No Arabic abstract
We present an extended corona model based on ray-tracing simulations to investigate X-ray time lags in Active Galactic Nuclei (AGN). This model consists of two axial point sources illuminating an accretion disc that produce the reverberation lags. These lags are due to the time delays between the directly observed and reflection photons and are associated with the light-travel time between the source and the disc, so they allow us to probe the disc-corona geometry. We assume the variations of two X-ray sources are triggered by the same primary variations, but allow the two sources to respond in different ways (i.e. having different source responses). The variations of each source induce a delayed accretion disc response and the total lags consist of a combination of both source and disc responses. We show that the extended corona model can reproduce both the low-frequency hard and high-frequency soft (reverberation) lags. Fitting the model to the timing data of PG~1244+026 reveals the hard and soft X-ray sources at $sim6r_{text{g}}$ and $sim11r_{text{g}}$, respectively. The upper source produces small amounts of reflection and can be interpreted as a relativistic jet, or outflowing blob, whose emission is beamed away from the disc. This explains the observed lag-energy in which there is no soft lag at energies $<1$~keV as they are diluted by the soft continuum of the upper source. Finally, our models suggest that the fluctuations propagating between the two sources of PG~1244+026 are possible but only at near the speed of light.
We investigate the X-ray time lags of a recent ~630ks XMM-Newton observation of PG 1211+143. We find well-correlated variations across the XMM-Newton EPIC bandpass, with the first detection of a hard lag in this source with a mean time delay of up to ~3ks at the lowest frequencies. We find that the energy-dependence of the low-frequency hard lag scales approximately linearly with log(E) when averaged over all orbits, consistent with the propagating fluctuations model. However, we find that the low-frequency lag behaviour becomes more complex on timescales longer than a single orbit, suggestive of additional modes of variability. We also detect a high-frequency soft lag at ~10^{-4}Hz with the magnitude of the delay peaking at <0.8ks, consistent with previous observations, which we discuss in terms of small-scale reverberation.
We develop a physically motivated, spherical corona model to investigate the frequency-dependent time lags in AGN. The model includes the effects of Compton up-scattering between the disc UV photons and coronal electrons, and the subsequent X-ray reverberation from the disc. The time lags are associated with the time required for multiple scatterings to boost UV photons up to soft and hard X-ray energies, and the light crossing time the photons take to reach the observer. This model can reproduce not only low-frequency hard and high-frequency soft lags, but also the clear bumps and wiggles in reverberation profiles which should explain the wavy-residuals currently observed in some AGN. Our model supports an anti-correlation between the optical depth and coronal temperatures. In case of an optically thin corona, time delays due to propagating fluctuations may be required to reproduce observed time lags. We fit the model to the lag-frequency data of 1H0707-495, Ark 564, NGC 4051 and IRAS 13224-3809 estimated using the minimal bias technique so that the observed lags here are highest-possible quality. We find their corona size is ~7-15 r_g having the constrained optical depth ~2-10. The coronal temperature is ~150-300 keV. Finally, we note that the reverberation wiggles may be signatures of repeating scatters inside the corona that control the distribution of X-ray sources.
Characteristic signatures that X-ray reverberation from an extended corona can manifest in the observed PSD of AGN are investigated. The presence of two X-ray blobs illuminating an accretion disc can cause the interference between two reprocessing-echo components and produce distinct physical features in the PSD. The oscillatory structures (e.g., dips and humps) are seen but, contrarily to the lamp-post case, the strongest dip is not always the one at the lowest frequency. Instead, we find the frequency where the strongest dip is seen associates to the lower-source height while the lowest frequency where the first dip appears links with the upper-source height. This is because the reverberation timescales increase with the source height. Accurate modelling of the PSD then helps put constraints to the lower and upper limit of the corona extent. Furthermore, the reverberation signatures are less pronounced with increasing number of sources that do not produce reflection (e.g., additional X-rays from fast, relativistic outflows). The amplitude of the oscillations also depends on the amount of dilution contributed by the X-ray sources, thus encodes information about their relative brightness. Due to stronger dilutions, robust detection of these signatures with the current observations will become even more difficult if the corona is extended. Future observations made by Athena will enable us to fit these characteristics in statistically significant details, and to reveal the nature of the disc-corona system.
The X-ray emission from bright active galactic nuclei (AGNs) is believed to originate in a hot corona lying above a cold, geometrically thin accretion disk. A highly concentrated corona located within $sim10$ gravitational radii above the black hole is inferred from observations. Based on the accretion of interstellar medium/wind, a disk corona model has been proposed in which the corona is well coupled to the disk by radiation, thermal conduction, as well as by mass exchange citep{Liu2015, Qiao2017}. Such a model avoids artificial energy input to the corona and has been used to interpret the spectral features observed in AGN. In this work, it is shown that the bulk emission size of the corona is very small for the extended accretion flow in our model. More than 80% of the hard X-ray power is emitted from a small region confined within 10 Schwarzschild radii around a non-spinning black hole, which is expected to be even smaller accordingly for a spinning black hole. Here, the corona emission is more extended at higher Eddington ratios. The compactness parameter of the corona, $l={Lover R}{sigma_{rm T}over m_{rm e} c^3}$, is shown to be in the range of 1-33 for Eddington ratios of 0.02 - 0.1. Combined with the electron temperature in the corona, this indicates that electron--positron pair production is not dominant in this regime. A positive relation between the compactness parameter and photon index is also predicted. By comparing the above model predictions with observational features, we find that the model is in agreement with observations.
We performed a detailed timing study of the Atoll source 4U 1705-44 in order to understand the accretion disk geometry. Cross correlation function (CCF) studies were performed between soft (3-5 keV) and hard energy (15-30 keV) bands using the AstroSat LAXPC data. We detected hard as well as soft lags of the order of few ten to hundred seconds. A dynamical CCF study was performed in the same energy bands for one of the light curves and we found smaller lags of few tens of seconds ($<$ 50 s) suggesting that the variation is probably originating from the corona. We found a broad noise component around $sim$ 13 Hz in the 3-10 keV band which is absent in 10-20 keV band. We interpret the observed lags as the readjustment timescales of the corona or a boundary layer around the neutron star and constrain the height of this structure to few tens of km. We independently estimated the coronal height to be around 15 km assuming that the 13 Hz feature in the PDS is originating from the oscillation of the viscous shell around the neutron star.