arXiv subjects

Dmitry Kobyakov

Publications and source records attributed to Dmitry Kobyakov.

6 recordsLinked to original sources

arXiv2026

The mean-field theory of superfluid-superconducting vortex states in the outer core of neutron stars

Purpose: Characterize superfluid-superconducting vortex states at arbitrary pressures with $T_{cp}\neq T_{cn}$, assuming both proton and neutron mean-fields are formed by spin-0 Cooper pairs. Method: The existing mean-field theory is extended to account for $T_{cp}\neq T_{cn}$. The pressure dependence of the pairing gap energy $\Delta_{\alpha0}$ is quantitatively established on the basis of the effective chiral field theory. To link $T_{c\alpha}$ with $\Delta_{\alpha0}$, I use the weak-coupling result $T_{c\alpha}\approx0.57\Delta_{\alpha0}$. A quadratic scaled-temperature ($T/T_{cp}$) dependence of the thermodynamic magnetic field is postulated in analogy with pure superconductors. The $T/T_{c\alpha}$-dependence of the gap $\Delta_{\alpha T}$ is inferred from the many-body approximations for the pure neutron matter. Results: An empirical $T/T_{c\alpha}$-dependence for the mean-field is constructed to account for the interplay between the condensation and the magnetic energies. The superfluid entrainment is found to increase the size of the vortex core and to decrease the effective magnetic penetration depth. The size of the neutron vortex core is found to be larger than the magnetic penetration depth in the outer core. Conclusions: The usual approximation of infinitely thin vortex line (the London's approximation) for the neutron vortex is found to be irrelevant in the entire outer core and for the proton vortex is found to be limited to vicinity of the crust-core transition. The developed mean-field theory paves the way to study the vortex microscopic structure, the angular momentum, the magnetization and the vortex-fluxtube interaction energy.

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arXiv2024

Inner crust of neutron stars: Polymorphism and superconductivity in the liquid drop model

Within the liquid drop model built up with the nuclear interaction parametrization Sk$\chi$450, which is based on the chiral effective field theory, we calculate numerically the internal energy density for each of nuclear pasta phases and for the uniform nuclear matter. We provide quantitative arguments in favor of coexistence of various nuclear matter phases at a significant range of total pressure within the inner crust of neutron stars, a concept known as crystal polymorphism. Specifically, we find that differences of the internal energy per baryon for various phases are typically less than the thermal energy per a freedom degree at temperature about $10^8$--$10^9$ K, which sets the energetic scale for thermal fluctuations of state of Fermi liquid from the ground state. The nuclear energy contributions are described using the same parametrization Sk$\chi$450 for the bulk, plain surface and curvature terms. We find that the introduction of the curvature correction changes the ground state in a relevant way. This may be understood as a consequence of the corresponding change in size of the nucleus, which significantly modifies the phase transition densities. Using the calculated structural parameters from liquid drop model, we explore the physical consequences of the expected Cooper pairing of protons in lasagna phase. In this case, we find a crossover between the discreet layered and the three-dimensional anisotropic regimes of superconductivity. Additionally, we study the magnetic stress in lasagna accounting for a rotational lag between superfluid neutrons and the crystal lattice, which is believed to develop naturally in pulsars and magnetars. Our results offer a preliminary insight into rich magnetic properties of the inner crust of neutron stars.

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arXiv2023

Some properties of plasma surrounding brown dwarfs

Recently, brown dwarfs have emerged as a new topic for the astrophysical studies. These objects are intermediate between solar-type stars and giant gaseous planets. In this article, the analogies between brown dwarfs and the planet Jupiter are considered with a focus on the surrounding plasma. I consider the magnetohydrodynamic version of the Rayleigh-Taylor instability (or so called ``interchange instability'') as a minimal model of the expansion of the plasma disc surrounding Jupiter. By comparing the theoretical prediction for the radial expansion rate of the disc with the observations I quantitatively confirm the existing qualitative result, which predicts that the Rayleigh-Taylor instability provides too quick expansion. Therefore, in the realistic plasma disc yet another mechanism must operate which slows down the expansion. I suggest that similar mechanisms take place in the observed radiation belts of brown dwarfs.

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arXiv2023

Location and symmetry of superconductivity in neutron stars

Earlier, it was a standard assumption that the entire core of neutron stars is superconducting. However, the matter contents in the inner core has been unknown even qualitatively, because the density of matter in that region is expected to be higher than the nuclear saturation density 0.16 $\mathrm{fm}^{-3}$. As a consequence, no reliable model exists that would describe the neutron star matter in the inner core of neutron stars. Thus, a possibility of presence of normal, nonsuperconducting, plasma in the inner core cannot be excluded as of today. This point is supported by the numerical calculations performed in [1]. The calculations are based on the equation of state and the proton Cooper pairing gap energy derived from the chiral effective field theory. The numerical results show that the superconducting gap goes to zero beyond the depth about 1 km below the crust-core boundary. Given that the stellar radius is of the order of 12 km, therefore the superconducting proton matter is expected to exist only in a thin layer at the tip of the outer core. Recently it has been realized that the symmetry of superconductor is anisotropic in the lasagna region of the pasta phases located at the bottom of the crust. However the question of whether this symmetry is continuous or discreet was unsolved. The numerical calculations performed in [1] have shown that the tunneling rate between the adjacent slabs in the entire range of the corresponding densities is negligibly small. Thus, a discreet model is necessary for the description of the lasagna region. Uncertainties and future directions of the research are discussed.

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arXiv2023

Unified description of superconductivity in neutron stars

In this paper, I study the location and symmetry of superconducting protons. Solving the Tolman-Oppenheimer-Volkoff (TOV) equations based on the unified Barcelona-Catania-Paris-Madrid equation of state (BCPM EoS) and on the pairing gap calculations by Lim and Holt [1], I find that roughly 500 meters of the liquid core (with isotropic and continuous symmetry) and roughly 100-150 meters of the core-crust interface (with anisotropic symmetry) are superconducting, while the rest of the star is normal. To specify whether the superconducting symmetry is discreet in the pasta phase, I study the coexistence of the saturated nuclear and the pure neutron matter using EoS based on the chiral effective field theory (ChEFT). I find that the maximum pressure at coexistence is $P_{*}\simeq0.5\;{\rm MeV\,fm^{-3}}$. To verify the precision of the coexistence calculations I evaluate the surface and the Coulomb corrections using the compressible liquid drop model. I calculate the proton tunneling rate in the perfectly ordered slab region of the pasta phase and conclude that for the chosen EoS, the proton supercurrent tunneling between the adjacent slabs is negligible and the slab region should be described as a discreet symmetry system of quasi two-dimensional layers.

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arXiv2023

On the screening condition in the core of neutron stars

Earlier, the screening condition in neutron star core has been formulated as equality of velocities of superconducting protons and the electrons $\mathbf{v}_p=\mathbf{u}_e$ at wavenumbers $q\ll\lambda^{-1}$ ($\lambda$ is the London penetration depth) and has been used to derive the force exerted by the electrons on a moving flux tube. By calculating the current-current response, I find that $\mathbf{v}_p\neq\mathbf{u}_e$ for $l^{-1}<q\ll\lambda^{-1}$ ($l$ is the electron mean free path). I show that at typical realistic parameters the electric field induced by a moving (relative to the electrons) flux tube is not screened by the electron currents. The implication is that the existing picture of the momentum exchange between the electrons and the flux tubes must be reassessed.

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