Three‐dimensional Parameterization of the Stellar Locus with Application to QSO Color Selection

Abstract

A straightforward method for parameterizing and visualizing a locus of points in n-space is presented. The algorithm applies directly to the problem of distinguishing QSOs from Galactic stars in multicolor space. When applied to an existing four-filter data set (photometric errors of sigma ~ 0.1 mag and BJ < 0.01 mag) of the Catalogue of WBVR Magnitudes of Northern Sky Bright Stars (V < 7.2) yields the first look at the intrinsic width in the Galactic star color distribution. The stellar locus is found to populate a ribbon-like subset of color-color-color space. In the G to early-K star region, the cross section of the stellar locus has a FWHM of 0.07 mag in the wide direction. We attribute the majority of the width to metallicity differences between the stars, although there may be some contribution from other sources such as differential reddening. The FWHM in the thin direction is 0.03 mag or less. The locus is parameterized from late-B stars through M stars. We reproduce the metallicities of 64 F and G dwarfs with an rms error of 0.13. The distribution of bright stars along the locus is also presented. The algorithm can be applied to parameterize any one-dimensional set of data that is distributed in n-dimensional space.