Quasar Black Hole Mass Estimates in the Era of Time Domain Astronomy

We investigate the dependence of the normalization of the high-frequency part of the X-ray and optical power spectral densities (PSD) on black hole mass for a sample of 39 active galactic nuclei (AGN) with black hole masses estimated from reverberation mapping or dynamical modeling. We obtained new Swift observations of PG 1426+015, which has the largest estimated black hole mass of the AGN in our sample. We develop a novel statistical method to estimate the PSD from a lightcurve of photon counts with arbitrary sampling, eliminating the need to bin a lightcurve to achieve Gaussian statistics, and we use this technique to estimate the X-ray variability parameters for the faint AGN in our sample. We find that the normalization of the high-frequency X-ray PSD is inversely proportional to black hole mass. We discuss how to use this scaling relationship to obtain black hole mass estimates from the short time-scale X-ray variability amplitude with precision ~ 0.38 dex. The amplitude of optical variability on time scales of days is also anti-correlated with black hole mass, but with larger scatter. Instead, the optical variability amplitude exhibits the strongest anti-correlation with luminosity. We conclude with a discussion of the implications of our results for estimating black hole mass from the amplitude of AGN variability.Comment: 19 pages, 10 figures, emulateapj format, submitted to Ap

The Impact of the Uncertainty in Single-Epoch Virial Black Hole Mass Estimates on the Observed Evolution of the Black Hole - Bulge Scaling Relations

Recent observations of the black hole (BH) - bulge scaling relations usually report positive redshift evolution, with higher redshift galaxies harboring more massive BHs than expected from the local relations. All of these studies focus on broad line quasars with BH mass estimated from virial estimators based on single-epoch spectra. Since the sample selection is largely based on quasar luminosity, the cosmic scatter in the BH-bulge relation introduces a statistical bias leading to on average more massive BHs given galaxy properties at high redshift (Lauer et al. 2007). We here emphasize a previously under-appreciated statistical bias resulting from the uncertainty of single-epoch virial BH mass estimators and the shape of the underlying (true) BH mass function, which leads to on average overestimation of the true BH masses at the high-mass end (Shen et al. 2008). We demonstrate that the latter virial mass bias can contribute a substantial amount to the observed excess in BH mass at fixed bulge properties, comparable to the Lauer et al. bias. The virial mass bias is independent of the Lauer et al. bias, hence if both biases are at work, they can largely (or even fully) account for the observed BH mass excess at high redshift.Comment: Replaced with the accepted version

Comparing Single-Epoch Virial Black Hole Mass Estimators for Luminous Quasars

Single-epoch virial black hole (BH) mass estimators utilizing broad emission lines have been routinely applied to high-redshift quasars to estimate their BH masses. Depending on the redshift, different line estimators (Halpha, Hbeta, MgII, CIV) are often used with optical/near-infrared spectroscopy. Here we use a homogeneous sample of 60 intermediate-redshift (z~1.5-2.2) SDSS quasars with optical and near-infrared spectra covering CIV through Halpha to investigate the consistency between different line estimators. We critically compare restframe UV line estimators (CIV, CIII], and MgII) with optical estimators (Hbeta and Halpha) in terms of correlations between line widths and between continuum/line luminosities, for the high-luminosity regime (L_5100>10^45.4 erg/s) probed by our sample. The continuum luminosities of L_1350 and L_3000, and the broad line luminosities are well correlated with L_5100. We found that the MgII FWHM correlates well with the FWHMs of the Balmer lines, and that the MgII line estimator can be calibrated to yield consistent virial mass estimates with those based on the Hbeta/Halpha estimators, thus extending earlier results on less luminous objects. The CIV FWHM is poorly correlated with the Balmer line FWHMs, and the scatter between the CIV and Hbeta FWHMs consists of an irreducible part (~0.12 dex), and a part that correlates with the blueshift of the CIV centroid relative to that of Hbeta. The CIII] FWHM is found to correlate with the CIV FWHM, and hence is also poorly correlated with the Hbeta FWHM. While the CIV and CIII] lines can be calibrated to yield consistent virial mass estimates as Hbeta on average, the scatter is substantially larger than MgII, and the usage of CIV/CIII] FWHM in the mass estimators does not improve the agreement with the Hbeta estimator. (Abridged)Comment: 17 emulateapj pages; submitted to Ap

Adapting the Customer Satisfaction Index to the Lodging Industry: Foreign Customers\u27 Evaluations

As a standard form of measuring customer satisfaction, the Customer Satisfaction Index (CSI) has been utilized in many countries. By using the Korean Customer Satisfaction Index (KCSI) methodology, this study attempted to investigate foreign customers’ evaluations of luxury hotels in Seoul, South Korea. In doing so, some efforts were made to overcome the methodological problems associated with the KCSI for the lodging industry. Data for this study were collected through a mall intercept survey using a self-administered questionnaire. Precisely 783 responses, collected solely from foreign guests who had stayed at a luxury hotel in Seoul, were included in the study

Calibrating CIV-based black hole mass estimators

We present the single-epoch black hole mass estimators based on the CIV (1549 A) broad emission line, using the updated sample of the reverberation-mapped AGNs and high-quality UV spectra. By performing multi-component spectral fitting analysis, we measure the CIV line widths (FWHM_CIV) and line dispersion (sigma_CIV) and the continuum luminosity at 1350 A (L_1350) to calibrate the CIV-based mass estimators. By comparing with the Hbeta reverberation-based masses, we provide new mass estimators with the best-fit relationships, i.e., M_BH \propto L_1350 ^ (0.50+-0.07) sigma_CIV ^2 and M_BH \propto L_1350 ^ (0.52+-0.09) FWHM_CIV ^ (0.56+-0.48). The new CIV-based mass estimators show significant mass-dependent systematic difference compared to the estimators commonly used in the literature. Using the published Sloan Digital Sky Survey QSO catalog, we show that the black hole mass of high-redshift QSOs decreases on average by ~0.25 dex if our recipe is adopted.Comment: 12 pages, 7 figures, ApJ in press, figure revise

The Lick AGN Monitoring Project: Recalibrating Single-Epoch Virial Black Hole Mass Estimates

We investigate the calibration and uncertainties of black hole mass estimates based on the single-epoch (SE) method, using homogeneous and high-quality multi-epoch spectra obtained by the Lick Active Galactic Nucleus (AGN) Monitoring Project for 9 local Seyfert 1 galaxies with black hole masses < 10^8 M_sun. By decomposing the spectra into their AGN and stellar components, we study the variability of the single-epoch Hbeta line width (full width at half-maximum intensity, FWHM_Hbeta; or dispersion, sigma_Hbeta) and of the AGN continuum luminosity at 5100A (L_5100). From the distribution of the "virial products" (~ FWHM_Hbeta^2 L_5100^0.5 or sigma_Hbeta^2 L_5100^0.5) measured from SE spectra, we estimate the uncertainty due to the combined variability as ~ 0.05 dex (12%). This is subdominant with respect to the total uncertainty in SE mass estimates, which is dominated by uncertainties in the size-luminosity relation and virial coefficient, and is estimated to be ~ 0.46 dex (factor of ~ 3). By comparing the Hbeta line profile of the SE, mean, and root-mean-square (rms) spectra, we find that the Hbeta line is broader in the mean (and SE) spectra than in the rms spectra by ~ 0.1 dex (25%) for our sample with FWHM_Hbeta < 3000 km/s. This result is at variance with larger mass black holes where the difference is typically found to be much less than 0.1 dex. To correct for this systematic difference of the Hbeta line profile, we introduce a line-width dependent virial factor, resulting in a recalibration of SE black hole mass estimators for low-mass AGNs.Comment: Accepted for publication in ApJ. 18 pages, 17 figure

The Mass of the Black Hole in Arp 151 from Bayesian Modeling of Reverberation Mapping Data

Supermassive black holes are believed to be ubiquitous at the centers of galaxies. Measuring their masses is extremely challenging yet essential for understanding their role in the formation and evolution of cosmic structure. We present a direct measurement of the mass of a black hole in an active galactic nucleus (Arp 151) based on the motion of the gas responsible for the broad emission lines. By analyzing and modeling spectroscopic and photometric time series, we find that the gas is well described by a disk or torus with an average radius of 3.99 +- 1.25 light days and an opening angle of 68.9 (+21.4, -17.2) degrees, viewed at an inclination angle of 67.8 +- 7.8 degrees (that is, closer to face-on than edge-on). The black hole mass is inferred to be 10^(6.51 +- 0.28) solar masses. The method is fully general and can be used to determine the masses of black holes at arbitrary distances, enabling studies of their evolution over cosmic time.Comment: Accepted for publication in ApJ Letter

Skewed recoil polarization in (e,e'p) reactions from polarized nuclei

The general formalism describing $\vec{A}(\vec{e},e'\vec{p})B$ reactions, involving polarization of the electron beam, target and ejected proton, is presented within the framework of the relativistic plane wave impulse approximation for medium and heavy nuclei. It is shown that the simultaneous measurement of the target and ejected proton polarization can provide new information which is not contained in the separate analysis of the $\vec{A}(\vec{e},e'p)B$ and $A(\vec{e},e'\vec{p})B$ reactions. The polarization transfer mechanism in which the electron interacts with the initial nucleon carrying the target polarization, making the proton exit with a fractional polarization in a different direction, is referred to here as ``skewed polarization''. The new observables characterizing the process are identified, and written in terms of polarized response functions and asymmetries which are of tensor nature. The corresponding half-off-shell single-nucleon responses are analyzed using different prescriptions for the electromagnetic vertex and for different kinematics. Numerical predictions are presented for selected perpendicular and parallel kinematics in the case of $^{39}$K as polarized target.Comment: 30 pages, 8 figure