Hipparcos Tycho catalog: surface density

Sloan Digital Sky Survey Telescope Technical Note 19970901

Contents

• Introduction
• Tycho catalog surface density
• Conclusions

Introduction

Astrometric calibration of the Sloan Digital Sky Survey (SDSS) will be based on the ACT Reference Catalog of the U.S. Naval Observatory. This catalog provides improved proper motions for the Hipparcos Tycho catalog using data from the photographic plate based AC 2000 catalog. The ACT contains 93% of the Tycho catalog stars.

Below a certain frequency, telescope tracking errors are expected to be measured and removed using the ACT catalog. The lower the surface density of these stars on the sky, the more stringent the requirement on telescope tracking error to avoid degrading the astrometric accuracy of the SDSS. Consequently, it is useful to know the surface density distribution of Tycho stars. For this purpose, catalog entries for stars within 12°x6° region centered at 12h 20m right ascension and 33° declination were examined. This region includes the north galactic pole and the center of the northern survey. Stars brighter than V = 8.5 were excluded since they are likely to saturate the astrometric CCDs.

Tycho catalog surface density

In Figure 1, the distribution in Johnson V magnitude of all Tycho catalog entries for stars within 12°x6° region centered at 12h 20m right ascension and 33° declination is plotted. About 91% of the stars are fainter than the V = 8.5 astrometric CCD saturation limit. The parallax for these stars is plotted in Figure 2. A negative parallax can occur when the measurement error is larger than the parallax.The distribution of these stars on the sky is plotted in Figure 3. As one might expect, clumps and holes are apparent.

The region between 180° and 190° right ascension and 30° and 35° declination (50 sq. deg.) was arbitrarily divided into fifty rectangles 0.4° right ascension by 2.5° declination. (Lines of constant right ascension are not parallel so these are only approximately rectangles. This is ignored in the following discussion. Its effect is to underestimate the surface densities by a bit under 20%.) Such a 1 sq. deg. rectangle is scanned by the leading or trailing astrometric array every 1.6 minutes of time. The number of catalog entries in each rectangle was counted (Figure 4). The mean surface density is 7.8 per sq. deg. and the standard deviation is 2.9 per sq. deg. The minimum count was 1 and the maximum count was 15. Rebinning the same data into forty-eight overlapping 0.8° x 2.5° rectangles gives a mean of 7.8 per sq. deg., a standard deviation of 2.2 per sq. deg., a minimum count of 4 and a maximum of 24. These data are adequately described by a normal distribution and have a standard deviation of root(N), i.e., they are consistent with shot noise.

Figure 1: Distribution of magnitude in Johnson V. This is for the 510 stars from the Tycho catalog in a 12°x6° area in the center of the northern survey region.

Figure 2: Distribution of parallax. This is for the 462 stars from the Tycho catalog in a 12°x6° area in the center of the northern survey region that are fainter than V = 8.5.

Figure 3: Locations of Tycho catalog stars. This is for the 462 stars from the Tycho catalog in a 12°x6° area in the center of the northern survey region that are fainter than V = 8.5.

Figure 4: Surface density distribution. This is a histogram of the number of stars in each of fifty 0.4° x 2.5° rectangles that tile 180° to 190° right ascension and 30° to 35° declination.

Conclusions:

The Tycho catalog has a mean surface density of 7.8 per sq. deg. in a 50 sq. deg. region at the north galactic pole. Correcting for the cosine of the declination, the density is 9.3 per sq. deg. This is not significantly different than the 10 per sq. deg. quoted in the SDSS NASA proposal (the black book). The number of stars in fifty 1 sq. deg. rectangles (0.4° right ascension by 2.5° declination and corresponding to a drift scan interval of 1.6 minutes) varies from 1 to 15 per rectangle. The distribution is gaussian and the standard deviation is consistent with shot noise, i.e., root(N).

Date created: 09/01/97
Last modified: 01/26/98
Copyright © 1997, 1998, Walter A. Siegmund
Walter A. Siegmund