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Qingjuan Yu

Publications and source records attributed to Qingjuan Yu.

At least 19 recordsLinked to original sources
arXiv2025

Enhanced Localization of Dark Lensed Gravitational Wave Events Enables Host Galaxy Identification and Precise Cosmological Inference

Lensed gravitational wave (GW) events are expected to be powerful new probes of cosmology, contingent on redshift measurement by electromagnetic observations. Host galaxy identification is thus crucial but challenging due to poor localization by GW signal alone. In this paper, we show that the third-generation ground-based GW detectors will detect a population of lensed events with three or more detectable images (including the central one), each arriving at distinct times and Earth locations in the space, forming an effective network that reduces the typical localization area to $\sim0.01$ deg$^2$. For at least $90\%$ (or $50\%$) of these events, the localization improves by more than a factor of $10$ (or $30$) comparing with unlensed cases. Such precise localization and multiple-image detections enable robust host-galaxy identification and, through lens modelling, further yield sub-arcsecond position. As ``dark lensed sirens", these events become powerful probes of cosmological parameters. Using simulated lensed compact-binary mergers, we show that two-year or longer observations with third-generation GW detectors can measure the Hubble constant to $\lesssim1$\% precision via ``dark lensed sirens" (even when relying solely on lensed stellar-mass binary black hole events), while simultaneously constraining other cosmological parameters. This approach will provide an independent, complementary avenue for measuring cosmological parameters.

astro-ph.CO↗
arXiv2024

Constraining the Binarity of Massive Black Holes in the Galactic Center and Some Nearby Galaxies via Pulsar Timing Array Observations of Gravitational Waves

Massive black holes (MBHs) exist in the Galactic center (GC) and other nearby galactic nuclei. As natural outcome of galaxy mergers, some MBHs may have a black hole (BH) companion. In this paper, assuming that the MBHs in the GC and some nearby galaxies are in binaries with orbital periods ranging from months to years (gravitational-wave frequency $\sim1-100$\,nHz), we investigate the detectability of gravitational-waves from these binary MBHs (BBHs) and constraints on the parameter space for the existence of BBHs in the GC, LMC, M31, M32, and M87, that may be obtained by current/future pulsar timing array (PTA) observations. We find that a BBH in the GC, if any, can be revealed by the Square Kilometer Array PTA (SKA-PTA) if its mass ratio $q\gtrsim10^{-4}-10^{-3}$ and semimajor axis $a\sim20-10^3$\,AU. The existence of a BH companion of the MBH can be revealed by SKA-PTA with $\sim20$-year observations in M31 if $q\gtrsim10^{-4}$ and $a\sim10^2-10^4$\,AU or in M87 if $q\gtrsim10^{-5}$ and $a\sim10^3-2\times10^4$\,AU, but not in LMC and M32 if $q\ll1$. If a number of milli-second stable pulsars with distances $\lesssim0.1-1$\,pc away from the central MBH in the GC, LMC, M32, or M31, can be detected in future and applied to PTAs, the BH companion with mass even down to $\sim100M_\odot$, close to stellar masses, can be revealed by such PTAs. Future PTAs are expected to provide an independent way to reveal BBHs and low-mass MBH companions in the GC and nearby galaxies, improving our understandings of the formation and evolution of MBHs and galaxies.

astro-ph.HE↗
arXiv2024

Constraining the origin of the nanohertz gravitational-wave background by pulsar timing array observations of both the background and individual supermassive binary black holes

The gravitational waves (GWs) from supermassive binary black holes (BBHs) are long sought by pulsar timing array experiments (PTAs), in the forms of both a stochastic GW background (GWB) and individual sources. The evidence for a GWB was reported recently by several PTAs with origins to be determined. Here we use a BBH population synthesis model to investigate the detection probability of individual BBHs by the Chinese PTA (CPTA) and the constraint on the GWB origin that may be obtained by PTA observations of both GWB and individual BBHs. If the detected GWB signal is entirely due to BBHs, a significantly positive redshift evolution ($\propto(1+z)^{2.07}$) of the mass scaling relation between supermassive black holes and their host galaxies is required. In this case, we find that the detection probability of individual BBHs is $\sim85\%$ or 64% if using a period of 3.4-year CPTA observation data, with an expectation of $\sim1.9$ or 1.0 BBHs detectable with a signal-to-noise ratio $\geq3$ or $5$, and it is expected to increase to $>95\%$ if extending the observation period to $5$ years or longer. Even if the contribution from BBHs to the GWB power signal is as small as $\sim10\%$, a positive detection of individual BBHs can still be expected within an observation period of $\sim10$ years. A non-detection of individual BBHs within several years from now jointly with the detected GWB signal can put a strong constraint on the upper limit of the BBH contribution to the GWB signal and help identify/falsify a cosmological origin.

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arXiv2023

Pulsar timing array detections of supermassive binary black holes: implications from the detected common process signal and beyond

Pulsar timing arrays (PTAs) are anticipated to detect the stochastic gravitational wave background (GWB) from supermassive binary black holes (BBHs) as well as the gravitational waves from individual BBHs. Recently, a common process signal was reported by several PTAs. In this paper, we investigate the constraints on the BBH population model(s) by current PTA observations and further study the detections of both the GWB and individual BBHs by current/future PTAs. We find that the MBH--host galaxy scaling relation, an important ingredient of the BBH population model, is required to either evolve significantly with redshift or have a normalization $\sim0.86-1.1$ dex higher than the empirical ones, if the GWB is the same as the common process signal. For both cases, the estimated detection probability for individual BBHs is too small for a positive detection by current PTAs. By involving either the constrained scaling relations or those empirical ones into the BBH population models, we estimate that the GWB may be detected with a signal-to-noise ratio $\gtrsim3$ by the PTAs based on the Five hundred meter Aperture Spherical radio Telescope (CPTA) and the Square Kilometer Array (SKAPTA) after $\sim2-3$ (or $\sim6-11$) years' observation, if it is the same as (or an order of magnitude lower than) the common process signal. The detection time of individual BBHs by CPTA and SKAPTA is close to that of the GWB detection. We show that the BBH population model can be strongly constrained by the number and property distributions of BBHs to be detected by future PTAs.

astro-ph.HE↗
arXiv2023

The correlations of stellar tidal disruption rates with properties of massive black holes and their host galaxies

Stars can be either disrupted as tidal disruption events (TDEs) or swallowed as a whole by massive black holes (MBHs) at galactic centers when they approach sufficiently close to these MBHs. In this work, we investigate the correlations of such stellar consumption rates with both the MBH mass $M_{\rm bh}$ and the inner slope of the host galaxy mass density distribution $\alpha$. We introduce a simplified analytical power-law model with a power-law stellar mass density distribution surrounding MBHs and separate the contributions of two-body relaxation and stellar orbital precession for the stellar orbital angular momentum evolution in nonspherical galaxy potentials. The stellar consumption rates derived from this simplified model can be well consistent with the numerical results obtained with a more realistic treatment of stellar distributions and dynamics around MBHs, providing an efficient way to estimate TDE rates. The origin of the correlations of stellar consumption rates with $M_{\rm bh}$ and $\alpha$ are explained by the dependence of this analytical model on those MBH/host galaxy properties and by the separation of the stellar angular momentum evolution mechanisms. We propose that the strong positive correlation between the rates of stellar consumption due to two-body relaxation and $\alpha$ provides one interpretation for the overrepresentation of TDEs found in some rare E+A/poststarburst galaxies. We find high TDE rates for giant stars, up to those for solar-type stars. The understanding of the origin of the correlations of the stellar consumption rates will be necessary for obtaining the demographics of MBHs and their host galaxies via TDEs.

astro-ph.HE↗
arXiv2022

On Detecting Nearby Nano-Hertz Gravitational Wave Sources via Pulsar Timing Arrays

Massive binary black holes (MBBHs) in nearby galactic centers, if any, may be nano-Hertz gravitational wave (GW) sources for pulsar timing arrays (PTAs) to detect. Normally the objective GWs for PTA experiments are approximated as plane waves because its sources are presumably located faraway. For nearby GW sources, however, this approximation may be inaccurate due to the curved GW wave front and the GW strength changes along the paths of PTA pulsar pulses. In this paper, we analyze the near-field effect in the PTA detection of nearby sources and find it is important if the source distance is less than a few tens Mpc, and ignoring this effect may lead to a significant signal-to-noise underestimation especially when the source distance is comparable to the pulsar distances. As examples, we assume a nano-Hertz MBBH source located at either the Galactic Center (GC) or the Large Magellanic Cloud (LMC) according to the observational constraints/hints on the MBBH parameter space, and estimate its detectability by current/future PTAs. We find that the GC MBBH may be detectable by the Square Kilometer Array (SKA) PTA. It is challenging for detecting the LMC MBBH; however, if a number ($N\gtrsim10$) of stable millisecond pulsars can be found in the LMC center, the MBBH may be detectable via a PTA formed by these pulsars. We further illustrate the near-field effects on the PTA detection of an isotropic GW background contributed mainly by nearby GW sources, and the resulting angular correlation is similar to the Hellings-Downs curve.

astro-ph.HE↗
arXiv2021

Investigating the existence of gravitomagnetic monopole in M87*

We examine the possibility for the existence of gravitomagnetic monopole ($n_*$) in M87* by using the results obtained from its first Event Horizon Telescope image. By numerically deducing the shadow sizes in Kerr-Taub-NUT (KTN) spacetime, we show that the shadow size increases with increasing $|n_*|$ for a fixed Kerr parameter $|a_*|$ in case of the KTN black hole, whereas for a KTN naked singularity it increases with increasing $n_*$ for a fixed $a_* > 0$ if $n_* > -\cot 17^{\circ}$ . In general, the asymmetry of shadow shape increases if the central dark object in M87 is a KTN/Kerr naked singularity instead of a KTN/Kerr black hole. We find that a non-zero gravitomagnetic monopole is still compatible with the current EHT observations, in which case the upper limit of $n_*$ cannot be greater than $1.1$, i.e., $n_* \lesssim 1.1$ for the prograde rotation ($a_* > 0$), and the lower limit of $n_*$ cannot be less than $-1.1$, i.e., $ n_* \gtrsim -1.1$ for the retrograde rotation ($a_* < 0$). Moreover, if the circularity of the shadow can be measured on a precision of $\lesssim 1\%$, the Kerr and KTN naked singularities can be falsified for M87*.

astro-ph.HE↗
arXiv2020

Cosmic distributions of stellar tidal disruptions by massive black holes at galactic centers

Stars can be consumed (either tidally disrupted or swallowed whole) by massive black holes (MBHs) at galactic centers when they move into the vicinity of the MBHs. In this study, we investigate the rates of stellar consumption by central MBHs and their cosmic distributions, including the effects of triaxial galaxy shapes in enhancing the reservoir of low-angular-momentum stars and incorporating realistic galaxy distributions. We find that the enhancement in the stellar consumption rates due to triaxial galaxy shapes can be significant, by a factor of ~3 for MBH mass $M_{\rm BH}\sim10^5$-$10^6$Msun and up to more than one order of magnitude for $M_{\rm BH}\gtrsim10^8$Msun. Only for $M_{\rm BH}\lesssim10^7$Msun are the stellar consumption rates significantly higher in galaxies with steeper inner surface brightness profiles. The average (per galaxy) stellar consumption rates correlate with central MBH masses positively for $M_{\rm BH}\gtrsim10^7$Msun and negatively for $M_{\rm BH}\lesssim10^7$Msun. The volumetric stellar tidal disruption rates are ~$3\times10^{-5}$/yr/Mpc$^3$ for MBHs in the mass range of $10^5$-$10^8$Msun at z=0; and the volumetric stellar consumption rates by MBHs with higher masses are ~$10^{-6}$/yr/Mpc$^3$, which can be the stellar tidal disruption rate if the high-mass BHs are extremely spinning Kerr BHs or the rate of being swallowed if those BHs are Schwarzschild ones. The volumetric stellar consumption rates decrease with increasing redshift, and the decrease is relatively mild for $M_{\rm BH}\sim10^5$-$10^7$Msun and stronger for higher $M_{\rm BH}$. Most of the stellar tidal disruption events (TDEs) at z=0 occur in galaxies with mass $M_{\rm gal}\lesssim10^{11}$Msun, and about 1%-2% of the TDEs can occur in high-mass galaxies with $M_{\rm gal}\gtrsim10^{11}$Msun.

astro-ph.HE↗
arXiv2020

Dynamical evolution of cosmic supermassive binary black holes and their gravitational wave radiation

We investigate the evolution of supermassive binary black holes (BBHs) in galaxies with realistic property distributions and the gravitational-wave (GW) radiation from the cosmic population of these BBHs. We incorporate a comprehensive treatment of the dynamical interactions of the BBHs with their environments by including the effects of galaxy triaxial shapes and inner stellar distributions, and generate a large number of BBH evolution tracks. By combining these BBH evolution tracks, galaxy mass functions, galaxy merger rates, and supermassive black hole-host galaxy relations into our model, we obtain the statistical distributions of surviving BBHs, BBH coalescence rates, the strength of their GW radiation, and the stochastic GW background (GWB) contributed by the cosmic BBH population. About ~1%-3% (or ~10%) of supermassive BHs at nearby galactic centers are expected to be binaries with mass ratio >1/3 (or >1/100). The characteristic strain amplitude of the GWB at frequency 1/yr is estimated to be ~$2.0^{+1.4}_{-0.8}\times 10^{-16}$, and the upper bound of its results obtained with the different BH-host galaxy relations can be up to $5.4\times 10^{-16}$, which await testing by future experiments (e.g., the Square Kilometer Array, FAST, Next-Generation Very Large Array). The turnover frequency of the GWB spectrum is at ~0.25nHz. The uncertainties on the above estimates and prospects for detecting individual sources are also discussed. The application of the cosmic BBH population to the Laser Interferometer Space Antenna (LISA) band provides a lower limit to the detection rate of BBHs by LISA, ~0.9/yr.

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arXiv2019

The Origin of the Stellar Mass-Stellar Metallicity Relation in the Milky Way Satellites and beyond

Observations and semianalytical galaxy formation and evolution models (SAMs) have suggested the existence of a stellar mass-stellar metallicity relation (MZR), which is shown to be universal for different types of galaxies over a large range of stellar masses ($M_*\sim 10^3$-$10^{11}M_\odot$) and dark matter (DM) halo masses ($M_{\rm halo}\sim 10^9$-$10^{15}h^{-1}M_\odot$). In this work, we construct a chemical evolution model to investigate the origin of the MZR, including both the effects of gas inflows and outflows in galaxies. We solve the MZR from the chemical evolution model, by assuming that the cold gas mass ($M_{\rm cold}$) and the stellar feedback efficiency ($\beta$) follow some power-law scaling relationships with $M_*$ during the growth of a galaxy, i.e., $M_{\rm cold}\propto M_*^{\alpha_{\rm gs}}$ and $\beta\propto M_*^{\alpha_{\beta{\rm s}}}$. We use the SAM to obtain these power-law scaling relations, which appear to be roughly universal over a large range of stellar masses for both satellites and central galaxies within a large range of halo masses. The range of the MZRs produced by our models is in a narrow space, which provides support to the universality of the MZRs. The formation of the MZR is a result caused jointly by that the cold gas fraction decreases with increasing $M_*$ and by that the stellar feedback efficiency decreases with increasing $M_*$ in the galaxy growth, and the exponent in the MZR is around $-\alpha_{\beta{\rm s}}$ or $1-\alpha_{\rm gs}$. The MZR represents an ''average'' evolutional track for the stellar metallicity of a galaxy. The comparison of our model with some previous models for the origin of MZRs is also discussed.

astro-ph.GA↗
arXiv2019

Is the stellar mass-stellar metallicity relation universal in the Milky Way satellites and beyond?

Observations reveal a universal stellar mass-stellar metallicity relation (MZR) existing in Local Group dwarfs of different types, $Z_*\propto M_*^{\alpha}$ with $\alpha=0.30\pm0.02$. In this work, we investigate the "universality" of the MZRs for both satellites and central galaxies in a large number of different host dark matter halos covering a large mass range of $10^9$-$10^{15}h^{-1}M_\odot$, by using a semianalytical galaxy formation and evolution model. We obtain the following results. (1) The exponents ($\alpha$) for the MZRs of the satellites in halos with the same mass as the Milky Way halo but different individual assembly histories are mostly $\sim$0.2-0.4, i.e., having a scatter of $\sim 0.2$; and the scatter of $\alpha$ increases with decreasing halo masses. (2) The MZR relations are changed little by the variation of halo masses and the classification between central galaxies and satellites, if many halos with the same mass are stacked together. (3) A double power law exists in the MZR relations for both central galaxies and stacked satellites, with $\alpha\sim$0.2-0.4 at $10^3M_\odot< M_*<10^{8} M_\odot$ and a relatively higher $\alpha\sim0.5$ at $10^8M_\odot 10^8M_\odot$) existing mostly in high-mass halos can lead to an apparent increase of $\alpha$ (from $\sim0.2$ to $\sim0.4$) with increasing host halo masses shown in the single power law fitting results of stacked satellites. The universality of the MZR suggests the common physical processes in stellar formation and chemical evolution of galaxies can be unified over a large range of galaxy masses and halo masses.

astro-ph.GA↗
arXiv2017

Simulating the galaxy cluster "El Gordo": gas motion, kinetic Sunyaev-Zel'dovich signal, and X-ray line features

The massive galaxy cluster "El Gordo" (ACT-CL J0102--4915) is a rare merging system with a high collision speed suggested by multi-wavelength observations and the theoretical modeling. Zhang et al. (2015) propose two types of mergers, a nearly head-on merger and an off-axis merger with a large impact parameter, to reproduce most of the observational features of the cluster, by using numerical simulations. The different merger configurations of the two models result in different gas motion in the simulated clusters. In this paper, we predict the kinetic Sunyaev-Zel'dovich (kSZ) effect, the relativistic correction of the thermal Sunyaev-Zel'dovich (tSZ) effect, and the X-ray spectrum of this cluster, based on the two proposed models. We find that (1) the amplitudes of the kSZ effect resulting from the two models are both on the order of $\Delta T/T\sim10^{-5}$; but their morphologies are different, which trace the different line-of-sight velocity distributions of the systems; (2) the relativistic correction of the tSZ effect around $240 {\rm\,GHz}$ can be possibly used to constrain the temperature of the hot electrons heated by the shocks; and (3) the shift between the X-ray spectral lines emitted from different regions of the cluster can be significantly different in the two models. The shift and the line broadening can be up to $\sim 25{\rm\,eV}$ and $50{\rm\,eV}$, respectively. We expect that future observations of the kSZ effect and the X-ray spectral lines (e.g., by ALMA, XARM) will provide a strong constraint on the gas motion and the merger configuration of ACT-CL J0102--4915.

astro-ph.CO↗
arXiv2017

X-ray Eclipses of Active Galactic Nuclei

X-ray variation is a ubiquitous feature of active galactic nuclei (AGNs), however, its origin is not well understood. In this paper, we show that the X-ray flux variations in some AGNs, and correspondingly the power spectral densities (PSDs) of the variations, may be interpreted as being caused by absorptions of eclipsing clouds or clumps in the broad line region (BLR) and the dusty torus. By performing Monte-Carlo simulations for a number of plausible cloud models, we systematically investigate the statistics of the X-ray variations resulting from the cloud eclipsing and the PSDs of the variations. For these models, we show that the number of eclipsing events can be significant and the absorption column densities due to those eclipsing clouds can be in the range from 10^{21} to 10^{24} cm^{-2}, leading to significant X-ray variations. We find that the PSDs obtained from the mock observations for the X-ray flux and the absorption column density resulting from these models can be described by a broken double power law, similar to those directly measured from observations of some AGNs. The shape of the PSDs depend strongly on the kinematic structures and the intrinsic properties of the clouds in AGNs. We demonstrate that the X-ray eclipsing model can naturally lead to a strong correlation between the break frequencies (and correspondingly the break timescales) of the PSDs and the masses of the massive black holes (MBHs) in the model AGNs, which can be well consistent with the one obtained from observations. Future studies of the PSDs of the AGN X-ray (and possibly also the optical-UV) flux and column density variations may provide a powerful tool to constrain the structure of the BLR and the torus and to estimate the MBH masses in AGNs.

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arXiv2016

Prospects for constraining the spin of the massive black hole at the Galactic center via the relativistic motion of a surrounding star

In this paper, we investigate the quality of constraining the spin of the massive black hole (MBH) at the Galactic center (GC) by using full general relativistic simulations of the motion of a surrounding star. We obtain the dependence mapping of the spin-induced signals on any spin direction of the MBH for given example stars, which indicates the feasibility to test whether the spin direction is the same as the normal of the young stellar disk located at the GC, and, further to provide insights into the assembly history of the MBH. We demonstrate the quality of constraining the MBH spin that may be achieved, given any set of the astrometric and the redshift precisions of observational facilities. We find that in the ranges of the astrometric and the velocity precisions with 1--30$\mu$as and 0.1--10 km/s, an improvement in astrometric precision would be more effective at improving the quality of constraining the spin than an improvement in velocity precision. We obtain the parameter space of the semimajor axis and the eccentricity for the orbit of the target star that a high-precision constraint on the GC MBH spin can be obtained via the motion of the star. Our results show that the spin of the GC MBH can be constrained with 1-sigma error <~0.1 or even >~0.02 by monitoring the orbital motion of a star, if existing as expected, with semimajor axis <~300AU and eccentricity >~0.95 over a period shorter than a decade through future facilities.

astro-ph.HE↗
arXiv2016

A Baryonic Effect on the Merger Timescale of Galaxy Clusters

Accurate estimation of the merger timescale of galaxy clusters is important to understand the cluster merger process and further the formation and evolution of the large-scale structure of the universe. In this paper, we explore a baryonic effect on the merger timescale of galaxy clusters by using hydrodynamical simulations. We find that the baryons play an important role in accelerating the merger process. The merger timescale decreases with increasing the gas fraction of galaxy clusters. For example, the merger timescale is shortened by a factor of up to 3 for merging clusters with gas fractions 0.15, compared with the timescale obtained with zero gas fractions. The baryonic effect is significant for a wide range of merger parameters and especially more significant for nearly head-on mergers and high merging velocities. The baryonic effect on the merger timescale of galaxy clusters is expected to have impacts on the structure formation in the universe, such as the cluster mass function and massive substructures in galaxy clusters, and a bias of "no-gas" may exist in the results obtained from the dark matter-only cosmological simulations.

astro-ph.CO↗
arXiv2015

Simulating the galaxy cluster "El Gordo" and identifying the merger configuration

The observational features of the massive galaxy cluster "El Gordo" (ACT-CL J0102-4915), such as the X-ray emission, the Sunyaev-Zel'dovich (SZ) effect, and the surface mass density distribution, indicate that they are caused by an exceptional ongoing high-speed collision of two galaxy clusters, similar to the well-known Bullet Cluster. We perform a series of hydrodynamical simulations to investigate the merging scenario and identify the initial conditions for the collision in ACT-CL J0102-4915. By surveying the parameter space of the various physical quantities that describe the two colliding clusters, including their total mass (M), mass ratio (\xi), gas fractions (f_b), initial relative velocity (V), and impact parameter (P), we find out an off-axis merger with P~800h_{70}^{-1}kpc, V~2500km/s, M~3x10^{15}Msun, and \xi=3.6 that can lead to most of the main observational features of ACT-CL J0102-4915. Those features include the morphology of the X-ray emission with a remarkable wake-like substructure trailing after the secondary cluster, the X-ray luminosity and the temperature distributions, and also the SZ temperature decrement. The initial relative velocity required for the merger is extremely high and rare compared to that inferred from currently available Lambda cold dark matter (LCDM) cosmological simulations, which raises a potential challenge to the LCDM model, in addition to the case of the Bullet Cluster.

astro-ph.CO↗
arXiv2015

A probable Milli-Parsec Supermassive Binary Black Hole in the Nearest Quasar Mrk 231

Supermassive binary black holes (BBHs) are unavoidable products of galaxy mergers and are expected to exist in the cores of many quasars. Great effort has been made during the past several decades to search for BBHs among quasars; however, observational evidence for BBHs remains elusive and ambiguous, which is difficult to reconcile with theoretical expectations. In this paper, we show that the distinct optical-to-UV spectrum of Mrk 231 can be well interpreted as emission from accretion flows onto a BBH, with a semimajor axis of ~590AU and an orbital period of ~1.2 year. The flat optical and UV continua are mainly emitted from a circumbinary disk and a mini-disk around the secondary black hole (BH), respectively; and the observed sharp drop off and flux deficit at wavelength lambda ~ 4000-2500 Angstrom is due to a gap (or hole) opened by the secondary BH migrating within the circumbinary disk. If confirmed by future observations, this BBH will provide a unique laboratory to study the interplay between BBHs and accretion flows onto them. Our result also demonstrates a new method to find sub-parsec scale BBHs by searching for deficits in the optical-to-UV continuum among the spectra of quasars.

astro-ph.HE↗