Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts

We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class $\mathcal B$), the Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff dimension greater than 1. Hence, the hyperbolic dimension of the Julia set is greater than 1.Comment: 7 pages, 1 figur

Neutron drip transition in accreting and nonaccreting neutron star crusts

The neutron-drip transition in the dense matter constituting the interior of neutron stars generally refers to the appearance of unbound neutrons as the matter density reaches some threshold density $\rho_\textrm{drip}$. This transition has been mainly studied under the cold catalyzed matter hypothesis. However, this assumption is unrealistic for accreting neutron stars. After examining the physical processes that are thought to be allowed in both accreting and nonaccreting neutron stars, suitable conditions for the onset of neutron drip are derived and general analytical expressions for the neutron drip density and pressure are obtained. Moreover, we show that the neutron-drip transition occurs at lower density and pressure than those predicted within the mean-nucleus approximation. This transition is studied numerically for various initial composition of the ashes from X-ray bursts and superbursts using microscopic nuclear mass models.Comment: 24 pages, accepted for publication in Physical Review

Neutron star radii and crusts: uncertainties and unified equations of state

The uncertainties in neutron star (NS) radii and crust properties due to our limited knowledge of the equation of state (EOS) are quantitatively analysed. We first demonstrate the importance of a unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core EOS based on models with different properties at nuclear matter saturation, the uncertainties can be as large as $\sim 30\%$ for the crust thickness and $4\%$ for the radius. Necessary conditions for causal and thermodynamically consistent matchings between the core and the crust are formulated and their consequences examined. A large set of unified EOS for purely nucleonic matter is obtained based on 24 Skyrme interactions and 9 relativistic mean-field nuclear parametrizations. In addition, for relativistic models 17 EOS including a transition to hyperonic matter at high density are presented. All these EOS have in common the property of describing a $2\;M_\odot$ star and of being causal within stable NS. A span of $\sim 3$ km and $\sim 4$ km is obtained for the radius of, respectively, $1.0\;M_\odot$ and $2.0\;M_\odot$ star. Applying a set of nine further constraints from experiment and ab-initio calculations the uncertainty is reduced to $\sim 1$ km and $2$ km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the EOS near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope $L$ which exhibits a linear correlation with the stellar radius, particularly for masses $\sim 1.0\;M_\odot$. Potential constraints on $L$, the NS radius and the EOS from observations of thermal states of NS are also discussed. [Abriged]Comment: Submitted to Phys. Rev. C. Supplemental material not include

Nuclear symmetry energy and the r-mode instability of neutron stars

We analyze the role of the symmetry energy slope parameter $L$ on the {\it r}-mode instability of neutron stars. Our study is performed using both microscopic and phenomenological approaches of the nuclear equation of state. The microscopic ones include the Brueckner--Hartree--Fock approximation, the well known variational equation of state of Akmal, Pandharipande and Ravenhall, and a parametrization of recent Auxiliary Field Diffusion Monte Carlo calculations. For the phenomenological approaches, we use several Skyrme forces and relativisic mean field models. Our results show that the {\it r}-mode instability region is smaller for those models which give larger values of $L$. The reason is that both bulk ($\xi$) and shear ($\eta$) viscosities increase with $L$ and, therefore, the damping of the mode is more efficient for the models with larger $L$. We show also that the dependence of both viscosities on $L$ can be described at each density by simple power-laws of the type $\xi=A_{\xi}L^{B_\xi}$ and $\eta=A_{\eta}L^{B_\eta}$. Using the measured spin frequency and the estimated core temperature of the pulsar in the low-mass X-ray binary 4U 1608-52, we conclude that observational data seem to favor values of $L$ larger than $\sim 50$ MeV if this object is assumed to be outside the instability region, its radius is in the range $11.5-12$($11.5-13$) km, and its mass $1.4M_\odot$($2M_\odot$). Outside this range it is not possible to draw any conclusion on $L$ from this pulsar.Comment: 10 pages, 6 figures. Version published in Physical Review

Equation-of-state dependence of the gravitational-wave signal from the ring-down phase of neutron-star mergers

Neutron-star (NS) merger simulations are conducted for 38 representative microphysical descriptions of high-density matter in order to explore the equation-of-state dependence of the postmerger ring-down phase. The formation of a deformed, oscillating, differentially rotating very massive NS is the typical outcome of the coalescence of two stars with 1.35 $M_{\odot}$ for most candidate EoSs. The oscillations of this object imprint a pronounced peak in the gravitational-wave (GW) spectra, which is used to characterize the emission for a given model. The peak frequency of this postmerger GW signal correlates very well with the radii of nonrotating NSs, and thus allows to constrain the high-density EoS by a GW detection. In the case of 1.35-1.35 $M_{\odot}$ mergers the peak frequency scales particularly well with the radius of a NS with 1.6 $M_{\odot}$, where the maximum deviation from this correlation is only 60 meters for fully microphysical EoSs which are compatible with NS observations. Combined with the uncertainty in the determination of the peak frequency it appears likely that a GW detection can measure the radius of a 1.6 $M_{\odot}$ NS with an accuracy of about 100 to 200 meters. We also uncover relations of the peak frequency with the radii of nonrotating NSs with 1.35 $M_{\odot}$ or 1.8 $M_{\odot}$, with the radius or the central energy density of the maximum-mass Tolman-Oppenheimer-Volkoff configuration, and with the pressure or sound speed at a fiducial rest-mass density of about twice nuclear saturation density. Furthermore, it is found that a determination of the dominant postmerger GW frequency can provide an upper limit for the maximum mass of nonrotating NSs. The prospects for a detection of the postmerger GW signal and a determination of the dominant GW frequency are estimated to be in the range of 0.015 to 1.2 events per year with the upcoming Advanced LIGO detector.Comment: 29 pages, 28 figures, accepted for publication in Phys. Rev.

Formation of the seed black holes: a role of quark nuggets?

Strange quark nuggets (SQNs) could be the relics of the cosmological QCD phase transition, and they could very likely be the candidate of cold quark matter if survived the cooling of the later Universe, although the formation and evolution of these SQNs depend on the physical state of the hot QGP (quark-gluon plasma) phase and the state of cold quark matter. We reconsider the possibility of SQNs as cold dark matter, and find that the formation of black holes in primordial halos could be significantly different from the standard scenario. In a primordial halo, the collision between gas and SQNs could be frequent enough, and thus the viscosity acting on each SQN would decrease its angular momentum and make it to sink into the center of the halo, as well as heat the gas. The SQNs with baryon numbers less than $10^{35}$ could assemble in the center of the halo before the formation of primordial stars. A black hole could form by merger of these SQNs, and then its mass could quickly become about $10^3\ M_\odot$ or higher, by accreting the surrounding SQNs or gas. The black holes formed in this way could be the seeds for the supermassive black holes at redshift as high as $z\sim 6$.Comment: 15 page

RX J0720.4--3125 as a Possible Example of the Magnetic Field Decay of Neutron Stars

We studied possible evolution of the rotational period and the magnetic field of the X-ray source RX J0720.4-3125 assuming this source to be an isolated neutron star accreting interstellar medium. Magnetic field of the source is estimated to be $10^6 - 10^9$ G, and it is difficult to explain observed rotational period 8.38 s without invoking hypothesis of the magnetic field decay. We used the model of ohmic decay of the crustal magnetic field. The estimates of accretion rate ($10^{-14} - 10^{-16} M_\odot/yr$), velocity of the source relative to interstellar medium ($10 - 50$ km/s), neutron star age ($2\cdot 10^9 - 10^{10}$ yrs) are obtained.Comment: 12 pages (LATEX), 2 PostScript figures. Also available at http://xray.sai.msu.su/~polar/ (with the Russian variant of the article

Temperature profiles of accretion discs around rapidly rotating strange stars in general relativity: a comparison with neutron stars

We compute the temperature profiles of accretion discs around rapidly rotating strange stars, using constant gravitational mass equilibrium sequences of these objects, considering the full effect of general relativity. Beyond a certain critical value of stellar angular momentum ($J$), we observe the radius ($r_{\rm orb}$) of the innermost stable circular orbit (ISCO) to increase with J (a property seen neither in rotating black holes nor in rotating neutron stars). The reason for this is traced to the crucial dependence of $dr_{\rm orb}/dJ$ on the rate of change of the radial gradient of the Keplerian angular velocity at $r_{\rm orb}$ with respect to $J$. The structure parameters and temperature profiles obtained are compared with those of neutron stars, as an attempt to provide signatures for distinguishing between the two. We show that when the full gamut of strange star equation of state models, with varying degrees of stiffness are considered, there exists a substantial overlap in properties of both neutron stars and strange stars. However, applying accretion disc model constraints to rule out stiff strange star equation of state models, we notice that neutron stars and strange stars exclusively occupy certain parameter spaces. This result implies the possibility of distinguishing these objects from each other by sensitive observations through future X-ray detectors.Comment: Contains 10 figures, uses psbox.tex. Accepted for publication in A&A main journa

Internal Heating of Old Neutron Stars: Contrasting Different Mechanisms

Context: The standard cooling models of neutron stars predict temperatures $T10^{7}$ yr. However, the likely thermal emission detected from the millisecond pulsar J0437-4715, of spin-down age $t_s \sim 7\times10^9$ yr, implies a temperature $T\sim 10^5$ K. Thus, a heating mechanism needs to be added to the cooling models in order to obtain agreement between theory and observation. Aims: Several internal heating mechanisms could be operating in neutron stars, such as magnetic field decay, dark matter accretion, crust cracking, superfluid vortex creep, and non-equilibrium reactions ("rotochemical heating"). We study these mechanisms in order to establish which could be the dominant source of thermal emission from old pulsars. Methods: We show by simple estimates that magnetic field decay, dark matter accretion, and crust cracking mechanism are unlikely to have a significant effect on old neutron stars. The thermal evolution for the other mechanisms is computed using the code of Fern\'andez and Reisenegger. Given the dependence of the heating mechanisms on the spin-down parameters, we study the thermal evolution for two types of pulsars: young, slowly rotating "classical" pulsars and old, fast rotating millisecond pulsars. Results: We find that magnetic field decay, dark matter accretion, and crust cracking do not produce detectable heating of old pulsars. Rotochemical heating and vortex creep can be important both for classical pulsars and millisecond pulsars. More restrictive upper limits on the surface temperatures of classical pulsars could rule out vortex creep as the main source of thermal emission. Rotochemical heating in classical pulsars is driven by the chemical imbalance built up during their early spin-down, and therefore strongly sensitive to their initial rotation period.Comment: 7 pages, 5 figures, accepted version to be published in A&

Jacobi-like bar mode instability of relativistic rotating bodies

We perform some numerical study of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity. In the Newtonian limit, this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by viscous dissipation. We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter $M/R = 0-0.275$. We find that general relativity weakens the Jacobi like bar mode instability, but the stabilizing effect is not very strong. According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy $(T/|W|)_{\rm crit}$ for compaction parameter as high as 0.275 is only 30% higher than the Newtonian value. The critical value of the eccentricity depends very weakly on the degree of relativity and for $M/R=0.275$ is only 2% larger than the Newtonian value at the onset for the secular bar mode instability. We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion.Comment: 15 pages, 8 figures, submitted to Phys. Rev.