by Patrick Wils (email: | ) |

A lot of the principles mentioned in the following sections are applicable not only to the NSVS database, but to other surveys as well. Note that the condition for the standard deviation to be higher than average will not be used here. Only specific properties of the magnitude distribution will be used to find eclipsing binaries.

*EA _{1}* = (

The value of 2 was chosen so that it includes the large majority of eclipsing binaries and excludes a large fraction of other variable star types. A plot for this statistic against median magnitude is given in Fig. 2.

*γ _{1}* >= 0.8

This excludes some EW type eclipsing binaries, but since systematic searches have already been done for those, the number of stars of this type left undiscovered may be small.

*MSSD* <= 0.75

Note that this might exclude a number of eclipsing binaries with a period very close to (an integer fraction of) one (sidereal) day.
Taking observations exactly one day apart might mimick the behaviour of a long period (eclipsing) variable,
see UW Boo with a period of 1.0047108 days for an example
(note that UW Boo *does* satisfy the above condition).

Stars not satisfying the *MSSD* condition, and certainly those with *MSSD* >= 0.9, will very likely be long period variables,
as is the case for XY Cam.

*EA _{2}* = standard deviation faint points/standard deviation bright points >= 2

Fig. 3 shows how this statistic is related to median magnitude.

*EA _{3}* >= 0.8

perl nsvsstats.pl NNNX >NNNX.txt

with NNNX the NSVS field name. The zipped NSVS data file should be in the current directory.

Knowledge of Perl is not required to use this script, only a Perl runtime is needed, e.g. ActivePerl provided by ActiveState for a number of operating systems.
The output of the script is a tab delimited list of NSVS identification numbers and the following statistics on magnitude:
maximum, average, minimum, number, 2nd percentile, median, 98th percentile, standard deviation, skewness, kurtosis,
mean of successive squared differences, and the three *EA _{i}* indexes defined above.
The data are filtered on the flags (mask = 15636) described in Wils et al. (2006),
and only objects with 50 or more data points are listed.
Standard spreadsheet programs can then be used to filter the objects.
Note that these statistics are not only useful for finding eclipsing binaries, but may be used for other purposes as well.

The script nsvsstats.pl will use the binary file "Skydot-Frames.bin" to create tab delimited data files for each of the objects satisfying the conditions determined in the previous section. These data files are called NSVSxxx.dat with "xxx" the NSVS id of the object. They contain lines with HJD - 2450000, the magnitude, the uncertainty on the magnitude and the flag values for the object in question. Those files may then be used by period determination software.

For EA type eclipsing binaries however the usual period search methods may regularly fail. It is often the case that most observations are made near maximum with little scatter. Only a few faint points are available, with large periods in between. Most of the information is therefore in the times of minimum, not necessarily in the magnitudes. Using a trial period, an integer number of cycles between the times of minimum can be determined and a least squares fit done to improve that period. This can be repeated for a number of trial periods, the best periods selected and verified in a phase plot with all the data.

To facilitate searches based on the above method, the Excel workbook OCEASE.xls was developed. Here is how it works (see Fig. 5): Fill in the list of minima in the A column of the "Calculate" sheet. Make sure there are at least three times of minimum and that no two lines refer to the same minimum. Put the smallest period you want to test in cell E2 and the largest one in E7 (or leave the latter blank for testing the largest possible period). Cell E6 contains the number of minima per cycle (either 1 or 2). Generally keep it equal to 1, so that for e.g. in the case of EW variables half the real period will be found (remember to set the period limits accordingly). Don't change other cells, and press the "Calculate" button. It will test all possible cycle counts (least squares fitting) over the entire timespan. When it has finished, the best period found is shown in E4, the epoch in E3.

The other worksheet needs to contain the data for a star. The plot on the "Calculate" sheet is based on these data points. It gives a phase diagram, based on the period found. Copy the HJD values to the A column and magnitudes to column B of the "Data" sheet (this may be done with one "Select All/Copy/Paste" action from the object data files; the uncertainties will be copied to column C; don't forget to remove extra lines with data from a previous object). Make sure the phases are calculated in columns E and F for each of the points (drag the contents to the last data line if necessary).

The "Data" sheet can be used to determine the times of eclipse as well. Just sort the data in reverse order according to magnitude and select the times of the faintest points for copy in column A of the Calculate worksheet. Remove the times corresponding to the same eclipse as a previous line (e.g. data points from the same night).

With the phase plot, it is easy to see whether the period found is correct. Since the calculated period is based only on times of minimum, not on all the data, it is quite possible that the phase plot shows points at maximum near phase 0. This means that the period found is not correct, possibly too short (doubling the period might give a better result in these cases; a quick check can be done by halving the cycle count in cell D4). Therefore, after the calculation, all other periods tested are provided in the H, I and J columns with respectively the period, the sum of squared deviations (= SSD), and the cycle count over the total timespan. These are sorted in order of increasing SSD. So after the calculation, the period in E4 will be a copy of H1, the cycle count in D4 a copy of J1, and the SSD in E5 a copy of I1. If the first period is not good, try one of the others by copying one of the cycle counts from the J column into D4, or retry the calculation with other minimum and maximum limits for the period. It may also be necessary to choose a different set of times of minimum. Indeed some points may be erroneous or may be from an eccentrically placed secondary minimum. The latter may not be treated very well by the above procedure. In some cases combining the data with those from "synonyms" of the object (the same star but observed in another NSVS field and therefore with another NSVS number) may help in finding the period or improve it.

The table of new eclipsing binaries contains the NSVS id (with a hyperlink to the source data), the position for equinox 2000, the NSVS field, maximum and minimum magnitude (actually the 2nd and 98th percentile), an epoch of minimum (HJD - 2450000), the period and a phase plot. The real period may be double or halve the value given in the table. The stars 2191928, 2224071, 2226910 and 2282774 are eccentric eclipsing binaries.