This is a simple interface to the EBOP lightcurve model that is useful for finding starting parameters for a full lightcurve model fit with jktebop.


Instructions for use

The lightcurve model is based on the EBOP code written by Paul B Etzel. You should cite Popper & Etzel (1981AJ.....86..102P) and Etzel (1981psbs.conf..111E) for EBOP. The following subset of parameters from the lightcurve model available to the user. (Star 1 is the star eclipsed at phase 0).

Surface brightness ratio
Surface brightness at the centre of the stellar disc for star 2 compared to star 1. The surface brightness is related to the effective temperature of the star.
Sum of fractional radii
(R1+R2)/a where R 1,2  are the radii of the stars and a is the semi-major axis of the orbit. For a circular orbit, a is the separation of the stars.
Ratio of the radii
Angle between the normal to the orbital plane and the line of sight in degrees, i.e., i=90 for an edge-on orbit.
e.cos(ω), e.sin(ω)
The eccentricity of the orbit is given by e (=0 for a circular orbit). The orientation of an eccentric orbit is given by the angle ω (longitude of periastron). Rather than using these parameters in the lightcurve model, we use e.cos(ω), e.sin(ω) because these are directly related to the phase and width of the secondary eclipse compared to the primary eclipse, respectively.

In addition, the program will automatically adjust the mean magnitude of the lightcurve and apply a phase shift to produce the best match to the observed lightcurve. There are a few other parameters that have a small effect on the lightcurve model so they are hidden from the user, e.g., limb darkening is fixed at 0.5 for both stars.

The program starts by prompting the user for the input file of the data to be fitted and some parameters used to model and display the data, e.g., the width of the eclipses. The input file is a text file with three columns containing the time of observation, the observed magnitude and its standard error. The program produces two output text files, a fit file that repeats the input data plus an extra column with the lightcurve model, and a model file that contains the lightcurve model tabulated as a function of phase.

The user is then prompted for the lightcurve model parameters. The data and model for these parameters is displayed on the selected PGPLOT device and the prompt Re-try? appears on the command line. The user should reply Yes to this prompt (or just hit return) and try new lightcurve parameters until the model lightcurve gives a reasonable match to the observed lightcurve. The default value for the parameters is the last value entered, so the user only needs to enter the new value for parameters to be adjusted, for unchanged parameters
the user can hit return at the prompt.

Once the user has a reasonable match to the observed lightcurve they enter "N" at the Re-try? prompt. The program then uses the Numerical Recipes amoeba implementation of the simplex algorithm to optimize the fit the observed lightcurve (this can take some time). The new values of the lightcurve parameters and the χ2 value for the fit are reported and the new fit displayed. The user is then prompted with Re-fit?, which enables them to repeat the process of entering parameters and re-fitting. Otherwise, the fit can be re-plotted to a new pgplot device (e.g., a postscript file), and the program then ends.

Dr Pierre Maxted
Last updated 30 Sep 2011