R.W. Clay , B.R.Dawson , L. Kewley , M. Johnston-Hollitt, PASA, 17 (3), 207.
Next Section: Application to the SUGAR
Title/Abstract Page: The Two Point Angular
Previous Section: Cosmic Ray Directions and
The Two Point Angular Autocorrelation Function
The two point angular autocorrelation function has been described by Peebles (1980). It involves the analysis of an ensemble of data points with known angular locations. The two point angular autocorrelation function is then the joint probability of finding an object in both of two elements of solid angle placed at an angular separation of as a function of . In practice, the probability can be found by comparing the number of ensemble pairs having a particular separation (in a given separation interval) with the number derived for a random ensemble which contains the same number of directions. We can express the function (w) and its uncertainty (dw derived from a consideration of Poisson statistical uncertainties) through the ratio of the number found in the experimental data to the number in the random data (at a particular angular separation and within an angular range) minus one. A positive value at small angular separations indicates a clustering of the data points.
A significant observational difficulty in applying this procedure is in determining a suitable random dataset for the comparison data. The experimental dataset may contain clustering information but it will also contain the effects of non-uniformity of sky coverage, which might have changed over the period of the data acquisition.
In order to determine the function for our complete catalogue of SUGAR data, we created a randomised SUGAR dataset through a procedure which shuffled components of the real SUGAR data. The SUGAR dataset available to us did not contain the altitude and azimuth of the events. We determined these from the event times and the celestial coordinates of the event arrival directions. A new dataset was then generated using randomly chosen Julian dates for the events from the ensemble of dates within the real catalogue. The catalogue was then used to assign horizontal coordinates for each of these events and corresponding celestial coordinates derived as though events from those directions had been observed at the randomly selected Julian dates. In this way, the new ensemble contained the real on-time properties of the array and it also contained the altitude and azimuthal properties of the array. In each case for our analysis of a subset of SUGAR events, we generated 1000 shuffled datasets so that it was possible to determine the number of real events with a particlar angular separation together with the chance probability that such a number would have been exceeded (the number of times the random sets gave a larger value divided by 1000, the number of random trials).
Angular |
|
| number |
interval | |||
0-5 | 8.4 | 14.2 | 278 |
5-10 | -5.3 | 8.0 | 670 |
10-15 | 8.0 | 6.5 | 161 |
15-20 | -7.3 | 5.2 | 830 |
20-25 | 6.8 | 5.0 | 148 |
25-30 | 3.5 | 4. 5 | 255 |
30-35 | -0.7 | 4.1 | 541 |
35-40 | -1.5 | 3.9 | 600 |
40-45 | 5.9 | 3.9 | 122 |
45-50 | -3.6 | 3.6 | 747 |
50-55 | -1.9 | 3.6 | 654 |
55-60 | 3.0 | 3.6 | 259 |
60-65 | -8.5 | 3.3 | 957 |
65-70 | -3.0 | 3.5 | 732 |
70-75 | 2.5 | 3.6 | 286 |
75-80 | -1.4 | 3.5 | 590 |
80-85 | 5.3 | 3.7 | 131 |
85-90 | -7.2 | 3.6 | 937 |
90-95 | -4.6 | 3.7 | 812 |
95-100 | 1.6 | 3.9 | 369 |
100-105 | 2.9 | 4.0 | 297 |
Angular |
|
| number |
interval | |||
0-5 | -47.9 | 14.2 | 766 |
5-10 | 6.0 | 22.6 | 357 |
10-15 | 25.8 | 18.2 | 109 |
15-20 | 9.9 | 14.7 | 253 |
20-25 | -5.2 | 12.2 | 569 |
25-30 | 5.4 | 11.9 | 333 |
30-35 | 17.9 | 11.8 | 105 |
35-40 | -20.3 | 9.3 | 908 |
40-45 | 4.9 | 10.2 | 339 |
45-50 | 1.1 | 9.9 | 432 |
50-55 | -14.1 | 9.0 | 837 |
55-60 | -22.3 | 8.4 | 952 |
60-65 | -14.2 | 8.9 | 851 |
65-70 | -27.0 | 8.1 | 978 |
70-75 | 7.1 | 9.9 | 263 |
75-80 | 20.7 | 10.6 | 43 |
80-85 | 11.0 | 10.0 | 183 |
85-90 | 14.5 | 10.5 | 118 |
90-95 | -5.7 | 9.6 | 635 |
95-100 | 10.7 | 10.7 | 200 |
100-105 | -3.2 | 10.3 | 553 |
Angular |
|
| number |
interval | |||
0-5 | -100 | undef. | 585 |
5-10 | 86.4 | 59.0 | 47 |
10-15 | 22.3 | 35.3 | 212 |
15-20 | 24.6 | 31.1 | 182 |
20-25 | 39.7 | 29.8 | 100 |
25-30 | 24.6 | 25.4 | 165 |
30-35 | 10.8 | 22.6 | 180 |
35-40 | -40.1 | 16.0 | 910 |
40-45 | 2.9 | 20.2 | 371 |
45-50 | -37.3 | 15.7 | 896 |
50-55 | -3.2 | 15.7 | 884 |
55-60 | -29.3 | 15.8 | 851 |
60-65 | -27.3 | 16.2 | 816 |
65-70 | -22.0 | 16.6 | 757 |
70-75 | -14.0 | 17.5 | 642 |
75-80 | 22.4 | 21.0 | 160 |
80-85 | 18.1 | 20.9 | 209 |
85-90 | 23.8 | 22.6 | 151 |
90-95 | 2.6 | 20.9 | 387 |
95-100 | 78.4 | 28.2 | 1 |
100-105 | -1.8 | 22.0 | 433 |
Next Section: Application to the SUGAR
Title/Abstract Page: The Two Point Angular
Previous Section: Cosmic Ray Directions and
© Copyright Astronomical Society of Australia 1997