Multiperiodicity, modulations and flip-flops in variable star light curves I. Carrier fit method

Context. The light curves of variable stars are commonly described using simple trigonometric models, that make use of the assumption that the model parameters are constant in time. This assumption, however, is often violated, and consequently, time series models with components that vary slowly in time are of great interest. Aims. In this paper we introduce a class of data analysis and visualization methods which can be applied in many different contexts of variable star research, for example spotted stars, variables showing the Blazhko effect, and the spin-down of rapid rotators. The methods proposed are of explorative type, and can be of significant aid when performing a more thorough data analysis and interpretation with a more conventional method. Methods. Our methods are based on a straightforward decomposition of the input time series into a fast "clocking" periodicity and smooth modulating curves. The fast frequency, referred to as the carrier frequency, can be obtained from earlier observations (for instance in the case of photometric data the period can be obtained from independently measured radial velocities), postulated using some simple physical principles (Keplerian rotation laws in accretion disks), or estimated from the data as a certain mean frequency. The smooth modulating curves are described by trigonometric polynomials or splines. The data approximation procedures are based on standard computational packages implementing simple or constrained least-squares fit -type algorithms. Results. Using both artificially generated data sets and observed data, we demonstrate the utility of the proposed methods. Our interest is mainly focused on cases where multiperiodicity, trends or abrupt changes take place in the variable star light curves. Conclusions. The presented examples show that the proposed methods significantly enrich the traditional toolbox for variable star researchers. Applications of the methods to solve problems of astrophysical interest will be presented in the next papers of the series.