The 2MASS Beam

The 2MASS survey mode is to scan across the sky along the declination axis, sampling each piece of the sky multiple times in the process. A single raw frame consists of 2" pixels, while the camera optics are designed such that the incoming beam is approximately 2" (for each band). The PSF is therefore undersampled. The multiple sampling was carried out in such a way that the sub-pixel sampling was optimized to minimize deleterious sub-pixel effects and to minimized the "seeing" profile. The resultant combined samples (representing the Atlas or "coadd" images) have 1" pixels and a FWHM that is typically 2.5" when the seeing is good, and symmetric circular shapes resistent to afocal distortions. The extended source processor uses the coadd images to detect, characterize and extract sources.

PSF Characterization


The PSF is characterized with a generalized radially symmetric Sersic exponential function:
where f0 is the central surface brightness, r is the radius in arcsec, and alpha and beta 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 (beta close to unity) to ellipsoidal galaxies (beta > 1, de Vaucouleurs law). The scale-length, alpha, and the modifier, beta, are generally quite correlated, so we combine them "shape parameter," alpha X beta. 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.

Stellar Ridgeline Determination


The mean "shape" is determined from an ensemble of isolated stars spatially clustered along the 2MASS in-scan (declination) direction. The sample population must be free of extended sources (galaxies) and double stars to be a meaningful measure of the PSF. We perform a robust separation of isolated stars from the larger population (of the spatially correlated sample) by employing an iterative selection method that is keyed by using an initial boot-strap from the lower quartile of the total population histogram. Since isolated stars will have an inherently smaller "shape" value than extended sources (or double stars), the lower quartile (25%) is dominated by isolated stars and conversely, the upper quartile by galaxies. Hence, the distribution lower quartile serves as a good first guess to the actual mean shape value of isolated stars. The idea is to exclude truely extended sources from the stellar shape determination. Once the lower quartile is identified, we can iteratively search a restricted range in the histogram to arrive at a stable and robust estimation of the true mean shape value for isolated stars. The initial restricted range corresponds -3sigma to +2sigma of the lower quartile, where s is the scatter in the "shape" value. In the first iteration we use an a priori determination of s. For each iteration thereafter, we set hard limits of +-2sigma. The final "shape" value corresponds to the median (50% central quartile) of the restricted histogram sample, and the s to the rms scatter or standard deviation of the population.

An example of stellar ridge line is given here. The plots show the median "shape" values (large triangles) along the scan. Extracted sources (including stars and galaxies) are denoted with small points. This is an example of good seeing conditions.

Width of the Point Spread Function


The radial shape of the PSF is roughly gaussian, and hence we may relate the alpha X beta "shape" (see above) to the standard FWHM. Here is an example of a Ks-band point spread function as derived from the Atlas or "coadd" image for a scan with good seeing: Measuring the FWHM width of stars from scans of a wide-variety of seeing, the relation to the "shape" is roughly: So for a "shape" value of 1.0 (see stellar ridgeline above), the corresponding FWHM is 3.2", representing a convolution of the atmospheric "seeing", camera optics, and the coadd resampling.

For a similar analysis of the "raw" (or "frame") PSF, see 2MASS Seeing and Image Shape Statistics.

The PSF and Small Galaxies

Extended sources are resolved down to diameters of ~10 arcsec. For these small galaxies, representing most of the catalog, the PSF is circularizing the nuclear and bulge light. The end result is that the axis ratio for small galaxies is systematically biased toward circular orientation. The user must take great care when interpreting the sizes and ellipticities of small galaxies, including the "effective" or half-light metric. Take for example the compact Seyfert galaxy, MRK 231. The half-light radius is floored at 2.5", corresponding to the PSF-circularized region of the radial profile. The axis ratio, and correspondingly the half-light radius, cannot be reliabily measured for a galaxy this small. The partial solution is to apply de-convolution techniques to attempt recovery of radial information within the PSF boundaries (see e.g., Masters et al., 2003, ApJ submitted).

[Last Updated: 2003 Feb 10; by Tom Jarrett]