The object of this task is to simulate the 2-D profiles of stars as they would look on real 2MASS/Protocam frames.
From the Protocam data, we know that stellar profiles have a shape that is something between a gaussian and lorentzian profile; i.e.,
Preliminary results indicate that a lorentzian profile is adequate for these simulations. The first figure shows radial profiles of four PSFs. Figure 1a has the profile for a PSF determined from data taken on the night of 6/1/94. Figures 1b-d show the profile determined by Kamphot for model lorentzian stars, in a field of moderate (b=25) density, with ``seeings'' (FWHM) of 1.5, 2.0, and 2.5 arcseconds, respectively. The model most consistent with the 6/1/94 data is the FWHM = 2.0 arcsec profile. The error bars represent the 1- deviation spread in the radial profile values; this effect is due to the undersampling of the true PSF. We adopt the lorenzian probability distribution for our stellar 2-D profile simulations.
Figure 1: Radial profiles of the PSF extracted from real and simulated data.
Stars have a brightness distribution (luminosity function) described by a power law:
where the power coefficient is a function of the galactic position (l,b), with typical values between 0.3 and 0.33. The LF power law coefficient and the stellar number density are taken from the starcount models of Jarrett (1992); see Table 1.
The total number of stars in a field (frame or set of frames) is simply
where area is the field area in degrees and density is the total number of stars brighter than K per square degree. Figure 2 shows the cumulative K-band star counts predicted for a field toward the NGP (b=90). The filled circles and filled squares represent starcount values for real data, 2MASS/Protocamera and Elias (1978).
Figure 2: Cumulative K-band starcounts predicted toward NGP.
The stars are positioned randomly on a 256X256 frame with a brightness as described above. We build the stars with a lorentzian profile function, with a width (FWHM) given by the input ``seeing" disk. Poisson noise in the form of background counts and background variations, as well as gaussian noise in the form of read noise, are chosen to match closely those of the protocamera data (June '94). For sub-pixel response, we include ``dead zone" regions of the pixel: center of pixel of radius = 0.075, and border of pixel of width 0.075. These values were determined empirically in the lab by M. Skrutskie. There is a probable large uncertainty in this value.
In-scan offsetting is applied to each frame. The typical inscan offset is 42 pixels; thus, six frames would completely cover a specific region of the sky. Sub-pixel dithering is also included in order to simulate the slight rotation angle of the array with respect to the scanning direction. For example, the total frame to frame default (nominal) offsets are shown in Table 2.