Dissipation in relativistic superfluid neutron stars

We analyze damping of oscillations of general relativistic superfluid neutron stars. To this aim we extend the method of decoupling of superfluid and normal oscillation modes first suggested in [Gusakov & Kantor PRD 83, 081304(R) (2011)]. All calculations are made self-consistently within the finite temperature superfluid hydrodynamics. The general analytic formulas are derived for damping times due to the shear and bulk viscosities. These formulas describe both normal and superfluid neutron stars and are valid for oscillation modes of arbitrary multipolarity. We show that: (i) use of the ordinary one-fluid hydrodynamics is a good approximation, for most of the stellar temperatures, if one is interested in calculation of the damping times of normal f-modes; (ii) for radial and p-modes such an approximation is poor; (iii) the temperature dependence of damping times undergoes a set of rapid changes associated with resonance coupling of neighboring oscillation modes. The latter effect can substantially accelerate viscous damping of normal modes in certain stages of neutron-star thermal evolution.Comment: 25 pages, 9 figures, 1 table, accepted for publication in MNRA

Quasi-normal modes of superfluid neutron stars

We study non-radial oscillations of neutron stars with superfluid baryons, in a general relativistic framework, including finite temperature effects. Using a perturbative approach, we derive the equations describing stellar oscillations, which we solve by numerical integration, employing different models of nucleon superfluidity, and determining frequencies and gravitational damping times of the quasi-normal modes. As expected by previous results, we find two classes of modes, associated to superfluid and non-superfluid degrees of freedom, respectively. We study the temperature dependence of the modes, finding that at specific values of the temperature, the frequencies of the two classes of quasi-normal modes show avoided crossings, and their damping times become comparable. We also show that, when the temperature is not close to the avoided crossings, the frequencies of the modes can be accurately computed by neglecting the coupling between normal and superfluid degrees of freedom. Our results have potential implications on the gravitational wave emission from neutron stars.Comment: 16 pages, 7 figures, 2 table

Population status of Bupleurum aureum (Apiaceae), a Critically Endangered plant species in a region of European Russia

Protected Areas are considered as an important and widely applied tool for biodiversity conservation. They are especially relevant for conservation of threatened species populations. This paper presents study aimed to investigate population status and suitability of habitat conditions of a regionally Critically Endangered plant species, Bupleurum aureum (Apiaceae). Our research has been conducted in National Park “Smolny” (European Russia). The field studies were carried out in 2008, 2013–2018 in two study sites (Plot1, Plot2). In each study sites, square plots (1×1 m) were established to cover the most number of B. aureum individuals. The population status was assessed on the basis of the morphometric traits of individuals (height of generative individuals, number of umbellulas per umbella, number of schizocarpiums per umbellula), number of individuals per population, age structure of populations, composition of accompanying flora. We analysed relationships between environmental conditions (shadiness, soil moisture, salt regime of soil, soil nitrogen, soil pH, soil moisture variability) and morphometric and population traits of B. aureum to reveal the most influencing environmental factors. We found that at the north-western limit of the range, B. aureum has relatively low abundance and height of individuals in compare to available data from other parts of its range. The population age structure indicated higher habitat suitability in Plot1 due to presence of both vegetative and generative individuals. At the same time, in Plot2, B. aureum population is under serious threat due to a lack of vegetative individuals noted during almost whole study period. We suppose a forthcoming threat of probable loss of this B. aureum population. Environment data obtained in both habitats of B. aureum populations in National Park “Smolny” (Russia) indicated high relationships between soil moisture and the number of inflorescences formed by plants. We suppose a threat of extinction of the B. aureum population due to the building activity of Castor fiber inhabiting the small river Bakhmustika located nearby of study area. If the small river will be dammed, it could lead to decrease in B. aureum population in both studied sites due to the increase in ground water level

Seismic signatures of strange stars with crust

We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l the fundamental mode (without radial nodes) has a frequency ~300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies >=20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (have approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.Comment: 15 pages, 3 figures, Accepted for publication in MNRA

Neutron star inner crust: reduction of shear modulus by nuclei finite size effect

The elasticity of neutron star crust is important for adequate interpretation of observations. To describe elastic properties one should rely on theoretical models. The most widely used is Coulomb crystal model (system of point-like charges on neutralizing uniform background), in some works it is corrected for electron screening. These models neglect finite size of nuclei. This approximation is well justified except for the innermost crustal layers, where nuclei size becomes comparable with the inter-nuclear spacing. Still, even in those dense layers it seems reasonable to apply the Coulomb crystal result, if one assumes that nuclei are spherically symmetric: Coulomb interaction between them should be the same as interaction between point-like charges. This argument is indeed correct, however, as we point here, shear of crustal lattice generates (microscopic) quadrupole electrostatic potential in a vicinity of lattice cites, which induces deformation on the nuclei. We analyze this problem analytically within compressible liquid drop model, using ionic spheroid model (which is generalization of well known ion sphere model). In particular, for ground state crust composition the effective shear modulus is reduced for a factor of $1-u^{5/3}/(2+3\,u-4\,u^{1/3})$, where u is the filling factor (ratio of the nuclei volume to the volume of the cell). This result is universal and does not depend on the applied nucleon interaction model. For the innermost layers of inner crust u~0.2 leading to reduction of the shear modulus by ~25%, which can be important for correct interpretation of quasi-periodic oscillations in the tails of magnetar flares.Comment: 7 pages, submitted to MNRAS on Sept.