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Register a new userOn reverberation and cross-correlation estimates of the size of the broad-line region in active galactic nuclei
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Alexander Melnikov Dr.
Publication date
2008
fields
Physics
and research's language is
English
Authors
Alexander V. Melnikov
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It is known that the dependence of the emission-line luminosity of a typical cloud in the active galactic nuclei broad-line regions (BLRs) upon the incident flux of ionizing continuum can be nonlinear. We study how this nonlinearity can be taken into account in estimating the size of the BLR by means of the reverberation methods. We show that the BLR size estimates obtained by cross-correlation of emission-line and continuum light curves can be much (up to an order of magnitude) less than the values obtained by reverberation modelling. This is demonstrated by means of numerical cross-correlation and reverberation experiments with model continuum flares and emission-line transfer functions and by means of practical reverberation modelling of the observed optical spectral variability of NGC 4151. The time behaviour of NGC 4151 in the H_alpha and H_beta lines is modelled on the basis of the observational data by Kaspi et al. (1996, ApJ, 470, 336) and the theoretical BLR model by Shevchenko (1984, Sov. Astron. Lett., 10, 377; 1985, Sov. Astron. Lett., 11, 35). The values of the BLR parameters are estimated that allow to judge on the size and physical characteristics of the BLR. The small size of the BLR, as determined by the cross-correlation method from the data of Kaspi et al. (1996, ApJ, 470, 336), is shown to be an artifact of this method. So, the hypothesis that the BLR size varies in time is not necessitated by the observational data.
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We reinvestigate the relationship between the characteristic broad-line region size (R_blr) and the Balmer emission-line, X-ray, UV, and optical continuum luminosities. Our study makes use of the best available determinations of R_blr for a large number of active galactic nuclei (AGNs) from Peterson et al. Using their determinations of R_blr for a large sample of AGNs and two different regression methods, we investigate the robustness of our correlation results as a function of data sub-sample and regression technique. Though small systematic differences were found depending on the method of analysis, our results are generally consistent. Assuming a power-law relation R_blr propto L^alpha, we find the mean best-fitting alpha is about 0.67+/-0.05 for the optical continuum and the broad Hbeta luminosity, about 0.56+/-0.05 for the UV continuum luminosity, and about 0.70+/-0.14 for the X-ray luminosity. We also find an intrinsic scatter of about 40% in these relations. The disagreement of our results with the theoretical expected slope of 0.5 indicates that the simple assumption of all AGNs having on average same ionization parameter, BLR density, column density, and ionizing spectral energy distribution, is not valid and there is likely some evolution of a few of these characteristics along the luminosity scale.
Broad emission lines in active galactic nuclei (AGNs) mainly arise from gas photoionized by continuum radiation from an accretion disk around a central black hole. The shape of the broad-line profile, described by ${cal D}_{_{rm Hbeta}}={rm FWHM}/sigma_{_{rm Hbeta}}$, the ratio of full width at half maximum to the dispersion of broad H$beta$, reflects the dynamics of the broad-line region (BLR) and correlates with the dimensionless accretion rate ($dot{mathscr{M}}$) or Eddington ratio ($L_{rm bol}/L_{rm Edd}$). At the same time, $dot{mathscr{M}}$ and $L_{rm bol}/L_{rm Edd}$ correlate with ${cal R}_{rm Fe}$, the ratio of optical Fe II to H$beta$ line flux emission. Assembling all AGNs with reverberation mapping measurements of broad H$beta$, both from the literature and from new observations reported here, we find a strong bivariate correlation of the form $log(dot{mathscr{M}},L_{rm bol}/L_{rm Edd})=alpha+beta{cal D}_{_{rm Hbeta}}+gamma{cal R}_{rm Fe},$ where $alpha=(2.47,0.31)$, $beta=-(1.59,0.82)$ and $gamma=(1.34,0.80)$. We refer to this as the fundamental plane of the BLR. We apply the plane to a sample of $z < 0.8$ quasars to demonstrate the prevalence of super-Eddington accreting AGNs are quite common at low redshifts.
The masses and emission-line region sizes of Active Galactic Nuclei (AGNs) can be measured by ``reverberation-mapping (measuring the lag of the emission-line luminosity after changes in the continuum). We use tis technique to calibrate similar size and mass estimates made by photoionization models of the AGN line-emitting regions. We compile a sample of 19 AGNs with reliable reverberation and spectroscopy data, twice the number available previously. The data provide strong evidence that the BLR size and the emission-line width measure directly the central mass. Two methods are used to estimate the distance of the broad emission-line region (BLR) from the ionizing source: the photoionization method (available for many AGNs but has large intrinsic uncertainties), and the reverberation method (gives very reliable distances, but available for only a few objects). The distance estimate is combined with the velocity dispersion, derived from the broad Hb line profile, to estimate the virial mass. Comparing the central masses calculated with the reverberation method to those calculated using a photoionization model, we find a highly significant, nearly linear correlation. This provides a calibration of the photoionization method on the objects with presently available reverberation data, which should enable mass estimates for all AGNs with measured Hb line width. Comparing the BLR sizes given by the two methods also enables us to estimate the ionizing EUV luminosity which is directly unobservable. We find it to be typically ten times the visible (monochromatic luminosity at 5100A). The inferred Eddington ratio of the individual objects in our sample are 0.001-0.03 (visible luminosity) and 0.01-0.3 (ionizing luminosity).
Most results of the reverberation monitoring of active galaxies showed a universal scaling of the time delay of the Hbeta emission region with the monochromatic flux at 5100 A, with very small dipersion. Such a scaling favored the dust-based formation mechanism of the Broad Line Region (BLR). Recent reverberation measurements showed that actually a significant fraction of objects exhibits horter lags than the previously found scaling. Here we demonstrate that these shorter lags can be explained by the old concept of scaling of the BLR size with the ionization parameter. Assuming a universal value of this parameter and universal value of the cloud density reproduces the distribution of observational points in the time delay vs. monochromatic flux plane, provided that a range of black hole spins is allowed. However, a confirmation of the new measurements for low/moderate Eddington ratio sources is strongly needed before the dust-based origin of the BLR can be excluded.
The combination of the linear size from reverberation mapping (RM) and the angular distance of the broad line region (BLR) from spectroastrometry (SA) in active galactic nuclei (AGNs) can be used to measure the Hubble constant $H_0$. Recently, Wang et al. (2020) successfully employed this approach and estimated $H_0$ from 3C 273. However, there may be a systematic deviation between the response-weighted radius (RM measurement) and luminosity-weighted radius (SA measurement), especially when different broad lines are adopted for size indicators (e.g., hb for RM and pa for SA). Here we evaluate the size deviations measured by six pairs of hydrogen lines (e.g., hb, ha and pa) via the locally optimally emitting cloud (LOC) models of BLR. We find that the radius ratios $K$(=$R_{rm SA}$/$R_{rm RM}$) of the same line deviated systematically from 1 (0.85-0.88) with dispersions between 0.063-0.083. Surprisingly, the $K$ values from the pa(SA)/hb(RM) and ha(SA)/hb(RM) pairs not only are closest to 1 but also have considerably smaller uncertainty. Considering the current infrared interferometry technology, the pa(SA)/hb(RM) pair is the ideal choice for the low redshift objects in the SARM project. In the future, the ha(SA)/hb(RM) pair could be used for the high redshift luminous quasars. These theoretical estimations of the SA/RM radius pave the way for the future SARM measurements to further constrain the standard cosmological model.
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