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Studying the orbital motion of stars around Sagittarius A* in the Galactic Center provides a unique opportunity to probe the gravitational potential near the supermassive black hole at the heart of our Galaxy. Interferometric data obtained with the GRAVITY instrument at the Very Large Telescope Interferometer (VLTI) since 2016 has allowed us to achieve unprecedented precision in tracking the orbits of these stars. GRAVITY data have been key to detecting the in-plane, prograde Schwarzschild precession of the orbit of the star S2, as predicted by General Relativity. By combining astrometric and spectroscopic data from multiple stars, including S2, S29, S38, and S55 - for which we have data around their time of pericenter passage with GRAVITY - we can now strengthen the significance of this detection to an approximately $10 \sigma$ confidence level. The prograde precession of S2's orbit provides valuable insights into the potential presence of an extended mass distribution surrounding Sagittarius A*, which could consist of a dynamically relaxed stellar cusp comprised of old stars and stellar remnants, along with a possible dark matter spike. Our analysis, based on two plausible density profiles - a power-law and a Plummer profile - constrains the enclosed mass within the orbit of S2 to be consistent with zero, establishing an upper limit of approximately $1200 \, M_\odot$ with a $1 \sigma$ confidence level. This significantly improves our constraints on the mass distribution in the Galactic Center. Our upper limit is very close to the expected value from numerical simulations for a stellar cusp in the Galactic Center, leaving little room for a significant enhancement of dark matter density near Sagittarius A*., Comment: Submitted to A&A on September 17, 2024

Large-scale cosmic filaments may have played an important role in shaping the properties of galaxies. Meanwhile, cosmic filaments are believed to harbor a substantial portion of the missing baryons at redshift z < 2. To inspect the role of filaments in these issues, many properties of filaments need to be examined, including their lengths, thicknesses, and density profiles. However, measuring some of these properties poses challenges. This study concentrates on estimating filament width/thickness, investigating potential correlations between the local width of filaments and the properties of dark matter halos within filaments. We find that the local width of filaments generally increases with the mass of dark matter halos embedded in filaments per unit length, roughly following a secondorder polynomial, although with notable scatter. We probe and discuss means that may refine our findings. After further verification and improvements, this relation could be applied to filament samples constructed from the observed galaxy distribution, aiding in understanding the roles of cosmic filaments in galaxy evolution and uncovering the missing baryons., Comment: 11 pages, 7 figures, accepted to ApJ

Future observations with next-generation large-area radio telescopes are expected to discover radio pulsars (PSRs) closely orbiting around Sagittarius~A* (Sgr~A*), the supermassive black hole (SMBH) dwelling at our Galactic Center (GC). Such a system can provide a unique laboratory for testing General Relativity (GR), as well as the astrophysics around the GC. In this paper, we provide a numerical timing model for PSR-SMBH systems based on the post-Newtonian (PN) equation of motion, and use it to explore the prospects of measuring the black hole (BH) properties with pulsar timing. We further consider the perturbation caused by the dark matter (DM) distribution around Sgr~A*, and the possibility of constraining DM models with PSR-SMBH systems. Assuming a 5-year observation of a normal pulsar in an eccentric ($e=0.8$) orbit with an orbital period $P_b = 0.5\,$yr, we find that -- with weekly recorded times of arrival (TOAs) and a timing precision of 1 ms -- the power-law index of DM density distribution near the GC can be constrained to about 20%. Such a measurement is comparable to those measurements at the Galactic length scale but can reveal small-scale properties of the DM., Comment: 12 pages, 13 figures, accepted by PRD

M60, an elliptical galaxy located 16.5~Mpc away, has an active nucleus with a very low luminosity and an extremely low accretion rate. Its central supermassive black hole has a mass of $M_{\rm BH}\sim4.5\times10^{9}\, M_{\odot}$ and a Schwarzschild radii corresponding to $R_{\rm S}\sim5.4\,\mu\mathrm{as}$. To investigate the nature of its innermost radio nucleus, data from the Very Long Baseline Array (VLBA) at 4.4 and 7.6~GHz were reduced. The VLBA images reveal a compact component with total flux densities of $\sim$20~mJy at both frequencies, a size of $\leq$0.27~mas (99.7$\%$ confidence level), about 0.022~pc ($50\,R_{\rm S}$) at 7.6~GHz, and a brightness temperature of $\geq6\times10^{9}$~K. This suggests that the observed centi-parsec-scale compact core could be attributed to a nonthermal jet base or an advection-dominated accretion flow (ADAF) with nonthermal electrons. The extremely compact structure also supports the presence of an SMBH in the center. Our results indicate that M60 is a promising target for broad-band VLBI observations at millimeter wavelengths to probe ADAF scenarios and tightly constrain the potential photon ring (about 28\,$\mu$as) around its SMBH., Comment: 15 pages, 5 figures, 3 tables, accepted for publication in Astrophysical Journal

In this study we present a novel Monte-Carlo code, referred to as GNC, which enables the investigation of dynamical relaxation in clusters comprising multiple mass components in the vicinity of supermassive black holes at the centers of galaxies. Our method is based on two-dimensional Fokker-Planck equations in the energy and angular momentum space, and allows the evolution of multiple mass components, including stars and compact objects. The code demonstrates remarkable flexibility to incorporate additional complex dynamics, such as resonant relaxations and gravitational wave orbital decay. By employing a weighting method, we effectively enhance the statistical accuracy of rare particle results. In this initial publication, we present the fundamental version of our method, focusing on two-body relaxations and loss cone effects. Through comparisons with previous studies, we establish consistent outcomes in terms of relaxation processes, energy and angular momentum distributions, density profiles, and loss cone consumption rates. We consistently observe the development of tangential anisotropy within the cluster, while the outer regions tend to retain near-isotropic characteristics. Moving forward, GNC holds great promise for exploring a wide range of intriguing phenomena within galactic nuclei, in particular relativistic stellar dynamics, providing detailed and insightful outcomes., Comment: Submitted. Comments welcome. The code is made publicly available

We investigate the impact of cosmic filaments on the gas accretion rate, $\dot{M}_{\rm{gas}}$, of dark matter halos in filaments, based on cosmological hydrodynamic simulation. We find that for halos less massive than $10^{12.0}\ \rm{M_{\odot}}$, $\dot{M}_{\rm{gas}}$ of halos residing in prominent filaments (with width $D_{\rm{fil}}>3\ \rm{Mpc}/h$) is lower than halos residing in tenuous filaments ($D_{\rm{fil}}<3\ \rm{Mpc}/h$) by $20-30\%$ at $z=0.5$, and by a factor of 2-3 at $z=0$. However, $\dot{M}_{\rm{gas}}$ depends weakly on the physical distance between halo center and the spine of filaments from high redshift to $z=0$, only shows clear difference between the inner and outer regions in prominent filaments at $z=0$. We further probe the thermal properties of gas in prominent and tenuous filaments, which appear in relatively highly and intermediate overdense regions, respectively. The gas in prominent filaments is hotter. Around $26\%$, $38\%$ and $45\%$ of gases in prominent filaments are hotter than $10^6$ K at $z=1.0, 0.5$ and $z=0.0$ respectively. The corresponding fractions in tenuous filaments are merely $\sim 6\%, 9\%$ and $11\%$. The suppressed gas accretion rate for low-mass halos in prominent filaments at $z \lesssim 0.5$ may result from the hotter ambient gas, which could provide a physical processing mechanism to cut down the supply of gas to halos before they enter clusters. This process meets partially the need of the preheating mechanism implemented in some semi-analytical models of galaxy formation, but works only for $\sim 20\%$ of halos at $z < 1$., Comment: 16 pages, 12 figures. published version in The Astrophysical Journal

X-ray quasi-periodic eruptions (QPEs) are discovered recently in active galaxies with unknown driven mechanism. Under the assumption that QPEs are caused by star-disc collisions, we adopt full relativistic method and show that both the orbital parameters of the star and also the mass and spinning of the massive black hole (MBH) can be revealed by using the time of arrival (TOA) of the QPEs. By applying the model to the observed QPEs of GSN069, we find that the star is in a near-circular orbit ( $e_\bullet=0.05^{+0.02}_{-0.02}$) with semimajor axis of $\sim 365^{+54}_{-49}r_{\rm g}$ around a MBH with $M_\bullet=3.0^{+0.9}_{-0.6} \times10^5M_\odot$. The alternative short and long recurring time of the QPEs of GSN069 can be well explained by the small eccentricity and the orbital precession of the star. We find that the QPEs of GSN069 are possibly driven by a striped stellar core colliding with accretion disc after partial tidal disruption event around the MBH. For GSN069-like galaxies, if continuous X-ray monitoring of QPE events can be accumulated with uncertainties of TOA $\lesssim 100-150$s, the spin of massive black hole can be constrained by fitting to QPEs. Our results show that the timing of QPEs can provide a unique probe for measuring the spinning of MBH and tests of no-hair theorem., Comment: Accepted for publication in ApJ Letters, 10 pages, 5 figures

We study the stellar binary black holes (BBHs) inspiralling/merging in galactic nuclei based on our numerical method GNC. We find that $3-40\%$ of all new born BBHs will finally merge due to various dynamical effects. In a five year's mission, up to $10^4$, $10^5$, $\sim100$ of BBHs inspiralling/merging in galactic nuclei can be detected with SNR$>8$ in aLIGO, Einstein/DECIGO, TianQin/LISA/TaiJi, respectively. About tens are detectable in both LISA/TaiJi/TianQin and aLIGO. These BBHs have two unique characteristics: (1) Significant eccentricities. $1-3\%$, $2-7\%$, or $30-90\%$ of them is with $e_i>0.1$ when they enter into aLIGO, Einstein, or space observatories, respectively. Such high eccentricities provide a possible explanation for that of GW 190521. Most highly-eccentric BBHs are not detectable in LISA/Tianqin/TaiJi before entering into aLIGO/Einstein as their strain become significant only at $f_{\rm GW}\gtrsim0.1$ Hz. DECIGO become an ideal observatory to detect those events as it can fully cover the rising phase. (2) Up to $2\%$ of BBHs can inspiral/merge at distances $\lesssim10^3 r_{\rm SW}$ from the massive black hole (MBH), with significant accelerations, such that the Doppler phase drift of $\sim10-10^5$ of them can be detectable with SNR$>8$ in space observatories. The energy density of the gravitational wave backgrounds (GWB) contributed by these BBHs deviate from the powerlaw slope of $2/3$ at $f_{\rm GW}\lesssim 1$mHz. The high eccentricity, significant accelerations and different profile of GWB of these sources make them distinguishable, thus interesting for future GW detections and tests of relativities., Comment: Published in ApJ. 32 pages, 13 figures, typos corrected

A large portion of the baryons at low redshifts are still missing from detection. Most of the missing baryons are believed to reside in large scale cosmic filaments. Understanding the distribution of baryons in filaments is crucial for the search for missing baryons. We investigate the properties of cosmic filaments since $z=4.0$ in a cosmological hydrodynamic simulation, focusing on the density and temperature profiles perpendicular to the filament spines. Our quantitative evaluation confirm the rapid growth of thick and prominent filaments after $z=2$. We find that the local linear density of filaments shows correlation with the local diameter since $z=4.0$. The averaged density profiles of both dark matter and baryonic gas in filaments of different width show self-similarity, and can be described by an isothermal single-beta model. The typical gas temperature increases as the filament width increasing, and is hotter than $10^6$ K for filaments with width $D_{fil} \gtrsim 4.0 \rm{Mpc}$, which would be the optimal targets for the search of missing baryons via thermal Sunyaev-Zel'dovich (SZ) effect. The temperature rises significantly from the boundary to the inner core regime in filaments with $D_{fil} \gtrsim 4.0 \rm{Mpc}$, probably due to heating by accretion shock, while the temperature rise gently in filaments with $D_{fil}< 4.0 \rm{Mpc}$., Comment: 15 pages, 8 figures, accepted for publication in The Astrophysical Journal

Radiative efficiencies of QSOs and its distribution encode rich information on the evolution of both masses and spins of massive black holes (MBHs) across cosmic time. In this paper, we develop a maximum likelihood method to statistically extract the intrinsic relation between radiative efficiency ($\epsilon$) and mass ($M_{\bullet}$) of QSOs from their distribution on the luminosity-(empirically estimated virial) mass plane. By using mock samples, we find that strong constraint can be put on the $\epsilon-M_{\bullet}$ relation at redshift $z\lesssim 0.4$ from uniform QSO samples similar to those in Sloan Digital Sky Survey, and from QSO samples at $z \sim 0.6$ (or $\lesssim 1.0$) if the magnitude limit of the survey can be $\sim 1-2$ (or $2-3$) magnitude deeper. Applying this method to the SDSS DR7 QSOs with $z\lesssim 0.7$, we find $\epsilon \propto M_{\bullet}^{0\sim 1.1}$ (or $\epsilon \propto M_{\bullet}^{-1.0\sim 0}$) correlation for QSOs with the masses obtained according to the H$\beta$ (or Mg II) empirical mass estimator. These contradictory results may be due to the unknown systematic errors in the two mass estimators, preventing an accurate constraint on the $\epsilon-M_{\bullet}$ relation by using current available QSO samples. We find that both the estimates of MBH mass and Eddington ratio distribution functions can be affected by the $\epsilon-M_\bullet$ relation, suggesting that the determination of this relation is important for understanding the accretion and growth history of MBHs. In future, the intrinsic $\epsilon-M_{\bullet}$ relation is expected to be strongly constrained by using QSO samples obtained from surveys deeper than SDSS if the host galaxy contamination and systematic errors of the mass estimator(s) can be well modeled or removed., Comment: Resubmitted to ApJ after the second referee's report

We study the dynamical evolution of the stellar mass binary black holes (BBHs) in a galactic nucleus that contains a massive black hole (MBH). For a comprehensive study of their merging events, we consider simultaneously the non-resonant and resonant relaxations of the BBHs, the binary-single encounters of the BBHs with the field stars, the Kozai-Lidov (KL) oscillation and the close encounters between the BBHs and the central MBH, which usually lead to binaries' tidal disruptions. As the BBHs are usually heavier than the background stars, they sink to the center by mass segregation, making the KL oscillation an important effect in merging BBHs. The binary-single encounters can not only lead to softening and ionization of the BBHs, it can also make them hardening, that increases the merging rates significantly. The mergers of BBHs are mainly contributed by galaxies containing MBHs less massive than $10^8 M_\odot$ and the total event rates are likely in orders of $1$--$10$ Gpc$^{-3}$ yr$^{-1}$, depending on the detailed assumptions of the nucleus clusters. About $3-10\%$ of these BBH mergers are with eccentricity $\ge 0.01$ when their gravitational wave oscillating frequencies enter the LIGO band ($10$\,Hz). Our results show that merging the BBHs within galactic nuclei can be an important source of the merging events detected by the Advanced LIGO/Virgo detectors, and they can be distinguished from BBH mergers from the galactic fields and globular clusters when enough events are accumulated., Comment: 31 pages, 14 figures, Accepted for publication in the Astrophysical Journal

The scattering of fast radio bursts (FRBs) by the intergalactic medium (IGM) is explored using cosmological hydrodynamical simulations. We confirm that the scattering by the clumpy IGM has significant line-of-sight variations. We demonstrate that the scattering by the IGM in the voids and walls of the cosmic web is weak, but it can be significantly enhanced by the gas in clusters and filaments. The observed non-monotonic dependence of the FRB widths on the dispersion measures (DM) cannot determine whether the IGM is an important scattering matter or not. The IGM may dominate the scattering of some FRBs, and the host galaxy dominates others. For the former case, the scattering should be primarily caused by the medium in clusters. A mock sample of 500 sources shows that $\tau_{\rm{IGM}} \propto \rm{DM_{IGM}}^{1.6-2.1}$ at $z<1.5$. Assuming that the turbulence follows Kolmogorov scaling, we find that an outer scale of $L_0\sim 5\,$pc is required to make $\tau_{\rm{IGM}} \sim 1-10\,$ms at $\nu=1\, $ GHz. The required $L_0\sim 5\, $pc can alleviate the tension in the timescales of turbulent heating and cooling but is still $\sim 4$ orders of magnitude lower than the presumed injection scale of turbulence in the IGM. The gap is expected to be effectively shortened if the simulation resolution is further increased. The mechanisms that may further reduce the gap are shortly discussed. If future observations can justify the role of the IGM in the broadening of FRBs, it can help to probe the gas in clusters and filaments., Comment: 11 pages, 9 figures, accepted for publication in The Astrophysical Journal

One of the major unsolved questions on the understanding of the AGN population is the origin of the dichotomy between radio-quiet and radio-loud quasars. The most promising explanation is provided by the spin paradigm, which suggests radio-loud quasars have higher black hole spin. However, the measurement of black hole spin remains extremely challenging. We here aim at comparing the mean radiative efficiencies of carefully matched samples of radio-loud and radio-quiet SDSS quasars at 0.3

Pulsars around the Massive Black Hole (MBH) in the Galactic Center (GC) are expected to be revealed by the incoming facilities (e.g., the Square Kilometre Array). Under a full relativistic framework with the pulsar approximated as a test particle, we investigate the constraints on the spinning of the MBH by monitoring the timing of surrounding pulsars. For GC pulsars orbiting closely around the MBH (e.g., $\lesssim1000$AU), we find that full relativistic treatment in modeling accurately their timing signals can be necessary, as the relativistic signals are orders of magnitude larger than the time of arrival measurement accuracies. Although usually there are near-degeneracies among MBH spin parameters, the constraints on the spinning of the MBH are still very tight. By continuously monitoring a normal pulsar in orbits with a period of $\sim2.6$yr and an eccentricity of $0.3-0.9$ under timing precision of $1-5$ms, within $\sim 8$yr the spin magnitude and the orientations of the GC MBH can be constrained with $2\sigma$ error of $10^{-3}-10^{-2}$ and $10^{-1}-10^\circ$, respectively. Even for pulsars in orbits similar to the detected star S2/S0-2 or S0-102, we find that the spinning of the MBH can still be constrained within $4-8$yr, with the most significant constraints provided near the pericenter passage. If the proper motion of the pulsars with astrometric accuracy of $10\mu$as can also be collected along with the timing measurement, then the position, velocity, mass and the distance to the Solar System of the MBH can be constrained about $\sim10\mu$as, $\sim1\mu$as$/$yr, $\sim 10 M_\odot$ and $\sim1$pc, respectively., Comment: Accepted for publication in the Astrophysical Journal

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., Comment: 25 pages, 10 figures

Detailed numerical analyses of the orbital motion of a test particle around a spinning primary are performed. They aim to investigate the possibility of using the post-Keplerian (pK) corrections to the orbiter's periods (draconitic, anomalistic and sidereal) as a further opportunity to perform new tests of post-Newtonian (pN) gravity. As a specific scenario, the S-stars orbiting the Massive Black Hole (MBH) supposedly lurking in Sgr A$^\ast$ at the center of the Galaxy is adopted. We, first, study the effects of the pK Schwarzchild, Lense-Thirring and quadrupole moment accelerations experienced by a target star for various possible initial orbital configurations. It turns out that the results of the numerical simulations are consistent with the analytical ones in the small eccentricity approximation for which almost all the latter ones were derived. For highly elliptical orbits, the size of all the three pK corrections considered turn out to increase remarkably. The periods of the observed S2 and S0-102 stars as functions of the MBH's spin axis orientation are considered as well. The pK accelerations considered lead to corrections of the orbital periods of the order of 1-100d (Schwarzschild), 0.1-10h (Lense-Thirring) and 1-10^3s (quadrupole) for a target star with a=300-800~AU and e ~ 0.8, which could be possibly measurable by the future facilities., Comment: Accepted for publication in ApJ

The S-stars discovered in the Galactic center (GC) are expected to provide unique dynamical tests of the Kerr metric of the massive black hole (MBH) orbited by them. In order to obtain unbiased measurements of its spin and the related relativistic effects, a comprehensive understanding of the gravitational perturbations of the stars and stellar remnants around the MBH is quite essential. Here, we study the perturbations on the observables of a typical target star, i.e., the apparent orbital motion and the redshift, due to both the spin-induced relativistic effects and the Newtonian attractions of a single or a cluster of disturbing object(s). We find that, in most cases, the Newtonian perturbations on the observables are mainly attributed to the perturbed orbital period of the target star, rather than the Newtonian orbital precessions. The Newtonian perturbations have their unique features when they peak around the pericenter passage in each revolution, which is quite different from those of the spin-induced effects. Looking at the currently detected star S2/S0-2, we find that its spin-induced effects on both the image position and redshift are very likely obscured by the gravitational perturbations from the star S0-102 alone. We also investigate and discuss the Newtonian perturbations on a hypothetical S-star located inside the orbits of the currently detected ones. By considering a number of possible stellar distributions near the central MBH, we find that the spin-induced effects on the apparent position and the redshift dominate over the stellar perturbations for target stars with orbital semimajor axis smaller than $100-400$AU if the MBH is maximally spinning. Our results suggest that, in principle, the stellar perturbations can be removed as they have distinctive morphologies comparing to those of the relativistic Kerr-type signatures., Comment: Accepted for publication in the Astrophysical Journal

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., Comment: 10 pages, 7 figures, updated to the journal version

The S-stars in the Galactic center (GC) are anticipated to provide unique dynamical constraint on the spin of the GC massive black hole (MBH). In this paper, we develop a fast full general relativistic method to simultaneously constrain the MBH mass, spin, and spin direction by considering both the motion of a star and the propagation of photons from the star to a distant observer. Assuming some example stars, we demonstrate that the spin-induced effects on the projected trajectory and redshift curve of a star depend on both the value and the direction of the spin. The maximum effects over a full orbit can differ by a factor upto more than one order of magnitude for cases with significantly different spin directions. Adopting the Markov Chain Monte Carlo fitting technique, we illustrate that the spin of the GC MBH is likely to be well constrained by using the motion of S0-2/S2 over a period of ~45yr if it is close to one and the astrometric and spectroscopic precisions (sigma_p,sigma_Z) can be as high as (10muas, 1km/s). In the mean time, the distance from the sun to the GC and the MBH mass can also be constrained to an unprecedented accuracy (0.01%-0.1%). If there exists a star with semimajor axis significantly smaller than that of S0-2/S2 and eccentricity larger than that of S0-2/S2, the MBH spin can be constrained with high accuracy over a period of <~10yr for (sigma_p,sigma_Z) ~ (10muas,1km/s), even if the spin is only moderately large (>~0.2)., Comment: 29 pages, 17 figures

Pulsars, if existing and detectable in the immediate vicinity of the massive black hole (MBH) in the Galactic center (GC), may be used as a superb tool to probe both the environment and the metric of the central MBH. The recent discovery of a magnetized pulsar in the GC suggests that many more pulsars should exist near the MBH. In this paper, we estimate the number and the orbital distribution of pulsars in the vicinity of the MBH in the GC by assuming that the pulsar progenitors, similar to the GC S-stars, were captured to orbits tightly bound to the MBH through the tidal breakup of stellar binaries. We use the current observations on both the GC S-stars and the hypervelocity stars to calibrate the injection rate(s) of and the dynamical model(s) for the stellar binaries. By including the relaxation processes, supernova kicks, and gravitational wave radiation in our simulations, we estimate that ~97-190 (9-14) pulsars may presently orbit the central MBH with semimajor axes <=4000AU (<=1000AU), which is compatible with the current observational constraints on the number of the GC pulsars. The semimajor axis and the pericenter distance of the pulsar closest to the central MBH are probably in the range of ~120-460AU and ~2-230AU, respectively. Future telescopes, such as the SKA, may be able to detect a significant number of pulsars with semimajor axis smaller than a few thousand AU in the GC. Long-term monitoring of these pulsars would be helpful in constraining both the environment and the metric of the central MBH. Our preferred model also results in about ten hyperfast pulsars with velocity >~1500km/s moving away from the Milky Way., Comment: 9 pages, 3 figures, accepted for publication in the Astrophysical Journal

We estimate the radiative efficiency (epsilon) of individual type 1 SDSS QSOs by using their bolometric luminosities (L_{bol}) and accretion rates (\dot{M}_{\bullet,acc}), which may be related to the assembly histories and spins of the central massive black holes (MBHs). We estimate L_{bol} by using the empirical spectral energy distributions of QSOs and \dot{M}_{\bullet,acc} by fitting the observed optical luminosity(/-ies) with the thin accretion disk model, assuming the MBH masses given by the virial mass estimator(s) (M_{\bullet,vir}). We find an apparent correlation between epsilon and M_{\bullet,vir}, which is strong at redshift z \la 1.8, weak at z \ga 2, and consistent with that found by Davis & Laor (2011) for 80 PG QSOs at z \leq 0.5. To investigate whether this correlation is intrinsic or not, we construct a mock sample of QSOs according to the true MBH mass and Eddington ratio distributions given in Kelly & Shen (2013). By comparing the results obtained from the mock sample with that from the SDSS sample, we demonstrate that the apparent epsilon-M_{\bullet,vir} correlation can be produced by and mainly due to the selection effects of the SDSS sample and the bias induced by the usage of M_{\bullet,vir} as the true MBH mass. The mean values of epsilon of those SDSS QSOs are consistent with being a constant \simeq 0.11-0.16 over the redshift range of 0.3 \la z \la 4. We conclude that the current SDSS QSO data is consistent with no strong intrinsic correlation between radiative efficiency and true MBH mass and no significant redshift evolution of radiative efficiencies., Comment: 16 pages, 10 figures, accepted for publication in MNRAS

In this paper, we investigate the link between the hypervelocity stars (HVSs) discovered in the Galactic halo and the S-stars moving in the Galactic center (GC), under the hypothesis that they are both the products of the tidal breakup of the same population of stellar binaries by the central massive black hole (MBH). By adopting several hypothetical models for binaries to be injected into the vicinity of the MBH and doing numerical simulations, we realize the tidal breakup processes of the binaries and their follow-up evolution. We find that many statistical properties of the detected HVSs and S-stars can be reproduced under some binary injecting models, and their number ratio can be reproduced if the stellar initial mass function is top-heavy (e.g., with slope ~-1.6). The total number of the captured companions is ~50 that have masses in the range ~3-7Msun and semimajor axes <~4000 AU and survive to the present within their main-sequence lifetime. The innermost one is expected to have a semimajor axis ~300-1500 AU and a pericenter distance ~10-200 AU, with a significant probability of being closer to the MBH than S2. Future detection of such a closer star would offer an important test to general relativity. The majority of the surviving ejected companions of the S-stars are expected to be located at Galactocentric distances <~20 kpc, and have heliocentric radial velocities ~-500-1500 km/s and proper motions up to ~5-20 mas/yr. Future detection of these HVSs may provide evidence for the tidal-breakup formation mechanism of the S-stars., Comment: updated to match the published version, 18 pages, 7 figures

Hypervelocity stars (HVSs) found in the Galactic halo are probably the dynamical products of interactions between (binary) stars and the massive black hole(s) (MBH) in the Galactic center (GC). It has been shown that the detected HVSs are spatially consistent with being located on two thin disks (Lu et al.), one of which has the same orientation as the clockwise-rotating stellar disk in the GC. Here we perform a large number of three-body experiments of the interactions between the MBH and binary stars bound to it, and find that the probability of ejecting HVSs is substantially enhanced by multiple encounters between the MBH and binary stars at distances substantially larger than the initial tidal breakup radii. Assuming that the HVS progenitors are originated from the two disks, the inclination distribution of the HVSs relative to the disk planes can be reproduced by either the mechanism of tidal breakup of binary stars or the mechanism of ejecting HVSs by a hypothetical binary black hole (BBH) in the GC. However, an isotropical origination of HVS progenitors is inconsistent with the observed inclination distribution. Assuming that the HVSs were ejected out by the tidal breakup mechanism, its velocity distribution can be reproduced if their progenitors diffuse onto low angular momentum orbits slowly and most of the progenitors were broken up at relatively large distances due to multiple encounters. Assuming that the HVSs were ejected out by a BBH within the allowed parameter space in the GC, our simulations produce relatively flatter velocity spectra compared to the observed ones; however, the BBH mechanism cannot be statistically ruled out, yet. Future surveys of HVSs and better statistics of their spatial and velocity distributions should enable to distinguish the ejection mechanisms of HVSs and shed new light on the dynamical environment of the MBH.(abridged), Comment: 19 pages, 16 figures

Hypervelocity stars (HVSs) escaping away from the Galactic halo are dynamical products of interactions of stars with the massive black hole(s) (MBH) in the Galactic Center (GC). They are mainly B-type stars with their progenitors unknown. OB stars are also populated in the GC, with many being hosted in a clockwise-rotating young stellar (CWS) disk within half a parsec from the MBH and their formation remaining puzzles. In this paper, we demonstrate that HVSs can well memorize the injecting directions of their progenitors using both analytical arguments and numerical simulations, i.e., the ejecting direction of an HVS is almost anti-parallel to the injecting direction of its progenitor. Therefore, the spatial distribution of HVSs maps the spatial distribution of the parent population of their progenitors directly. We also find that almost all the discovered HVSs are spatially consistent with being located on two thin disk planes. The orientation of one plane is consistent with that of the (inner) CWS disk, which suggests that most of the HVSs originate from the CWS disk or a previously existed disk-like stellar structure with an orientation similar to it. The rest of HVSs may be correlated with the plane of the northern arm of the mini-spiral in the GC or the plane defined by the outer warped part of the CWS disk. Our results not only support the GC origin of HVSs but also imply that the central disk (or the disk structure with a similar orientation) should persist or be frequently rejuvenated over the past 200 Myr, which adds a new challenge to the stellar disk formation and provides insights to the longstanding problem of gas fueling into massive black holes., Comment: 7 pages, 5 figures