Page author: TJR Last edit: 2016-03-19

Southern Eclipsing Binaries Project

Investigating Period Change

This is an astrophysically important, yet relatively simple, analysis you can make of the minima you’ve recorded in the Minima Analysis Form for your target system. Add to your form minima you find in the literature, to give (hopefully) a reasonable coverage since the time of discovery. Enter them in increasing HJD order. The best sources for minima can be obtained through the AAVSO VSX portal, under References (try Bob Nelson’s O-C files), and also External Links for your target system. Try O-C Gateway, Atlas of O-C Diagrams, ADS Biblio, and SIMBAD. If you come up with nothing much except the discovery light elements - which is common enough - your minima become very important for future period change work. Incidentally you may find your period disagrees quite a bit from the discovery period. That’s quite common - discoveries were often made from patrol photographic plates way back when. It need not indicate period change so much as a poorly measured period. That’s for you to judge! In your Minima Analysis Form, the “active” set of light elements automatically fill in most columns in the table except for your minima entries. What matters now are the columns for orbital cycle number and the (O-C) value (expressed in days) and its uncertainty. (O-C) is simply the difference between your (or another’s) Observed minimum, and that Calculated by the active light elements. Now simply construct an Excel scatter plot of (O-C) against cycle number. The result is called an O-C diagram. If the plot is sensibly linear, the binary has a constant period. If it’s horizontal, the period P in the active LE set is correct; if it slopes upward the calculated P is a bit too short - the slope is the correction to apply to P. Fiddle to find the correct P. Things get interesting if the plot is not linear. It can have a sudden change of slope from one linear slope to another, indicating a sudden change of period. Fiddle with your light elements on each straight-line part get it horizontal - then you have its period. Frequently though, the plot is parabolic, indicating a constant rate of change in P. If the parabola is open upwards, P is increasing linearly, conversely if open downwards. A discussion of how to derive from your parabolic (O-C) curve the quadratic light elements describing the period change is beyond this simple introduction, but is not tricky. Here is an article on deriving quadratic light elements from period change measures. This O-C diagram (from H. Dreschel et al, A & A 110, 246, reproduced in R.W. Hilditch, Introduction to Close Binary Stars, Cambridge 2001) demonstrates period decrease in the EB binary SV Cen over a 30- year period. The authors fitted a parabola to the (O- C) data, indicating a constant period decrease. But arguably these data points could have been fitted by two straight lines, signalling a sudden period change around cycle 0. More minima after cycle 1000 would resolve the ambiguity - showing the importance of continuous long-term minima measurements.

Reporting

If you’re the first to detect period change, it’s certainly worth a paper, along with your minima and light elements. If it’s already recorded, does your data fit in? Keep on getting minima every year and recording them in the Dropbox ‘Minima & LEs ’ spreadsheet.

Forging Ahead

If you have filtered magnitude data, move on to getting a phased light curve. Otherwise, start again on another target.