An important diagnostic of the inner structure of accretion flows onto supermassive black holes are the stochastic flux variations at X-ray wavelengths. Despite its significance, a systematic characterization of the statistical properties of the X-ray variability to the highest Eddington ratios and most massive black holes is still lacking. In this paper, we address this issue using SRG/eROSITA (Spectrum-Roentgen-Gamma/extended ROentgen Survey with an Imaging Telescope Array) five-epoch light curves to characterize the mean X-ray variability of optically selected Sloan Digital Sky Survey quasars extending to black holes masses of 10(10) solar and accretion rates close to the Eddington limit. The adopted variability statistic is the ensemble normalized excess variance, which is measured using a novel hierarchical Bayesian model (EBEXVAR) tailored to the Poisson nature of the X-ray light curves. We find a clear anticorrelation of the ensemble variability with black hole mass, extending previous results to time-scales of months. This can be interpreted as evidence for an X-ray corona size and/or physical conditions that scale with black holes mass. We also find an unexpected increase of the ensemble normalized excess variance close to the Eddington limit, which is contrary to the predictions of empirical variability models. This result suggests an additional variability component for fast growing black holes that may be related to systematic variations of the hot corona size with Eddington ratio or shielding of the hot corona by an inner puffed-up disc and/or outflows.

Active galactic nuclei (AGN) emit radiation via accretion across the entire energy spectrum. While the standard disk and corona model can somewhat describe this emission, it fails to predict specific features such as the soft X-ray excess, the short-term optical/UV variability, and the observed UV/X-ray correlation in AGN. In this context, the fraction of AGN emission in different bands (i.e., bolometric corrections) can be useful to better understand the accretion physics of AGN. Past studies have shown that the X-ray bolometric corrections are strongly dependent on the physical properties of AGN, such as their luminosities and Eddington ratios. However, since these two parameters depend on each other, it has been unclear which is the main driver of the X-ray bolometric corrections. We present here results from a large study of hard-X-ray-selected (14-195 keV) nearby (z < 0.1) AGN. Based on our systematic analysis of the simultaneous optical-to-X-ray spectral energy distributions of 236 unobscured AGN, we found that the primary parameter controlling the X-ray bolometric corrections is the Eddington ratio. Our results show that, while the X-ray bolometric correction increases with the bolometric luminosity for sources with intermediate Eddington ratios (0.01-1), this dependence vanishes for sources with lower Eddington ratios (<0.01). This could be used as evidence for a change in the accretion physics of AGN at low Eddington ratios.

Over the last years, a number of broadband reverberation mapping campaigns have been conducted to explore the short-term UV and optical variability of nearby AGN. Despite the extensive data collected, the origin of the observed variability is still debated in the literature. Frequency-resolved time lags offer a promising approach to distinguish between different scenarios, as they probe variability on different time scales. In this study, we present the expected frequency-resolved lags resulting from X-ray reprocessing in the accretion disk. The predicted lags are found to feature a general shape that resembles that of observational measurements, while exhibiting strong dependence on various physical parameters. Additionally, we compare our model predictions to observational data for the case of NGC 5548, concluding that the X-ray illumination of the disk can effectively account for the observed frequency-resolved lags and power spectra in a self-consistent way. To date, X-ray disk reprocessing is the only physical model that has successfully reproduced the observed multi-wavelength variability, in both amplitude and time delays, across a range of temporal frequencies.

Active Galactic Nuclei (AGN) are believed to be powered by accretion of matter onto a supermassive black hole. A fundamental ingredient in shaping our understanding of AGN is their variability across the entire electromagnetic spectrum. Variability studies have the potential to help us understand the geometry of the emitting regions (in various energy bands), their causal relations, and the physics of the accretion processes. This review focuses on the observational properties of AGN variability in the optical/UV/X-ray bands (where most of the AGN luminosity is emitted) and their dependence on the AGN physical parameters (i.e. mass, luminosity, accretion rate). We also discuss possible interpretations in the context of accreting compact systems, and we review the use of variability as a tool to discover AGN and trace their properties across cosmic time, using both ground and space facilities. Finally, we discuss the opportunities and challenges provided by current and next-generation optical/X-ray surveys, to use variability as an effective tool to probe the growth of super massive black holes in the Universe.

We study the X-ray power spectrum of Active Galactic Nuclei (AGN) to investigate whether Seyfert I and II power spectra are similar or not, whether the AGN variability depends on black hole mass and accretion rate, and to compare the AGN power spectra with the Galactic X-ray black hole binaries power-spectra. We used 14-195 keV band light curves from the 157th SWIFT/BAT hard X-ray survey and we computed the mean power spectrum and excess variance of AGN in narrow black-hole mass/luminosity bins. We fitted a power-law model to the AGN power spectra, and we investigated whether the power spectrum parameters and the excess variance depend on black hole mass, luminosity and accretion rate. The Seyfert I and Seyfert II power spectra are identical, in agreement with AGN unification models. The mean AGN X-ray power spectrum has the same, power-law like shape with a slope of -1 in all AGN, irrespective of their luminosity and BH mass. We do not detect any flattening to a slope of zero at frequencies as low as 10e-9 Hz. We detect an anti-correlation between the PSD amplitude and the accretion rate, similar to what has been seen in the past in the 2-10 keV band. This implies that the variability amplitude in AGN decreases with increasing accretion rate. The universal AGN power-spectrum is consistent with the mean, 2-9 keV band Cyg X-1 power spectrum in its soft state. The mean, low frequency AGN X-ray power spectrum is consistent with the extension of the mean, 0.01-25 Hz Cyg X-1 power spectrum to lower frequencies. The agreement between the AGN and the Cyg X-1 power spectrum (either in the soft or the hard state) over many decades in frequency indicates that the X-ray variability process is probably the same in all accreting objects, irrespective of the mass of the compact object. We plan to investigate this issue further in the near future.

Context. Recently, nearby bright galaxies have been the subject of long monitoring surveys in the X-rays, UV, and optical. All of these campaigns revealed a strong correlation between the various UV and optical bands, with time lags that increase with wavelength. In a series of papers, we have demonstrated that a scenario in which an X-ray source located on the rotation axis of the central black hole illuminating the accretion disc is a viable explanation for the observed correlations. However, some of the monitored sources showed low or moderate correlation between the X-rays and the UV, which could challenge this scenario. Aims. In this paper, we analyse the time-averaged and the variable broadband X-ray/UV/optical spectral energy distributions (SEDs) of NGC 5548, one of the most intensely monitored Seyfert 1 galaxies, using Swift, HST, and ground-based telescopes. The aim of this paper is to test whether the broadband spectral behaviour of the source could be explained with the X-ray illumination hypothesis, despite the apparently moderate correlation between the X-rays and longer wavelength. Methods. We modelled the broadband time-averaged SED, from the Space Telescope and Optical Reverberation Mapping (STORM) monitoring campaign of the source performed using the KYNSED model, which assumes X-ray illumination of the disc. We also modelled 15 time-resolved SEDs extracted from the same campaign to check whether this model can account for the spectral variability seen in the various wavebands during the monitoring. We assumed in our modelling that the X-ray corona is powered via the accretion process. Results. Our results show that the proposed scenario could describe the time-averaged and the time-resolved SEDs of NGC 5548 perfectly well. In this scenario, the height of the corona, the X-ray photon index, and the power that is transferred to the corona all vary. This would explain the variability behaviour at the various wavelengths. The best-fit model is obtained for a non-spinning black hole accreting at a constant rate of 5% of its Eddington limit. Since each of the variable parameters will affect the observed flux in a particular way, the combined variability of all of these parameters will then account for the moderate correlation between the X-rays and UV/optical. Conclusions. We demonstrate in this paper that X-ray illumination of the accretion disc can actually explain the observed properties of NGC 5548. In fact, this model not only fits the broadband spectra of the source well, but it also explains the time-lag behaviour as a function of wavelength as well as the power spectral distribution, providing a complete description of the behaviour of this source.

Aims. We study the X-ray power spectrum of active galactic nuclei (AGN) in order to investigate whether Seyfert I and II power spectra are similar or not and whether AGN variability depends on the mass and accretion rate of black holes as well as to compare the power spectra of AGN with the power spectra of Galactic X-ray black hole binaries. Method. We used 14–195 keV band light curves from the 157-month Swift/BAT hard X-ray survey, and we computed the mean power spectrum and excess variance of AGN in narrow black hole mass and AGN luminosity bins. We fitted a power-law model to the AGN power spectra, and we investigated whether the power spectrum parameters and the excess variance depend on the black hole mass, luminosity, and accretion rate of AGN. Results. We found the Seyfert I and Seyfert II power spectra to be identical, in agreement with AGN unification models. The mean AGN X-ray power spectrum has the same power-law like shape, with a slope of −1 in all AGN irrespective of their luminosity and black hole mass. We did not detect any flattening to a slope of zero at frequencies as low as 10−9 Hz. We detected an anti-correlation between the power spectral density function (PSD) amplitude and the accretion rate, similar to what has been seen in the past in the 2–10 keV band. This implies that the variability amplitude in AGN decreases with an increasing accretion rate. The universal AGN power spectrum is consistent with the mean 2–9 keV band Cyg X-1 power spectrum in its soft state. We detected a small difference in amplitude, but this is probably due to the difference in energy. Conclusions. The mean low-frequency AGN X-ray power spectrum is consistent with the extension of the mean 0.01–25 Hz Cyg X-1 power spectrum in its soft state to lower frequencies. We cannot prove that the mean AGN PSD is analogous to the mean Cyg X-1 PSD in its soft state, as we do not know the location of the high-frequency break in the hard X-ray AGN PSDs. However, if this is the case, then the accretion disc in AGN probably extends to the radius of the innermost circular stable orbit (as is probably the case with the black hole binaries in their soft state). The X-ray corona will then be located on top, illuminating the disc and producing the X-ray reflection and disc reverberation phenomena commonly observed in these objects. Furthermore, the agreement between the PSD amplitude in AGN and the Cyg X-1 (either in the soft or the hard state) over many decades in frequency indicates that the X-ray variability process is probably the same in all accreting objects, irrespective of the mass of the compact object. We plan to investigate this issue further in the near future.

ABSTRACT We study the connection between the variations in the far-ultraviolet (FUV), near-ultraviolet (NUV), and X-ray band emission from NGC 4051 using 4 d long AstroSat observations performed during 5–9 June 2016. NGC 4051 showed rapid variability in all three bands with the strongest variability amplitude in the X-ray band ($F_{\mathrm{ var}} \sim 37~{{\ \rm per\ cent}}$) and much weaker variability in the UV bands ($F_{\mathrm{ var}} \sim 3{\!-\!}5~{{\ \rm per\ cent}}$). Cross-correlation analysis performed using interpolated cross-correlation functions and discrete cross-correlation functions revealed a robust correlation (∼0.75) between the UV and X-ray light curves. The variations in the X-ray band are found to lead those in the FUV and NUV bands by ∼7.4 ks and ∼24.2 ks, respectively. The UV lags favour the thermal disc reprocessing model. The FUV and NUV bands are strongly correlated (∼0.9) and the variations in the FUV band lead those in the NUV band by ∼13 ks. Comparison of the UV lags found using the AstroSat observations with those reported earlier and the theoretical model for thermal reverberation timelag suggests a possible change in either the geometry of the accretion disc/corona or the height of the corona.

Context: Extensive, multi-wavelength monitoring campaigns of nearby and higher redshift active galactic nuclei (AGN) have shown that the UV/optical variations are well correlated with time delays which increase with increasing wavelength. Such behaviour is expected in the context of the X-ray thermal reverberation of the accretion disc in AGN. Aims: Our main objective is to use time-lag measurements of luminous AGN and fit them with sophisticated X-ray reverberation time-lags models. In this way we can investigate whether X-ray reverberation can indeed explain the observed continuum time lags, and whether time-lag measurements can be used to measure physical parameters such as the X-ray corona height and the spin of the black hole (BH) in these systems. Methods: We use archival time-lag measurements for quasars from different surveys, and we compute their rest frame, mean time-lags spectrum. We fit the data with analytical X-ray reverberation models, using χ^2 statistics, and fitting for both maximal and non spinning BHs, for various colour correction values and X-ray corona heights. Results: We found that X-ray reverberation can explain very well the observed time lags, assuming the measured BH mass, accretion rate and X-ray luminosity of the quasars in the sample. The model agrees well with the data both for non-rotating and maximally rotating BHs, as long as the corona height is larger than ∼ 40 gravitational radii. This is in agreement with previous results which showed that X-ray reverberation can also explain the disc radius in micro-lensed quasars, for the same corona heights. The corona height we measure depends on the model assumption of a perfectly flat disc. More realistic disc models may result in lower heights for the X-ray corona.

Context. Quasar variability has proven to be a powerful tool to constrain the properties of their inner engine and the accretion process onto supermassive black holes. Correlations between UV/optical variability and physical properties have been long studied with a plethora of different approaches and time-domain surveys, although the detailed picture is not yet clear. Aims. We analysed archival data from the SDSS Stripe-82 region to study how the quasar power spectral density (PSD) depends on the black hole mass, bolometric luminosity, accretion rate, redshift, and rest-frame wavelength. We developed a model-independent analysis framework that could be easily applied to upcoming large surveys such as the Legacy Survey of Space and Time (LSST). Methods. We used light curves of 8042 spectroscopically confirmed quasars, observed in at least six yearly seasons in five filters ugriz . We split the sample into bins of similar physical properties containing at least 50 sources, and we measured the ensemble PSD in each of them. Results. We find that a simple power law is a good fit to the power spectra in the frequency range explored. Variability does not depend on the redshift at a fixed wavelength. Instead, both PSD amplitude and slope depend on the black hole mass, accretion rate, and rest-frame wavelength. We provide scaling relations to model the observed variability as a function of the physical properties, and discuss the possibility of a universal PSD shape for all quasars, where frequencies scale with the black hole mass, while normalization and slope(s) are fixed (at any given wavelength and accretion rate).

We present a multiwavelength spectral study of NGC 4151 based on five epochs of simultaneous AstroSat observations in the near-ultraviolet (NUV) to hard X-ray band (similar to 0.005-80 keV) during 2017-2018. We derived the intrinsic accretion disk continuum after correcting for internal and Galactic extinction, contributions from broad- and narrow-line regions, and emission from the host galaxy. We found a bluer continuum at brighter UV flux, possibly due to variations in the accretion disk continuum or the UV reddening. We estimated the intrinsic reddening, E(B - V) similar to 0.4, using high-resolution Hubble Space Telescope (HST)/STIS spectrum acquired in 2000 March. We used thermal Comptonization, neutral and ionized absorption, and X-ray reflection to model the X-ray spectra. We obtained the X-ray absorbing neutral column varying between N H similar to 1.2 and 3.4 x 1023 cm-2, which are similar to 100 times larger than that estimated from UV extinction, assuming the Galactic dust-to-gas ratio. To reconcile this discrepancy, we propose two plausible configurations of the obscurer: (a) a two-zone obscurer consisting of dust-free and dusty regions, divided by the sublimation radius, or (b) a two-phase obscurer consisting of clumpy, dense clouds embedded in a low-density medium, resulting in a scenario where a few dense clouds obscure the compact X-ray source substantially, while the bulk of UV emission arising from the extended accretion disk passes through the low-density medium. Furthermore, we find a positive correlation between the X-ray absorption column and NUV - far-UV color and UV flux, indicative of enhanced winds possibly driven by the "bluer-when-brighter" UV continuum.

Context. Active galactic nuclei (AGNs) are known to be variable across all wavelengths. Significant observational efforts have been invested in the last decade in studying their ultraviolet (UV) and optical variability. Long and densely sampled, multi-wavelength monitoring campaigns of numerous Seyfert galaxies have been conducted with the aim of determining the X-ray/UV/optical continuum time lags. Time-lag studies can be used to constrain theoretical models. The observed time lags can be explained by thermal reprocessing of the X-rays illuminating the accretion disc (known as the X-ray reverberation model). However, the observed light curves contain more information that can be used to further constrain physical models. Aims. Our primary objective is to investigate whether, in addition to time lags, the X-ray reverberation model can also explain the UV/optical variability amplitude of nearby Seyferts. Methods. We measured the excess variance of four sources (namely Mrk 509, NGC 4151, NGC 2617, and Mrk 142) as a function of wavelength using data from archival long, multi-wavelength campaigns with Swift, and ground-based telescopes. We also computed the model excess variance in the case of the X-ray reverberation model by determining the disc's transfer function and assuming a bending power law for the X-ray power spectrum. We tested the validity of the model by comparing the measured and model variances for a range of accretion rates and X-ray source heights. Results. Our main result is that the X-ray thermal reverberation model can fit both the continuum, UV/optical time lags, as well as the variance (i.e. the variability amplitude) in these AGNs, for the same physical parameters. Our results suggest that the accretion disc is constant and that all the observed UV/optical variations, on timescales of days and up to a few weeks, can be fully explained by the variable X-rays as they illuminate the accretion disc.

The black hole mass MBH is crucial in constraining the growth of supermassive BHs within their host galaxies. Since direct measurements of MBH with dynamical methods are restricted to a limited number of nearly quiescent nearby galaxies and a small minority of active galactic nuclei (AGN), we must rely on indirect methods. In this work, we utilize an unbiased, volume-limited, hard X-ray selected sample of AGN to compare the reliability of some commonly used indirect methods, emphasising those that can be applied to obscured AGN. Based on a subsample of AGN with MBH determined via dynamical methods, our study suggests that X-ray based techniques, such as the scaling method and the one based on the variability measured through the excess variance, are in good agreement with the dynamical methods. On the other hand, the M-sigma correlation based on inactive galaxies tends to systematically overestimate MBH, regardless of the level of obscuration. We provide a correcting factor that produces an acceptable agreement with dynamical values and can be used to quickly correct the MBH computed with this method. We also derive an alternative M-sigma correlation based on this unbiased sample of AGN with a slope considerably shallower than the ones obtained using inactive galaxies, suggesting that the latter correlation may not be appropriate to compute the MBH in AGN. Finally, we find that no quick fix can be applied to correct the MBH obtained from the fundamental plane of black hole activity, casting doubts on the reliability of this method.

We study the ensemble X-ray variability properties of Active Galactic Nuclei (AGN) over a large range of timescales (20 ks $\leq T\leq$ 14 yrs), redshift ($0\leq z \lesssim 3$), luminosities ($10^{40}$ erg s$^{-1}\leq L_X\leq 10^{46}$ erg s$^{-1}$) and black hole (BH) masses ($10^6 \leq $M$_\odot \leq 10^9$). We propose the use of the variance-frequency diagram, as a viable alternative to the study of the power spectral density (PSD), which is not yet accessible for distant, faint and/or sparsely sampled AGN. We show that the data collected from archival observations and previous literature studies are fully consistent with a universal PSD form which does not show any evidence for systematic evolution of shape or amplitude with redshift or luminosity, even if there may be differences between individual AGN at a given redshift or luminosity. We find new evidence that the PSD bend frequency depends on BH mass and, possibly, on accretion rate. We finally discuss the implications for current and future AGN population and cosmological studies.

Optical polarimeters are typically calibrated using measurements of stars with known and stable polarization parameters. However, there is a lack of such stars available across the sky. Many of the currently available standards are not suitable for medium and large telescopes due to their high brightness. Moreover, as we find, some of the used polarimetric standards are in fact variable or have polarization parameters that differ from their cataloged values. Our goal is to establish a sample of stable standards suitable for calibrating linear optical polarimeters with an accuracy down to $10^{-3}$ in fractional polarization. For five years, we have been running a monitoring campaign of a sample of standard candidates comprised of 107 stars distributed across the northern sky. We analyzed the variability of the linear polarization of these stars, taking into account the non-Gaussian nature of fractional polarization measurements. For a subsample of nine stars, we also performed multiband polarization measurements. We created a new catalog of 65 stars (see Table 2) that are stable, have small uncertainties of measured polarimetric parameters, and can be used as calibrators of polarimeters at medium- and large-size telescopes.

We study accretion disk-corona connection in Seyfert 1 galaxies using simultaneous UV/X-ray observations of NGC 4593 (July 14-18, 2016) and NGC 7469 (October 15-19, 2017) performed with AstroSat. We use the X-ray (0.5-7.0 keV) data acquired with the Soft X-ray Telescope (SXT) and the UV (FUV: 130-180 nm, NUV: 200-300 nm) data obtained with the Ultra-Violet Imaging Telescope (UVIT). We also use the contemporaneous Swift observations of NGC 4593 and demonstrate AstroSat's capability for X-ray/UV correlation studies. We performed UV/X-ray cross-correlation analysis using the Interpolated and the Discrete Cross-Correlation Functions and found similar results. In the case of NGC 4593, we found that the variations in the X-rays lead to those in the FUV and NUV bands by 38 ks and 44 ks, respectively. These UV lags favour the disk reprocessing model, they are consistent with the previous results within uncertainties. In contrast, we found an opposite trend in NGC 7469 where the soft X-ray variations lag those in the FUV and NUV bands by 41 ks and 49 ks, respectively. The hard lags in NGC 7469 favour the Thermal Comptonization model. Our results may provide direct observational evidence for the variable intrinsic UV emission from the accretion disk which acts as the seed for thermal Comptonization in a hot corona in a lamp-post like geometry. The non-detection of disk reverberation photons in NGC 7469, using AstroSat data, is most likely due to a high accretion rate resulting in a hot accretion disk and large intrinsic emission.

ABSTRACT We present a 140 ks observation of NGC 4593 with XMM–Newton providing simultaneous and continuous pn X-ray and OM UV (UVW1 2910 Å) light curves, which sample short-time-scale variations better than previous observations. These observations were simultaneous with 22 d of Swift X-ray and UV/optical monitoring reported previously, and 4 d of AstroSat Soft X-ray Telescope (SXT), far (FUV 1541 Å) and near (NUV 2632 Å) UV allowing lag measurements between them and the highly-sampled XMM. From the XMM, we find that UVW1 lags behind the X-rays by 29.5 ± 1.3 ks, ∼half the lag previously determined from the Swift monitoring. Re-examination of the Swift data reveals a bimodal lag distribution, with evidence for both the long and short lags. However, if we detrend the Swift light curves by LOWESS filtering with a 5 d width, only the shorter lag (23.8 ± 21.2 ks) remains. The NUV observations, compared to pn and SXT, confirm the ∼30 ks lag found by XMM, and after 4 d filtering is applied to remove the long-time-scale component, the FUV shows a lag of ∼23 ks. The resultant new UVW1, FUV, and NUV lag spectrum extends to the X-ray band without requiring additional X-ray to UV lag offset, which if the UV arises from reprocessing of X-rays implies direct illumination of the reprocessor. By referencing previous Swift and HST lag measurements, we obtain an X-ray to optical lag spectrum, which agrees with a model using the KYNreverb disc-reprocessing code, assuming the accepted mass of 7.63 × 106 M⊙ and a spin approaching maximum. Previously noted lag contribution from the BLR in the Balmer and Paschen continua are still prominent.

In this paper, we present an updated version of our model (KYNXiltr) which considers thermal reverberation of a standard Novikov-Thorne accretion disc illuminated by an X-ray point-like source. Previously, the model considered only two cases of black hole spins, and assumed a colour correction factor $f_{\rm col} = 2.4$. Now, we extend the model to any spin value and colour correction. In addition, we consider two scenarios of powering the X-ray corona, either via accretion, or external to the accretion disc. We use KYNXiltr to fit the observed time lags obtained from intense monitoring of four local Seyfert galaxies (NGC 5548, NGC 4395, Mrk 817, and Fairall 9). We consider various combinations of black hole spin, colour correction, corona height, and fraction of accretion power transferred to the corona. The model fits well the overall time-lags spectrum in these sources (for a large parameter space). For NGC 4593 only, we detect a significant excess of delays in the U-band. The contribution of the diffuse BLR emission in the time-lags spectrum of this source is significant. It is possible to reduce the large best-fitting parameter space by combining the results with additional information, such as the observed Eddington ratio and average X-ray luminosity. We also provide an update to the analytic expression provided by Kammoun et al., for an X-ray source that is not powered by the accretion process, which can be used for any value of colour correction, and for two values of the black hole spin (0 and 0.998).

$\require{mediawiki-texvc}$ We study accretion disk emission from eight Seyfert $1 - 1.5$ active galactic nuclei (AGN) using far ultra-violet ($1300-1800$ ${\AA}$) slit-less grating spectra acquired with AstroSat/UVIT. We correct for the Galactic and intrinsic extinction, contamination from the host galaxies, narrow and broad-line regions, Fe II emission and Balmer continuum, and derive the intrinsic continua. We use HST COS/FOS spectra to account for the emission/absorption lines in the low-resolution UVIT spectra. We find generally redder power-law ($f_\nu \propto \nu^{\alpha}$) slopes ($\alpha \sim -1.1 - 0.3$) in the far UV band than predicted by the standard accretion disk model in the optical/UV band. We fit accretion disk models such as the multi-temperature disk blackbody ($\texttt{DISKBB}$) and relativistic disk ($\texttt{ZKERRBB}$, $\texttt{OPTXAGNF}$) models to the observed intrinsic continuum emission. We measure the inner disk temperatures using the $\texttt{DISKBB}$ model for seven AGN. These temperatures in the range $\sim 3.6-5.8$ eV are lower than the peak temperatures predicted for standard disks around maximally spinning super-massive black holes accreting at Eddington rates. The inner disks in two AGN, NGC 7469 and Mrk 352, appear to be truncated at $\sim 35-125r_{g}$ and $50-135r_{g}$, respectively. While our results show that the intrinsic FUV emission from the AGN are consistent with the standard disks, it is possible that UV continua may be affected by the presence of soft X-ray excess emission, X-ray reprocessing, and thermal Comptonisation in the hot corona. Joint spectral modeling of simultaneously acquired UV/X-ray data may be necessary to further investigate the nature of accretion disks in AGN.

We study the Fourier time-lags due to the Comptonization of disc-emitted photons in a spherical, uniform, and stationary X-ray corona, which located on the rotational axis of the black hole. We use Monk, a general relativistic Monte-Carlo radiative transfer code, to calculate Compton scattering of photons emitted by a thin disc with a Novikov-Thorne temperature profile. We find that the model time-lags due to Comptonization remain constant up to a characteristic frequency and then rapidly decrease to zero at higher frequencies. We provide equations which can be used to determine the time-lags and cross spectra for a wide range of values for the corona radius, temperature, optical depth, height, and for various accretion rates and black hole masses. We also provide an equation for the X-ray luminosity of a single corona, as a function of the its characteristics and location above the disc. Remarkably, the observed X-ray time-lags of nearby, bright active galaxies can be successfully reproduced by inverse Comptonization process of multiple dynamic coronae.