Radial Profile Shape & the Generalized Point Spread Function
The unique shape of the 2MASS point spread function (PSF) derives from a combination of factors: the optics, large 2² pixels (frame images), dithering pattern of the six samples that comprise the coadd, focus, sampling/convolution algorithm to generate the coadds, and atmospheric. As such, the PSF corresponding to frame-coadded images is not well fit with a gaussian function. It is adequately characterized by a generalized exponential function (see below) out to a radius ~2´ FWHM, which is sufficient for star-galaxy discrimination.
The 2MASS PSF typically varies on time scales of ~minutes due to two effects: atmospheric "seeing" and variable telescope focus (thermally driven). The 2MASS telescopes are designed to be mostly free of afocal PSFs (under most conditions), but experience has shown that 2MASS images can be slightly out of focus during periods of rapid change in the air temperature – conditions that generally only occur during the hottest summer months. Out of focus images have the ill-desired property of possessing elongated PSFs. Fortunately, under most/typical observing conditions for the survey, the PSFs are symmetrically round throughout the focal plane. That leaves the atmospheric seeing as the primary dynamic to the radial size of the PSF. Given the long exposure times per sample (1.3 sec) and the six-sample coaddition (with optimal dithering to produce round PSFs), seeing changes result in a symmetric ‘puffing’ in and out of the resultant coadd PSF. We can represent the image PSF with the generalized radially symmetric exponentialof the form:
where f0 is the central surface brightness, r is the radius in arcsec, and a and b are free parameters. This versatile function not only describes the 2MASS PSF, but it also used to characterize the radial profiles of galaxies, from disk-dominated spirals (b close to unity) to ellipsoidal galaxies (b ~ 4, de Vaucouleurs law). The scale-length, a, and the modifier, b, are generally quite correlated, so we combine them "shape parameter," a ´ b. This parameter is a powerful discriminate: galaxies tend to have larger values of both a and b than compared to stars; thus, the multiplicative join of the exponential fitting parameters amplifies the difference between point sources and extended sources.
More information on atmospheric seeing and tracking, click here.