Allen Keel
Summer Research Student
Center of Excellence in Information Systems
(1 Aug 2000)

Our first interest in this investigation was to approximate the sensitivity of the guide camera in the automatic spectroscopic telescope (AST). To estimate its sensitivity, we used images of the sky (Orion) that Mike Williamson had taken with a 25-mm, f/1.4 (D=0.7 in.) camera lens. The cutoff stellar magnitude for the faintness stars in these images was measured in order to estimate the faintness limit of the images to be captured by the AST. 8-second, 4-second, 2-second, and 0.5-second exposures of the Orion constellation were optimized with a photo editor and subsequently compared with the same field from the Megastar database. The Megastar software contains a graphical catalog and pertinent information (namely the stellar magnitude) of stars and other cosmic bodies, which can be located by field coordinates. Using the Megastar program, the faint limit on the magnitude filter was altered until a reasonable match was found. The resulting limiting V-magnitude was recorded to be used later in calculations to determine the faintest stellar magnitude that can be detected on the AST's images. Results are as follows: for the 8-sec exposure (Figure 1.1), V = 7.5 - 8.0; for the 2-sec exposure, V = ~7.5; for the 0.5-sec exposure (Figure 1.2), V = 4 - 4.5.

Figure 1.1 (8-second exposure)

Figure 1.2 (1/2-second exposure)

The exposure time in an image will be proportional to the flux per diode (pixel) in the camera. This is simply proportional to the area of the aperture divided by the number of pixels in the image. For the telescope, the images will be of the order of 1 arcsecond, which we can scale to the camera (0.5 in. corresponds to 500 pixels or 3 arminutes, giving 3 pixels/sec). The camera lens, to first order, is diffraction limited, so its image is (~10 arcsec in size. This corresponds to 1.25 microns, which is much smaller than one pixel of this camera. The camera’s image will thus cover at least one pixel. So the area of the telescope is (80/0.7)2 = 13,060 times that of the lens, but the image is (3/1)2 = 9 times as large. Therefore, by calculating the ratio between the estimated flux per pixel for the systems, the flux will be 1450 times (logarithmic equivalent is 7.9 mag) as great. This gives a limiting magnitude of V = 15.7 for the 8-sec exposure with the telescope, or about 12.5 for a 0.5-sec exposure.

Given these expected limiting magnitudes, we then took two approaches to determine the availability of potential guidestars within random star fields. The first approach involved the investigation of random star fields around the sky, and the second approach used previously identified fields containing a program star, usually of a bright stellar magnitude, thus making those particular star fields easier targets for the AST to locate.

First, random fields were investigated to find the median brightness magnitude of a star in a random 4 min. x 4 min. field, which is somewhat bigger than the field of view of the telescope. We chose a grid of positions to give roughly even coverage over the sky sampled by the Palomer Sky Survey (PSS) (declinations at –33 degrees, 0 degrees, +33 degrees, +48 degrees, and +60 degrees were the ones of interest, with right ascensions at all integral hour angles from 0 to 23). We then printed images of these star fields, taken from the STScI digitized PSS. The two brightest stars in each field were recorded by identifying them with the Megastar program, and an absence of a star in the Megastar database was designated a negligible 18^th magnitude brightness. Unfortunately, the accuracy of the results was compromised by the incompleteness of the Megastar catalog. The resulting histogram (Figure 2.1) for the random fields showed a roughly bell-shaped distribution, with the exception a sharp skew caused by a heavy concentration of brightnesses in the 18^th magnitude. The median average stellar magnitude, determined by locating the 50^th percentile in the cumulative distribution, was roughly 14. According to the histogram, for a 0.5-sec exposure, roughly 21% of randomly selected fields will have at least one star bright enough for guiding, and between 65-78% for both an 8-sec and 2-sec exposure.

Figure 2.1

Next, designated fields containing known program stars, which are generally bright enough to observe with the AST, were investigated in order to identify any potential guidestars nearby program stars. These stars were program stars for Greg Henry’s precision photometry of Sun-like stars. Using HD numbers, sky survey coordinates for the program stars were found within 3 min. x 3min. fields, which is approximately the actual scope of the telescope. Stellar magnitudes for the two brightest stars in each field were recorded from the Megastar database. The resulting distribution was sharply skewed to the left, and the median brightness was of the 16^th magnitude. A separate distribution included only the brightest star in each field produced a significantly different histogram. The shape of the "1 star/field" distribution (Figure 2.2) was considerably more symmetric than the "2 stars/field" distribution (Figure 2.3), and the median dropped down to an interval between the 14^th and 15^th magnitudes. For the "1 star/field" case, about 12% of the program star fields will have a minimum of one star above the limiting magnitude for a 0.5-sec exposure, and between 65-75% for both an 8-sec and 2-sec exposure. However, only 7% of the fields in the "2 star/field" distribution will include one star bright enough to use as a guidestar for a 0.5-sec exposure, and from 48% to 56% for both an 8-sec and 2-sec exposure.

Figure 2.2

Figure 2.3