We present the use of continuous-time autoregressive moving average (CARMA) models as a method for estimating the variability features of a light curve, and in particular its power spectral density (PSD). CARMA models fully account for irregular sampling and measurement errors, making them valuable for quantifying variability, forecasting and interpolating light curves, and variability-based classification. We show that the PSD of a CARMA model can be expressed as a sum of Lorentzian functions, which makes them extremely flexible and able to model a broad range of PSDs. We present the likelihood function for light curves sampled from CARMA processes, placing them on a statistically rigorous foundation, and we present a Bayesian method to infer the probability distribution of the PSD given the measured light curve. Because calculation of the likelihood function scales linearly with the number of data points, CARMA modeling scales to current and future massive time-domain data sets. We conclude by applying our CARMA modeling approach to light curves for an X-ray binary, two active galactic nuclei, a long-period variable star, and an RR Lyrae star in order to illustrate their use, applicability, and interpretation.

In this work, we have developed a new stochastic model for the fluctuations in light curves of accreting black holes. The model is based on a linear combination of stochastic processes and is also the solution to the linear diffusion equation perturbed by a spatially correlated noise field. This allows flexible modeling of the power spectral density (PSD), and we derive the likelihood function for the process, enabling one to estimate the parameters of the process, including break frequencies in the PSD. Our statistical technique is computationally efficient, unbiased by aliasing and red noise leak, and fully accounts for irregular sampling and measurement errors. We show that our stochastic model provides a good approximation to the X-ray light curves of galactic black holes, and the optical and X-ray light curves of active galactic nuclei (AGNs). We use the estimated timescales of our stochastic model to recover the correlation between characteristic timescale of the high-frequency X-ray fluctuations and black hole mass for AGNs, including two new "detections" of the timescale for Fairall 9 and NGC 5548. We find a tight anti-correlation between the black hole mass and the amplitude of the driving noise field, which is proportional to the amplitude of the high-frequency X-ray PSD, and we estimate that this parameter gives black hole mass estimates to within ∼0.2 dex precision, potentially the most accurate method for AGNs yet. We also find evidence that ≈13% of AGN optical PSDs fall off flatter than 1/f 2 and, similar to previous work, find that the optical fluctuations are more suppressed on short timescales compared to the X-rays, but are larger on long timescales, suggesting that the optical fluctuations are not solely due to reprocessing of X-rays.

We present the results from the spectral analysis of more than 7500 Rossi X‐ray Timing Explorer (RXTE) spectra of 10 active galactic nuclei (AGN). Our main goal was to study their long‐term X‐ray spectral variability. The sources in the sample are nearby, X‐ray bright, and they have been observed by RXTE regularly over a long period of time (∼7–11 yr). High‐frequency breaks have been detected in their power spectra, and these characteristic frequencies imply time‐scales of the order of a few days or weeks. Consequently, the RXTE observations we have used most probably sample most of the flux and spectral variations that these objects exhibit. Thus, the RXTE data are ideal for our purpose. Fits to the individual spectra were performed in the 3–20 keV energy band. We modelled the data in a uniform way using simple phenomenological models (a power law with the addition of Gaussian line and/or edge to model the iron Kα emission/absorption features, if needed) to consistently parametrize the shape of the observed X‐ray continuum of the sources in the sample. We found that the average spectral slope does not correlate with source luminosity or black hole mass, while it correlates positively with the average accretion rate. We have also determined the (positive) spectral slope–flux relation for each object, over a flux range larger than before. We found that this correlation is similar in all objects, except for NGC 5548 which displays limited spectral variations for its flux variability. We discuss this global spectral slope–flux trend in the light of current models for spectral variability. We consider (i) intrinsic variability, expected, for example, from Comptonization processes, (ii) variability caused by absorption of X‐rays by a single absorber whose ionization parameter varies proportionally to the continuum flux variations, (iii) variability resulting from the superposition of a constant reflection component and an intrinsic power law which is variable in flux but constant in shape and (iv) variability resulting from the superposition of a constant reflection component and an intrinsic power law which is variable both in flux and in shape. Our final conclusion is that scenario (iv) provides the best fit to the data of all objects, except for NGC 5548.

Recently, several ultraluminous X-ray (ULX) sources were shown to host a neutron star (NS) accretor. We perform a suite of evolutionary calculations which show that, in fact, NSs are the dominant type of ULX accretor. Although black holes (BH) dominate early epochs after the star-formation burst, NSs outweigh them after a few 100 Myr and may appear as late as a few Gyr after the end of the star formation episode. If star formation is a prolonged and continuous event (i.e., not a relatively short burst), NS accretors dominate ULX population at any time in solar metallicity environment, whereas BH accretors dominate when the metallicity is sub-solar. Our results show a very clear (and testable) relation between the companion/donor evolutionary stage and the age of the system. A typical NS ULX consists of a ∼ 1.3 M NS and ∼ 1.0 M Red Giant. A typical BH ULX consist of a ∼ 8 M BH and ∼ 6 M main-sequence star. Additionally, we find that the very luminous ULXs (L X 10 41 erg/s) are predominantly BH systems (∼ 9 M ) with Hertzsprung gap donors (∼ 2 M ). Nevertheless, some NS ULX systems may also reach extremely high X-ray luminosities ( 10 41 erg/s).

We study the γ -ray variability of 13 blazars observed with the Fermi/Large Area Telescope (LAT). These blazars have the most complete light curves collected during the first four years of the Fermi sky survey. We model them with the Ornstein-Uhlenbeck (OU) process or a mixture of the OU processes. The OU process has power spectral density (PSD) proportional to 1/f α with α changing at a characteristic timescale, τ 0 , from 0 (τ τ 0 ) to 2 (τ τ 0 ). The PSD of the mixed OU process has two characteristic timescales and an additional intermediate region with 0 < α < 2. We show that the OU model provides a good description of the Fermi/LAT light curves of three blazars in our sample. For the first time, we constrain a characteristic γ -ray timescale of variability in two BL Lac sources, 3C 66A and PKS 2155-304 (τ 0 25 days and τ 0 43 days, respectively, in the observer's frame), which are longer than the soft X-ray timescales detected in blazars and Seyfert galaxies. We find that the mixed OU process approximates the light curves of the remaining 10 blazars better than the OU process. We derive limits on their long and short characteristic timescales, and infer that their Fermi/LAT PSD resemble power-law functions. We constrain the PSD slopes for all but one source in the sample. We find hints for sub-hour Fermi/LAT variability in four flat spectrum radio quasars. We discuss the implications of our results for theoretical models of blazar variability.