# Determining the Time of Minimum

This is one step that is unique to observing eclipsing binaries.  Once you're taken images of the star field through an eclipse, and produced a time series of V-C magnitudes (and C-K to ensure quality), you must now determine the mid-time of the eclipse.  If your data is of good quality, and the star is not badly spotted, the time series will be symmetric around the midpoint of the eclipse.  Most algorithms for determining the ToM assume this is so.  They numerically "fold" the time series around a hypothesized midpoint, and compute how well the ingress and egress legs match.  The algorithm will do this for many hypothesized midpoints, and choose the one that minimizes mismatch between the two legs.

There are a number of software packages that will do this for you (see Software Resources page for links):

• AVE is a free package that can determine ToMs, and do some period analysis.  The menus are in Spanish, but this doesn't present much difficulty.
• minima25 by Bob Nelson is also free.  It computes ToMs using several methods that can be compared.
• Peranso is a shareware program (with a free trial period) that computes ToMs and performs many other useful data analysis functions.  Ensure you update to the latest version, as versions prior to 2.50 sometimes produced erroneous ToMs.

All of the above run on the Microsoft Windows platform.  AAVSO's analysis program VStar, which is Java-based and platform independent, does not presently include a time of minimum determination method.

Once you have derived a ToM, it is very instructive, and recommended for checking purposes, that you time-reverse your data series (reflect it around the ToM) and overplot the forward and reversed versions.  Do this by making a new forward time value of JDfwd=JD-ToM, and a reversed time value of JDrev=ToM-JD axis.  Plot each magnitude against JDfwd and JDrev, on the same graph.  If the forward and reverse versions do not match, you should investigate.  This could be caused by, e.g., unfiltered observation using a comparison star that is of substantially different colour than your eclipsing star, observed through greatly changing airmass.  Of course, you observation will be flagged as unfiltered, offering a warning to data users.

Sometimes stars have extensive transient starspots (like giant sunspots!) that cause the ingress and egress legs of a light curve to differ.  In such a case there is nothing wrong with your photometry, but the determined ToM partially reflects other astrophysical phenomena, not just the geometric eclipse time.

Whatever program you use, it should report an uncertainty value, not just the time.  By plotting your data time reversed, you may also wish to assess whether you think the reported uncertainty is appropriate.  Sometimes the uncertainties reported by the KvW algorithm seem too small and it may be reasonable to report a slightly larger uncertainty.