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Register a new userIs Quasar Optical Variability a Damped Random Walk?
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Ying Zu
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The damped random walk (DRW) model is increasingly used to model the variability in quasar optical light curves, but it is still uncertain whether the DRW model provides an adequate description of quasar optical variability across all time scales. Using a sample of OGLE quasar light curves, we consider four modifications to the DRW model by introducing additional parameters into the covariance function to search for deviations from the DRW model on both short and long time scales. We find good agreement with the DRW model on time scales that are well sampled by the data (from a month to a few years), possibly with some intrinsic scatter in the additional parameters, but this conclusion depends on the statistical test employed and is sensitive to whether the estimates of the photometric errors are correct to within ~10%. On very short time scales (below a few months), we see some evidence of the existence of a cutoff below which the correlation is stronger than the DRW model, echoing the recent finding of Mushotzky et al. (2011) using quasar light curves from Kepler. On very long time scales (> a few years), the light curves do not constrain models well, but are consistent with the DRW model.
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Studies have shown that UV/optical light curves of quasars can be described with the prevalent damped random walk (DRW, also known as Ornstein-Uhlenbeck process) model. A white noise power spectral density (PSD) is expected at low frequency in this model, however, direct observational constraint to the low frequency PSD slope is hard due to limited lengths of the light curves available. Meanwhile, quasars show too large scatter in their DRW parameters to be attributed to the uncertainties in the measurements and the dependence of variation to known physical factors. In this work we present simulations showing that, if the low frequency PSD deviates from DRW, the red noise leakage can naturally produce large scatter in variation parameters measured from simulated light curves. The steeper the low frequency PSD slope is, the larger scatter we expect. Based on the observations of SDSS Stripe 82 quasars, we find the low frequency PSD slope should be no steeper than -1.3. The actual slope could be flatter, which consequently requires that quasar variabilities should be influenced by other unknown factors. We speculate that magnetic field and/or metallicity could be such additional factors.
A damped random walk is a stochastic process, defined by an exponential covariance matrix that behaves as a random walk for short time scales and asymptotically achieves a finite variability amplitude at long time scales. Over the last few years, it has been demonstrated, mostly but not exclusively using SDSS data, that a damped random walk model provides a satisfactory statistical description of observed quasar variability in the optical wavelength range, for rest-frame timescales from 5 days to 2000 days. The best-fit characteristic timescale and asymptotic variability amplitude scale with the luminosity, black hole mass, and rest wavelength, and appear independent of redshift. In addition to providing insights into the physics of quasar variability, the best-fit model parameters can be used to efficiently separate quasars from stars in imaging surveys with adequate long-term multi-epoch data, such as expected from LSST.
We model the time variability of ~9,000 spectroscopically confirmed quasars in SDSS Stripe 82 as a damped random walk. Using 2.7 million photometric measurements collected over 10 years, we confirm the results of Kelly et al. (2009) and Koz{l}owski et al. (2010) that this model can explain quasar light curves at an impressive fidelity level (0.01-0.02 mag). The damped random walk model provides a simple, fast [O(N) for N data points], and powerful statistical description of quasar light curves by a characteristic time scale (tau) and an asymptotic rms variability on long time scales (SF_inf). We searched for correlations between these two variability parameters and physical parameters such as luminosity and black hole mass, and rest-frame wavelength. We find that tau increases with increasing wavelength with a power law index of 0.17, remains nearly constant with redshift and luminosity, and increases with increasing black hole mass with power law index of 0.21+/-0.07. The amplitude of variability is anti-correlated with the Eddington ratio, which suggests a scenario where optical fluctuations are tied to variations in the accretion rate. The radio-loudest quasars have systematically larger variability amplitudes by about 30%, when corrected for the other observed trends, while the distribution of their characteristic time scale is indistinguishable from that of the full sample. We do not detect any statistically robust differences in the characteristic time scale and variability amplitude between the full sample and the small subsample of quasars detected by ROSAT. Our results provide a simple quantitative framework for generating mock quasar light curves, such as currently used in LSST image simulations. (abridged)
We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending on the increment law, there are several regimes with different limit distributions for this length. Among other tools, a representation of the convex minorant of a random walk in terms of uniform random permutations is utilized.
Broad absorption lines (BALs) in quasar spectra identify high velocity outflows that likely exist in all quasars and could play a major role in feedback to galaxy evolution. Studying the variability in these BALs can help us understand the structure, evolution, and basic physical properties of these outflows. We are conducting a BAL monitoring program, which so far includes 163 spectra of 24 luminous quasars, covering time-scales from sim 1 week to 8 years in the quasar rest-frame. We investigate changes in both the CIV {lambda}1550 and SiIV {lambda}1400 BALs, and we report here on some of the results from this program.
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