arXiv subjects

Xian Chen

Publications and source records attributed to Xian Chen.

At least 127 records · Page 7Linked to original sources

arXiv2016

Relativistic mergers of black hole binaries have large, similar masses, low spins and are circular

Gravitational waves are a prediction of general relativity, and with ground-based detectors now running in their advanced configuration, we will soon be able to measure them directly for the first time. Binaries of stellar-mass black holes are among the most interesting sources for these detectors. Unfortunately, the many different parameters associated with the problem make it difficult to promptly produce a large set of waveforms for the search in the data stream. To reduce the number of templates to develop, one must restrict some of the physical parameters to a certain range of values predicted by either (electromagnetic) observations or theoretical modeling. In this work we show that "hyperstellar" black holes (HSBs) with masses $30 \lesssim M_{\rm BH}/M_{\odot} \lesssim 100$, i.e black holes significantly larger than the nominal $10\,M_{\odot}$, will have an associated low value for the spin, i.e. $a<0.5$. We prove that this is true regardless of the formation channel, and that when two HSBs build a binary, each of the spin magnitudes is also low, and the binary members have similar masses. We also address the distribution of the eccentricities of HSB binaries in dense stellar systems using a large suite of three-body scattering experiments that include binary-single interactions and long-lived hierarchical systems with a highly accurate integrator, including relativistic corrections up to ${\cal O}(1/c^5)$. We find that most sources in the detector band will have nearly zero eccentricities. This correlation between large, similar masses, low spin and low eccentricity will help to accelerate the searches for gravitational-wave signals.

astro-ph.CO↗

arXiv2015

The Gamma-ray Afterglows of Tidal Disruption Events

A star wandering too close to a supermassive black hole (SMBH) will be tidally disrupted. Previous studies of such "tidal disruption event" (TDE) mostly focus on the stellar debris that are bound to the system, because they give rise to luminous flares. On the other hand, half of the stellar debris in principle are unbound and can stream to a great distance, but so far there is no clear evidence that this "unbound debris stream" (UDS) exists. Motivated by the fact that the circum-nuclear region around SMBHs is usually filled with dense molecular clouds (MCs), here we investigate the observational signatures resulting from the collision between an UDS and a MC, which is likely to happen hundreds of years after a TDE. We focus on $γ$-ray emission ($0.1-10^5$ GeV), which comes from the encounter of shock-accelerated cosmic rays with background protons and, more importantly, is not subject to extinction. We show that because of the high proton density inside a MC, the peak $γ$-ray luminosity, about $10^{39}~{\rm erg~s^{-1}}$, is at least $100$ times greater than that in the case without a MC (only with a smooth interstellar medium). The luminosity decays on a time-scale of decades, depending on the distance of the MC, and about a dozen of these "TDE afterglows" could be detected within a distance of about $16$ Mpc by the future Cherenkov Telescope Array. Without careful discrimination, these sources potentially could contaminate the searches for starburt galaxies, galactic nuclei containing millisecond pulsars or dark-matter annihilation signals.

astro-ph.HE↗

arXiv2015

Continuous-time Markov decision processes under the risk-sensitive average cost criterion

This paper studies continuous-time Markov decision processes under the risk-sensitive average cost criterion. The state space is a finite set, the action space is a Borel space, the cost and transition rates are bounded, and the risk-sensitivity coefficient can take arbitrary positive real numbers. Under the mild conditions, we develop a new approach to establish the existence of a solution to the risk-sensitive average cost optimality equation and obtain the existence of an optimal deterministic stationary policy.

math.OC↗

arXiv2015

Unbound Debris Streams and Remnants Resulting From the Tidal Disruptions of Stars by Supermassive Black Holes

The kinetic energy of a star in orbit about a supermassive black hole is a significant fraction of its rest mass energy when its periapse is comparable to its tidal radius. Upon its destruction, a fraction of this energy is extracted and injected into the stellar debris, half of which becomes unbound from the black hole, with the fastest material moving at $\sim 0.03 c$. In this paper, we present a formalism for determining the fate of these unbound debris streams (UDSs) as they depart from the black hole and interact with the surrounding gas. As the density and velocity varies along the length of a UDS, we find that hydrodynamical drag quickly shapes UDSs into loop-like structures, with the densest portions of the streams leading portions of lower density. As UDSs travel outwards, their drag against the ISM increases quadratically with distance, which causes UDSs to deposit their momentum and energy into the ambient medium before the surrounding shocked ISM has a chance to cool. This sudden injection of $\sim 10^{50}$ erg into the ambient medium generates a Sedov-like unbound debris remnant (UDR) that mimics supernova remnants (SNRs) in energetics and appearance, accelerates particles which will produce cosmic rays and synchrotron emission, and provides momentum feedback into the molecular clouds surrounding a black hole. We estimate that a few of these UDRs might be present within a couple degrees of the Galactic Center masquerading as SNRs, and that the UDR scenario is a plausible explanation for Sgr A East.

astro-ph.HE↗

arXiv2015

The Midpoint Mixed Model with a Missingness Mechanism (M5): A Likelihood-Based Framework for Quantification of Mass Spectrometry Proteomics Data (Preprint)

Statistical models for proteomics data often estimate protein fold changes between two samples, A and B, as the average peptide intensity from sample A divided by the average peptide intensity from sample B. Such average intensity ratios fail to take full advantage of the experimental design which eliminates unseen confounding variables by processing peptides from both samples under identical conditions. Typically this structure is exploited through the estimation of a protein ratio as the median ratio of matched peptide intensities. This simple solution fails to account for a substantial missing data bias which has led to the development of more sophisticated average intensity models. Here we develop the first statistical model that accounts for nonignorable missingness while utilizing peptide level matched pairs across samples. Our simulation analysis shows that models which fail to utilize peptide level ratios, su.er astonishing losses to accuracy with basic ANOVA estimates having an average MSE 371% higher than median ratio estimates. In turn, median ratio estimates have an average MSE 35% higher than our model estimates. An analysis of breast cancer data reinforces these relationships and shows that our model is capable of increasing the number of proteins estimated by 22%.

stat.AP↗

arXiv2015

Stability of Gas Clouds in Galactic Nuclei: An Extended Virial Theorem

Cold gas entering the central $1$ to $10^2$ pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulate a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to include an external tidal field, crucial for the stability in the region of interest -- in dense star clusters, around SMBHs. We apply our extended Virial theorem to find the correct solutions to practical problems that until now were controversial, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly-used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.

astro-ph.GA↗

arXiv2015

Determination of the stretch tensor for structural transformations

The transformation stretch tensor plays an essential role in the evaluation of conditions of compatibility between phases and the use of the Cauchy-Born rule. This tensor is difficult to measure directly from experiment. We give an algorithm for the determination of the transformation stretch tensor from x-ray measurements of structure and lattice parameters. When evaluated on some traditional and emerging phase transformations the algorithm gives unexpected results.

cond-mat.mtrl-sci↗

arXiv2014

Sculpting the Stellar Cusp in the Galactic Center

Observations of the innermost parsec surrounding Sgr A$^*$ ---the supermassive black hole in the center of our Galaxy--- have revealed a diversity of structures whose existence and characteristics apparently defy the fundamental principles of dynamics. In this article, we review the challenges to the dynamics theories that have been brought forth in the past two decades by the observations of the Galactic center (GC). We outline the theoretical framework that has been developed to reconcile the discrepancies between the theoretical predictions and the observational results. In particular, we highlight the role of the recently discovered sub-parsec stellar disk in determining the dynamics and resolving the inconsistencies. We also discuss the implications for the recent activity of Sgr A$^*$.

astro-ph.GA↗

arXiv2014

Descope of the ALIA mission

The present work reports on a feasibility study commissioned by the Chinese Academy of Sciences of China to explore various possible mission options to detect gravitational waves in space alternative to that of the eLISA/LISA mission concept. Based on the relative merits assigned to science and technological viability, a few representative mission options descoped from the ALIA mission are considered. A semi-analytic Monte Carlo simulation is carried out to understand the cosmic black hole merger histories starting from intermediate mass black holes at high redshift as well as the possible scientific merits of the mission options considered in probing the light seed black holes and their coevolution with galaxies in early Universe. The study indicates that, by choosing the armlength of the interferometer to be three million kilometers and shifting the sensitivity floor to around one-hundredth Hz, together with a very moderate improvement on the position noise budget, there are certain mission options capable of exploring light seed, intermediate mass black hole binaries at high redshift that are not readily accessible to eLISA/LISA, and yet the technological requirements seem to within reach in the next few decades for China.

gr-qc↗

arXiv2014

Markov jump processes in modeling coalescent with recombination

Genetic recombination is one of the most important mechanisms that can generate and maintain diversity, and recombination information plays an important role in population genetic studies. However, the phenomenon of recombination is extremely complex, and hence simulation methods are indispensable in the statistical inference of recombination. So far there are mainly two classes of simulation models practically in wide use: back-in-time models and spatially moving models. However, the statistical properties shared by the two classes of simulation models have not yet been theoretically studied. Based on our joint research with CAS-MPG Partner Institute for Computational Biology and with Beijing Jiaotong University, in this paper we provide for the first time a rigorous argument that the statistical properties of the two classes of simulation models are identical. That is, they share the same probability distribution on the space of ancestral recombination graphs (ARGs). As a consequence, our study provides a unified interpretation for the algorithms of simulating coalescent with recombination, and will facilitate the study of statistical inference on recombination.

math.ST↗

arXiv2014

Continuous-time Markov Decision Processes with Finite-horizon Expected Total Cost Criteria

This paper deals with the unconstrained and constrained cases for continuous-time Markov decision processes under the finite-horizon expected total cost criterion. The state space is denumerable and the transition and cost rates are allowed to be unbounded from above and from below. We give conditions for the existence of optimal policies in the class of all randomized history-dependent policies. For the unconstrained case, using the analogue of the forward Kolmogorov equation in the form of conditional expectation, we show that the finite-horizon optimal value function is the unique solution to the optimality equation and obtain the existence of an optimal deterministic Markov policy. For the constrained case, employing the technique of occupation measures, we first give an equivalent characterization of the occupation measures, and derive that for each occupation measure generated by a randomized history-dependent policy, there exists an occupation measure generated by a randomized Markov policy equal to it. Then using the compactness and convexity of the set of all occupation measures, we obtain the existence of a constrained-optimal randomized Markov policy. Moreover, the constrained optimization problem is reformulated as a linear program, and the strong duality between the linear program and its dual program is established. Finally, a controlled birth and death system is used to illustrate our main results.

math.OC↗

arXiv2014

A rapid evolving region in the Galactic Center: Why S-stars thermalize and more massive stars are missing

The existence of "S-stars" within a distance of 1" from SgrA$^*$ contradicts our understanding of star formation, due to the forbiddingly violent environment. A suggested possibility is that they form far and have been brought in by some fast dynamical process, since they are young. Nonetheless, all conjectured mechanisms either fail to reproduce their eccentricities --without violating their young age-- or cannot explain the problem of "inverse mass segregation": The fact that lighter stars (the S-stars) are closer to SgrA$^*$ and more massive ones, Wolf-Rayet (WR) and O-stars, are farther out. In this Letter we propose that the responsible for both, the distribution of the eccentricities and the paucity of massive stars, is the Kozai-Lidov-{\em like} resonance induced by a sub-parsec disk recently discovered in the Galactic center. Considering that the disk probably extended to smaller radius in the past, we show that in as short as (a few) $10^6$ years, the stars populating the innermost 1" region would redistribute in angular-momentum space and recover the observed "super-thermal" distribution. Meanwhile, WR and O-stars in the same region intermittently attain ample eccentricities that will lead to their tidal disruptions by the central massive black hole. Our results provide new evidences that SgrA$^*$ was powered several millions years ago by an accretion disk as well as by tidal stellar disruptions.

astro-ph.GA↗

arXiv2013

The fragmenting past of the disk at the Galactic Center : The culprit for the missing red giants

Since 1996 we have known that the Galactic Center (GC) displays a core-like distribution of red giant branch (RGB) stars starting at ~ 10", which poses a theoretical problem, because the GC should have formed a segregated cusp of old stars. This issue has been addressed invoking stellar collisions, massive black hole binaries, and infalling star clusters, which can explain it to some extent. Another observational fact, key to the work presented here, is the presence of a stellar disk at the GC. We postulate that the reason for the missing stars in the RGB is closely intertwined with the disk formation, which initially was gaseous and went through a fragmentation phase to form the stars. Using simple analytical estimates, we prove that during fragmentation the disk developed regions with densities much higher than a homogeneous gaseous disk, i.e. "clumps", which were optically thick, and hence contracted slowly. Stars in the GC interacted with them and in the case of RGB stars, the clumps were dense enough to totally remove their outer envelopes after a relatively low number of impacts. Giant stars in the horizontal branch (HB), however, have much denser envelopes. Hence, the fragmentation phase of the disk must have had a lower impact in their distribution, because it was more difficult to remove their envelopes. We predict that future deeper observations of the GC should reveal less depletion of HB stars and that the released dense cores of RGB stars will still be populating the GC.

astro-ph.CO↗

arXiv2013

Study of the cofactor conditions: conditions of supercompatibility between phases

The cofactor conditions, introduced in James and Zhang, are conditions of compatibility between phases in martensitic materials. They consist of three subconditions: i) the condition that the middle principal stretch of the transformation stretch tensor $\mathbf U$ is unity ($λ_2 = 1$), ii) the condition $\mathbf a \cdot \mathbf U\, \cof (\mathbf U^2 - \mathbf I)\mathbf n = 0$, where the vectors $\mathbf a$ and $\mathbf n$ are certain vectors arising in the specification of the twin system, and iii) the inequality ${\rm tr} \mathbf U^2 + \det \mathbf U^2 -(1/4) |\mathbf a|^2 |\mathbf n|^2\ge 2$. Together, these conditions are necessary and sufficient for the equations of the crystallographic theory of martensite to be satisfied for the given twin system but for any volume fraction f of the twins, $0 \le f \le 1$. This contrasts sharply with the generic solutions of the crystallographic theory which have at most two such volume fractions for a given twin system of the form $f^*$ and $1-f^*$. In this paper we simplify the form of the cofactor conditions, we give their specific forms for various symmetries and twin types, we clarify the extent to which the satisfaction of the cofactor conditions for one twin system implies its satisfaction for other twin systems. In particular, we prove that the satisfaction of the cofactor conditions for either Type I or Type II twins implies that there are solutions of the crystallographic theory using these twins that have no elastic transition layer. We show that the latter further implies macroscopically curved, transition-layer-free austenite/martensite interfaces for Type I twins, and planar transition-layer-free interfaces for Type II twins which nevertheless permit significant flexibility of the martensite. We identify some real material systems nearly satisfying the cofactor conditions.

math-ph↗

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.

astro-ph.CO↗

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.

astro-ph.GA↗

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.

astro-ph.GA↗

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.

astro-ph.CO↗