Persistency Checking of Gaussians

Newsletter #12
March 5, 2002

Persistency Checking of Gaussians
Steve Fulton

Thus far, approximately 20 million distinct Gaussians have passed data integrity testing. For these signals we standardized the score such that there were on average an equal number of Gaussians in each workunit group with scores greater than or equal to 1.0. (See "An Explanation of Score Correction" below for details.) This standardization left 1.25 million Gaussians of interest to be examined further.

From these signals we then determine which Gaussians have been detected in the same location of the sky on multiple occasions. This process is called persistency checking. For our first pass through the data, we performed an analysis with very restrictive bounds on matches. Gaussians were considered matches if they conformed to the following criteria:

Their detection location matched within 10 arc minutes of right ascension (RA) and declination (DEC).
Their barycentric frequencies matched within 125 Hz
Their detections were at least 900 seconds apart

The right ascension and declination restrictions approximate the beam size at Arecibo. Barycentric frequency is used to correct for the Doppler effects caused by Earth's rotation and its orbit around the sun. The barycentric frequency divergence across a beam at Arecibo is approximately 125Hz. The final bounds on the time remove the possibility of detecting multiple images of the Gaussian from a single observation.

1,397 multiplets (multiply-detected Gaussians) meet the above criteria. Future analyses will identify the best candidates from this group.

An Explanation of Score Correction

The SETI@home feed at Arecibo moves at varying rates as the opposing feed tracks objects in the sky. At faster rates, the SETI@home client obtains fewer points over a fixed angular separation. With fewer data points false detections are more likely, and hence the client detects more Gaussians and higher scoring Gaussians as the rate of telescopic movement increases. (See Figure 1, where (uncorrected) Gaussian score is on the y-axis and the width of the Gaussian (sigma) is on the x-axis.) This slew-rate detection dependence creates problems when looking for persistent signals. Persistency detection assumes that there is an equal chance of detecting a Gaussian each time the telescope passes a given point in the sky; the analysis uses this assumption to rank persistent multiplets and reject temporal rfi. To fix the problem, we corrected the factors used to calculate score such that the number of signals in a workunit group with significant scores is constant across slew rate.

Figure 1 (click to enlarge)

Figure 2 (click to enlarge)

Statistically, the score of a Gaussian is defined as the peak-power/chi-square. The chi-square is a measure of the Gaussian's fit (i.e., how well the signal matches a classic Gaussian curve, with a lower score representing a better fit). Since both the peak-power and chi-square terms reported back by the client were dependent on the telescope slew rate, a simple correction function was needed for each of the terms. The resulting "flattened" peak power and chi-square were used to define the new (corrected) score (Figure 2). (Note that the Y-axis in Figure 2 is mislabelled--instead of "Score uncorrected", it should read "Score corrected".)

The normalization was set so that on average each workunit group would have 4 Gaussians with a score 1.0 or greater. This score approximates a chi_square cutoff of 8.8 (uncorrected) at low slew rates, which is the threshold used by the client.