arXiv subjects

Xian Chen

Publications and source records attributed to Xian Chen.

At least 73 records · Page 4Linked to original sources

arXiv2023

The appearance of a merging binary black hole very close to a spinning supermassive black hole

The mass and distance of a binary black hole (BBH) are fundamental parameters to measure in gravitational-wave (GW) astronomy. It is well-known that the measurement is affected by cosmological redshift, and recent works also showed that Doppler and gravitational redshifts could further affect the result if the BBH coalesces close to a supermassive black hole (SMBH). Here we consider the additional lensing effect induced by the nearby SMBH on the measurement. We compute the null geodesics originating within $10$ gravitational radii of a Kerr SMBH to determine the redshift and magnification of the GWs emitted by the BBH. We find a positive correlation between redshift and demagnification, which results in a positive correlation between the mass and distance of the BBH in the detector frame. More importantly, we find a higher probability for the signal to appear redshifted and demagnified to a distant observer, rather than blueshifted and magnified. Based on these results, we show that a binary at a cosmological redshift of $z_{\rm cos}=(10^{-2}-10^{-1})$ and composed of BHs of $(10-20)M_\odot$ could masquerade as a BBH at a redshift of $z_{\rm cos}\sim1$ and containing BHs as large as $(44-110)M_\odot$. In the case of extreme demagnification, we also find that the same BBH could appear to be at $z_{\rm cos}>10$ and contain subsolar-mass BHs. Such an effect, if not accounted for, could bias our understanding of the origin of the BHs detected via GWs.

astro-ph.HE↗

arXiv2023

Moving gravitational wave sources at cosmological distances: Impact on the measurement of the Hubble constant

Standard sirens - GW sources with an EM counterpart - can be used to measure H_0 directly which should help to ease the existing Hubble tension. However, if the source has a relative velocity to the expanding universe on top of its motion due to the Hubble flow, a relativistic redshift affects the redshift of the EM counterpart and the apparent distance of the GW source, and thus it needs to be corrected to obtain accurate measurements. We study the effect of such a relative velocity on GWs for a source in an expanding universe showing that the total redshift of the wave is equal to the product of the relativistic redshift and the cosmological redshift. We, further, find that a relative velocity of the source changes its apparent distance by a factor (1+z_rel)^2 in contrast to a linear factor for the cosmological redshift. We discuss that the additional factor for the relativistic redshift is a consequence of a velocity-dependent amplitude for GWs. We consider the effect of the relative velocity on the chirp mass and the apparent distance of the source an observer would infer when ignoring this velocity. We find that for different astrophysical scenarios the error can range between 0.1 % and 7 % for the chirp mass while the error in the apparent distance can be between 0.25 % and 15 %. Furthermore, we consider the error introduced in the measurement of H_0 using standard sirens for two cases: (i) when the effect of velocity on the redshift of the EM counterpart is considered but not on the apparent distance obtained from GWs and (ii) when the effect of the relative velocity is ignored completely. We find that in the first case the error can reach 1 % for a source moving due to the peculiar velocity of its host galaxy and that in the second case the error can be more than 5 % for a source at the distance of GW150914 with the same velocity.

astro-ph.CO↗

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.

astro-ph.HE↗

arXiv2023

Detecting Accelerating Eccentric Binaries in the LISA Band

Many gravitational wave (GW) sources in the LISA band are expected to have non-negligible eccentricity. Furthermore, many of them can undergo acceleration because they reside in the presence of a tertiary. Here we develop analytical and numerical methods to quantify how the compact binary's eccentricity enhances the detection of its peculiar acceleration. We show that the general relativistic precession pattern can disentangle the binary's acceleration-induced frequency shift from the chirp-mass-induced frequency shift in GW template fitting, thus relaxing the signal-to-noise ratio requirement for distinguishing the acceleration by a factor of $10\sim100$. Moreover, by adopting the GW templates of the accelerating eccentric compact binaries, we can enhance the acceleration measurement accuracy by a factor of $\sim100$, compared to the zero-eccentricity case, and detect the source's acceleration even if it does not change during the observational time. For example, a stellar-mass binary black hole (BBH) with moderate eccentricity in the LISA band yields an error of the acceleration measurement $\sim10^{-7}m\cdot s^{-2}$ for $\rm{SNR}=20$ and observational time of $4$ yrs. In this example, we can measure the BBHs' peculiar acceleration even when it is $\sim1\rm pc$ away from a $4\times 10^{6}\rm M_{\odot}$ SMBH. Our results highlight the importance of eccentricity to the LISA-band sources and show the necessity of developing GW templates for accelerating eccentric compact binaries.

astro-ph.HE↗

arXiv2022

Synchronizing the EMRIs and IMRIs in AGN accretion disks

Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals (IMRIs) are important gravitational-wave (GW) sources for the Laser Interferometer Space Antenna (LISA). So far, their formation and evolution are considered to be independent, but recent theories suggest that stellar-mass black holes (sBHs) and intermediate-mass black hole (IMBHs) can coexist in the accretion disk of an active galactic nucleus (AGN), which indicates that EMRIs and IMRIs may form in the same place. Motivated by the fact that a gas giant migrating in a protoplanetary disk could trap planetesimals close to its orbit, we study in this paper a similar interaction between a gap-opening IMBH in an AGN disk and the sBHs surrounding it. We analyse the torques imposed on the sBHs by the disk as well as by the IMBH, and show that the sBHs can be trapped by the IMBH if they are inside the orbit of the IMBH. Then we implement the torques in our numerical simulations to study the migration of an outer IMBH and an inner sBH, both embedded in an AGN disk. We find that their migration is synchronized until they reach a distance of about ten Schwarzschild radii from the central supermassive black hole, where the pair breaks up due to strong GW radiation. This result indicates that LISA may detect an EMRI and an IMRI within several years from the same AGN. Such a GW source will bring rich information about the formation and evolution of sBHs and IMBHs in AGNs.

astro-ph.HE↗

arXiv2022

Piecewise deterministic Markov process for condition-based imperfect maintenance models

In this paper, a condition-based imperfect maintenance model based on piecewise deterministic Markov process (PDMP) is constructed. The degradation of the system includes two types: natural degradation and random shocks. The natural degradation is deterministic and can be nonlinear. The damage increment caused by a random shock follows a certain distribution, and its parameters are related to the degradation state. Maintenance methods include corrective maintenance and imperfect maintenance. Imperfect maintenance reduces the degradation degree of the system according to a random proportion. The maintenance action is delayed, and the system will suffer natural degradations and random shocks while waiting for maintenance. At each inspection time, the decision-maker needs to make a choice among planning no maintenance, imperfect maintenance and perfect maintenance, so as to minimize the total discounted cost of the system. The impulse optimal control theory of PDMP is used to determine the optimal maintenance strategy. A numerical study dealing with component coating maintenance problem is presented. Relationship with optimal threshold strategy is discussed. Sensitivity analyses on the influences of discount factor, observation interval and maintenance cost to the discounted cost and optimal actions are presented.

eess.SY↗

arXiv2022

Binaries Wandering Around Supermassive Black Holes Due To Gravito-electromagnetism

Extreme-mass-ratio inspirals (EMRIs) are important sources for space-borne gravitational-wave (GW) detectors. Such a source normally consists of a stellar-mass black hole (BH) and a Kerr supermassive BH (SMBH), but recent astrophysical models predict that the small body could also be a stellar-mass binary BH (BBH). A BBH reaching several gravitational radii of a SMBH will induce rich observable signatures in the waveform, but the current numerical tools are insufficient to simulate such a triple system while capturing the essential relativistic effects. Here we solve the problem by studying the dynamics in a frame freely falling alongside the BBH. Since the BBH is normally non-relativistic and much smaller than the curvature radius of the Kerr background, the evolution in the free-fall frame reduces to essentially Newtonian dynamics, except for a perturbative gravito-electromagnetic (GEM) force induced by the curved background. We use this method to study the BBHs on near-circular orbits around a SMBH and track their evolution down to a distance of $2-3$ gravitational radii from the SMBH. Our simulations reveal a series of dynamical effects which are not shown in the previous studies using conventional methods. The most notable one is a radial oscillation and azimuthal drift of the BBH relative to the SMBH. These results provide new insight into the evolution and detection of the EMRIs containing BBHs.

astro-ph.HE↗

arXiv2022

Subnanometer Accuracy of Surface Characterization by Reflected-Light Differential Interference Microscopy

We theorize the surface step characterization by reflected incoherent-light differential interference microscopy with consideration of the optical diffraction effect. With the integration of localization analysis, we develop a quantitative differential interference optical system, by which we demonstrate that the axial resolution of measuring surface height variation is sensitive to the shear distance between the two spatially differentiated beams. We fabricate three nanometer-size steps by photolithography, and successfully characterize their 1D height variations with 0.13 nm Hz^(-1/2) axial precision. Our result suggests that the optical differential interference microscopy can be used for real-time characterization of surface structure with a subnanometer accuracy and a large field of view, which is greatly beneficial to the surface characterization of micro/nano-electromechanical systems.

physics.optics↗

arXiv2022

The Eccentric and Accelerating Stellar Binary Black Hole Mergers in Galactic Nuclei: Observing in Ground and Space Gravitational Wave Observatories

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.

astro-ph.HE↗

arXiv2022

A Higher Probability of Detecting Lensed Supermassive Black Hole Binaries by LISA

Gravitational lensing of gravitational waves (GWs) is a powerful probe of the matter distribution in the universe. Here we revisit the wave-optics effects induced by dark matter (DM) halos on the GW signals of merging massive black hole binaries (MBHBs), and we study the possibility of discerning these effects using the Laser Interferometer Space Antenna (LISA). In particular, we include the halos in the low-mass range of $\rm 10^5-10^8\, M_\odot$ since they are the most numerous according to the cold DM model. We simulate the lensed signals corresponding to a wide range of impact parameters, and we find distinguishable deviation from the standard best-fit GW templates even when the impact parameter is as large $y\simeq50$. Consequently, we estimate that over $(0.1-1.6)\%$ of the MBHBs in the mass range of $\rm 10^{5.0}-10^{6.5}\, M_\odot$ and the redshift range of $4-10$ should show detectable wave-optics effects. This probability is one order of magnitude higher than that derived in previous works. The uncertainty comes mainly from the mass function of the DM halos. Not detecting any signal during the LISA mission would imply that DM halos with $\rm 10^5-10^8\, M_\odot$ are less numerous than what the cold DM model predicts.

astro-ph.CO↗

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.

astro-ph.HE↗

arXiv2021

Revised event rates for extreme and extremely large mass-ratio inspirals

One of the main targets of the Laser Interferometer Space Antenna (LISA) is the detection of extreme mass-ratio inspirals (EMRIs) and extremely large mass-ratio inspirals (X-MRIs). Their orbits are expected to be highly eccentric and relativistic when entering the LISA band. Under these circumstances, the inspiral time-scale given by Peters' formula loses precision and the shift of the last-stable orbit (LSO) caused by the massive black hole spin could influence the event rates estimate. We re-derive EMRIs and X-MRIs event rates by implementing two different versions of a Kerr loss-cone angle that includes the shift in the LSO, and a corrected version of Peters' time-scale that accounts for eccentricity evolution, 1.5 post-Newtonian hereditary fluxes, and spin-orbit coupling. The main findings of our study are summarized as follows: (1) implementing a Kerr loss-cone changes the event rates by a factor ranging between 0.9 and 1.1; (2) the high-eccentricity limit of Peters' formula offers a reliable inspiral time-scale for EMRIs and X-MRIs, resulting in an event rate estimate that deviates by a factor of about 0.9 to 3 when compared to event rates computed with the corrected version of Peters' time-scale and the usual loss-cone definition. (3) Event rates estimates for systems with a wide range of eccentricities should be revised. Peters' formula overestimates the inspiral rates of highly eccentric systems by a factor of about 8 to 30 compared to the corrected values. Besides, for e$_0 \lesssim$0.8, implementing the corrected version of Peters' formula would be necessary to obtain accurate estimates.

astro-ph.GA↗

arXiv2021

Excitation of gravitational wave modes by a center-of-mass velocity of the source

Most gravitational wave (GW) sources are moving relative to us. This motion is often closely related to the environment of the source and can thus provide crucial information about the formation of the source and its host. Recently, LIGO and Virgo detected for the first time the subdominant modes of GWs. We show that a motion of the center-of-mass of the source can affect these modes, where the effect is proportional to the velocity of the source. The effect on the GW modes in turn affects the overall frequency of the GW, thus leading to a phase shift. We study the impact of this effect on LIGO/Virgo detections and show that it is detectable for sources with high mass ratios and inclinations. This effect breaks the degeneracy between mass and Doppler shift in GW observations, and opens a new possibility of detecting the motion of a GW source even for constant velocities.

astro-ph.CO↗

arXiv2021

Moderate and $L^p$ maximal inequalities for diffusion processes and conformal martingales

The $L^p$ maximal inequalities for martingales are one of the classical results in the theory of stochastic processes. Here we establish the sharp moderate maximal inequalities for one-dimensional diffusion processes, which include the $L^p$ maximal inequalities as special cases. Moreover, we apply our theory to many specific examples, including the Ornstein-Uhlenbeck (OU) process, Brownian motion with drift, reflected Brownian motion with drift, Cox-Ingersoll-Ross process, radial OU process, and Bessel process. The results are further applied to establish the moderate maximal inequalities for some high-dimensional processes, including the complex OU process and general conformal local martingales.

math.PR↗

arXiv2021

Exciting modes due to the aberration of gravitational waves: Measurability for extreme-mass-ratio inspirals

Gravitational waves from a source moving relative to us can suffer from special-relativistic effects such as aberration. The required velocities for these to be significant are on the order of $1000\,\textrm{km s}^{-1}$. This value corresponds to the velocity dispersion that one finds in clusters of galaxies. Hence, we expect a large number of gravitational-wave sources to have such effects imprinted in their signals. In particular, the signal from a moving source will have its higher modes excited, i.e., $(3,3)$ and beyond. We derive expressions describing this effect, and study its measurability for the specific case of a circular, non-spinning extreme-mass-ratio inspiral. We find that the excitation of higher modes by a peculiar velocity of $1000\,\textrm{km\,s}^{-1}$ is detectable for such inspirals with signal-to-noise ratios of $\gtrsim20$. Using a Fisher matrix analysis, we show that the velocity of the source can be measured to a precision of just a few percent for a signal-to-noise ratio of 100. If the motion of the source is ignored parameter estimates could be biased, e.g., the estimated masses of the components through a Doppler shift. Conversely, by including this effect in waveform models, we could measure the velocity dispersion of clusters of galaxies at distances inaccessible to light.

gr-qc↗

arXiv2021

Energy conversion from heat to electricity by highly reversible phase-transforming ferroelectrics

Searching for performant multiferroic materials attracts general research interests in energy science as they have been increasingly exploited as the conversion media among thermal, electric, magnetic and mechanical energies by using their temperature-dependent ferroic properties. Here we report a material development strategy that guides us to discover a reversible phase-transforming ferroelectric material exhibiting enduring energy harvesting from small temperature differences. The material satisfies the crystallographic compatibility condition between polar and nonpolar phases, which shows only 2.5C thermal hysteresis and high figure of merit. It stably generates 15uA electricity in consecutive thermodynamic cycles in absence of any bias fields. We demonstrate our device to consistently generate 6uA/cm2 current density near 100C over 540 complete phase transformation cycles without any electric and functional degradation. The energy conversion device can light up a LED directly without attaching an external power source. This promising material candidate brings the low-grade waste heat harvesting closer to a practical realization, e.g. small temperature fluctuations around the water boiling point can be considered as a clean energy source.

cond-mat.mtrl-sci↗

arXiv2021

Amplification of gravitational wave by a Kerr black hole

Binary black hole may form near a supermassive black hole. The background black hole (BH) will affect the gravitational wave (GW) generated by the binary black hole. It is well known that the Penrose process may provide extra energy due to the ergosphere. In the present paper we investigate the energy amplification of the gravitational wave by a Kerr black hole background. In particular and different from the earlier studies, we compare the energies of the waves in the cases with and without a nearby Kerr BH. We find that only when the binary black hole is moving relative to the Kerr background can the GW energy be amplified. Otherwise, the energy will be suppressed by the background Kerr black hole. This finding is consistent with the inequality found by Wald for Penrose process. Taking into account realistic astrophysical scenarios, we find that the Kerr black hole background can amplify the GW energy by at most 5 times.

gr-qc↗

arXiv2021

Merging stellar and intermediate-mass black holes in dense clusters: implications for LIGO, LISA and the next generation of gravitational wave detectors

We study the formation of intermediate-mass ratio inspirals (IMRIs) triggered by the interactions between two stellar black holes (BHs) and an intermediate-mass BH (IMBH) inhabiting the centre of a dense star cluster. We exploit $N$-body models varying the IMBH mass, the stellar BH mass spectrum, and the star cluster properties. These simulations are coupled with a semi-analytic procedure to characterise the evolution of the remnant IMBH. The IMRIs formation probability attains values $\sim 5-50\%$, with larger values corresponding to larger IMBH masses. IMRIs map out the stellar BH mass spectrum, thus they might be used to unravel BH populations in star clusters harboring an IMBH. After the IMRI phase, an IMBH initially nearly maximal(almost non-rotating) tends to decrease(increase) its spin. If IMBHs grow mostly via repeated IMRIs, we show that only IMBH seeds sufficiently massive ($M_{\rm seed} > 300$ M$_\odot$) can grow up to $M_{\rm imbh} >10^3$ M$_\odot$ in dense globular clusters. Assuming that these seeds form at a redshift $z\sim 2-6$, we find that around $1-5\%$ of them would reach masses $\sim 500-1500$ M$_\odot$ at redshift $z=0$ and would exhibit low-spins, $S_{\rm imbh} < 0.2$. Measuring the mass and spin of IMBHs involved in IMRIs could help unravelling their formation mechanisms. We show that LISA can detect IMBHs in Milky Way globular clusters with a signal-to-noise ratio SNR$=10-100$, or in the Large Magellanic Cloud with an SNR$=8-40$. We provide the IMRIs merger rate for LIGO ($Γ_{\rm LIG} = 0.003-1.6$ yr$^{-1}$), LISA ($Γ_{\rm LIS} = 0.02-60$ yr$^{-1}$), ET ($Γ_{\rm ET} = 1-600$ yr$^{-1}$), and DECIGO ($Γ_{\rm DEC} = 6-3000$ yr$^{-1}$). Our simulations show that IMRIs' mass and spin encode crucial insights on the mechanisms that regulate IMBH formation and that the synergy among different detectors would enable us to fully unveil them. (Abridged)

astro-ph.GA↗