arXiv subjects

F. K. Liu

Publications and source records attributed to F. K. Liu.

At least 19 recordsLinked to original sources

arXiv2026

A model for the enhanced production rate of early-type hypervelocity stars in the Galactic halo

About twenty late B-type hypervelocity stars (HVSs) traveling faster than the Galactic escape velocity have been discovered in the Galactic halo, many of which were ejected from the Galactic center (GC). Recently, we have advocated that these HVSs most likely formed in the nuclear star cluster (NSC) $150$--$500\, \rm{Myr}$ ago and were predominantly ejected via the gravitational slingshot of a past intermediate-mass black hole (IMBH) orbiting the supermassive black hole (SMBH) Sgr~A$^{*}$. Here we explore the constraints of the production rate of young HVSs on the star formation region of the NSC. We propose that the young HVS progenitors are born in a lopsided eccentric disk that is comparable in radius to the NSC. By numerically tracking the orbital evolution of disk stars, we find that they undergo rapid angular momentum relaxation at formation due to eccentric disk instability, and that their slingshot interactions with the SMBH-IMBH binary at distances $\simeq 100\, \rm{au}$ produce HVSs at a rate of $10^{-5}$--$10^{-4}\, \rm{yr}^{-1}$. The rate is expected to trace the disk formation history, increasing with the accumulation of disk stars and dropping rapidly after the star formation stopped at $150\, \rm{Myr}$ ago. The rate is consistent with the observation and orders of magnitude higher than that expected for an old relaxed population in the literature, enhanced due to the gravitational torque from the non-spherical GC potential and radial velocity anisotropies of the disk stars. Our results imply that young HVSs should have a distinct radial and angular distribution from old ones.

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arXiv2024

Formation Rate of Quasiperiodic Eruptions in Galactic Nuclei Containing Single and Dual Supermassive Black Holes

Quasiperiodic eruptions (QPEs) are a novel class of transients recently discovered in a few extragalactic nuclei. It has been suggested that a QPE can be produced by a main-sequence star undergoing repeated partial disruptions by the tidal field of a supermassive black hole (SMBH) immediately after getting captured on a tightly bound orbit through the Hills mechanism. In this Letter, we investigate the period-dependent formation rate of QPEs for this scenario, utilizing scattering experiments and the loss-cone theory. We calculate the QPE formation rates in both a single-SMBH and a dual-SMBH system, motivated by the overrepresentation of postmerger galaxies as QPE hosts. We find that for SMBHs of mass $10^{6}$--$10^{7}M_{\odot}$, most QPEs formed in this scenario have periods longer than $\simeq 100$ days. A single-SMBH system generally produces QPEs at a negligible rate of $10^{-10}$--$10^{-8}\ \rm{yr}^{-1}$ due to inefficient two-body relaxation. Meanwhile, in a dual-SMBH system, the QPE rate is enhanced by 3-4 orders of magnitude, mainly due to a boosted angular momentum evolution under tidal perturbation from the companion SMBH (galaxy). The QPE rate in a postmerger galactic nucleus hosting two equal-mass SMBHs separated by a few parsecs could reach $10^{-6}$--$10^{-5}\ \rm{yr}^{-1}$. Our results suggest that a nonnegligible fraction ($\simeq 10$--$90\%$) of long-period QPEs should come from postmerger galaxies.

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arXiv2023

Absence of the predicted 2022 October outburst of OJ 287 and implications for binary SMBH scenarios

The project MOMO (Multiwavelength Observations and Modelling of OJ 287) was set up to test predictions of binary supermassive black hole (SMBH) scenarios and to understand disk-jet physics of the blazar OJ 287. After a correction, the precessing binary (PB) SMBH model predicted the next main outburst of OJ 287 in 2022 October, no longer in July, making the outburst well observable and the model testable. We have densely covered this period in our ongoing multi-frequency radio, optical, UV, and X-ray monitoring. The predicted outburst was not detected. Instead, OJ 287 was at low optical-UV emission levels, declining further into November. The predicted thermal bremsstrahlung spectrum was not observed either, at any epoch. Further, applying scaling relations, we estimate a SMBH mass of OJ 287 of 10^8 M_sun. The latest in a sequence of deep low-states that recur every 1-2 yrs is used to determine an upper limit on the Eddington ratio and on the accretion-disk luminosity. This limit is at least a factor of 10 lower than required by the PB model with its massive primary SMBH of >10^{10} M_sun. All these results favor alternative binary SMBH models of OJ 287 that neither require strong orbital precession nor a very large mass of the primary SMBH.

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arXiv2023

MOMO VI: Multifrequency radio variability of the blazar OJ 287 from 2015-2022, absence of predicted 2021 precursor-flare activity, and a new binary interpretation of the 2016/2017 outburst

Based on our dedicated Swift monitoring program, MOMO, OJ 287 is one of the best-monitored blazars in the X-ray--UV--optical regime. Here, we report results from our accompanying, dense, multi-frequency (1.4--44 GHz) radio monitoring of OJ 287 between 2015 and 2022 covering a broad range of activity states. Fermi gamma-ray observations are added. We characterize the radio flux and spectral variability in detail, including DCF and other variability analyses, and discuss its connection with the multiwavelength emission. Deep fades of radio and optical--UV fluxes are found to occur every 1--2 years. Further, it is shown that a precursor flare of thermal bremsstrahlung predicted by one of the binary supermassive black hole (SMBH) models of OJ 287 was absent. We then focus on the nature of the extraordinary, nonthermal 2016/2017 outburst that we initially discovered with Swift. We interpret it as the latest of the famous optical double-peaked outbursts of OJ 287, favoring binary scenarios that do not require a highly precessing secondary SMBH.

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arXiv2023

Tracing the Evolution of SMBHs and Stellar Objects in Galaxy Mergers: An Multi-mass Direct N-body Model

By using direct N-body numerical simulations, we model the dynamical co-evolution of two supermassive black holes (SMBHs) and the surrounding stars in merging galaxies. In order to investigate how different stellar components evolve during the merger, we generate evolved stellar distributions with an initial mass function. Special schemes have also been developed to deal with some rare but interesting events, such as tidal disruption of main sequence stars, the plunge of low mass stars, white dwarfs, neutron stars and stellar mass black holes, and the partial tidal disruption of red giants or asymptotic giant branch stars. Our results indicate that the formation of a bound supermassive black hole binary (SMBHB) will enhance the capture rates of stellar objects by the SMBHs. Compared to the equal stellar mass model, the multi-mass model tends to result in a higher average mass of disrupted stars. Instead of being tidally disrupted by the SMBH, roughly half of the captured main sequence stars will directly plunge into the SMBH because of their small stellar radius. Giant stars, on the other hand, can be stripped of their envelopes if they are close enough to the SMBH. Though most remnants of the giant stars can survive after the disruption, a small fraction still could plunge into the SMBH quickly or after many orbital periods. Our results also indicate significant mass segregation of compact stars at the beginning of the merger, and then this effect is destroyed as the two SMBHs form a bound binary.

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arXiv2021

Milli-Hertz Gravitational Wave Background Produced by Quasi-Periodic Eruptions

Extreme-mass-ratio inspirals (EMRIs) are important targets for future space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Sapce Antenna (LISA). Recent works suggest that EMRI may reside in a population of newly discovered X-ray transients called "quasi-periodic eruptions" (QPEs). Here we follow this scenario and investigate the detectability of the five recently discovered QPEs by LISA. We consider two specific models in which the QPEs are made of either stellar-mass objects moving on circular orbits around massive black holes (MBHs) or white dwarfs (WDs) on eccentric orbits around MBHs. We find that in either case each QPE is too weak to be resolvable by LISA. However, if QPEs are made of eccentric WD-MBH binaries, they radiate GWs in a wide range of frequencies. The broad spectra overlap to form a background which, between $0.003-0.02$ Hz, exceeds the background known to exist due to other types of sources. Presence of this GW background in the LISA band could impact the future search for the seed black holes at high redshift as well as the stellar-mass binary black holes in the local universe.

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arXiv2020

Measuring black hole masses from tidal disruption events and testing the $M_{\rm BH}-σ_*$ relation

Liu and collaborators recently proposed an elliptical accretion disk model for tidal disruption events (TDEs). They showed that the accretion disks of optical/UV TDEs are large and highly eccentric and suggested that the broad optical emission lines with complex and diverse profiles originate in the cool eccentric accretion disk of random inclination and orientation. In this paper, we calculate the radiation efficiency of the elliptical accretion disk and investigate the implications for the observations of TDEs. We compile observational data for the peak bolometric luminosity and total radiation energy after peak brightness of 18 TDE sources and compare these data to the predictions from the elliptical accretion disk model. Our results show that the observations are consistent with the theoretical predictions and that the majority of the orbital energy of the stellar debris is advected into the black hole (BH) without being converted into radiation. Furthermore, we derive the masses of the disrupted stars and the masses of the BHs of the TDEs. The BH masses obtained in this paper are also consistent with those calculated with the $M_{\rm BH} - σ_*$ relation. Our results provide an effective method for measuring the masses of BHs in large numbers of TDEs to be discovered in ongoing and next-generation sky surveys, regardless of whether the BHs are located at the centers of galactic nuclei or wander in disks and halos.

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arXiv2019

Direct n-body simulations of tidal disruption rate evolution in unequal-mass galaxy mergers

The hierarchical galaxy formation model predicts supermassive black hole binaries (SMBHBs) in galactic nuclei. Due to the gas poor environment and the limited spatial resolution in observations they may hide in the center of many a galaxy. However, a close encounter of a star with one of the supermassive black holes (SMBHs) may tidally disrupt it to produce a tidal disruption event (TDE) and temporarily light up the SMBH. In a previous work, we investigated with direct N-BODY simulations the evolution of TDE rates of SMBHB systems in galaxy mergers of equal mass. In this work we extend to unequal mass mergers. Our results show that, when two SMBHs are far away from each other, the TDE rate of each host galaxy is similar as in an isolated galaxy. As the two galaxies and their SMBHs separation shrinks, the TDE rate is increasing gradually until it reaches a maximum shortly after the two SMBHs become bound. In this stage, the averaged TDE rate can be enhanced by several times to an order of magnitude relative to isolated single galaxies. Our simulations show that the dependence of the TDE accretion rate on the mass ratio in this stage can be well fitted by power law relations for both SMBHs. After the bound SMBHB forms, the TDE rate decreases with its further evolution. We also find that in minor mergers TDEs of the secondary SMBH during and after the bound binary formation are mainly contributed by stars from the other galaxy.

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arXiv2018

A large accretion disk of extreme eccentricity in the TDE ASASSN-14li

In the canonical model for tidal disruption events (TDEs), the stellar debris circularizes quickly to form an accretion disk of size about twice the orbital pericenter of the star. Most TDEs and candidates discovered in the optical/UV have broad optical emission lines with complex and diverse profiles of puzzling origin. Liu et al. recently developed a relativistic elliptical disk model of constant eccentricity in radius for the broad optical emission lines of TDEs and well reproduced the double-peaked line profiles of the TDE candidate PTF09djl with a large and extremely eccentric accretion disk. In this paper, we show that the optical emission lines of the TDE ASASSN-14li with radically different profiles are well modelled with the relativistic elliptical disk model, too. The accretion disk of ASASSN-14li has an eccentricity 0.97 and semimajor axis of 847 times the Schwarzschild radius (r_S) of the black hole (BH). It forms as the consequence of tidal disruption of a star passing by a massive BH with orbital pericenter 25r_S. The optical emission lines of ASASSN-14li are powered by an extended X-ray source of flat radial distribution overlapping the bulk of the accretion disk and the single-peaked asymmetric line profiles are mainly due to the orbital motion of the emitting matter within the disk plane of inclination about 26\degr and of pericenter orientation closely toward the observer. Our results suggest that modelling the complex line profiles is powerful in probing the structures of accretion disks and coronal X-ray sources in TDEs.

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arXiv2017

Disk origin of broad optical emission lines of the TDE candidate PTF09djl

An otherwise dormant supermassive black hole (SMBH) in a galactic nucleus flares up when it tidally disrupts a star passing by. Most of the tidal disruption events (TDEs) and candidates discovered in the optical/UV have broad optical emission lines with complex and diverse profiles of puzzling origin. In this Letter, we show that the double-peaked broad Halpha line of the TDE candidate PTF09djl can be well modelled with a relativistic elliptical accretion disk and the peculiar substructures with one peak at the line rest wavelength and the other redshifted to about 3.5x10^4 km/s are mainly due to the orbital motion of the emitting matter within the disk plane of large inclination 88\degr and pericenter orientation nearly vertical to the observer. The accretion disk has an extreme eccentricity 0.966 and semimajor axis of 340 BH Schwarzschild radii. The viewing angle effects of large disk inclination lead to significant attenuation of He emission lines originally produced at large electron scattering optical depth and to the absence/weakness of He emission lines in the spectra of PTF09djl. Our results suggest that the diversities of line intensity ratios among the line species in optical TDEs are probably due to the differences of disk inclinations.

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arXiv2016

Boosted Tidal Disruption by Massive Black Hole Binaries During Galaxy Mergers FROM The View of N-Body Simulation

Supermassive black hole binaries (SMBHBs) are productions of the hierarchical galaxy formation model. There are many close connections between central SMBH and its host galaxy because the former plays very important roles on the formation and evolution of a galaxy. For this reason, the evolution of SMBHBs in merging galaxies is an essential problem. Since there are many discussions about SMBHB evolution in gas rich environment, we focus on the quiescent galaxy, using tidal disruption as a diagnostic tool. Our study is based on a series of numerical large particle number direct N-body simulations for dry major mergers. According to the simulation results, the evolution can be divided into three phases. In phase I, the tidal disruption rate for two well separated SMBHs in merging system has similar level to single SMBH in isolate galaxy. After two SMBHs getting close enough to form a bound binary in phase II, the disruption rate can be enhanced for ~ 2 order of magnitudes within a short time. This "boosted" disruption stage finishes after the SMBHB evolving to compact binary system in phase III, corresponding to a drop back of disruption rate to a level of a few times higher than that in Phase I. How to correctly extrapolate our N-body simulation results to reality, and implications of our results to observations, are discussed too.

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arXiv2016

Growth of supermassive black holes, galaxy mergers and supermassive binary black holes

The study of galaxy mergers and supermassive binary black holes (SMBBHs) is central to our understanding of the galaxy and black hole assembly and (co-)evolution at the epoch of structure formation and throughout cosmic history. Galaxy mergers are the sites of major accretion episodes, they power quasars, grow supermassive black holes (SMBHs), and drive SMBH-host scaling relations. The coalescing SMBBHs at their centers are the loudest sources of gravitational waves (GWs) in the universe, and the subsequent GW recoil has a variety of potential astrophysical implications which are still under exploration. Future GW astronomy will open a completely new window on structure formation and galaxy mergers, including the direct detection of coalescing SMBBHs, high-precision measurements of their masses and spins, and constraints on BH formation and evolution in the high-redshift universe.

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arXiv2014

A milliparsec supermassive black hole binary candidate in the galaxy SDSS J120136.02+300305.5

Galaxy mergers play a key role in the evolution of galaxies and the growth of their central supermassive black holes (SMBHs). A search for (active) SMBH binaries (SMBHBs) at the centers of the merger remnants is currently ongoing. Perhaps the greatest challenge is to identify the inactive SMBHBs, which might be the most abundant, but are also the most difficult to identify. Liu et al. predicted characteristic drops in the light curves of tidal disruption events (TDEs), caused by the presence of a secondary SMBH. Here, we apply that model to the light curve of the optically inactive galaxy SDSS J120136.02+300305.5, which was identified as a candidate TDE with XMM-Newton. We show that the deep dips in its evolving X-ray light curve can be well explained by the presence of a SMBHB at its core. A SMBHB model with a mass of the primary of M_BH = 10^7 M_sun, a mass ratio q=0.08, and a semimajor axis a_b = 0.6 mpc is in good agreement with the observations. Given that primary mass, introducing an orbital eccentricity is needed, with e_b = 0.3. Alternatively, a lower mass primary of M_BH = 10^6 M_sun in a circular orbit fits the light curve well. Tight binaries like this one, which have already overcome the "final parsec problem," are prime sources of gravitational wave radiation once the two SMBHs coalesce. Future transient surveys, which will detect TDEs in large numbers, will place tight constraints on the SMBHB fraction in otherwise non-active galaxies.

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arXiv2013

Enhanced off-center stellar tidal disruptions by supermassive black holes in merging galaxies

Off-center stellar tidal disruption flares have been suggested to be a powerful probe of recoiling supermassive black holes (SMBHs) out of galactic centers due to anisotropic gravitational wave radiations. However, off-center tidal flares can also be produced by SMBHs in merging galaxies. In this paper, we computed the tidal flare rates by dual SMBHs in two merging galaxies before the SMBHs become self-gravitationally bounded. We employ an analytical model to calculate the tidal loss-cone feeding rates for both SMBHs, taking into account two-body relaxation of stars, tidal perturbations by the companion galaxy, and chaotic stellar orbits in triaxial gravitational potential. We show that for typical SMBHs with mass 10^7 M_\sun, the loss-cone feeding rates are enhanced by mergers up to Γ~ 10^{-2} yr^{-1}, about two order of magnitude higher than those by single SMBHs in isolated galaxies and about four orders of magnitude higher than those by recoiling SMBHs. The enhancements are mainly due to tidal perturbations by the companion galaxy. We suggest that off-center tidal flares are overwhelmed by those from merging galaxies, making the identification of recoiling SMBHs challenging. Based on the calculated rates, we estimate the relative contributions of tidal flare events by single, binary, and dual SMBH systems during cosmic time. Our calculations show that the off-center tidal disruption flares by un-bound SMBHs in merging galaxies contribute a fraction comparable to that by single SMBHs in isolated galaxies. We conclude that off-center tidal disruptions are powerful tracers of the merging history of galaxies and SMBHs.

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arXiv2012

Is there an intermediate massive black hole in the Galactic center: Imprints on the stellar tidal-disruption rate

It has been suggested that an intermediate-massive black hole (IMBH) with mass $10^{3-5} M_\odot$ could fall into the galactic center (GC) and form a massive black hole binary (MBHB) with the central supermassive black hole, but current observations are not sensitive to constrain all mass and distance ranges. Motivated by the recent discovery that MBHBs could enhance the rate of tidal-disruption events (TDEs) of stellar objects, we investigate the prospect of using stellar-disruption rate to probe IMBHs in the GC. We incorporated the perturbation by an IMBH into the loss-cone theory and calculated the stellar-disruption rates in the GC. We found that an IMBH heavier than $2000 M_\odot$ could distinguishably enhance the stellar-disruption rate. By comparing observations of Sgr A* with the fall-back model for stellar debris, we suggested that the TDE rate in our Galaxy should not significantly exceed $0.002 yr^{-1}$, therefore a fraction of the parameter space for the IMBH, concentrating at the high-mass end, can already be excluded. To derive constraint in the remaining parameter space, it is crucial to observationally confirm or reject the stellar-disruption rate between $10^{-4}$ and $10^{-2} yr^{-1}$, and we discussed possible strategies to make such measurements.

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arXiv2012

Mass estimate of the Swift J 164449.3+573451 supermassive black hole based on the 3:2 QPO resonance hypothesis

A dormant Swift source J 164449.3+573451 (Sw 164449+57)recently experienced a powerful outburst, caused most probably by a tidal disruption of a star by the super-massive black hole at the center of the source. During the outburst, a quasi periodic oscillation (QPO) was detected in the observed X-ray flux from Sw 164449+57. We show that if the observed QPO belongs to a "3:2 twin peak QPO" (with the second frequency not observed), the mass of the black hole in Sw 164449+57 is rather low, M ~ 10^5 M_sun, and the source belongs to a class of intermediate mass black holes. The low mass of the source has been pointed out previously by several authors.

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arXiv2012

Interaction of Recoiling Supermassive Black Holes with Stars in Galactic Nuclei

Supermassive black hole binaries (SMBHBs) are the products of frequent galaxy mergers. The coalescence of the SMBHBs is a distinct source of gravitational wave (GW) radiation. The detections of the strong GW radiation and their possible electromagnetic counterparts are essential. Numerical relativity suggests that the post-merger supermassive black hole (SMBH) gets a kick velocity up to 4000 km/s due to the anisotropic GW radiations. Here we investigate the dynamical co-evolution and interaction of the recoiling SMBHs and their galactic stellar environments with one million direct N-body simulations including the stellar tidal disruption by the recoiling SMBHs. Our results show that the accretion of disrupted stars does not significantly affect the SMBH dynamical evolution. We investigate the stellar tidal disruption rates as a function of the dynamical evolution of oscillating SMBHs in the galactic nuclei. Our simulations show that most of stellar tidal disruptions are contributed by the unbound stars and occur when the oscillating SMBHs pass through the galactic center. The averaged disruption rate is ~10^{-6} M_\odot yr^{-1}, which is about an order of magnitude lower than that by a stationary SMBH at similar galactic nuclei. Our results also show that a bound star cluster is around the oscillating SMBH of about ~ 0.7% the black hole mass. In addition, we discover a massive cloud of unbound stars following the oscillating SMBH. We also investigate the dependence of the results on the SMBH masses and density slopes of the galactic nuclei.

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arXiv2011

Recoiling Supermassive Black Holes in Spin-flip Radio Galaxies

Numerical relativity simulations predict that coalescence of supermassive black hole (SMBH) binaries not only leads to a spin flip but also to a recoiling of the merger remnant SMBHs. In the literature, X-shaped radio sources are popularly suggested to be candidates for SMBH mergers with spin flip of jet-ejecting SMBHs. Here we investigate the spectral and spatial observational signatures of the recoiling SMBHs in radio sources undergoing black hole spin flip. Our results show that SMBHs in most spin-flip radio sources have mass ratio $q\ga 0.3$ with a minimum possible value $q_{\rm min} \simeq 0.05$. For major mergers, the remnant SMBHs can get a kick velocity as high as $2100 km s^{-1}$ in the direction within an angle $\la 40^\circ$ relative to the spin axes of remnant SMBHs, implying that recoiling quasars are biased to be with high Doppler-shifted broad emission lines while recoiling radio galaxies are biased to large apparent spatial off-center displacements. We also calculate the distribution functions of line-of-sight velocity and apparent spatial off-center for spin-flip radio sources with different apparent jet reorientation angles. Our results show that the larger the apparent jet reorientation angle is, the larger the Doppler-shifting recoiling velocity and apparent spatial off-center displacement will be. We investigate the effects of recoiling velocity on the dust torus in spin-flip radio sources and suggest that recoiling of SMBHs would lead to "dust poor" AGNs. Finally, we collect a sample of 19 X-shaped radio objects and for each object give the probability of detecting the predicted signatures of recoiling SMBH.

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