A Bayesian Approach to Estimate the Size and Structure of the Broad-line Region in Active Galactic Nuclei Using Reverberation Mapping Data

This is the first paper in a series devoted to systematic study of the size and structure of the broad-line region (BLR) in active galactic nuclei (AGNs) using reverberation mapping (RM) data. We employ a recently developed Bayesian approach that statistically describes the variabibility as a damped random walk process and delineates the BLR structure using a flexible disk geometry that can account for a variety of shapes, including disks, rings, shells, and spheres. We allow for the possibility that the line emission may respond non-linearly to the continuum, and we detrend the light curves when there is clear evidence for secular variation. We use a Markov Chain Monte Carlo implementation based on Bayesian statistics to recover the parameters and uncertainties for the BLR model. The corresponding transfer function is obtained self-consistently. We tentatively constrain the virial factor used to estimate black hole masses; more accurate determinations will have to await velocity-resolved RM data. Application of our method to RM data with Hbeta monitoring for about 40 objects shows that the assumed BLR geometry can reproduce quite well the observed emission-line fluxes from the continuum light curves. We find that the Hbeta BLR sizes obtained from our method are on average ~20% larger than those derived from the traditional cross-correlation method. Nevertheless, we still find a tight BLR size-luminosity relation with a slope of alpha=0.55\pm0.03 and an intrinsic scatter of ~0.18 dex. In particular, we demonstrate that our approach yields appropriate BLR sizes for some objects (such as Mrk 142 and PG 2130+099) where traditional methods previously encountered difficulties.Comment: 17 pages, 10 figures, 2 tables; minor reversion to match the published versio

DebCSE: Rethinking Unsupervised Contrastive Sentence Embedding Learning in the Debiasing Perspective

Several prior studies have suggested that word frequency biases can cause the Bert model to learn indistinguishable sentence embeddings. Contrastive learning schemes such as SimCSE and ConSERT have already been adopted successfully in unsupervised sentence embedding to improve the quality of embeddings by reducing this bias. However, these methods still introduce new biases such as sentence length bias and false negative sample bias, that hinders model's ability to learn more fine-grained semantics. In this paper, we reexamine the challenges of contrastive sentence embedding learning from a debiasing perspective and argue that effectively eliminating the influence of various biases is crucial for learning high-quality sentence embeddings. We think all those biases are introduced by simple rules for constructing training data in contrastive learning and the key for contrastive learning sentence embedding is to mimic the distribution of training data in supervised machine learning in unsupervised way. We propose a novel contrastive framework for sentence embedding, termed DebCSE, which can eliminate the impact of these biases by an inverse propensity weighted sampling method to select high-quality positive and negative pairs according to both the surface and semantic similarity between sentences. Extensive experiments on semantic textual similarity (STS) benchmarks reveal that DebCSE significantly outperforms the latest state-of-the-art models with an average Spearman's correlation coefficient of 80.33% on BERTbase

A New Approach to Constrain Black Hole Spins in Active Galaxies Using Optical Reverberation Mapping

A tight relation between the size of the broad-line region (BLR) and optical luminosity has been established in about 50 active galactic nuclei studied through reverberation mapping of the broad Hbeta emission line. The R_blr-L relation arises from simple photoionization considerations. Using a general relativistic model of an optically thick, geometrically thin accretion disk, we show that the ionizing luminosity jointly depends on black hole mass, accretion rate, and spin. The non-monotonic relation between the ionizing and optical luminosity gives rise to a complicated relation between the BLR size and the optical luminosity. We show that the reverberation lag of Hbeta to the varying continuum depends very sensitively to black hole spin. For retrograde spins, the disk is so cold that there is a deficit of ionizing photons in the BLR, resulting in shrinkage of the hydrogen ionization front with increasing optical luminosity, and hence shortened Hbeta lags. This effect is specially striking for luminous quasars undergoing retrograde accretion, manifesting in strong deviations from the canonical R_blr-L relation. This could lead to a method to estimate black hole spins of quasars and to study their cosmic evolution. At the same time, the small scatter of the observed R_blr-L relation for the current sample of reverberation-mapped active galaxies implies that the majority of these sources have rapidly spinning black holes.Comment: 6 pages, 5 figures, to appear in ApJ

Rarefied Broad-Line Regions in Active Galactic Nuclei: Anomalous Responses in Reverberation Mapping and Implications for Weak-Emission Line Quasars

Reverberation mapping (RM) is a widely-used method for probing the physics of broad-line regions (BLRs) in active galactic nuclei (AGNs). There are increasing preliminary evidences that the RM behaviors of broad emission lines are influenced by BLR densities, however, the influences have not been investigated systematically from theoretical perspective. In the present paper, we adopt locally optimally emitting cloud model and use CLOUDY to obtain the one-dimensional transfer functions of the prominent UV and optical emission lines for different BLR densities. We find that the influences of BLR densities to RM behaviors have mainly three aspects. First, rarefied BLRs (with low gas densities) may show anomalous responses in RM observations. Their emission-line light curves inversely response the variations of continuum light curves, which may have been observed in some UV RM campaigns. Second, the different BLR densities in AGNs may result in correlations between the time lags and equivalent widths of emission lines, and may contribute to the scatters of the radius-luminosity relationships. Third, the variations of BLR densities may explain the changes of time lags in individual objects in different years. Some weak emission-line quasars (WLQs) are probably extreme cases of rarefied BLRs. We predict that their RM observations may show the anomalous responses.Comment: 28 pages, 12 figures, accepted for publication in The Astrophysical Journa