for a given feature in respect to the reference feature is given by
Next: A Reduction and Analysis Pipeline for ROSAT PSPC Data
Previous: Detection of Variable Sources
Table of Contents --- Search ---
PS reprint
L. Kogan
National Radio Astronomy Observatory,1 Socorro, NM 87801
1The National Radio Astronomy Observatory is a facility of the National Science Foundation, operated under cooperative agreement by Associated Universities, Inc.
Astrophysical masers often have spatial structures containing a number of well separated, compact features at each frequency. Interferometric observations of such structures produce fringe rate spectra with multiple peaks.
The fringe rate mapping method uses the fact that the fringe rate offset for a given feature in respect to the reference feature is given by
where u and v are the projected baseline components in
Equation (1) describes a straight line, along which the
emission corresponding to the measured 
must be located. If
there is only one feature (in space, and therefore in the fringe rate
spectrum) at the given velocity then we can determine its position by
measuring 
at different baselines and finding the
intersection of the relevant straight lines.
If there are multiple features in the same frequency channel several fringe rate peaks will be seen on each baseline. This will result in a set of parallel lines in the fringe rate map. The positions of the features in this case can be found using a criterion of maximum density of the lines crossing a given area. Some years ago, simple software for fringe rate mapping was developed for small databases by Giuffrida (1977) and Walker (1981).
Figure 1: A fringe rate spectrum.
Figure 1: PS 23 Kb
A new task FRMAP installed in the NRAO Astronomical Image Processing System ( AIPS) works in a wide range of baselines, time intervals, and frequency channels. The task estimates the fringe rates at the beginning and then creates the image itself. A new algorithm for fringe rate estimation has been developed. This algorithm reaches the best accuracy allowed by the data, and can eliminate erroneous peaks appearing in the fringe rate spectra as a result of the convolution of the true spectrum with the window function. Such peaks with a rather large amplitude occur at some frequencies due to the lack of data in some time intervals.
Figure 1 shows a fringe rate spectrum demonstrating 13 peaks of which 10 are definitely spurious. Evidently these 10 peaks are due to the convolution of the true peaks with the Fourier transform of the window function. The new algorithm works in three steps:
Figure 2: A fringe rate map. Four features are clearly seen.
Figure 2: PS 6 Kb
For the data displayed in Figure 1, the second stage rejects erroneous peaks and leaves only three features. At this stage, their frequencies are determined with the accuracy of 0.1 FFT step. The third stage of the algorithm (non linear least squares) yields more accurate values of the frequencies, amplitudes, and phases of the found three components achieving the accuracy which the data allow.
According to the mapping algorithm, the search window is divided into many small rectangles. The rectangles crossed by a number of lines exceeding the given threshold are selected. If the selected rectangles organize clusters the program selects the rectangle with the maximum number of intersections. The fringe rate straight lines can also be displayed on the screen or printed for visual inspection. Figure 2 shows an example of such a fringe rate map. The found coordinates of the features in RA and DEC altogether with their estimated fluxes are printed into a file.
The task is very useful for preliminary determination of source locations followed by the use of the CLEAN procedure in smaller windows near the determined locations.
The author is grateful to P. Diamond for initiating this work, and for helpful discussions during its course.
Walker, R. C. 1981, AJ, 86, 1323
