arXiv subjects

Kai-Xing Lu

Publications and source records attributed to Kai-Xing Lu.

At least 37 records · Page 2Linked to original sources

arXiv2021

Application of the space-based optical interferometer towards measuring cosmological distances of quasars

Measuring the quasar distance through joint analysis of spectroastrometry (SA) and reverberation mapping (RM) observations is a new method for driving the development of cosmology. In this paper, we carry out detailed simulation and analysis to study the effect of four basic observational parameters (baseline length, exposure time, equivalent diameter and spectral resolution) on the data quality of differential phase curves (DPCs), furthermore on the accuracy of distance measurement. In our simulation, we adopt an axis symmetrical disc model of broad line region (BLR) to generate differential phase signals. We find that the differential phases and their Poisson errors could be amplified by extending the baseline, while the influence of OPD (optical path difference) errors can be reduced during fitting the BLR model. Longer exposure time or larger equivalent diameter helps reduce the absolute Poisson error. Therefore, the relative error of DPCs could be reduce by increasing any of the above three parameters, then the accuracy of distance measurement could be improved. In contrast, the uncertainty of $D_{\rm{A}}$ ( absolute angular distances) could be improved with higher spectral resolution, although the relative error of DPCs would be amplified. We show how the uncertainty of distance measurement varies with the relative error of DPCs. For our specific set of model parameters, without considering more complicated structures and kinematics of BLRs in our simulation, it is found that the relative error of DPCs $<$ 20$\%$ is a limit for accurate distance measurement. The relative error of DPCs have a lower limit (roughly 5$\%$) and the uncertainty of distance measurement can be better than 2$\%$.

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arXiv2021

Reverberation Mapping Measurements of Black Hole Masses and Broad-Line Region Kinematics in Mrk 817 and NGC 7469

We present the results from a spectroscopic monitoring campaign to obtain reverberation-mapping measurements and investigate the broad-line region kinematics for active galactic nuclei (AGN) of Mrk~817 and NGC~7469. This campaign was undertaken with the Lijiang 2.4-meter telescope, the median spectroscopic sampling is 2.0 days for Mrk~817 and 1.0 days for NGC~7469. We detect time lags of the broad emission lines including H$β$, H$γ$, He~{\sc ii} and He~{\sc i} for both AGNs, and including Fe~{\sc ii} for Mrk~817 with respect to the varying AGN continuum at 5100~Å. Investigating the relationship between line widths and time lags of the broad emission lines, we find that the BLR dynamics of Mrk~817 and NGC~7469 are consistent with the virial prediction. We estimate the masses of central supermassive black hole (SMBH) and the accretion rates of both AGNs. Using the data of this campaign, we construct the velocity-resolved lag profiles of the broad H$γ$, H$β$, and He~{\sc i} lines for Mrk~817, which show almost the same kinematic signatures that the time lags in the red wing are slightly larger than the time lags in the blue wing. For NGC~7469, we only clearly construct the velocity-resolved lag profiles of the broad H$γ$ and H$β$, which show very similar kinematic signatures to the BLR of Mrk~817. These signatures indicate that the BLR of Keplerian motion in both AGNs seemingly has outflowing components during the monitoring period. We discuss the kinematics of the BLR and the measurements including SMBH mass and accretion rates.

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arXiv2021

Reverberation Mapping of Two Luminous Quasars: the Broad-line Region Structure and Black Hole Mass

We report the results of a multi-year spectroscopic and photometric monitoring campaign of two luminous quasars, PG~0923+201 and PG~1001+291, both located at the high-luminosity end of the broad-line region (BLR) size-luminosity relation with optical luminosities above $10^{45}~{\rm erg~s^{-1}}$. PG~0923+201 is for the first time monitored, and PG~1001+291 was previously monitored but our campaign has a much longer temporal baseline. We detect time lags of variations of the broad H$β$, H$γ$, Fe {\sc ii} lines with respect to those of the 5100~Å continuum. The velocity-resolved delay map of H$β$ in PG~0923+201 indicates a complicated structure with a mix of Keplerian disk-like motion and outflow, and the map of H$β$ in PG~1001+291 shows a signature of Keplerian disk-like motion. Assuming a virial factor of $f_{\rm BLR}=1$ and FWHM line widths, we measure the black hole mass to be $118_{-16}^{+11}\times 10^7 M_{\odot}$ for PG~0923+201 and $3.33_{-0.54}^{+0.62}\times 10^7 M_{\odot}$ for PG~1001+291. Their respective accretion rates are estimated to be $0.21_{-0.07}^{+0.06} \times L_{\rm Edd}\,c^{-2}$ and $679_{-227}^{+259}\times L_{\rm Edd}\,c^{-2}$, indicating that PG~0923+201 is a sub-Eddington accretor and PG~1001+291 is a super-Eddington accretor. While the H$β$ time lag of PG~0923+201 agrees with the size-luminosity relation, the time lag of PG~1001+291 shows a significant deviation, confirming that in high-luminosity AGN the BLR size depends on both luminosity and Eddington ratio. Black hole mass estimates from single AGN spectra will be over-estimated at high luminosities and redshifts if this effect is not taken into account.

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arXiv2021

A correction method for the telluric absorptions and application to Lijiang Observatory

Observing a telluric standard star for correcting the telluric absorption lines of spectrum will take a significant amount of precious telescope time, especially in the long-term spectral monitoring project. Beyond that, it's difficult to select a suitable telluric standard star near in both time and airmass to the scientific object. In this paper, we present a method of correcting the telluric absorption lines by combining the advantages of long slit spectroscopy. By rotating the slit, we observed the scientific object and a nearby comparison star in one exposure, so that the spectra of both objects should have the same telluric transmission spectrum. The telluric transmission spectrum was constructed by dividing the observed spectrum of comparison star by its stellar template, and was used to correct the telluric absorption lines of the scientific object. Using the long slit spectrograph of Lijiang 2.4-meter telescope, we designed a long-term spectroscopic observation strategy, and finished a four-year spectroscopic monitoring for a pair of objects (an active galactic nuclei and an non-varying comparison star). We applied this method to correct the telluric absorption lines of the long-term monitored spectra by Lijiang 2.4-meter telescope, and investigated the variation of the telluric absorptions at Lijiang Observatory. We found that the telluric absorption transparency is mainly modulated by the seasonal variability of the relative humidity, airmass and seeing. Using the scatter of the [O~III] $λ$5007 fluxes emitted from the narrow-line region of active galactic nuclei as an indicator, we found that the correction accuracy of the telluric absorption lines is 1%.

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arXiv2020

Broad-line Region of the Quasar PG 2130+099 from a Two-Year Reverberation Mapping Campaign with High Cadence

As one of the most interesting Seyfert 1 galaxies, PG 2130+099 has been the target of several reverberation mapping (RM) campaigns over the years. However, its measured broad H$β$ line responses have been inconsistent, with time lags of $\sim$200 days, $\sim$25 days, and $\sim$10 days being reported for different epochs while its optical luminosity changed no more than 40%. To investigate this issue, we conducted a new RM-campaign with homogenous and high cadence (about $\sim$3 days) for two years during 2017--2019 to measure the kinematics and structure of the ionized gas. We successfully detected time lags of broad H$β$, He II, He I, and Fe II lines with respect to the varying 5100Åcontinuum, revealing a stratified structure that is likely virialized with Keplerian kinematics in the first year of observations, but an inflow kinematics of the broad-line region from the second year. With a central black hole mass of $0.97_{-0.18}^{+0.15}\times 10^7~M_{\odot}$, PG 2130+099 has an accretion rate of $10^{2.1\pm0.5}L_{\rm Edd}c^{-2}$, where $L_{\rm Edd}$ is the Eddington luminosity and $c$ is speed of light, implying that it is a super-Eddington accretor and likely possesses a slim, rather than thin, accretion disk. The fast changes of the ionization structures of the three broad lines remain puzzling.

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arXiv2019

Active Galactic Nuclei with Ultra-fast Outflows Monitoring Project: The Broad-line Region of Mrk 79 as a Disk Wind

We developed a spectroscopic monitoring project to investigate the kinematics of the broad-line region (BLR) in active galactic nuclei (AGN) with ultra-fast outflows (UFOs). Mrk~79 is a radio-quiet AGN with UFOs and warm absorbers, had been monitored by three reverberation mapping (RM) campaigns, but its BLR kinematics is not understood yet. In this paper, we report the results from a new RM-campaign of Mrk~79, which was undertaken by Lijiang 2.4-m telescope. Mrk~79 is seeming to come out the faint state, the mean flux approximates a magnitude fainter than historical record. We successfully measured the lags of the broad emission lines including H$β~\lambda4861$, H$γ~\lambda4340$, He II $\lambda4686$ and He I $\lambda5876$ with respect to the varying AGN continuum. Based on the broad H$β~\lambda4861$ line, we measured black hole (BH) mass of $M_{\bullet}=5.13^{+1.57}_{-1.55}\times10^{7}M_{\odot}$, estimated accretion rates of ${\dot{M}_{\bullet}}=(0.05\pm0.02)~L_{\rm Edd}~c^{-2}$, indicating that Mrk~79 is a sub-Eddington accretor. We found that Mrk~79 deviates from the canonical Radius$-$Luminosity relationship. The marginal blueshift of the broad He II $\lambda4686$ line detected from rms spectrum indicates outflow of high-ionization gas. The velocity-resolved lag profiles of the broad H$γ~\lambda4340$, H$β~\lambda4861$, and He I $\lambda5876$ lines show similar signatures that the largest lag occurs in the red wing of the lines then the lag decreases to both sides. These signatures should suggest that the BLR of Keplerian motion probably exists the outflow gas motion. All findings including UFOs, warm absorbers, and the kinematics of high- and low-ionization BLR, may provide an indirect evidence that the BLR of Mrk~79 probably originates from disk wind.

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arXiv2019

A Possible ~20 yr Periodicity in Long-term Optical Photometric and Spectral Variations of the Nearby Radio-Quiet Active Galactic Nucleus Ark 120

We study the long-term variability in the optical monitoring database of Ark~120, a nearby radio-quiet active galactic nucleus (AGN) at a distance of 143 Mpc (z=0.03271). We compiled the historical archival photometric and spectroscopic data since 1974 and conducted a new two-year monitoring campaign in 2015-2017, resulting in a total temporal baseline over four decades. The long-term variations in the optical continuum exhibit a wave-like pattern and the Hbeta integrated flux series varies with a similar behavior. The broad Hbeta profiles have asymmetric double peaks, which change strongly with time and tend to merge into a single peak during some epochs. The period in the optical continuum determined from various period-search methods is about 20 yr and the estimated false alarm probability with null hypothesis simulations is about 1*10^-3. The overall variations of the broad Hbeta profiles also follow the same period. However, the present database only covers two cycles of the suggested period, which strongly encourages continued monitoring to track more cycles and confirm the periodicity. Nevertheless, in light of the possible periodicity and the complicated Hbeta profile, Ark~120 is one candidate of the nearest radio-quiet AGNs with possible periodic variability, and it is thereby a potential candidate host for a sub-parsec supermassive black hole binary.

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arXiv2019

Lijiang 2.4-meter Telescope and its Instruments

Lijiang 2.4-meter Telescope(LJT), the largest common-purpose optical telescope in China, has been applied to the world-wide astronomers since 2008. It is located at Gaomeigu site, Lijiang Observatory(LJO), the southwest of China. The site has very good observational conditions. Since 10-year operation, several instruments have been equipped on the LJT. Astronomers can perform both photometric and spectral observations. The main scientific goals of LJT include photometric and spectral evolution of supernova, reverberation mapping of active galactic nucleus, physical properties of binary star and near-earth object(comet and asteroid), identification of exoplanet, and all kinds of transients. Until now, the masses of 41 high accretion rate black holes have been measured, and more than 168 supernova have been identified by the LJT. More than 190 papers related to the LJT have been published. In this paper, the general observation condition of the Gaomeigu site is introduced at first. Then, the LJT structure is described in detail, including the optical, mechanical, motion and control system. The specification of all the instruments, and some detailed parameters of the YFOSC is also presented. Finally, some important scientific results and future expectations are summarized.

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arXiv2019

Supermassive black holes with high accretion rates in active galactic nuclei: X. Optical variability characteristics

We compiled a sample of 73 active galactic nuclei (AGNs) with reverberation mapping (RM) observations from RM campaigns including our ongoing campaign of monitoring super-Eddington accreting massive black holes (SEAMBHs). This sample covers a large range of black hole (BH) mass $(M_{\bullet}=10^{6-9}~M_\odot)$, dimensionless accretion rates $(\dot{\mathscr{M}}=10^{-2.7}-10^{2.7})$ and 5100~Å~luminosity $(L_{5100}=10^{42-46}~\rm erg~s^{-1})$, allowing us to systematically study the AGN variability and their relations with BH mass, accretion rates, and optical luminosity. We employed the damped random walk (DRW) model to delineate the optical variability of continuum at 5100~Å~and obtained damped variability timescale ($τ_{\rm d}$) and amplitude ($σ_{\rm d}$) using a Markov Chain Monte Carlo (MCMC) method. We also estimated the traditional variability amplitudes ($F_{\rm var}$), which provide a model-independent measure and therefore are used to test the DRW results. We found that AGN variability characteristics are generally correlated with $(M_{\bullet},\dot{\mathscr{M}},L_{5100})$. These correlations are smooth from sub-Eddington to super-Eddington accretion AGNs, probably implying that the AGN variability may be caused by the same physical mechanism.

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arXiv2019

Reverberation mapping of narrow-line Seyfert 1 galaxy I Zwicky 1: black hole mass

We report results of the first reverberation mapping campaign of I Zwicky 1 during $2014$-$2016$, which showed unambiguous reverberations of the broad H$β$ line emission to the varying optical continuum. From analysis using several methods, we obtain a reverberation lag of $τ_{\rm Hβ}=37.2^{+4.5}_{-4.9}\,$ days. Taking a virial factor of $f_{_{\rm BLR}}=1$, we find a black hole mass of $M_{\bullet}=9.30_{-1.38}^{+1.26}\times 10^6 M_{\odot}$ from the mean spectra. The accretion rate is estimated to be $203.9_{-65.8}^{+61.0}\,L_{\rm Edd}c^{-2}$, suggesting a super-Eddington accretor, where $L_{\rm Edd}$ is the Eddington luminosity and $c$ is the speed of light. By decomposing {\it Hubble Space Telescope} images, we find that the stellar mass of the bulge of its host galaxy is $\log (M_{\rm bulge}/M_{\odot}) = \rm 10.92\pm 0.07$. This leads to a black hole to bulge mass ratio of $\sim 10^{-4}$, which is significantly smaller than that of classical bulges and elliptical galaxies. After subtracting the host contamination from the observed luminosity, we find that I Zw 1 follows the empirical $R_{\rm BLR}\propto L_{5100}^{1/2}$ relation.

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arXiv2018

Reddening of the BLR and NLR in AGN From a Systematic Analysis of Balmer Decrement

We selected an active galactic nuclei (AGN) sample ($0 < z \le 0.35$) from Sloan Digital Sky Survey Data Release 7, and measured the broad- (${\rm Hα^{b}/Hβ^{b}}$) and narrow-line Balmer decrements (${\rm Hα^{n}/Hβ^{n}}$) of 554 selected AGNs. We found that the distributions of Balmer decrements can be fitted by a Gaussian function and give the best estimates of ${\rm Hα^{b}/Hβ^{b}} = 3.16$ with a standard deviation 0.07 dex, and ${\rm Hα^{n}/Hβ^{n}} = 4.37$ with a standard deviation 0.10 dex. We inspected the distributions of ${\rm Hα^{b}/Hβ^{b}}$ and ${\rm Hα^{n}/Hβ^{n}}$ in the Baldwin$-$Phillips$-$Terlevich (BPT) diagram and found that only narrow-line Balmer decrements depend on the physical conditions of the narrow-line region (NLR). We tested the relationship between ${\rm Hα^{b}/Hβ^{b}}$ and ${\rm Hα^{n}/Hβ^{n}}$, and found that ${\rm Hα^{b}/Hβ^{b}}$ does not correlate with ${\rm Hα^{n}/Hβ^{n}}$. We investigated the relationship between Balmer decrements and Seyfert sub-type, and found that only broad-line Balmer decrements correlate with Seyfert sub-type, We also examined the dependency of Balmer decrements on AGN properties, and found that Balmer decrements have no correlation with optical luminosity, but show some dependence on accretion rate. These results indicate that the NLR is subject to more reddening by dust than the broad-line region (BLR).

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arXiv2018

Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. VIII. Structure of the Broad-Line Region and Mass of the Central Black Hole in Mrk 142

This is the eighth in a series of papers reporting on a large reverberation mapping campaign to measure black hole (BH) mass in high accretion rate active galactic nuclei (AGNs). We employ the recently developed dynamical modeling approach for broad-line regions (BLRs) based on the method of Pancoast et al. to analyze the reverberation mapping dataset of Mrk 142 observed in the first monitoring season. In this approach, continuum variations are reconstructed using a damped random walk process, and BLR structure is delineated using a flexible disk-like geometry, in which BLR clouds move around the central BH with Keplerian orbits or inflow/outflow motion. The approach also includes the possibilities of anisotropic emission of BLR clouds, non-linear response of the line emission to the continuum, and different long-term trends in the continuum and emission-line variations. We implement the approach in a Bayesian framework that is apt for parallel computation and use a Markov Chain Monte Carlo technique to recover the parameters and uncertainties for the modeling, including mass of the central BH. We apply three BLR models with different prescriptions of BLR clouds distributions and find that the best model for fitting the data of Mrk 142 is a two-zone BLR model, consistent with the theoretical BLR model surrounding slim accretion disks. The best model yields a BH mass of $\log (M_\bullet/M_\odot)=6.23_{-0.45}^{+0.26}$, resulting in a virial factor of $\log f=-0.36_{-0.54}^{+0.33}$ for the full width at half maximum of the H$β$ line measured from the mean spectrum. The virial factors for the other measures of the H$β$ line width are also presented.

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arXiv2018

A High-Quality velocity-delay map of the broad-line region in NGC 5548

NGC 5548 has been well spectroscopically monitored for reverberation mapping of the central kinematics by 19 campaigns. Using the maximum entropy method in this Letter, we build up a high-quality velocity-delay map of the H$β$ emission line in the light curves of the continuum and the line variations observed between 2015-2016. The map shows the response strength and lags of the velocity fields of the H$β$ emitting regions. The velocity-delay structure of the map is generally symmetric, with strong red and blue wings at time lag $τ\leq 15$ days, a narrower velocity distribution at $τ\geq 15$ days, and a deficit of response in the core. This is suggestive of a disk geometry of the broad-line region (BLR). The relatively weaker H$β$ response at the longer lags in the red side indicates anisotropic emission from the outer part of the BLR. We also recover the velocity-delay maps of NGC 5548 from the historical data of 13 years to investigate the long-term variability of its BLR. In general, the BLR of NGC 5548 was switching between the inflow and virialized phases in the past years. The resultant maps of seven years reveal inflow signatures and show decreasing lags, indicating that the changes in the BLR size are related to the infalling BLR gas. The other four maps show potential disk signatures which are similar to our map.

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arXiv2018

Supermassive black holes with high accretion rates in active galactic nuclei. VII. Reconstruction of velocity-delay maps by maximum entropy method

As one of the series of papers reporting on a large reverberation mapping campaign, we apply the maximum entropy method (MEM) to 9 narrow-line Seyfert 1 galaxies with super-Eddington accretion rates observed during 2012-2013 for the velocity-delay maps of their Hβ and Hγ emission lines. The maps of 6 objects are reliably reconstructed using MEM. The maps of Hβ and Hγ emission lines of Mrk 335 indicate that the gas of its broad-line region (BLR) is infalling. For Mrk 142, its Hβ and Hγ lines show signatures of outflow. The Hβ and Hγ maps of Mrk 1044 demonstrate complex kinematics -- a virialized motion accompanied by an outflow signature, and the Hβ map of IRAS F12397+3333 is consistent with a disk or a spherical shell. The Hβ maps of Mrk 486 and MCG +06-26-012 suggest the presence of an inflow and outflow, respectively. These super-Eddington accretors show diverse geometry and kinematics. Brief discussions of their BLRs are provided for each individual object.

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arXiv2018

Optical and Gamma-Ray Variability Behaviors of 3C 454.3 from 2006 to 2011

We present our photometric monitoring of a flat spectrum radio quasar (FSRQ) 3C 454.3 at Yunnan observatories from 2006 to 2011. We find that the optical color of 3C 454.3 shows obvious redder-when-brighter trend, which reaches a saturation stage when the source is brighter than 15.15 mag at V band. We perform a simulation with multiple values of disk luminosity and spectral index to reproduce the magnitude-color diagram. The results show that the contamination caused by the disk radiation alone is difficult to produce the observed color variability. The variability properties during the outburst in December 2009 are also compared with $γ$-ray data derived from Fermi $γ$-ray space telescope. The flux variation of these two bands follow a linear relation with $F_γ \propto F_R^{1.14\pm0.07}$, which provides an observational evidence for external Compton process in 3C 454.3. Meanwhile, this flux correlation indicates that electron injection is the main mechanism for variability origin. We also explore the variation of the flux ratio $F_γ/F_R$ and the detailed structures in the lightcurves, and discuss some possible origins for the detailed variability behaviors.

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arXiv2018

Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. IX 10 New Observations of Reverberation Mapping and Shortened H$β$ Lags

As one of the series of papers reporting on a large reverberation mapping campaign of super-Eddington accreting massive black holes (SEAMBHs) in active galactic nuclei (AGNs), we present the results of 10 SEAMBHs monitored spectroscopically during 2015-2017. Six of them are observed for the first time, and have generally higher 5100 Å luminosities than the SEAMBHs monitored in our campaign from 2012 to 2015; the remaining four are repeat observations to check if their previous lags change. Similar to the previous SEAMBHs, the H$β$ time lags of the newly observed objects are shorter than the values predicted by the canonical $R_{\mathrm{Hβ}}$-$L_{5100}$ relation of sub-Eddington AGNs, by factors of $\sim2-6$, depending on the accretion rate. The four previously observed objects have lags consistent with previous measurements. We provide linear regressions for the $R_{\mathrm{Hβ}}$-$L_{5100}$ relation, solely for the SEAMBH sample and for low-accretion AGNs. We find that the relative strength of Fe II and the profile of the H$β$ emission line can be used as proxies of accretion rate, showing that the shortening of H$β$ lags depends on accretion rates. The recent SDSS-RM discovery of shortened H$β$ lags in AGNs with low accretion rates provides compelling evidence for retrograde accretion onto the black hole. These evidences show that the canonical $R_{\mathrm{Hβ}}$-$L_{5100}$ relation holds only in AGNs with moderate accretion rates. At low accretion rates, it should be revised to include the effects of black hole spin, whereas the accretion rate itself becomes a key factor in the regime of high accretion rates.

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arXiv2016

Improving the Flux Calibration in Reverberation Mapping by Spectral Fitting: Application to the Seyfert Galaxy MCG--6-30-15

We propose a method for the flux calibration of reverberation mapping spectra based on accurate measurement of [O III] $λ5007$ emission by spectral fitting. The method can achieve better accuracy than the traditional method of van Groningen & Wanders (1992), allowing reverberation mapping measurements for object with variability amplitudes as low as $\sim$ 5%. As a demonstration, we reanalyze the data of the Seyfert 1 galaxy MCG--6-30-15 taken from the 2008 campaign of the Lick AGN Monitoring Project, which previously failed to obtain a time lag for this weakly variable object owing to a relatively large flux calibration uncertainty. We detect a statistically significant rest-frame time lag of $6.38_{-2.69}^{+3.07}$ days between the H$β$ and $V$-band light curves. Combining this lag with FWHM(H$β$) = $1933\pm81$ $\rm km~s^{-1}$ and a virial coefficient of $f$ = 0.7, we derive a virial black hole mass of $3.26_{-1.40}^{+1.59}\times10^6$ $M_{\odot}$, which agrees well with previous estimates by other methods.

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arXiv2016

Reverberation Mapping of the Broad-line Region in NGC 5548: Evidence for Radiation Pressure?

NGC 5548 is the best-observed reverberation-mapped active galactic nucleus with long-term, intensive monitoring. Here we report results from a new observational campaign between January and July, 2015. We measure the centroid time lag of the broad H$β$ emission line with respect to the 5100 Åcontinuum and obtain $τ_{\rm cent} = 7.20^{+1.33}_{-0.35}$ days in the rest frame. This yields a black hole mass of $M_{\bullet}=8.71^{+3.21}_{-2.61} $x$ 10^{7}M_{\odot}$ using a broad H$β$ line dispersion of $3124\pm302$ km s$^{-1}$ and a virial factor of $f_{_{\rm BLR}}=6.3\pm1.5$ for the broad-line region (BLR), consistent with the mass measurements from previous H$β$ campaigns. The high-quality data allow us to construct a velocity-binned delay map for the broad H$β$ line, which shows a symmetric response pattern around the line center, a plausible kinematic signature of virialized motion of the BLR. Combining all the available measurements of H$β$ time lags and the associated mean 5100 Å luminosities over 18 campaigns between 1989 and 2015, we find that the H$β$ BLR size varies with the mean optical luminosity, but, interestingly, with a possible delay of $2.35_{-1.25}^{+3.47}$ yrs. This delay coincides with the typical BLR dynamical timescale of NGC 5548, indicating that the BLR undergoes dynamical changes, possibly driven by radiation pressure.

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