Optical Variability In Quasars: Scalings With Black Hole Mass And Eddington Ratio Depend On The Observed Time-Scales

ABSTRACT Quasars emission is highly variable, and this variability gives us clues to understand the accretion process onto supermassive black holes. We can expect variability properties to correlate with the main physical properties of the accreting black hole, i.e. its mass and accretion rate. It has been established that the relative amplitude of variability anticorrelates with the accretion rate. The dependence of the variance on black hole mass has remained elusive, and contradicting results, including positive, negative, or no correlation, have been reported. In this work, we show that the key to these contradictions lies in the times-cales of variability studied (e.g. the length of the light curves available). By isolating the variance on different time-scales in well-defined mass and accretion rate bins we show that there is indeed a negative correlation between black hole mass and variance and that this anticorrelation is stronger for shorter time-scale fluctuations. The behaviour can be explained in terms of a universal variability power spectrum for all quasars, resembling a broken power law where the variance is constant at low temporal frequencies and then drops continuously for frequencies higher than a characteristic (break) frequency fb, where fb correlates with the black hole mass. Furthermore, to explain all the variance results presented here, not only the normalization of this power spectrum must anticorrelate with the accretion rate, but also the shape of the power spectra at short time-scales must depend on this parameter as well.