Astron. Nachr. W(1988) 2, 121-131 zyxwvutsr Period search using the DMRT method: The properties of the test function I. L. ANDRONOV, Jena*) Universitats-Sternwarte Received 1987 February zyxwvutsrq 5 The test function for the method proposed by DUMONT, MORGULEFF, RUTILY, and TERZAN (1978) is investigated analytically and numerically for some examples with constant and variable periods. The properties of the test function of the DMRT method are discussed in comparison with that of the leastsquare method. Die Testfunktion fiir die von DUMONT, MORGULEFF, RUTILY und TERZAN (1978) vorgeschlagene Methode wurde anhand einiger Beispiele mit konstan- ten und veranderlichen Perioden untersucht. Die Eigenschaften der Testfunktion der DMRT-Methode werden im Vergleich zur Methode der kleinsten Quadrate erortert. zyxwvutsrqpon Key words: variable stars zyxwvutsrqp - period search 1. Introduction Many methods for the period search were proposed in the recent years. In the majority of them the whole sequence of observa- tions is used (e.g. LAFLER and KINMAN 1965, JURKEVICH 1971, PELJT 1975, DEEMING 1975, MARRAW and MUZZIO 1980,RENSON 1978, DWORETSKY 1983, ANDRONOV 1985, 1987). Moreover, some algorithms need equidistance in time observations (eg. auto- correlation analysis, see WEISKOPF et al. 1975). However, such methods cannot be practically used for the sure period deter- mination, if the signal shape and its amplitude underwent strong chadges during the time interval of the observations. The problem might become more correct, if not the whole curve, but only its characteristical points (eg. minima or maxima) are used for analysis. Until recent time only one method - least squares (LS) method - was mainly used to investigate the period and its changes (eg. TSESSEVICH 1970). In the Paper of DUMONT, MORGULEFF, RUTILY and TERZAN (1978, hereafter DMRT), a new method for the period search was proposed. In this article we investigate this method in comparison with the LS method and propose its modification to reduce the computational time. 2. Description of the methods It is common for all methods, that for a given “test period” P and fixed observations zyxw Si = zyx S(T,), i = 1 ... N, the value of the “test function” F(P; TI ... T,; S, ... S , ) might be computed. Here Ti are the moments of the observations and Si the corresponding values of the signal (eg. the bright- ness or the radial velocity of the variable star). If the test period differs significantly from the “true” one Po, one may see the fluctuations on the periodogram (the curve corresponding to the dependence F(P)). However, when Preaches Po the behaviour of F(P; Ti; Si) changes drastically and one may see a sharp extremum (maximum or minimum) at the periodogram. Its width corresponds to the accuracy of the period determination. The computation time strongly depends on the concrete type of the function F. Using only the moments of the characteristical points, one may strongly reduce the computation time. This “short” function F(P; Ti) is the case for both analysed methods - LS and DMRT. Mathematically one must determine the value of the period Po zyxwv E [Pmin, P,,,], which corresponds to the system of N equations: Ti = Mo + PoEi + p, , i = 1 ... N (1) where Ti are the used moments of time, Mo is the so-called “initial epoch”, Ei is the integer number (cycle number), and pi is the error of the time determination. In the LS method the values of Mo and Po correspond to the minimum value of One may see, that Mo is a very important point, connected with the cycle numeration. In some cases the value of Tl is used instead of M, for the first approximation. However, the accuracy of its determination can be worther compared with other values *) Guest investigator. Permanent address: Department of Astronomy of Odessa State University, T. G. Shevchenko Park, Odessa 270 zy 014 USSR.