arXiv subjects

Stephane Paltani

Publications and source records attributed to Stephane Paltani.

36 records · Page 2Linked to original sources

arXiv2018

The Large Area Detector onboard the eXTP mission

The eXTP (enhanced X-ray Timing and Polarimetry) mission is a major project of the Chinese Academy of Sciences (CAS) and China National Space Administration (CNSA) currently performing an extended phase A study and proposed for a launch by 2025 in a low-earth orbit. The eXTP scientific payload envisages a suite of instruments (Spectroscopy Focusing Array, Polarimetry Focusing Array, Large Area Detector and Wide Field Monitor) offering unprecedented simultaneous wide-band X-ray spectral, timing and polarimetry sensitivity. A large European consortium is contributing to the eXTP study and it is expected to provide key hardware elements, including a Large Area Detector (LAD). The LAD instrument for eXTP is based on the design originally proposed for the LOFT mission within the ESA context. The eXTP/LAD envisages a deployed 3.4 m2 effective area in the 2-30 keV energy range, achieved through the technology of the large-area Silicon Drift Detectors - offering a spectral resolution of up to 200 eV FWHM at 6 keV - and of capillary plate collimators - limiting the field of view to about 1 degree. In this paper we provide an overview of the LAD instrument design, including new elements with respect to the earlier LOFT configuration.

astro-ph.IM↗

arXiv2017

BAT AGN Spectroscopic Survey - V. X-ray properties of the Swift/BAT 70-month AGN catalog

Hard X-ray ($\geq 10$ keV) observations of Active Galactic Nuclei (AGN) can shed light on some of the most obscured episodes of accretion onto supermassive black holes. The 70-month Swift/BAT all-sky survey, which probes the 14-195 keV energy range, has currently detected 838 AGN. We report here on the broad-band X-ray (0.3-150 keV) characteristics of these AGN, obtained by combining XMM-Newton, Swift/XRT, ASCA, Chandra, and Suzaku observations in the soft X-ray band ($\leq 10$ keV) with 70-month averaged Swift/BAT data. The non-blazar AGN of our sample are almost equally divided into unobscured ($N_{\rm H}< 10^{22}\rm cm^{-2}$) and obscured ($N_{\rm H}\geq 10^{22}\rm cm^{-2}$) AGN, and their Swift/BAT continuum is systematically steeper than the 0.3-10 keV emission, which suggests that the presence of a high-energy cutoff is almost ubiquitous. We discuss the main X-ray spectral parameters obtained, such as the photon index, the reflection parameter, the energy of the cutoff, neutral and ionized absorbers, and the soft excess for both obscured and unobscured AGN.

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arXiv2017

The close environments of accreting massive black holes are shaped by radiative feedback

The large majority of the accreting supermassive black holes in the Universe are obscured by large columns of gas and dust. The location and evolution of this obscuring material have been the subject of intense research in the past decades, and are still highly debated. A decrease in the covering factor of the circumnuclear material with increasing accretion rates has been found by studies carried out across the electromagnetic spectrum. The origin of this trend has been suggested to be driven either by the increase in the inner radius of the obscuring material with incident luminosity due to the sublimation of dust; by the gravitational potential of the black hole; by radiative feedback; or by the interplay between outflows and inflows. However, the lack of a large, unbiased and complete sample of accreting black holes, with reliable information on gas column density, luminosity and mass, has left the main physical mechanism regulating obscuration unclear. Using a systematic multi-wavelength survey of hard X-ray-selected black holes, here we show that radiation pressure on dusty gas is indeed the main physical mechanism regulating the distribution of the circumnuclear material. Our results imply that the bulk of the obscuring dust and gas in these objects is located within the sphere of influence of the black hole (i.e., a few to tens of parsecs), and that it can be swept away even at low radiative output rates. The main physical driver of the differences between obscured and unobscured accreting black holes is therefore their mass-normalized accretion rate.

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arXiv2017

The Complete Calibration of the Color-Redshift Relation (C3R2) Survey: Survey Overview and Data Release 1

A key goal of the Stage IV dark energy experiments Euclid, LSST and WFIRST is to measure the growth of structure with cosmic time from weak lensing analysis over large regions of the sky. Weak lensing cosmology will be challenging: in addition to highly accurate galaxy shape measurements, statistically robust and accurate photometric redshift (photo-z) estimates for billions of faint galaxies will be needed in order to reconstruct the three-dimensional matter distribution. Here we present an overview of and initial results from the Complete Calibration of the Color-Redshift Relation (C3R2) survey, designed specifically to calibrate the empirical galaxy color-redshift relation to the Euclid depth. These redshifts will also be important for the calibrations of LSST and WFIRST. The C3R2 survey is obtaining multiplexed observations with Keck (DEIMOS, LRIS, and MOSFIRE), the Gran Telescopio Canarias (GTC; OSIRIS), and the Very Large Telescope (VLT; FORS2 and KMOS) of a targeted sample of galaxies most important for the redshift calibration. We focus spectroscopic efforts on under-sampled regions of galaxy color space identified in previous work in order to minimize the number of spectroscopic redshifts needed to map the color-redshift relation to the required accuracy. Here we present the C3R2 survey strategy and initial results, including the 1283 high confidence redshifts obtained in the 2016A semester and released as Data Release 1.

astro-ph.CO↗

arXiv2016

SED-dependent Galactic Extinction Prescription for Euclid and Future Cosmological Surveys

The outcome of upcoming cosmological surveys will depend on the accurate estimates of photometric redshifts. In the framework of the implementation of the photo-z algorithm for Euclid, we are exploring new avenues to improve template-fitting methods. The paper focusses on the prescription of the extinction of source light by dust in the Milky Way. Since Galactic extinction strongly correlates with wavelength and photometry is commonly obtained in broad-band filters, the amount of absorption depends on the source SED, a point often neglected as the SED is not known a-priori. A consequence of this is that the observed E(B-V) (=A_B-A_V) will be different from the E(B-V) used to normalise the absorption law k_lambda (=A_lambda/E(B-V)). Band-pass corrections are required to renormalise the law for a given SED. We assess the band-pass corrections of a range of SEDs and find they vary by up to 20%. We investigate how dust-to-reddening scaling factors depend of the sources used for their calibration. We derive scaling factors from the color excesses of z<0.4 SDSS red galaxies and show that band-pass corrections predict the observed differences. Extinction is then estimated for a range of SEDs and filters relevant to Euclid and other cosmological ground-based surveys. For high extinction line-of-sights (E(B-V)>0.1, ~8% of the Euclid survey), the variations in corrections can be ~0.1mag in the `bluer' optical filters and ~0.04mag in the NIR filters. An inaccurate correction of extinction critically affects photo-z. In particular, for high extinctions and z<0.5, the bias (mean D_z=z_phot-z_real) exceeds 0.2%(1+z), the precision required by weak-lensing analyses. Additional uncertainty on the MW extinction law further reduces the photo-z precision. We propose a new prescription of Galactic absorption for template-fitting algorithms that takes into consideration the dependence of extinction with SED.

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arXiv2015

Mapping the Galaxy Color-Redshift Relation: Optimal Photometric Redshift Calibration Strategies for Cosmology Surveys

Calibrating the photometric redshifts of >10^9 galaxies for upcoming weak lensing cosmology experiments is a major challenge for the astrophysics community. The path to obtaining the required spectroscopic redshifts for training and calibration is daunting, given the anticipated depths of the surveys and the difficulty in obtaining secure redshifts for some faint galaxy populations. Here we present an analysis of the problem based on the self-organizing map, a method of mapping the distribution of data in a high-dimensional space and projecting it onto a lower-dimensional representation. We apply this method to existing photometric data from the COSMOS survey selected to approximate the anticipated Euclid weak lensing sample, enabling us to robustly map the empirical distribution of galaxies in the multidimensional color space defined by the expected Euclid filters. Mapping this multicolor distribution lets us determine where - in galaxy color space - redshifts from current spectroscopic surveys exist and where they are systematically missing. Crucially, the method lets us determine whether a spectroscopic training sample is representative of the full photometric space occupied by the galaxies in a survey. We explore optimal sampling techniques and estimate the additional spectroscopy needed to map out the color-redshift relation, finding that sampling the galaxy distribution in color space in a systematic way can efficiently meet the calibration requirements. While the analysis presented here focuses on the Euclid survey, similar analysis can be applied to other surveys facing the same calibration challenge, such as DES, LSST, and WFIRST.

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arXiv2014

Suzaku observation of IRAS 00521-7054, a peculiar type-II AGN with a very broad feature at 6 keV

IRAS 00521$-$7054 is the first Seyfert 2 in which the presence of an extremely large Fe K$α$ line has been claimed. We report here on the analysis of a 100 ks Suzaku observation of the source. We confirm the existence of a very strong excess over the power-law X-ray continuum at $E\sim6$ keV ($EW\simeq 800$ eV), extending down to $\sim 4.5$ keV, and found that the X-ray spectrum of the source can be explained by two different models. i) An absorption scenario, in which the X-ray source is obscured by two fully-covering ionized absorbers, with a strong reflection component from neutral material ($R\sim 1.7$), a black body component and four narrow Gaussian lines (corresponding to Fe K$α$, Fe K$β$, Fe xxv and Fe xxvi). ii) A reflection scenario, in which the X-ray spectrum is dominated by an obscured ($\log N_{\rm\,H}\sim 22.9$) blurred reflection produced in an ionized disk around a rotating supermassive black hole with a spin of $a \geq 0.73$, and affected by light-bending ($R\sim 2.7$), plus two narrow Gaussian lines (corresponding to Fe K$α$ and Fe K$β$). The narrow Fe K$α$ and K$β$ lines are consistent with being produced by ionized iron, and in particular by Fe xiv-Fe xvi and Fe xii-Fe xvi for the absorption and reflection scenario, respectively. While the X-ray continuum varies significantly during the observation, the intensity of the broad feature appears to be constant, in agreement with both the absorption and reflection scenarios. For both scenarios we obtained a steep power-law emission ($Γ\sim 2.2-2.3$), and we speculate that the source might be an obscured narrow-line Seyfert 1.

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arXiv2014

Iron K$α$ emission in type-I and type-II Active Galactic Nuclei

The narrow Fe K$α$ line is one of the main signatures of the reprocessing of X-ray radiation from the material surrounding supermassive black holes, and it has been found to be omnipresent in the X-ray spectra of active galactic nuclei (AGN). In this work we study the characteristics of the narrow Fe K$α$ line in different types of AGN. Using the results of a large Suzaku study we find that Seyfert 2s have on average lower Fe K$α$ luminosities than Seyfert 1s for the same 10-50 keV continuum luminosity. Simulating dummy Sy1s and Sy2s populations using physical torus models of X-ray reflected emission, we find that this difference can be explained by means of different average inclination angles with respect to the torus, as predicted by the unified model. Alternative explanations include differences in the intensities of Compton humps or in the photon index distributions. We show that the ratio between the flux of the broad and narrow Fe K$α$ line in the 6.35-6.45 keV range depends on the torus geometry considered, and is on average $<25\%$ and $<15\%$ for type I and type II AGN, respectively. We find evidence of absorption of the narrow Fe K$α$ line flux in Compton-thick AGN, which suggests that part of the reflecting material is obscured. We estimate that on average in obscured AGN the reflected radiation from neutral material is seen through a column density which is 1/4 of that absorbing the primary X-ray emission. This should be taken into account in synthesis models of the CXB and when studying the luminosity function of heavily obscured AGN. We detect the first evidence of the X-ray Baldwin effect in Seyfert 2s, with the same slope as that found for Seyfert 1s, which suggests that the mechanism responsible for the decrease of the equivalent width with the continuum luminosity is the same in the two classes of objects.

astro-ph.GA↗

arXiv2014

The narrow Fe K$α$ line and the molecular torus in active galactic nuclei - an IR/X-ray view

The narrow component of the iron K$α$ is an almost ubiquitous feature in the X-ray spectra of active galactic nuclei (AGN) and is believed to originate in neutral material, possibly located in the molecular torus. This would imply a tight connection between the Fe K$α$ equivalent width (EW) and the physical properties of the torus. In a recent work we have shown that the decrease of the covering factor of the torus with the luminosity, as expected by luminosity-dependent unification models, would be able to explain the decrease of Fe K$α$ EW with the luminosity (i.e., the X-ray Baldwin effect). Recent developments in the study of the mid-IR (MIR) spectrum of AGN allow important parameters of the torus to be deduced, such as its covering factor ($f_{\rm\,obs}$) and equatorial column density ($N_{\rm\,H}^{\rm\,T}$), by applying clumpy torus models. Using XMM-Newton/EPIC observations of a sample of 24 type-I AGN, we investigate the relation between the physical parameters of the torus obtained by recent MIR works and the properties of the Fe K$α$ line. We correct the values of the Fe K$α$ EW by taking the inclination angle, the photon index, the equatorial column density, and half-opening angle of the torus into account using a physical torus model of X-ray reprocessed radiation. We find that the relation between Fe K$α$ EW and $f_{\rm\,obs}$ shows a slope that is consistent with the expected value, albeit with a low statistical significance. A trend that is consistent with the theoretical prediction is also found when comparing the Fe K$α$ EW to $N_{\rm\,H}^{\rm\,T}$. Our work seems to confirm that the bulk of the narrow Fe K$α$ line is produced by the same material responsible for the MIR emission.

astro-ph.GA↗

arXiv2013

The role of the Gamma-Eddington ratio relation on the X-ray Baldwin effect in Active Galactic Nuclei

The X-ray Baldwin effect is the inverse correlation between the equivalent width (EW) of the narrow component of the iron Kalpha line and the X-ray luminosity of active galactic nuclei (AGN). A similar trend has also been observed between Fe Kalpha EW and the Eddington ratio (lambda_Edd). Using Chandra/HEG results of Shu et al. (2010) and bolometric corrections we study the relation between EW and the lambda_Edd, and find that log EW = (-0.13+/-0.03)log(lambda_Edd) + 1.47. We explore the role of the known positive correlation between the photon index of the primary X-ray continuum (Gamma) and lambda_Edd on the X-ray Baldwin effect. We simulate the iron Kalpha line emitted by populations of unabsorbed AGN considering 3 different geometries of the reflecting material: toroidal, spherical-toroidal and slab. We find that the Gamma-lambda_Edd correlation cannot account for the whole X-ray Baldwin effect, unless a strong dependence of Gamma on lambda_Edd, such as the one recently found by Risaliti et al. (2009) and Jin et al. (2012), is assumed. No clear correlation is found between EW and Gamma. We conclude that a good understanding of the slope of the Gamma-lambda_Edd relation is critical to assess whether the trend plays a leading or rather a marginal role in the X-ray Baldwin effect.

astro-ph.HE↗

arXiv2013

Luminosity-dependent unification of Active Galactic Nuclei and the X-ray Baldwin effect

The existence of an anti-correlation between the equivalent width (EW) of the narrow core of the iron Kalpha line and the luminosity of the continuum (i.e. the X-ray Baldwin effect) in type-I active galactic nuclei has been confirmed over the last years by several studies carried out with XMM-Newton, Chandra and Suzaku. However, so far no general consensus on the origin of this trend has been reached. Several works have proposed the decrease of the covering factor of the molecular torus with the luminosity (in the framework of the luminosity-dependent unification models) as a possible explanation for the X-ray Baldwin effect. Using the fraction of obscured sources measured by recent X-ray and IR surveys as a proxy of the half-opening angle of the torus, and the recent Monte-Carlo simulations of the X-ray radiation reprocessed by a structure with a spherical-toroidal geometry by Ikeda et al. (2009) and Brightman & Nandra (2011), we test the hypothesis that the X-ray Baldwin effect is related to the decrease of the half-opening angle of the torus with the luminosity. Simulating the spectra of an unabsorbed population with a luminosity-dependent covering factor of the torus as predicted by recent X-ray surveys, we find that this mechanism is able to explain the observed X-ray Baldwin effect. Fitting the simulated data with a log-linear L_{2-10keV}-EW relation, we found that in the Seyfert regime (L_{2-10keV}< 10^44.2 erg s^-1) luminosity-dependent unification produces a slope consistent with the observations for average values of the equatorial column densities of the torus of log N_H^T > 23.1. In the quasar regime (L_{2-10 keV}> 10^44.2 erg s^-1) a decrease of the covering factor of the torus with the luminosity slower than that observed in the Seyfert regime (as found by recent hard X-ray surveys) is able to reproduce the observations for 23.2 < log N_H^T < 24.2.

astro-ph.CO↗

arXiv2012

Accretion and outflow of gas in Markarian 509

A major uncertainty in models for photoionised outflows in AGN is the distance of the gas to the central black hole. We present the results of a massive multiwavelength monitoring campaign on the bright Seyfert 1 galaxy Mrk 509 to constrain the location of the outflow components dominating the soft X-ray band. Mrk 509 was monitored by XMM-Newton, Integral, Chandra, HST/COS and Swift in 2009. We have studied the response of the photoionised gas to the changes in the ionising flux produced by the central regions. We were able to put tight constraints on the variability of the absorbers from day to year time scales. This allowed us to develop a model for the time-dependent photoionisation in this source. We find that the more highly ionised gas producing most X-ray line opacity is at least 5 pc away from the core; upper limits to the distance of various absorbing components range between 20 pc up to a few kpc. The more lowly ionised gas producing most UV line opacity is at least 100 pc away from the nucleus. These results point to an origin of the dominant, slow (v<1000 km/s) outflow components in the NLR or torus-region of Mrk 509. We find that while the kinetic luminosity of the outflow is small, the mass carried away is likely larger than the 0.5 Solar mass per year accreting onto the black hole. We also determined the chemical composition of the outflow as well as valuable constraints on the different emission regions. We find for instance that the resolved component of the Fe-K line originates from a region 40-1000 gravitational radii from the black hole, and that the soft excess is produced by Comptonisation in a warm (0.2-1 keV), optically thick (tau~10-20) corona near the inner part of the disk.

astro-ph.CO↗

arXiv2011

Reflection in Seyfert Galaxies and the Unified Model of AGN

We present a deep study of the average hard X-ray spectra of Seyfert galaxies. We analyzed all public INTEGRAL IBIS/ISGRI data available on all the 165 Seyfert galaxies detected at z<0.2. Our final sample consists of 44 Seyfert 1's, 29 Seyfert 1.5's, 78 Seyfert 2's, and 14 Narrow Line Seyfert 1's. We derived the average hard X-ray spectrum of each subsample in the 17-250keV energy range. All classes of Seyfert galaxies show on average the same nuclear continuum, as foreseen by the zeroth order unified model, with a cut-off energy of Ec>200keV, and a photon index of Gamma ~1.8. Compton-thin Seyfert 2's show a reflection component stronger than Seyfert 1's and Seyfert 1.5's. Most of this reflection is due to mildly obscured (10^23 cm^-2 < NH < 10^24 cm^-2) Seyfert 2's, which have a significantly stronger reflection component (R=2.2^{+4.5}_{-1.1}) than Seyfert 1's (R<=0.4), Seyfert 1.5's (R<= 0.4) and lightly obscured (NH < 10^23 cm^-2) Seyfert 2's (R<=0.5). This cannot be explained easily by the unified model. The absorber/reflector in mildly obscured Seyfert 2's might cover a large fraction of the X-ray source, and have clumps of Compton-thick material. The large reflection found in the spectrum of mildly obscured Seyfert 2's reduces the amount of Compton-thick objects needed to explain the peak of the cosmic X-ray background. Our results are consistent with the fraction of Compton-thick sources being ~10%. The spectra of Seyfert 2's with and without polarized broad lines do not show significant differences, the only difference between the two samples being the higher hard X-ray and bolometric luminosity of Seyfert 2's with polarized broad lines. The average hard X-ray spectrum of Narrow line Seyfert 1's is steeper than those of Seyfert 1's and Seyfert 1.5's, probably due to a lower energy of the cutoff.

astro-ph.CO↗

arXiv2011

Multiwavelength campaign on Mrk 509. IV. Optical-UV-X-ray variability and the nature of the soft X-ray excess

We present the analysis of XMM-Newton and Swift optical-UV and X-ray observations of the Seyfert-1/QSO Mrk 509, part of an unprecedented multi-wavelength campaign, investigating the nuclear environment of this AGN. The XMM-Newton data are from a series of 10 observations of about 60 ks each, spaced from each other by about 4 days, taken in Oct-Nov 2009. During our campaign, Mrk 509 was also observed with Swift for a period of about 100 days, monitoring the behaviour of the source before and after the XMM-Newton observations. With these data we have established the continuum spectrum in the optical-UV and X-ray bands and investigated its variability on the timescale of our campaign with a resolution time of a few days. In order to measure and model the continuum as far as possible into the UV, we also made use of HST/COS observations of Mrk 509 (part of our coordinated campaign) and of an archival FUSE observation. We have found that in addition to an X-ray power-law, the spectrum displays soft X-ray excess emission below 2 keV, which interestingly varies in association with the thermal optical-UV emission from the accretion disc. The change in the X-ray power-law component flux (albeit smaller than that of the soft excess), on the other hand, is uncorrelated to the flux variability of the soft X-ray excess and the disc component on the probed timescale. The results of our simultaneous broad-band spectral and timing analysis suggest that, on a resolution time of a few days, the soft X-ray excess of Mrk 509 is produced by the Comptonisation of the thermal optical-UV photons from the accretion disc by a warm (0.2 keV) optically thick (tau ~ 17) corona surrounding the inner regions of the disc. This makes Mrk 509, with a black hole mass of about 1-3 x 10^8 solar masses, the highest mass known system to display such behaviour and origin for the soft X-ray excess.

astro-ph.CO↗

arXiv2011

Hard X-ray Variability of the Brightest Swift/BAT AGN

Variability is one of the hallmarks of Active Galactic Nuclei. The Burst Alert Telescope onboard of Swift, with its homogeneous coverage of the sky is a formidable tool to study variability at hard X-rays. We present here the analysis of the 1-month binned Swift/BAT lightcurves of the 20 brightest Active Galactic Nuclei in the hard X-ray sky. The sample consists of 2 blazars, 3 radio galaxies, 6 Seyfert 1/1.5s, 8 Seyfert 2s and 1 Narrow Line Seyfert 1. We found that all the objects show variability, and most of them have a value of the fractional root mean squared variability amplitude of Fvar \sim 0.2 - 0.3. We did not find any significant correlation of Fvar with the column density or the luminosity in our sample.

astro-ph.HE↗

arXiv2007

Hard X-ray colours of Neutron Star and Black Hole Low Mass X-ray Binaries with INTEGRAL

The X-ray spectra of Low Mass X-ray Binaries (LMXB) can change on short time-scales, making it difficult to follow their spectral characteristics in detail through model fitting. Colour-colour (C-C) diagrams are therefore often used as alternative, model independent, tools to study the spectral variability of these sources. The INTEGRAL mission, with its high sensitivity, large field of view and good angular resolution, is well suited to study the hard X-ray properties of LMXBs. In particular the ISGRI imager on board of INTEGRAL allows the regular monitoring of the sources in the less frequently studied domain above 20 keV. In this proceeding, C-C diagrams have been made with data from the INTEGRAL public archive; a search is made for systematic differences in the C-C diagrams between black hole candidates (BH) and neutron stars (NS) in LMXBs using a moments analysis method.

astro-ph↗

arXiv2002

Dynamics of the Lyman alpha and C IV emitting gas in 3C 273

In this paper we study the variability properties of the Lyman alpha and C IV emission lines in 3C273 using archival IUE observations. Our data show for the first time the existence of variability on time scales of several years. We study the spatial distribution and the velocity field of the emitting gas by performing detailed analyses on the line variability using correlations, 1D and 2D response functions, and principal component analysis. In both lines we find evidence for two components, one which has the dynamic properties of gas in Keplerian motion around a black hole with a mass of the order of 10^9 Mo, and one which is characterized by high, blue-shifted velocities at large lag. There is no indication of the presence of optically thick emission medium neither in the Lya, nor in the Civ response functions. The component characterized by blue-shifted velocities, which is comparatively much stronger in Civ than in Lya, is more or less compatible with being the result of gas falling towards the central black hole with free-fall acceleration. We propose however that the line emission at high, blue-shifted velocities is better explained in terms of entrainment of gas clouds by the jet. This gas is therefore probably collisionally excited as a result of heating due to the intense infrared radiation from the jet, which would explain the strength of this component in Civ relative to Lya. This phenomenon might be a signature of disk-jet interaction.

astro-ph↗

arXiv1997

Rest-frame variability of quasars and Seyfert galaxies in the ultraviolet: Constraints on the discrete-event models

We determine the variability-luminosity relationship of quasars and Seyfert galaxies in the rest frame of the objects using IUE spectra. We find that the variability decreases with the luminosity. An important part of the scatter in the relationship may be explained if one tries to estimate the uncertainties on the variability due to the sampling. We discuss the variability using the concept of discrete events. The trend between variability and luminosity is described by a power-law with an index -0.08, which is incompatible with the power-law of index -1/2 predicted by the most general discrete-event models in which the change in average luminosity is due to differences in average event rates exclusively. We conclude that the -1/2 index is definitely inconsistent with the data. A flat relationship is however possible, if some bias has been underestimated. We propose different ways whereby discrete events may produce a different variability--luminosity relationship: by changing the luminosity or the life time of the events, or by introducing interdependence between the events. The latter possibility cannot produce a satisfactory relationship. Using the former possibilities, we do not find any "natural" explanation for the variability- luminosity relationship in the context of discrete-event models. This is possibly an indication that explanations in which variability is not expressed in terms of discrete events should be favoured.

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