Star - Galaxy Discrimination Parameters

Resolved galaxies tend to separate from stars in parameter space (e.g., image second moment vs. integrated flux) because they are extended with respect to the point spread function. At the sensitivity limit this separation breaks down and the space becomes degenerate. In addition, double stars and other multiple star objects also tend to mimic galaxies in a this parameter space AND most other simple forms of parameter space. It is therefore necessary to develop discrimination techniques that can handle both solitary stars (comprising most of the sky) and multiple stars, confined primarily to the galactic plane.

Score Parameters

A number of parameters are used to distinguish stars (point sources) from galaxies (extended sources). There are four basic kinds of parameters to this end: (1) image moments, (2) the peak flux versus integrated flux, (3) radial profile, and (4) emission located beyond the central peak and wings of a stellar PSF, and various combinations thereof. The central surface brightness to total brightness parameter is referred to as "mxdn". The radial profile parameters derive primarily from the radial profile function:

f = f0 * exp [- (r / alpha) ** (1/beta) ]
where f0 is the peak flux, r is the radial distance from the peak center, alpha and beta are the scaling parameters.

sh = alpha * beta
score = (sh - sh_0) / sigma_sh_0
where sh_0 and sigma_sh_0 are the shape and standard deviation of the shape for stars (the stellar ridge, see the above figures, e.g.)

SCMXDN vs Mag : "mxdn" score

The "mxdn" score is derived from the peak pixel brightness versus the integrated flux (using an adaptive circular aperture).

SCSH vs Mag : "sh" score

The "sh" score is derived from the radial profile, as discussed earlier in this memo. It is effective for most kinds of stars, except double stars and other multiple point source objects.

SCWSH vs Mag : "wsh" score

The "wsh" score (a.k.a. "wedge shape") is derived similar to the "sh" score, except that it employs a rotating wedge-shaped mask designed to exclude sections of the radial profile from the modified exponential function fit. It's primary purpose is to minimize contamination from double stars.

SCMsh vs Mag : "msh" score

Similar in function to the "wsh", we compute the median radial profile shape. The median is computed for circular annuli about the primary. The median tends to minimize the affect of the secondary component, thus the "msh" should be small for most double systems.

SCR23: "r23" score

Again, the vectored circular-radial profile is measured, expect that all possible vectors are measured, The vector with the minimum "sh" is thrown out, while the next two vectors with the minimum "sh" are averaged to construct the "r23" shape. In this way double stars, triple stars and any other asymmetric star system should have a small "r23" shape value, while galaxies (being extended in all directions) should have a large "r23" shape value. This parameter breaks down when there are so many stars that every radial direction is extended (generally this means a system with more than 3 stars, but a some triple configurations satisfy this condition). This parameter tends to work best when the primary star in the system is significantly brighter then the secondary (s).

SCVINT: "vint" score

The first step is to subtract the primary component and one secondary component using the PSF. The remaining flux surrounding the system is then integrated in small wedged chunks (symmetrically distributed around the primary). The integrated flux in the chunks is normalized by the peak brightness of the primary. The chunks with the second and third lowest flux are averaged. Triple stars should have normalized flux values that are low compared to galaxies (because galaxies should have substantial flux beyond the primary -- i.e., the core). There are several variations on this theme that are used (e.g., instead of using the integrated flux, the mean flux is used).

SCTRIP: trip" score

Several of the parameters described above are averaged togethor (with a weighting system that favors "wsh") to form this score. Since many of these parameters are correlated (some more than others) this score has limited affect, but it does nicely combine all the the multiple star killers into one score.

A new parameter under design takes advantage of the fact that the PSF for stars is fairly well measured for the coadds (via SEEMAN). Using the alpha and beta values for the PSF, GALWORKS deconvolves the galaxy candidate images using an iterative scheme similar to a Richardson-Lucy algorithm. It then counts the number of "local maxima" within 8" of the object central position. The general idea is to identify multiple-peaked objects, such as double and triple stars, as well as galaxies with two nuclei, or galaxies with stellar contamination. The parameter space is designed to separate multiple stars from galaxies: Galaxies should have a large "trip" score (> 5, e.g.,) and may have more than one peak, while double stars and triple stars should have a smaller "trip" score (< 10) with multiple peaks. Galaxies with multiple peaks tend to be the bigger and brighter of the set (but do not appear to be double nuclei).. The sources with zero peak correspond to faint objects (SNR < 10) in which the deconvolution was not attempted.

Final Remark: