arXiv subjects
Publications and source records attributed to Xiaoling Zhang.
This paper contributes to the study of the Matsumoto metric F=alpha^2/beta, where the alpha is a Riemannian metric and the beta is a one form. It is shown that such a Matsumoto metric F is of scalar flag curvature if and only if F is projectively flat.
In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric $F=α^2/β$ with constant curvature $K$ and $\|β\|_α=1$ is projectively flat if and only if $F$ is locally Minkowskian.
In this paper, the necessary and sufficient conditions for Matsumoto metrics $F=\frac{α^2}{α-β}$ to be Einstein are given. It is shown that if the length of $β$ with respect to $α$ is constant, then the Matsumoto metric $F$ is an Einstein metric if and only if $α$ is Ricci-flat and $β$ is parallel with respect to $α$. A nontrivial example of Ricci flat Matsumoto metrics is given.
In this paper, a characteristic condition of Einstein Kropina metrics is given. By the characteristic condition, we prove that a non-Riemannian Kropina metric $F=\frac{α^2}β$ with constant Killing form $β$ on an n-dimensional manifold $M$, $n\geq 2$, is an Einstein metric if and only if $α$ is also an Einstein metric. By using the navigation data $(h,W)$, it is proved that an n-dimensional ($n\geq2$) Kropina metric $F=\frac{α^2}β$ is Einstein if and only if the Riemannian metric $h$ is Einstein and $W$ is a unit Killing vector field with respect to $h$. Moreover, we show that every Einstein Kropina metric must have vanishing S-curvature, and any conformal map between Einstein Kropina metrics must be homothetic.
In this paper, we study how the distance spectral radius behaves when the graph is perturbed by grafting edges. As applications, we also determine the graph with $k$ cut vertices (respectively, $k$ cut edges) with the minimal distance spectral radius.
Understanding the properties of the hot corona is important for studying the accretion disks in black hole X-ray binary systems. Using the Monte-Carlo technique to simulate the inverse Compton scattering between photons emitted from the cold disk and electrons in the hot corona, we have produced two table models in the $XSPEC$ format for the spherical corona case and the disk-like (slab) corona case. All parameters in our table models are physical properties of the system and can be derived from data fitting directly. Applying the models to broad-band spectra of the black hole candidate XTE J2012+381 observed with BeppoSAX, we estimated the size of the corona and the inner radius of the disk. The size of the corona in this system is several tens of gravitational radius, and the substantial increase of the inner disk radius during the transit from hard-state to soft-state is not found.
For an accretion disk around a black hole, the strong relativistic effects affect every aspect of the radiation from the disk, including its spectrum, light-curve, and image. This work investigates in detail how the images of a thin disk around a black hole will be distorted, and what the observer will see from different viewing angles and in different energy bands.
Understanding the properties of the hot corona is very important for studying the accretion disks in black hole X-ray binary systems. Using the Monte-Carlo technique to simulate the inverse Compton scattering process between disk photons and electrons in the hot corona, we have produced two table models in the XSPEC package. Applying the models to the broad-band BeppoSAX observations of the black hole candidate XTE J2012+381, we demonstrate the power of this table model. Our results indicate that the electron distribution in the corona has a powerlaw shape with a spectral index around 4 and the size of the corona is just several tens of gravitational radius and the inclination angle of the disk is around 60 degrees.
Special and general relativistic effects on the X-ray emissions, especially the continuum spectra, from the accretion disks around black holes are investigated using the ray-tracing method. Because both the special and general relativistic effects are more important at distances closer to the black hole, the relativistic modifications to the emitted X-ray spectra are more significant at higher energies. In a simple accretion disk precession model, the relativistic effects can account for the energy dependence of the QPO amplitude and phase-lags observed in several black hole binaries. The dramatic QPO phase-lag transitions only show up when the central black hole is spinning rapidly. The narrow distribution of the observed system inclination angles of black hole binaries may be due to the selection effect caused by the relativistic effects around black holes.
Modeling of the x-ray spectra of the Galactic superluminal jet sources GRS 1915+105 and GRO J1655-40 reveal a three-layered atmospheric structure in the inner region of their accretion disks. Above the cold and optically thick disk of a temperature 0.2-0.5 keV, there is a warm layer with a temperature of 1.0-1.5 keV and an optical depth around 10. Sometimes there is also a much hotter, optically thin corona above the warm layer, with a temperature of 100 keV or higher and an optical depth around unity. The structural similarity between the accretion disks and the solar atmosphere suggest that similar physical processes may be operating in these different systems.