False periodicities in quasar time-domain surveys

Abstract

There have recently been several reports of apparently periodic variations in the light curves of quasars, e.g. PG 1302−102 by Graham et al. (2015a). Any quasar showing periodic oscillations in brightness would be a strong candidate to be a close binary supermassive black hole and, in turn, a candidate for gravitational wave studies. However, normal quasars -powered by accretion onto a single, supermassive black hole -usually show stochastic variability over a wide range of timescales. It is therefore important to carefully assess the methods for identifying periodic candidates from among a population dominated by stochastic variability. Using a Bayesian analysis of the light curve of PG 1302−102, we find that a simple stochastic process is preferred over a sinusoidal variations. We then discuss some of the problems one encounters when searching for rare, strictly periodic signals among a large number of irregularly sampled, stochastic time series, and use simulations of quasar light curves to illustrate these points. From a few thousand simulations of steep spectrum ('red noise') stochastic processes, we find many simulations that display few-cycle periodicity like that seen in PG 1302−102. We emphasise the importance of calibrating the false positive rate when the number of targets in a search is very large.

Gamma-ray and optical oscillations of 0716+714, MRK 421, and BL Lacertae

“…Examining the light curves of hundred thousands objects, only three apparently well established periodic cases have been found (Graham et al 2015a,b;Zheng et al 2016;Liu et al 2015;Charisi et al 2016), and ∼ 100 are considered as promising candidates. As Vaughan et al (2016) point out, when searching for rare events in large samples of noisy time series it is particularly import to properly evaluate the false positive rate and to treat with caution few-cycle periodicities that are selected by machine methods. The tests used in the above papers to asses the significance of the claimed quasiperiodicities, which also lack calibration against a red noise null hypothesis, could introduce phantom periodic detections.…”

Understanding extreme quasar optical variability with CRTS – I. Major AGN flares

“…This relation was derived from 100 000 isotropically selected sources that exhibited no significant sign of variability based on their Welch-Stetson variability index. However, errors at the brighter magnitudes are overestimated and those at fainter magnitudes (>18) are underestimated (Palaversa et al 2013;Drake et al 2014;Vaughan et al 2016). We have derived a multiplicative correction factor from CRTS observations of 350 000 sources in the Stripe 82 Standard Star catalogue (Ivezic et al 2007) that ensures that the mode of the reduced chi-squared variability in magnitude bins of width of mag = 0.05 is centred at unity (see Fig.…”

A 78 Day X-Ray Period Detected From NGC 5907 Ulx1 by Swift

“…We tested 920 trial periods between 30 and 140 days on a linearly sampled grid. The period range is set by our requirement that each cycle be covered by at least four observations during the lower-cadence portion of our program, and that the duration of our monitoring program would cover at least five cycles (see Vaughan et al 2016). To evaluate the likelihood that at any given period the folded profile deviates significantly from the null hypothesis of a flat profile, we used the L-statistic as described by Davies (1990).…”

“…Figure 2 also shows the maximum L-stat obtained for each of the 10,000 simulated data sets, which are all below that seen in the real data. In order to test for any dependence on the assumed form of the power spectrum (as discussed by, e.g., Vaughan et al 2016 for the case of quasar light curves), we also performed additional sets of simulations varying α by±0.5 and obtained identical results in both cases. We therefore conclude that the significance of the detection is comfortably in excess of the 3σ level.…”