Generating artificial light curves: revisited and updated

Abstract

The production of artificial light curves with known statistical and\nvariability properties is of great importance in astrophysics. Consolidating\nthe confidence levels during cross-correlation studies, understanding the\nartefacts induced by sampling irregularities, establishing detection limits for\nfuture observatories are just some of the applications of simulated data sets.\nCurrently, the widely used methodology of amplitude and phase randomisation is\nable to produce artificial light curves which have a given underlying power\nspectral density (PSD) but which are strictly Gaussian distributed. This\nrestriction is a significant limitation, since the majority of the light curves\ne.g. active galactic nuclei, X-ray binaries, gamma-ray bursts show strong\ndeviations from Gaussianity exhibiting `burst-like' events in their light\ncurves yielding long-tailed probability distribution functions (PDFs). In this\nstudy we propose a simple method which is able to precisely reproduce light\ncurves which match both the PSD and the PDF of either an observed light curve\nor a theoretical model. The PDF can be representative of either the parent\ndistribution or the actual distribution of the observed data, depending on the\nstudy to be conducted for a given source. The final artificial light curves\ncontain all of the statistical and variability properties of the observed\nsource or theoretical model i.e. same PDF and PSD, respectively. Within the\nframework of Reproducible Research, the code, together with the illustrative\nexample used in this manuscript, are both made publicly available in the form\nof an interactive Mathematica notebook.\n