arXiv subjects
Publications and source records attributed to Xiang-Dong Li.
In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation $\partial_t u=Lu$ associated with the time dependent Witten Laplacian on complete Riemannian manifolds equipped with a variant of the $(K, m)$-super Perelman Ricci flows and the $K$-super Perelman Ricci flows.
The discovery of the ultraluminous X-ray pulsar M82 X-2 has stimulated lively discussion on the nature of the accreting neutron star. In most of the previous studies the magnetic field of the neutron star was derived from the observed spin-up/down rates based on the standard thin, magnetized accretion disk model. However, under super-Eddington accretion the inner part of the accretion disk becomes geometrically thick. In this work we consider both radiation feedback from the neutron star and the sub-Keplerian rotation in a thick disk, and calculate the magnetic moment - mass accretion rate relations for the measured rates of spin change. We find that the derived neutron star's dipole magnetic field depends the maximum accretion rate adopted, but is likely $\lesssim 10^{13}$ G. The predicted accretion rate change can be used to test the proposed models by comparison with observations.
We present a timing analysis of two Rossi X-ray Timing Explorer observations of the microquasar GRS 1915+105 during the heartbeat state. The phase-frequency-power maps show that the intermediate-frequency aperiodic X-ray variability weakens as the source softens in the slow rise phase, and when the quasi-periodic oscillation disappears in the rise phase of the pulse of the double-peaked class its sub-harmonic is still present with a hard phase lag. In the slow rise phase, the energy-frequency-power maps show that most of the aperiodic variability is produced in the corona, and may also induce the aperiodic variability observed at low energies from an accretion disk, which is further supported by the soft phase lag especially in the intermediate-frequency range (with a time delay up to 20 ms). In the rise phase of the pulse, the low-frequency aperiodic variability is enhanced significantly and there is a prominent hard lag (with a time delay up to 50 ms), indicating that the variability is induced by extension of the disk toward small radii as implied by the increase in flux and propagates into the corona. However, during the hard pulse of the double-peaked class, the variability shows no significant lag, which may be attributed to an optically thick corona. These timing results are generally consistent with the spectral results presented by Neilsen et al. (2011, 2012) which indicated that the slow rise phase corresponds to a local Eddington limit and the rise phase of the pulse corresponds to a radiation pressure instability in the disk.
The mass transfer efficiency during the evolution of massive binaries is still uncertain. We model the mass transfer processes in a grid of binaries to investigate the formation of Wolf-Rayet+O (WR+O) binaries, taking into account two kinds of non-conservative mass transfer models: Model I with rotation-dependent mass accretion and Model II of half mass accretion. Generally the mass transfer in Model I is more inefficient, with the average efficiency in a range of $\sim0.2-0.7$ and $ \lesssim0.2 $ for Case A and Case B mass transfer, respectively. We present the parameter distributions for the descendant WR+O binaries. By comparing the modeled stellar mass distribution with the observed Galactic WR+O binaries, we find that highly non-conservative mass transfer is required.
Recent observations show that the white dwarfs (WDs) in cataclysmic Variables (CVs) have an average mass significantly higher than isolated WDs and WDs in post-common envelope binaries (PCEBs), which are thought to the progenitors of CVs. This suggests that either the WDs have grown in mass during the PCEB/CV evolution or the binaries with low-mass WDs are unable to evolve to be CVs. In this paper, we calculate the evolution of accreting WD binaries with updated hydrogen accumulation efficiency and angular momentum loss prescriptions. We show that thermal timescale mass transfer is not effective in changing the average WD mass distribution. The WD mass discrepancy is most likely related to unstable mass transfer in WD binaries in which an efficient mechanism of angular momentum loss is required.
Whether the progenitors of SNe Ia are single-degenerate or double-degenerate white dwarf (WD) systems is a highly debated topic. To address the origin of the Type Ia Tycho's supernova remnant (SNR), SN 1572, we have carried out a $^{12}$CO J=2-1 mapping and a 3-mm line survey toward the remnant using the IRAM 30 m telescope. We show that Tycho is surrounded by a clumpy molecular bubble at a local standard of rest velocity of $\sim 61$ km s$^{-1}$ which expands at a speed of $\sim 4.5$ km s$^{-1}$ and has a mass of $\sim 220$ M$_\odot$ (at the distance of 2.5 kpc). Enhanced $^{12}$CO J=2-1 line emission relative to $^{12}$CO J=1-0 emission and possible line broadenings (in velocity range $-64$ to $-60$ km s$^{-1}$) are found at the northeastern boundary of the SNR, where the shell is deformed and decelerated. These features, combined with the morphological correspondence between the expanding molecular bubble and Tycho, suggest that the SNR is associated with the bubble at the velocity range $-66$ to $-57$ km s$^{-1}$. The most plausible origin for the expanding bubble is the fast outflow (with velocity of hundreds km s$^{-1}$) driven from the vicinity of a WD as it accreted matter from a nondegenerate companion star. The SNR has been expanding in the low-density wind-blown bubble, and the shock wave has just reached the molecular cavity wall. The SNR has been expanding in the low-density wind-blown bubble, and the shock wave has just reached the molecular cavity wall. This is the first unambiguous detection of an expanding bubble driven by the progenitor of a Type-Ia SNR, which constitutes evidence for a single-degenerate progenitor for this SN Ia.
Millisecond pulsars (MSPs) are thought to originate from low-mass X-ray binaries (LMXBs). The discovery of eclipsing radio MSPs including redbacks and black widows indicates that evaporation of the donor star by the MSP's irradiation takes place during the LMXB evolution. In this work, we investigate the effect of donor evaporation on the secular evolution of LMXBs, considering different evaporation efficiencies and related angular momentum loss. We find that for widening LMXBs, the donor star leaves a less massive white dwarf than without evaporation; for contracting systems, evaporation can speed up the evolution, resulting in dynamically unstable mass transfer and possibly the formation of isolated MSPs.
The binding energy parameter $λ$ plays a vital role in common envelope evolution. Though it is well known that $λ$ takes different values for stars with different masses and varies during stellar evolution, it has been erroneously adopted as a constant in most of the population synthesis calculations. We have systematically calculated the values of $λ$ for stars of masses $1-60\,M_{\odot}$ by use of an updated stellar evolution code, taking into account contribution from both gravitational energy and internal energy to the binding energy of the envelope. We adopt the criterion for the core-envelope boundary advocated by \citet{Ivanova2011}. A new kind of $λ$ with the enthalpy prescription is also investigated. We present fitting formulae for the calculated values of various kinds of $λ$, which can be used in future population synthesis studies.
Neutron stars in high-mass X-ray binaries (HMXBs) generally accrete from the wind matter of their massive companion stars. Recently Shakura et al. (2012) suggested a subsonic accretion model for low-luminosity ($<4\times 10^{36}$ ergs$^{-1}$), wind-fed X-ray pulsars. To test the feasibility of this model, we investigate the spin period distribution of wind-fed X-ray pulsars with a supergiant companion star, using a population synthesis method. We find that the modeled distribution of supergiant HMXBs in the spin period - orbital period diagram is consistent with observations provided that the winds from the donor stars have relatively low terminal velocities ($\lesssim 1000$ kms$^{-1}$). The measured wind velocities in several supergiant HMXBs seem to favor this viewpoint. The predicted number ratio of wind-fed X-ray pulsars with persistent X-ray luminosities higher and lower than $4\times 10^{36}$ ergs$^{-1}$ is about $1:10$.
Binary population synthesis (BPS) study provides a comprehensive way to understand evolutions of binaries and their end products. Close white dwarf (WD) binaries have crucial characteristics in examining in uence of yetunresolved physical parameters on the binary evolution. In this paper, we perform Monte Carlo BPS simulations, investigating the population of WD/main sequence (WD/MS) binaries and double WD binaries, with a publicly available binary star evolution code under 37 different assumptions on key physical processes and binary initial conditions. We considered different combinations of the binding energy parameter (lambda_g:considering gravitational energy only, lambda_b: considering both gravitational energy and internal energy, and lambda_e:considering gravitational energy, internal energy, and entropy of the envelope, the values of them derived with the MESA code), CE effciency, critical mass ratio, initial primary mass function and metallicity. We find that a larger number of post-CE WD/MS binaries in tight orbits are formed when the binding energy parameters is set by lambda_e than the cases adopting the other prescriptions. We also find effects of the other input parameters on orbital period and mass distributions of post-CE WD/MS binaries as well. Containing at least one CO WD, the double WD system evolved from WD/MS binaries may explode as type Ia supernovae (SNe Ia) by merging. In this work, we also investigate a frequency of two WD mergers and compare it to the SNe Ia rate.
The properties of the Galactic Ridge X-ray Emission (GRXE) observed in the 2-10 keV band place fundamental constraints on various types of X-ray sources in the Milky Way. Although the primarily discrete origin of the emission is now well established, the responsible populations of these sources remain uncertain, especially at relatively low fluxes. To provide insights into this issue, we systematically characterize the Fe emission line properties of the candidate types of the sources in the solar neighborhood and compare them with those measured for the GRXE. Our source sample includes 6 symbiotic stars (SSs), 16 intermediate polars (IPs), 3 polars, 16 quiescent dwarf novae (DNe) and 4 active binaries (ABs). We find that the mean equivalent width ($EW_{6.7}$) of the 6.7-keV line and the mean 7.0/6.7-keV line ratio are $107\pm16.0$ eV and $0.71\pm 0.04$ for intermediate polars and $221\pm 135$ eV and $0.44\pm 0.14$ for polars, respectively, which are all substantially different from those ($490\pm15 $~eV and $0.2\pm 0.08$) for the GRXE. Instead, the GRXE values are better agreed by the $EW_{6.7}$ ($438\pm 84.6$~eV) and the ratio ($0.27\pm 0.06$) observed for the DNe. We further find that the $EW_{6.7}$ is strongly correlated with the 2-10-keV luminosity of the DNe, which can be characterized by the relation $EW_{6.7}=(438\pm95 {\rm~eV}) (L/10^{31}~{\rm~ergs~s^{-1} })^{(-0.31\pm0.15)}$. Accounting for this correlation, the agreement can be improved further, especially when the contributions from other classes sources to the GRXE are considered, which all have low $EW_{6.7}$ values. We conclude that the GRXE mostly consists of typically faint, but numerous DNe, plus ABs, while magnetic CVs are probably mainly the high-flux representatives of the responsible populations and dominate the GRXE only in harder energy bands.
In this paper, we prove logarithmic Sobolev inequalities and derive the Hamilton Harnack inequality for the heat semigroup of the Witten Laplacian on complete Riemannian manifolds equipped with $K$-super Perelman Ricci flow. We establish the $W$-entropy formula for the heat equation of the Witten Laplacian and prove a rigidity theorem on complete Riemannian manifolds satisfying the $CD(K, m)$ condition, and extend the $W$-entropy formula to time dependent Witten Laplacian on compact Riemannian manifolds with $(K, m)$-super Perelman Ricci flow, where $K\in \mathbb{R}$ and $m\in [n, \infty]$ are two constants. Finally, we prove the Li-Yau and the Li-Yau-Hamilton Harnack inequalities for positive solutions to the heat equation $\partial_t u=Lu$ associated to the time dependent Witten Laplacian on compact or complete manifolds equipped with variants of the $(K, m)$-super Ricci flow.
Currently, there are 24 black hole (BH) X-ray binary systems that have been dynamically confirmed in the Galaxy. Most of them are low-mass X-ray binaries (LMXBs) comprised of a stellar-mass BH and a low-mass donor star. Although the formation of these systems has been extensively investigated, some crucial issues remain unresolved. The most noticeable one is that, the low-mass companion has difficulties in ejecting the tightly bound envelope of the massive primary during the spiral-in process. While initially intermediate-mass binaries are more likely to survive the common envelope (CE) evolution, the resultant BH LMXBs mismatch the observations. In this paper, we use both stellar evolution and binary population synthesis to study the evolutionary history of BH LMXBs. We test various assumptions and prescriptions for the supernova mechanisms that produce BHs, the binding energy parameter, the CE efficiency, and the initial mass distributions of the companion stars. We obtain the birthrate and the distributions of the donor mass, effective temperature and orbital period for the BH LMXBs in each case. By comparing the calculated results with the observations, we put useful constraints on the aforementioned parameters. In particular, we show that it is possible to form BH LMXBs with the standard CE scenario if most BHs are born through failed supernovae.
We use the evolutionary population synthesis method to investigate the statistical properties of the wind-fed neutron star (NS) compact ($P_{\rm orb}<10$ days) high-mass X-ray binaries (HMXBs) in our Galaxy, based on different spin-down models. We find that the spin-down rate in the supersonic propeller phase given \textbf{by assuming that the surrounding material is treated as forming a quasi-static atmosphere} or \textbf{by assuming that the characteristic velocity of matter and the typical Alfv$\acute{e}$n velocity of material in the magnetospheric boundary layer are comparable to the sound speed in the external medium} is too low to produce the observed number of compact HMXBs. We also find that the models suggested \textbf{by assuming that the infalling material is ejected with the corotation velocity at the magnetospheric radius when the magnetospheric radius is larger than the corotation radius} and \textbf{by simple integration of the magnetic torque over the magnetosphere} with a larger spin-down rate than that given by \citet{dav81} or \citet{is75} can predict a reasonable number of observed wind-fed NS compact HMXBs. Our calculated results indicate that subsonic propeller phase may not exist at all by comparing with the observed particular distributions of wind-fed NS compact HMXBs in the $P_s-P_{orb}$ diagram. However, the spin-down rate suggested by \citet{wan85,dai06,jia05} and that given by \citet{dav73} both seem reasonable to produce the observed distribution of wind-fed NS compact HMXBs in the $P_s-P_{orb}$ diagram. We cannot find which spin-down rate seems more reasonable from our calculations.
We investigate the formation and evolutionary sequences of Galactic intermediate- and low-mass X-ray binaries (I/LMXBs) by combining binary population synthesis (BPS) and detailed stellar evolutionary calculations. Using an updated BPS code we compute the evolution of massive binaries that leads to the formation of incipient I/LMXBs, and present their distribution in the initial donor mass vs. initial orbital period diagram. We then follow the evolution of I/LMXBs until the formation of binary millisecond pulsars (BMSPs). We find that the birthrate of the I/LMXB population is in the range of $ 9\times10^{-6} - 3.4\times10^{-5} \, {\rm yr^{-1}}$, compatible with that of BMSPs which are thought to descend from I/LMXBs. We show that during the evolution of I/LMXBs they are likely to be observed as relatively compact binaries with orbital periods $ \lesssim $ 1 day and donor masses $\lesssim 0.3 M_{\odot}$. The resultant BMSPs have orbital periods ranging from less than 1 day to a few hundred days. These features are consistent with observations of LMXBs and BMSPs. We also confirm the discrepancies between theoretical predications and observations mentioned in the literature, that is, the theoretical average mass transfer rates ($ \sim 10^{-10} M_{\odot} $\,yr$^{-1}$) of LMXBs are considerably lower than observed, and the number of BMSPs with orbital periods $\sim 0.1-10$ day is severely underestimated. These discrepancies imply that something is missing in the modeling of LMXBs, which is likely to be related to the mechanisms of the orbital angular momentum loss.
The spin period (185 ms) and period derivative ($1.8\times10^{-17}\,\rm s\,s^{-1}$) of the double neutron star (DNS) system PSR J1930$-$1852 recently discovered indicate that the pulsar was mildly recycled through the process of Roche-lobe overflow. This system has the longest orbital period (45 days) of the known DNS systems, and can be formed from a helium star-NS binary if the initial mass of the helium star was $ \lesssim 4.0M_{\odot} $; otherwise the helium star would never fill its Roche-lobe \citep{t15}. At the moment of the supernova explosion, the mass of the helium star was $ \lesssim3.0M_{\odot} $. We find that the probability distribution of the velocity kick imparted to the new-born neutron star has a maximum at about $30 \,\rm km\,s^{-1}$ (and a tail up to $ 260 \,\rm km\,s^{-1}$), indicating that this NS most probably received a low kick velocity at birth.
Recent timing observation reported that the radio pulsar PSR J1734 - 3333 with a rotating period $P=1.17~\rm s$ is slowing down with a period derivative $\dot{P}=2.28\times 10^{-12}\rm s\,s^{-1}$. Its derived braking index $n=0.9 \pm 0.2$ is the lowest value among young radio pulsars with the measured braking indices. In this Letter, we attempt to investigate the influence of the braking torque caused by the interaction between the fall-back disk and the strong magnetic field of the pulsar on the spin evolution of PSR J1734 - 3333. Analytical result show that this braking torque is obviously far more than that by magnetic dipole radiation for pulsars with spin period of $> 0.1$ s, and play an important role during the spin-down of the pulsars. Our simulated results indicate that, for some typical neutron star parameters, the braking index and the period derivative approximately in agreement with the measured value of PSR J1734 - 3333 if the material inflow rate in the fallback disk is $2 \times 10^{17} \rm g\,s^{-1}$. In addition, our scenario can account for the measured braking indices of four young pulsars. However, our predicted X-ray luminosity are 1 -2 order of magnitude higher than the observation. We proposed that this discrepancy may originate from the instability of fall-back disk.
Recently, compact black hole X-ray binaries XTE J 1118+480 and A0620-00 have been reported to be experiencing a fast orbital period decay, which is two orders of magnitude higher than expected with gravitational wave radiation. Magnetic braking of an Ap/Bp star has been suggested to account for the period change when the surface magnetic field of the companion star $B_{\rm s}\ga 10^{4}$ G. However, our calculation indicates that anomalous magnetic braking cannot significantly contribute to the large orbital period decay rates observed in these two sources even if $B_{\rm s}\ga 10^{4}$ G. Observations have provided evidence that circumbinary disks around two compact black hole X-ray binaries may exist. Our analysis shows that, for some reasonable parameters, tidal torque between the circumbinary disk and the binary can efficiently extract the orbital angular momentum from the binary, and result in a large orbital period change rate. Based on the circumbinary disk model, we simulate the evolution of XTE J 1118+480 via a stellar evolution code. Our computations are approximatively in agreement with the observed data (the masses of two components, donor star radius, orbital period, and orbital period derivative). The mass transfer rate and circumbinary disk mass are obviously far greater than the inferred values from observations. Therefore, it seems that the circumbinary disk is unlikely to be the main cause of the rapid orbital decay observed in some compact black hole X-ray binaries.