & Glazebrook, K.G. 1996, AJ, 112, 359
Next: Grid OCL : A Graphical Object Connecting Language
Up: Applications
Previous: An IRAF Port of the New IUE Calibration Pipeline
Table of Contents -- Index -- PS reprint -- PDF reprint