An O−C (and light travel time) method suitable for application to large photometric databases

Abstract

The standard method of studying period changes in variable stars is to study the timing residuals or O−C values of light-curve maxima or minima. The advent of photometric surveys for variability, covering large parts of the sky and stretching over years, has made available measurementsofprobablyhundredsofthousandsofvariablestars,observedatrandomphases. Simple methodology is described which can be used to quickly check such measurements of a star for indications of period changes. Effectively, the low-frequency periodogram of a first-order estimate of the O−C function is calculated. In the case of light travel time (LTT) effects, the projected orbital amplitude follows by robust regression of a sinusoid on the O−C. The results can be used as input into a full non-linear least-squares regression directly on the observations. Extensive simulations of LTT configurations are used to explore the sensitivity of results to various parameter values (period of the variable star and signal to noise of measurements; orbital period and amplitude; number and time baseline of observations). The methodology is applied to observations of three previously studied stars.