arXiv subjects
Publications and source records attributed to Wenda Zhang.
Let $(X,G)$ be a $G$-action topological system, where $G$ is a countable infinite discrete amenable group and $X$ a compact metric space. In this paper we study the upper capacity entropy and packing entropy for systems with weaker version of specification. We prove that the upper capacity always carries full entropy while there is a variational principle for packing entropy of saturated sets.
The study of radiation emitted from black hole accretion discs represents a crucial way to understand the main physical properties of these sources, and in particular the black hole spin. Beside spectral analysis, polarimetry is becoming more and more important, motivated by the development of new techniques which will soon allow to perform measurements also in the X- and γ-rays. Photons emitted from black hole accretion discs in the soft state are indeed expected to be polarized, with an energy dependence which can provide an estimate of the black hole spin. Calculations performed so far, however, considered scattering as the only process to determine the polarization state of the emitted radiation, implicitly assuming that the temperatures involved are such that material in the disc is entirely ionized. In this work we generalize the problem by calculating the ionization structure of a surface layer of the disc with the public code CLOUDY , and then by determining the polarization properties of the emerging radiation using the Monte Carlo code STOKES . This allows us to account for absorption effects alongside scattering ones. We show that including absorption can deeply modify the polarization properties of the emerging radiation with respect to what is obtained in the pure-scattering limit. As a general rule, we find that the polarization degree is larger when absorption is more important, which occurs e.g. for low accretion rates and/or spins when the ionization of the matter in the innermost accretion disc regions is far from complete.
In this paper, we introduce the unstable topological pressure for C^1-smooth partially hyperbolic diffeomorphisms with sub-additive potentials. Moreover, without any additional assumption, we have established the expected variational principle which connects this unstable topological pressure and the unstable measure theoretic entropy, as well as the corresponding Lyapunov exponent.
Accretion disks around stellar-mass black holes (BHs) emit radiation peaking in the soft X-rays when the source is in the thermal state. The emerging photons are polarized and, for symmetry reasons, the polarization integrated over the source is expected to be either parallel or perpendicular to the (projected) disk symmetry axis, because of electron scattering in the disk. However, due to General Relativity effects photon polarization vectors will rotate with respect to their original orientation, by an amount depending on both the BH spin and the observer's inclination. Hence, X-ray polarization measurements may provide important information about strong gravity effects around these sources. Along with the spectral and polarization properties of radiation which reaches directly the observer once emitted from the disk, in this paper we also include the contribution of returning radiation, i.e. photons that are bent by the strong BH gravity to return again on the disk, where they scatter until eventually escaping to infinity. A comparison between our results and those obtained in previous works by different authors show an overall good agreement, despite the use of different code architectures. We finally consider the effects of absorption in the disk material by including more realistic albedo profiles for the disk surface. Our findings in this respect show that considering also the ionization state of the disk may deeply modify the behavior of polarization observables.
In this work, we measure two important phenomenological parameters of corona (and hot accretion flow) in black hole X-ray binaries: the photon index $Γ$ and the electron temperature $\te$. Thanks to the capability of {\it NuSTAR} in hard X-rays, we measure these two parameters over six orders of magnitude in the 0.1-100 keV X-ray luminosity $\lx$, from $\sim 5\times10^{38} \ergs$ down to as low as $\sim 5\times10^{32} \ergs$. We confirm the existence of a "V"-shaped correlation between $Γ$ and $\lx$. Surprisingly, we observe a "$Λ$"-shaped correlation between $\te$ and $\lx$. The "cooler when brighter" branch in the high luminosity regime ($\lx \ga 3\times 10^{36} \ergs$) agrees with previous results and can be understood under the existing model of Compton scattering in the corona. On the other hand, the apparent "cooler when fainter" (positive $\te$-$\lx$ correlation) branch in the low-luminosity regime ($\lx \la 3\times 10^{36} \ergs$) is unexpected, thus it puts a new challenge to existing models of hot accretion flow/corona.
The transport by materially coherent eddies is studied in a two-layer quasigeostrophic model of geophysical turbulence. The coherent eddies are identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. A series of flow regimes with different bottom friction strengths are considered---it is found that coherent eddies become more prevalent and longer-lasting as the strength of the bottom drag increases. These coherent eddies, with average core radius close to the deformation radius, propagate zonally with speeds close to the long baroclinic Rossby wave speed and meridionally with a preference for cyclones to propagate poleward and anticyclones to propagate equatorward. The meridional propagation preference of the coherent eddies gives rise to a systematic upgradient potential vorticity (PV) transport, which is in the opposite direction as the background PV transport and not captured by standard Lagrangian diffusivity estimates. The upgradient PV transport by coherent eddy cores is less than 10% of the total PV transport, but the PV transport by the periphery flow induced by the PV inside coherent eddies is significant and downgradient. This clarifies the distinct roles of the trapping and stirring effect of coherent eddies in PV transport in geophysical turbulence.
In this paper, we define and study unstable measure theoretic pressure for C^1-smooth partially hyperbolic diffeomorphisms with sub-additive potentials. For any ergodic measure, we show that this unstable metric pressure equals the corresponding unstable measure theoretic entropy plus the Lyapunov exponents with respect to the ergodic measure. On the other hand, we also define unstable topological and metric pressure in terms of the Bowen's picture and the capacity picture. We show that all these definitions of unstable metric pressure actually coincide for any ergodic measure.
For an inclined accretion flow around a rotating black hole, the combined effect of the Lense-Thirring precession and viscous torque tends to align the inner part of the flow with the black hole spin, leading to the formation of a warped disc, known as the Bardeen-Petterson effect (Bardeen & Petterson 1975). In tidal disruption events (TDEs) in which a super-massive black hole starts to accrete the bound debris, if the black hole is spinning, in general the stellar orbit is inclined with the black hole spin. So is the accretion disc formed following circularization and radiative cooling of the debris. Xiang-Gruess et al. (2016) studied in detail the stellar debris evolution and disc formation in TDEs when the stellar orbit is inclined, and found that a warped disc would form under certain conditions. In this work we investigate properties of time-resolved fluorescent iron line originating from a warped disc that is irradiated by the initial X-ray flare. We find that the time-resolved spectrum shows distinct features before and after a critical time. This critical time depends on the Bardeen-Petterson radius $r_{\rm BP}$, i.e., the outer boundary of the inner aligned disc; while the line width during the later stage of the X-ray flare is sensitive to the inclination of the outer disc flow. This demonstrates that time-resolved X-ray spectroscopy can be a powerful tool to probe the Bardeen-Petterson effect in TDE flares and can be used to measure the Bardeen-Petterson radius as well as put constraint on the black hole mass and spin.
The size and geometry of the X-ray emitting corona in AGNs are still not well constrained. Dovčiak & Done (2016) proposed a method based on calculations assuming a point-like lamp-post corona. To perform more self-consistent calculations of energy spectra of extended coronae, we develop monk, a Monte Carlo radiative transfer code dedicated to calculations of Comptonised spectra in the Kerr spacetime. In monk we assume Klein-Nishina scattering cross section and include all general relativistic effects. We find that for a corona located above the disc, the spectrum is not isotropic, but with harder and less luminous spectra towards observers at lower inclinations, owing to anisotropic illumination of the seed photons. This anisotropy also leads to an underestimated size of the corona if we assume the corona to be a point-like, isotropic source located on the black hole rotation axis, demonstrating the necessity of more self-consistent calculations. We also inspect the effect of motion and geometry of the corona on the emergent spectrum. Finally, we discuss the implication of anisotropic corona emission for the reflection spectrum in AGNs as well as black hole X-ray binaries (BHXRBs). We find that by assuming the corona emission to be isotropic, one may underestimate the soft excess in AGNs and the reflection continuum and iron K fluorescent line flux in BHXRBs.
We study the modulation of the observed radiation flux and the associated changes in the polarization degree and angle that are predicted by the orbiting spot model for flares from accreting black holes. The geometric shape of the emission region influences the resulting model lightcurves, namely, the emission region of a spiral shape can be distinguished from a simpler geometry of a small orbiting spot.
In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. The tightest statistical constraints on the dense matter equation of state will come from pulse profile modelling of accretion-powered pulsars, burst oscillation sources, and rotation-powered pulsars. Additional constraints will derive from spin measurements, burst spectra, and properties of the accretion flows in the vicinity of the neutron star. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Science, the eXTP mission is expected to be launched in the mid 2020s.
The eXTP (enhanced X-ray Timing and Polarimetry) mission is a major project of the Chinese Academy of Sciences (CAS) and China National Space Administration (CNSA) currently performing an extended phase A study and proposed for a launch by 2025 in a low-earth orbit. The eXTP scientific payload envisages a suite of instruments (Spectroscopy Focusing Array, Polarimetry Focusing Array, Large Area Detector and Wide Field Monitor) offering unprecedented simultaneous wide-band X-ray spectral, timing and polarimetry sensitivity. A large European consortium is contributing to the eXTP study and it is expected to provide key hardware elements, including a Large Area Detector (LAD). The LAD instrument for eXTP is based on the design originally proposed for the LOFT mission within the ESA context. The eXTP/LAD envisages a deployed 3.4 m2 effective area in the 2-30 keV energy range, achieved through the technology of the large-area Silicon Drift Detectors - offering a spectral resolution of up to 200 eV FWHM at 6 keV - and of capillary plate collimators - limiting the field of view to about 1 degree. In this paper we provide an overview of the LAD instrument design, including new elements with respect to the earlier LOFT configuration.
A K-theoretic classification is given for AF systems of cyclic groups with prime orders.
We studied the outburst properties of the hyper-luminous X-ray source ESO 243-49 HLX-1, using the full set of Swift monitoring observations. We quantified the increase in the waiting time, recurrence time, and e-folding rise timescale along the outburst sequence, and the corresponding decrease in outburst duration, total radiated energy, and e-folding decay timescale, which confirms previous findings. HLX-1 spends less and less time in outburst and more and more time in quiescence, but its peak luminosity remains approximately constant. We compared the HLX-1 outburst properties with those of bright Galactic low-mass X-ray binary transients (LMXBTs). Our spectral analysis strengthens the similarity between state transitions in HLX-1 and those in Galactic LMXBTs. We also found that HLX-1 follows the nearly linear correlations between the hard-to-soft state transition luminosity and the peak luminosity, and between the rate of change of X-ray luminosity during the rise phase and the peak luminosity, which indicates that the occurrence of the hard-to-soft state transition of HLX-1 is similar to those of Galactic LMXBTs during outbursts. We found that HLX-1 does not follow the correlations between total radiated energy and peak luminosity, and between total radiated energy and e-folding rise/decay timescales we had previously identified in Galactic LMXBTs. HLX-1 would follow those correlations if the distance were several hundreds of kiloparsecs. However, invoking a much closer distance for HLX-1 is not a viable solution to this problem, as it introduces other, more serious inconsistencies with the observations.
Tidal Disruption Events (TDEs) can be perfect probes of dormant SMBHs in normal galaxies. During the rising phase, the accretion luminosity can increase by orders of magnitude in several weeks and the emergent ionizing radiation illuminates the fresh accretion flow. In this paper, we simulated the evolution of the expected spectral line profile of iron due to such a flare by using a ray-tracing code with effects of general relativity (GR) taken into account. We found that the time-dependent profile changes significantly with black hole spin, inclination angle with respect to the black-hole equatorial plane, and the expansion velocity of the ionization front. At low values of spin, a "loop" feature appears in the line profile vs. time plot when the inclination is no less than $30^\circ$ and the expansion velocity $v_{\rm exp}$ is no less than half speed of light, due to a shadow in the emission of the truncated disk. In the light curve two peaks occur depending on the inclination angle. At large $v_{\rm exp}$, a shallow "nose" feature may develop ahead of the loop, its duration depends on the expansion velocity and the inclination angle. We explore the entire interval of black hole spin parameter ranging from extreme prograde to extreme retrograde rotation, $-1<a<1$. In the prograde case, a low-energy tail appears to be more pronounced in the evolving centroid energy of the line. Our results demonstrate the importance to search for X-ray spectral lines in the early phase of TDE flares in order to constrain black hole mass and spin, as well as properties of the innermost accretion flow.
We have studied the evolution of the Low Frequency Quasi-Periodic Oscillations (LFQPOs) during the rising phase of seven outbursts of the neutron star Soft X-ray Transient (SXT) Aql X$-$1 observed with the \textit{Rossi X-ray Timing Explorer (RXTE)}. The frequency correlation between the low frequency break and the LFQPO sampled on the time scale of $\sim$2 days was seen. Except for the peculiar 2001 outburst, the frequency of the LFQPOs increased with time before the hard-to-soft state transition up to a maximum $ν_{max}$ at $\sim$31 Hz, a factor of $\sim$5 higher than those seen in black hole transients such as GX 339$-$4, making the maximum QPO frequency a likely indicator of the mass of the central compact object. The characteristic frequencies increased by around ten percent per day in the early rising phase and accelerated to nearly one hundred percent per day since $\sim$2 days before the hard-to-soft state transition. We examined the dependence of the frequency $ν_{LF}$ on the source flux $f$ and found an anti-correlation between the maximum frequency of the LFQPOs and the corresponding X-ray luminosity of the hard-to-soft transition (or outburst peak luminosity) among the outbursts. We suggest that X-ray evaporation process can not be the only mechanism that drives the variation of the inner disk radius if either of the twin kHz QPO corresponds to the Keplerian frequency at the truncation radius.
SKA's large field of view and high sensitivity at low frequencies will provide almost a complete coverage of the very early rising phase of extragalactic and Galactic transients which undergo a flare or outburst due to an abrupt accretion onto either supermassive (such as tidal disruption events, TDEs) or stellar mass black hole transients (such as black hole LMXB) , when their broadband emission is supposed to be jet-dominated at low luminosities, allowing SKA to be the first facility to make source discoveries and to send out alerts for follow-up ground or space observations as compared with the sensitivity of future X-ray wide-field-view monitoring. On the other hand, due to extremely large rate-of-change in the mass accretion rate during the rising phase of TDE flares or transient outbursts, SKA will be able to cover an extremely large range of the mass accretion rate as well as its rate-of-change not accessible with observations in persistent black hole systems, which will shape our understanding of disk-jet coupling in accreting black holes in the non-stationary accretion regimes.
In this paper, a definition of entropy for $\mathbb{Z}_+^k(k\geq2)$-actions due to S. Friedland \cite{Friedland} is studied. Unlike the traditional definition, it may take a nonzero value for actions whose generators have finite (even zero) entropy as single transformations. Some basic properties are investigated and its value for the $\mathbb{Z}_+^k$-actions on circles generated by expanding endomorphisms is given. Moreover, an upper bound of this entropy for the $\mathbb{Z}_+^k$-actions on tori generated by expanding endomorphisms is obtained via the preimage entropies, which are entropy-like invariants depending on the "inverse orbits" structure of the system.