Estimating the distribution of rest-frame timescales for blazar jets: a statistical approach

In any flux-density limited sample of blazars, the distribution of the timescale modulation factor $\Delta t'/\Delta t$, which quantifies the change in observed timescales compared to the rest-frame ones due to redshift and relativistic compression follows an exponential distribution with a mean depending on the flux limit of the sample. In this work we produce the mathematical formalism that allows us to use this information in order to uncover the underlining rest-frame probability density function of measurable timescales of blazar jets. We extensively test our proposed methodology using a simulated FSRQ population with a 1.5 Jy flux-density limit in the simple case (where all blazars share the same intrinsic timescale), in order to identify limits of applicability and potential biases due to observational systematics and sample selection. We find that for monitoring with time intervals between observations longer than $\sim$30\% of the intrinsic timescale under investigation the method loses its ability to produce robust results. For time intervals of $\sim$3\% of the intrinsic timescale the error of the method is as low as 1\% in recovering the intrinsic rest-frame timescale. We applied our method to rotations of the optical polarization angle of blazars observed by RoboPol. We found that the intrinsic timescales of the longest-duration rotation event in each blazar follows a narrow distribution, well-described by a normal distribution with mean 87 days and standard deviation 5 days. We discuss possible interpretations of this result.