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With respect to the Hβ FWHM (FWHMHβ ), the broad Hβ line dispersion (σ Hβ ) was preferred as a velocity tracer to calculate the single-epoch supermassive black hole mass (M BH) suggested by Yu et al. For a compiled sample of 311 broad-line active galactic nuclei (AGNs) with measured hard X-ray photon index (z < 0.7), σ Hβ and the optical Fe ii relative strength (R Fe) are measured from their optical spectra, which are used to calculate σ Hβ -based virial M BH and dimensionless accretion rate ( M ̇ ). With respect to FWHMHβ , it is found that the mean value of σ Hβ -based M BH is on average larger by 0.26 dex and the mean value of σ Hβ -based M ̇ is on average smaller by 0.51 dex. It is found that there exists a nonlinear relationship between the Eddington ratio (L Bol/L Edd) and M ̇ , i.e., L Bol / L Edd ∝ M ̇ 0.56 ± 0.01 . This nonlinear relationship comes from the accretion efficiency η, which is smaller for AGNs with higher M ̇ . We find a strong bivariate correlation of the fraction of energy released in the corona F X with M ̇ and M BH, F X ∝ M ̇ − 0.57 ± 0.05 M BH − 0.54 ± 0.06 . The flat slope of −0.57 ± 0.05 favors the shear stress tensor of the accretion disk being proportional to the geometric mean of gas pressure and total pressure. We find a strong bivariate relation of Γ with M ̇ and F X, Γ ∝ M ̇ − 0.21 ± 0.02 F X 0.02 ± 0.04 . The hard X-ray spectrum becomes softer with increasing F X, although the scatter is large.
With respect to the Hβ FWHM (FWHMHβ ), the broad Hβ line dispersion (σ Hβ ) was preferred as a velocity tracer to calculate the single-epoch supermassive black hole mass (M BH) suggested by Yu et al. For a compiled sample of 311 broad-line active galactic nuclei (AGNs) with measured hard X-ray photon index (z < 0.7), σ Hβ and the optical Fe ii relative strength (R Fe) are measured from their optical spectra, which are used to calculate σ Hβ -based virial M BH and dimensionless accretion rate ( M ̇ ). With respect to FWHMHβ , it is found that the mean value of σ Hβ -based M BH is on average larger by 0.26 dex and the mean value of σ Hβ -based M ̇ is on average smaller by 0.51 dex. It is found that there exists a nonlinear relationship between the Eddington ratio (L Bol/L Edd) and M ̇ , i.e., L Bol / L Edd ∝ M ̇ 0.56 ± 0.01 . This nonlinear relationship comes from the accretion efficiency η, which is smaller for AGNs with higher M ̇ . We find a strong bivariate correlation of the fraction of energy released in the corona F X with M ̇ and M BH, F X ∝ M ̇ − 0.57 ± 0.05 M BH − 0.54 ± 0.06 . The flat slope of −0.57 ± 0.05 favors the shear stress tensor of the accretion disk being proportional to the geometric mean of gas pressure and total pressure. We find a strong bivariate relation of Γ with M ̇ and F X, Γ ∝ M ̇ − 0.21 ± 0.02 F X 0.02 ± 0.04 . The hard X-ray spectrum becomes softer with increasing F X, although the scatter is large.
Measuring broad emission-line widths in active galactic nuclei (AGN) is not straightforward owing to the complex nature of flux variability in these systems. Line width measurements become especially challenging when the signal-to-noise ratio is low, profiles are narrower, or spectral resolution is low. We conducted an extensive correlation analysis between emission-line measurements from the optical spectra of Markarian 142 (Mrk 142; a narrow-line Seyfert galaxy) taken with the Gemini North Telescope (Gemini) at a spectral resolution of 185.6 ± 10.2 km s−1 and the Lijiang Telescope (LJT) at 695.2 ± 3.9 km s−1 to investigate the disparities in the measured broad-line widths from both telescopes’ data. Due to its narrow broad-line profiles, which were severely affected by instrumental broadening in the lower-resolution LJT spectra, Mrk 142 posed a challenge. We discovered that allowing the narrow-line flux of permitted lines having broad and narrow components to vary during spectral fitting caused a leak in the narrow-line flux to the broad component, resulting in broader broad-line widths in the LJT spectra. Fixing the narrow-line flux ratios constrained the flux leak and yielded the Hβ broad-line widths from LJT spectra ∼54% closer to the Gemini Hβ widths than with flexible narrow-line ratios. The availability of spectra at different resolutions presented this unique opportunity to inspect how spectral resolution affected emission-line profiles in our data and adopt a unique method to accurately measure broad-line widths. Reconsidering line measurement methods while studying diverse AGN populations is critical for the success of future reverberation-mapping studies. Based on the technique used in this work, we offer recommendations for measuring line widths in narrow-line AGN.
Based on the spectral decomposition through a code of PrepSpec, the light curves (spanning 6.5 years in the observed frame) of the broad-line Balmer decrement, i.e., the flux ratio of the broad Hα to the broad Hβ line, are calculated for a sample of 44 Sloan Digital Sky Survey reverberation-mapped quasars (z < 0.53). It is found that the logarithm of the mean broad-line Balmer decrement is 0.62 with a standard deviation of 0.15 dex. The relations between the mean Balmer decrement and the SMBH accretion properties (the luminosity, black hole mass, Eddington ratio, accretion rate) are investigated and no obvious correlations are found. It is found that there are 27 quasars ($61\%$) showing strong negative correlations between the Balmer decrement variance and the continuum variance, i.e., the Balmer decrement would be smaller with larger continuum flux. Assuming that the dust obscuration leads to the variance in the Balmer decrement and the continuum, an expected slope is −1/3, which is not consistent with most of measured slopes. Using the interpolated cross-correlation function, the time delays between the inverse Balmer decrement and the continuum are measured for 14 quasars with the maximum correlation coefficient larger the 0.6. It suggests that the size corresponding to the Balmer decrement lag extends from the BLR size to the torus size.
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