arXiv subjects

Xiang-Dong Li

Publications and source records attributed to Xiang-Dong Li.

At least 163 records · Page 9Linked to original sources

arXiv2013

Population synthesis on high-mass X-ray binaries: prospects and constraints from the universal X-ray luminosity function

Using an updated population synthesis code initially developed by Hurley et al. we modeled the synthetic X-ray binary (XRB) populations for direct comparison with the universal, featureless X-ray luminosity function (XLF) of high mass X-ray binaries (HMXBs) in star-forming galaxies. Our main goal is to use the universal XLF to constrain the model parameters, given the current knowledge of binary evolution. We find that the one-dimensional (1D) Maxwellian velocity dispersion of the natal kick can be constrained to be of the order of ~150km/s, supporting earlier findings that neutron stars (NSs) formed in binaries seem to receive significantly smaller natal kicks than the velocities of Galactic single pulsars would indicate. The super-Eddington accretion factor is further confirmed in the framework of stellar mass black holes (BHs), revealing the true origin of the most of the ultraluminous X-ray sources (ULXs) may indeed be the high-luminosity extension of ordinary HMXBs which harbor stellar-mass BHs rather than exotic intermediate-mass BHs or ones. We present the detail properties of the model-predicted present-day HMXBs, which may be investigated by future high-resolution X-ray and optical observations of sources in nearby star-forming galaxies.

astro-ph.HE↗

arXiv2013

On the formation of the peculiar low-mass X-ray binary IGR J17480$-$2446 in Terzan 5

IGR J17480$-$2446 is an accreting X-ray pulsar in a low-mass X-ray binary harbored in the Galactic globular cluster Terzan 5. Compared with other accreting millisecond pulsars, IGR J17480$-$2446 is peculiar in its low spin frequency (11 Hz), which suggests that it might be a mildly recycled neutron star at the very early phase of mass transfer. However, this model seems to be in contrast with the low field strength deduced from the kiloHertz quasi-periodic oscillations observed in IGR J17480$-$2446. Here we suggest an alternative interpretation, assuming that the current binary system was formed during an exchange encounter either between a binary (which contains a recycled neutron star) and the current donor, or between a binary and an isolated, recycled neutron star. In the resulting binary, the spin axis of the neutron star could be parallel or anti-parallel with the orbital axis. In the later case, the abnormally low frequency of IGR J17480$-$2446 may result from the spin-down to spin-up evolution of the neutron star. We also briefly discuss the possible observational implications of the pulsar in this scenario.

astro-ph.HE↗

arXiv2013

Population synthesis of young isolated neutron stars: the effect of fallback disk accretion and magnetic field evolution

The spin evolution of isolated neutron stars (NSs) is dominatd by their magnetic fields. The measured braking indices of young NSs show that the spin-down mechanism due to magnetic dipole radiation with constant magnetic fields is inadequate. Assuming that the NS magnetic field is buried by supernova fallback matter and re-emerges after accretion stops, we carry out Monte-Carlo simulation of the evolution of young NSs, and show that most of the pulsars have the braking indices ranging from -1 to 3. The results are compatible with the observational data of NSs associated with supernova remnants. They also suggest that the initial spin periods of NSs might occupy a relatively wide range.

astro-ph.HE↗

arXiv2013

On the $L^p$-estimates for Beurling-Ahlfors and Riesz transforms on Riemannian manifolds

In our previous papers \cite{Li2008, Li2011}, we proved some martingale transform representation formulas for the Riesz transforms and the Beurling-Ahlfors transforms on complete Riemannian manifolds, and proved some explicit $L^p$-norm estimates for these operators on complete Riemannian manifolds with suitable curvature conditions. In this paper we correct a gap contained in \cite{Li2008, Li2011} and prove that the $L^p$-norm of the Riesz transforms $R_a(L)=\nabla(a-L)^{-1/2}$ can be explicitly bounded by $C(p^*-1)^{3/2}$ if $Ric+\nabla^2ϕ\geq -a$ for $a\geq 0$, and the $L^p$-norm of the Riesz transform $R_0(L)=\nabla(-L)^{-1/2}$ is bounded by $2(p^*-1)$ if $Ric+\nabla^2ϕ=0$. We also prove that the $L^p$-norm estimates for the Beurling-Ahlfors transforms obtained in \cite{Li2011} remain valid. Moreover, we prove the time reversal martingale transform representation formulas for the Riesz transforms and the Beurling-Ahlfors transforms on complete Riemannian manifolds.

math.PR↗

arXiv2013

On the $L^p$-estimates of Riesz transforms on forms over complete Riemanian manifolds

In our previous paper \cite{Li2010}, we proved a martingale transform representation formula for the Riesz transforms on forms over complete Riemannian manifolds, and proved some explicit $L^p$-norm estimates for the Riesz transforms on complete Riemannian manifolds with suitable curvature conditions. In this paper we correct a gap contained in \cite{Li2010} and prove that the main result obtained in \cite{Li2010} on the $L^p$-norm estimates for the Riesz transforms on forms remain valid. Moreover, we prove a time reversal martingale transform representation formula for the Riesz transforms on forms. Finally, we extend our approach and result to the Riesz transforms acting on Euclidean vector bundles over complete Riemannian manifolds with suitable curvature conditions.

math.PR↗

arXiv2013

From the Boltzmann $H$-theorem to Perelman's $W$-entropy formula for the Ricci flow

In 1870s, L. Boltzmann proved the famous $H$-theorem for the Boltzmann equation in the kinetic theory of gas and gave the statistical interpretation of the thermodynamic entropy. In 2002, G. Perelman introduced the notion of $W$-entropy and proved the $W$-entropy formula for the Ricci flow. This plays a crucial role in the proof of the no local collapsing theorem and in the final resolution of the Poincaré conjecture and Thurston's geometrization conjecture. In our previous paper \cite{Li11a}, the author gave a probabilistic interpretation of the $W$-entropy using the Boltzmann-Shannon-Nash entropy. In this paper, we make some further efforts for a better understanding of the mysterious $W$-entropy by comparing the $H$-theorem for the Boltzmann equation and the Perelman $W$-entropy formula for the Ricci flow. We also suggest a way to construct the "density of states" measure for which the Boltzmann $H$-entropy is exactly the $W$-entropy for the Ricci flow.

math.DG↗

arXiv2013

Strange star equation of state fits the refined mass measurement of 12 pulsars and predicts their radii

There are three categories of stars whose masses have been found accurately in recent times: (1) two for which Shapiro delay is used which is possible due to GR light bending as the partner is heavy : PSR J1614-2230 and PSR J1903+0327 (2) six eclipsing stars for which numerical Roche Lobe geometry is used and (3) 3 stars for which spectroscopic methods are used and in fact for these three the mass and radii both are estimated. Motivated by large color (N_c) expansion using a modified Richardson potential, along with density dependent quark masses thereby allowing chiral symmetry restoration, we get compact strange stars fitting all the observed masses.

astro-ph.HE↗

arXiv2013

Generalized Dyson Brownian motion, McKean-Vlasov equation and eigenvalues of random matrices

Using Itô's calculus and the mass optimal transportation theory, we study the generalized Dyson Brownian motion (GDBM) and the associated McKean-Vlasov evolution equation with an external potential $V$. Under suitable condition on $V$, we prove the existence and uniqueness of strong solution to SDE for GDBM. Standard argument shows that the family of the process of empirical measures $L_N(t)$ of GDBM is tight and every accumulative point of $L_N(t)$ in the weak convergence topology is a weak solution of the associated McKean-Vlasov evolution equation, which can be realized as the gradient flow of the Voiculescu free entropy on the Wasserstein space over $\mathbb{R}$. Under the condition $V''\geq -K$ for some constant $K\geq 0$, we prove that the McKean-Vlasov equation has a unique solution $μ(t)$ and $L_N(t)$ converges weakly to $μ(t)$ as $N\rightarrow \infty$. For $C^2$ convex potentials, we prove that $μ(t)$ converges to the equilibrium measure $μ_V$ with respect to the $W_2$-Wasserstein distance on $\mathscr{P}_2(\mathbb{R})$ as $t\rightarrow \infty$. Under the uniform convexity or a modified uniform convexity condition on $V$, we prove that $μ(t)$ converges to $μ_V$ with respect to the $W_2$-Wasserstein distance on $\mathscr{P}_2(\mathbb{R})$ with an exponential rate as $t\rightarrow \infty$. Finally, we discuss the double-well potentials and raise some conjectures.

math.PR↗

arXiv2012

Could SXP 1062 be an Accreting Magnetar?

In this work we explore the possible evolutionary track of the neutron star in the newly discovered Be/X-ray binary SXP 1062, which is believed to be the first X-ray pulsar associated with a supernova remnant. Although no cyclotron feature has been detected to indicate the strength of the neutron star's magnetic field, we show that it may be $\ga 10^{14} $G. If so SXP 1062 may belong to the accreting magnetars in binary systems. We attempt to reconcile the short age and long spin period of the pulsar taking account of different initial parameters and spin-down mechanisms of the neutron star. Our calculated results show that, to spin down to a period $\sim 1000 $s within $10-40 $kyr requires efficient propeller mechanisms. In particular, the model for angular momentum loss under energy conservation seems to be ruled out.

astro-ph.HE↗

arXiv2012

Formation of Millisecond Pulsars from Intermediate- and Low-Mass X-ray Binaries

We present a systematic study of the evolution of intermediate- and low-mass X-ray binaries consisting of an accreting neutron star of mass $1.0-1.8 M_{\odot}$ and a donor star of mass $1.0-6.0 M_{\odot}$. In our calculations we take into account physical processes such as unstable disk accretion, radio ejection, bump-induced detachment, and outflow from the $L_{2}$ point. Comparing the calculated results with the observations of binary radio pulsars, we report the following results. (1) The allowed parameter space for forming binary pulsars in the initial orbital period - donor mass plane increases with increasing neutron star mass. This may help explain why some MSPs with orbital periods longer than $\sim 60$ days seem to have less massive white dwarfs than expected. Alternatively, some of these wide binary pulsars may be formed through mass transfer driven by planet/brown dwarf-involved common envelope evolution. (2) Some of the pulsars in compact binaries might have evolved from intermediate-mass X-ray binaries with anomalous magnetic braking. (3) The equilibrium spin periods of neutron stars in low-mass X-ray binaries are in general shorter than the observed spin periods of binary pulsars by more than one order of magnitude, suggesting that either the simple equilibrium spin model does not apply, or there are other mechanisms/processes spinning down the neutron stars.

astro-ph.HE↗

arXiv2012

On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking Ricci solitons

We prove a lower bound estimate for the first non-zero eigenvalue of the Witten-Laplacian on compact Riemannian manifolds. As an application, we derive a lower bound estimate for the diameter of compact gradient shrinking Ricci solitons. Our results improve some previous estimates which were obtained by the first author and Y. Sano in [12], and by B. Andrews and L. Ni in [1]. Moreover, we extend the diameter estimate to compact self-similar shrinkers of mean curvature flow.

math.DG↗

arXiv2011

Angular Momentum Loss Mechanisms in Cataclysmic Variables below the Period Gap

Mass transfer in cataclysmic variables (CVs) is usually considered to be caused by angular momentum loss (AML) driven by magnetic braking and gravitational radiation (GR) above the period gap, and solely by GR below the period gap. The best-fit revised model of CV evolution recently by \citet{kbp11}, however, indicates that AML rate below the period gap is $2.47(\pm 0.22)$ times the GR rate, suggesting the existence of some other AML mechanisms. We consider several kinds of consequential AML mechanisms often invoked in the literature: isotropic wind from the accreting white dwarfs, outflows from the Langrangian points, and the formation of a circumbinary disk. We found that neither isotropic wind from the white dwarf nor outflow from the $L_1$ point can explain the extra AML rate, while ouflow from the $L_2$ point or a circumbinary disk can effectively extract the angular momentum provided that $\sim (15-45)%$ of the transferred mass is lost from the binary. A more promising mechanism is a circumbinary disk exerting gravitational torque on the binary. In this case the mass loss fraction can be as low as $\lesssim 10^{-3}$.

astro-ph.SR↗

arXiv2011

Strong field effects on emission line profiles: Kerr black holes and warped accretion disks

If an accretion disk around a black hole is illuminated by hard X-rays from non-thermal coronae, fluorescent iron lines will be emitted from the inner region of the accretion disk. The emission line profiles will show a variety of strong field effects, which may be used as a probe of the spin parameter of the black hole and the structure of the accretion disk. In this paper we generalize the previous relativistic line profile models by including both the black hole spinning effects and the non-axisymmetries of warped accretion disks. Our results show different features from the conventional calculations for either a flat disk around a Kerr black hole or a warped disk around a Schwarzschild black hole by presenting, at the same time, multiple peaks, rather long red tails and time variations of line profiles with the precession of the disk. We show disk images as seen by a distant observer, which are distorted by the strong gravity. Although we are primarily concerned with the iron K-shell lines in this paper, the calculation is general and is valid for any emission lines produced from a warped accretion disk around a black hole.

astro-ph.HE↗

arXiv2011

On Pulsar-Driven Mass Ejection in Low-Mass X-ray Binaries

There is accumulating evidence for mass ejection in low-mass X-ray binaries (LMXBs) driven by radio pulsar activity during X-ray quiescence. In this paper we consider the condition for mass ejection by comparing the radiation pressure from a millisecond pulsar, and the gas pressure at the inner Lagrange point or at the surrounding accretion disk. We calculate the critical spin period of the pulsar below which mass ejection is allowed. Combining with the evolution of the mass transfer rate, we present constraints on the orbital periods of the systems. We show that mass ejection could happen in both wide and compact LMXBs. It may be caused by transient accretion due to thermal instability in the accretion disks in the former, and irradiation-driven mass-transfer cycles in the latter.

astro-ph.HE↗

arXiv2011

He star evolutionary channel to intermediate-mass binary pulsar PSR J1802-2124

The intermediate-mass binary pulsars (IMBPs) are characterized by relatively long spin periods (10 - 200 ms) and massive ($\ga 0.4 M_{\odot}$) white dwarf (WD) companions. Recently, precise mass measurements have been performed for the pulsar and the WD in the IMBP PSR J1802-2124. Some observed properties, such as the low mass of the pulsar, the high mass of the WD, the moderately long spin period, and the tight orbit, imply that this system has undergone a peculiar formation mechanism. In this work, we attempt to simulate the detailed evolutionary history of PSR J1802-2124. We propose that a binary system consisting of a neutron star (NS, of mass $1.3 M_{\odot}$) and an He star (of mass $1.0 M_{\odot}$), and with an initial orbital period of 0.5 d, may have been the progenitor of PSR J1802-2124. Once the He star overflows its Roche lobe, He-rich material is transferred onto the NS at a relatively high rate of $\sim 10^{-7}-10^{-6} M_{\odot}\,\rm yr^{-1}$, which is significantly higher than the Eddington accretion rate. A large amount of the transferred material is ejected from the vicinity of the NS by radiation pressure and results in the birth of a mildly recycled pulsar. Our simulated results are consistent with the observed parameters of PSR J1802-2124. Therefore, we argue that the NS + He star evolutionary channel may be responsible for the formation of most IMBPs with orbital periods $\la 3 \rm d$.

astro-ph.HE↗

arXiv2011

The contribution of X-ray binaries to the evolution of late-type galaxies: Evolutionary population synthesis simulations

X-ray studies of normal late-type galaxies have shown that non-nuclear X-ray emission is typically dominated by X-ray binaries, and provides a useful measure of star formation activity. We have modeled the X-ray evolution of late-type galaxies over the $\sim$ 14 Gyr of cosmic history, with an evolutionary population synthesis code developed by Hurley et al. Our calculations reveal a decrease of the X-ray luminosity-to-mass ratio $L_{\rm X}/M$ with time, in agreement with observations (Fig.~7$a$). We show that this decrease is a natural consequence of stellar and binary evolution and mass accumulating process in galaxies. The X-ray-to-optical luminosity ratio $L_{\rm X}/L_{\rm B}$ is found to be fairly constant (around $\sim 10^{30}$ erg\,s$^{-1}$$L_{\rm B,\odot}^{-1}$, Fig.~7$b$), and insensitive to the star formation history in the galaxies. The nearly constant value of $L_{\rm X}/L_{\rm B}$ is in conflict with the observed increase in $L_{\rm X}/L_{\rm B}$ from $z=0$ to 1.4. The discrepancy may be caused by intense obscured star formation activity that leads to nonlinear relationship between X-ray and B-band emission.

astro-ph.HE↗

arXiv2011

KHz QPOs in LMXBs, relations between different frequencies and compactness of stars

We suggest that the mass of four compact stars SAX J1808.4$-$3658, KS 1731$-$260, SAX J1750.8$-$2900 and IGR J17191$-$2821 can be determined from the difference in the observed kiloHertz quasi periodic oscillations (kHz QPO-s) of these stars. The stellar radius is very close to the marginally stable orbit $R_{ms}$ as predicted by Einstein's general relativity. It may be noted that the first of these stars was suggested to be a strange star more than a decade back by Li \emph{et al.} (1999) from the unique millisecond X-ray pulsations with an accurate determination of its rotation period. It showed kHz QPO-s eight years back and so far it is the only set that has been observed. This is the first time we give an estimate of the mass of the star and of three other compact stars in Low-Mass X-ray Binaries using their observed kHz QPO-s.

astro-ph.HE↗

arXiv2011

Can eccentric binary millisecond pulsars form by accretion induced collapse of white dwarfs?

Binary radio pulsars are generally believed to have been spun up to millisecond periods (i.e. recycling) via mass accretion from their donor stars, and they are the descendants of neutron star low-mass X-ray binaries. However, some studies indicate that the formation of pulsars from the accretion-induced collapse (AIC) of accreting white dwarfs (WDs) cannot be excluded. In this work, we use a population synthesis code to examine if the AIC channel can produce eccentric binary millisecond pulsars (BMSPs) in the Galaxy. Our simulated results indicate that, only when the natal MSPs receive a relatively strong kick ($\ga100\rm km\,s^{-1}$), can the AIC channel produce $\sim 10-180$ eccentric ($e>0.1$) BMSPs in the Galaxy, most of which are accompanied by a Helium star. Such a kick seems to be highly unlikely in the conventional AIC process, hence the probability of forming eccentric BMSPs via the AIC channel can be ruled out. Even if a high kick is allowed, the AIC channel cannot produce eccentric BMSPs with an orbital period of $\ga 20$ days. Therefore, we propose that the peculiar BMSP PSR J1903+0327 cannot be formed by the AIC channel. However, the AIC evolutionary channel may produce some fraction of isolated millisecond pulsars, and even sub-millisecond pulsars if they really exist.

astro-ph.HE↗