We calculate the finite-temperature r-mode spectrum of a slowly rotating superfluid Newtonian neutron star neglecting the entrainment between neutron and proton liquid components (i.e., neglecting ...the off-diagonal element of the entrainment matrix). We show that for `minimal' NS core composition (neutrons, protons, and electrons) only two \(m=2\) r-modes exist --- normal mode, which is similar to ordinary r-mode in a nonsuperfluid star, and a superfluid temperature-dependent mode. Accounting for muons in the core dramatically modifies the oscillation spectrum, resulting in an infinite set of superfluid r-modes, whose frequencies vary with temperature. We demonstrate that the normal r-mode can exhibit avoided crossings with superfluid modes at certain `resonance' temperatures, where it dissipates strongly, which leads to substantial suppression of the r-mode instability near these temperatures. The corresponding instability windows are calculated and discussed.
We calculate the spectrum of inertial oscillation modes in a slowly rotating superfluid neutron star, including, for the first time, both the effects of finite temperatures and entrainment between ...superfluid neutrons and protons. We work in the Newtonian limit and assume minimal core composition (neutrons, protons and electrons). We also developed an approximate method that allows one to calculate the superfluid r-mode analytically. Finally, we derive and analyze dispersion relations for inertial modes in the superfluid NS matter in the short wavelength limit.
The relativistic dynamic equations are derived for a superfluid-superconducting mixture coupled to the electromagnetic field. For definiteness, and bearing in mind possible applications of our ...results to neutron stars, it is assumed that the mixture is composed of superfluid neutrons, superconducting protons, and normal electrons. Proton superconductivity of both I and II types is analysed, and possible presence of neutron and proton vortices (or magnetic domains in the case of type-I proton superconductivity) is allowed for. The derived equations neglect all dissipative effects except for the mutual friction dissipation and are valid for arbitrary temperatures (i.e. they do not imply that all nucleons are paired), which is especially important for magnetar conditions. It is demonstrated that these general equations can be substantially simplified for typical neutron stars, for which a kind of magnetohydrodynamic approximation is justified. Our results are compared to the nonrelativistic formulations existing in the literature and a number of discrepancies are found. In particular, it is shown that, generally, the electric displacement \({\pmb D}\) does not coincide with the electric field \({\pmb E}\), contrary to what is stated in the previous works. The relativistic framework developed here is easily extendable to account for more sophisticated microphysics models and it provides the necessary basis for realistic modelling of neutron stars.
Buoyancy of proton vortices is considered as one of the important mechanisms of magnetic field expulsion from the superconducting interiors of neutron stars. Here we show that the generally accepted ...expression for the buoyancy force is not correct and should be modified. The correct expression is derived for both neutron and proton vortices. It is argued that this force is already contained in the coarse-grained hydrodynamics of Bekarevich & Khalatnikov and its various multifluid extensions, but is absent in the hydrodynamics of Hall. Some potentially interesting buoyancy-related effects are briefly discussed.
To put new constraints on the r-mode instability window, we analyse the formation of millisecond pulsars (MSPs) within the recycling scenario, making use of three sets of observations: (a) X-ray ...observations of neutron stars (NSs) in low-mass X-ray binaries; (b) timing of millisecond pulsars; and (c) X-ray and UV observations of MSPs. As shown in previous works, r-mode dissipation by shear viscosity is not sufficient to explain observational set (a), and enhanced r-mode dissipation at the red-shifted internal temperatures \(T^\infty\sim 10^8\) K is required to stabilize the observed NSs. Here, we argue that models with enhanced bulk viscosity can hardly lead to a self-consistent explanation of observational set (a) due to strong neutrino emission, which is typical for these models (unrealistically powerful energy source is required to keep NSs at the observed temperatures). We also demonstrate that the observational set (b), combined with the theory of internal heating and NS cooling, provides evidence of enhanced r-mode dissipation at low temperatures, \(T^\infty\sim 2\times 10^7\) K. Observational set (c) allows us to set an upper limit on the internal temperatures of MSPs, \(T^\infty<2\times 10^7\) K (assuming a canonical NS with the accreted crust). Recycling scenario can produce MSPs at these temperatures only if r-mode instability is suppressed in the whole MSP spin frequency range (\(\nu\lesssim 750\) Hz) at temperatures \(2\times 10^7\lesssim T^\infty\lesssim 3 \times 10^7\) K, providing thus a new constraint on the r-mode instability window. These observational constraints are analysed in more details in application to the resonance uplift scenario of Gusakov et al. Phys. Rev. Lett., 112 (2014), 151101.
We constrain the parameters of neutron superfluidity in the cores of neutron stars making use of the recently proposed effect of resonance stabilization of \(r\)-modes. To this end, we, for the first ...time, calculate the finite-temperature \(r\)-mode spectra for realistic models of rotating superfluid neutron stars, accounting for both muons and neutron-proton entrainment in their interiors. We find that the ordinary (normal) \(r\)-mode exhibits avoided crossings with superfluid \(r\)-modes at certain stellar temperatures and spin frequencies. Near the avoided crossings, the normal \(r\)-mode dissipates strongly, which leads to substantial suppression of the \(r\)-mode instability there. The extreme sensitivity of the positions of avoided crossings to the neutron superfluidity model allows us to constrain the latter by confronting the calculated spectra with observations of rapidly rotating neutron stars in low-mass X-ray binaries.
New experimental and theoretical results on the silicon di‐interstitial (I2) and its interactions with oxygen and carbon impurity atoms in Si crystals are reported. Electronic structure calculations ...indicate that I2 has an acceptor and a donor level in the gap, which are close to the conduction and the valence band edges, respectively. Experimental results, which support the theoretically predicted high mobility of I2, are discussed. It is argued that mobile I2 can be trapped by oxygen and carbon impurities. The I2O center has a donor level at Ev +0.09 eV. Two absorption bands at 936 and 929 cm−1 are assigned to the local vibrational modes of the I2O defect in the neutral and positively charged states, respectively. The binding energy of I2O relative to the separated I2 and Oi species is 0.22 eV. The disappearance of the I2O complex upon thermal annealing occurs in the temperature range 50–100 °C and is accompanied by the introduction of another defect, which gives rise to two hole emission signals from energy levels at Ev +0.54 and Ev +0.45 eV. It is argued that these levels are related to a complex consisting of interstitial carbon and interstitial silicon atoms (CiI). The stable configurations of the CiI pair have been found.
A new class of neutron stars (NSs) -- hot rapidly rotating non-accreting NSs, which we propose to call HOFNARs (HOt and Fast Non-Accreting Rotators) or "hot widows" (in analogy with "black widow" ...pulsars) -- is suggested. We argue that such stars should originate from the low-mass X-ray binaries (LMXBs) provided that they were unstable with respect to excitation of \(r\)-modes at the end of accretion epoch (when their low-mass companions ceased to fill the Roche lobe). High temperature of "hot widows"/HOFNARs is maintained by \(r\)-mode dissipation rather than by accretion. We analyse observational properties of "hot widows"/HOFNARs and demonstrate that these objects form a specific separate class of neutron stars. In particular, some of the most stable X-ray sources among the candidates to quiescent LMXB systems (qLMXBs), can, in fact, belong to that new class. We formulate observational criteria which allow to distinguish "hot widows"/HOFNARs from qLMXB systems, and argue that available observations of X-ray sources 47 Tuc X5 and X7 satisfy (or, at least, do not contradict) these criteria. In addition, we discuss indirect evidences in favor of "hot widows"/HOFNARs existence, following from the analysis of observations and predictions of population synthesis theories. If that new class of NSs does exist, it would prove the possibility to emit gravitational waves by mass-current multipole. Various applications of our results, such as prospects for constraining superdense matter properties with hot widows"/HOFNARs, are analyzed.
In a previous paper M. E. Gusakov, A. I. Chugunov, and E. M. Kantor, Phys. Rev. Lett. 112, 151101 (2014), we introduced a new scenario that explains the existence of rapidly rotating warm neutron ...stars (NSs) observed in low-mass X-ray binaries (LMXBs). Here it is described in more detail. The scenario takes into account the interaction between superfluid inertial modes and the normal (quadrupole) \(m=2\) \(r\)-mode, which can be driven unstable by Chandrasekhar-Friedman-Schutz (CFS) mechanism. This interaction can only occur at some fixed "resonance" stellar temperatures; it leads to formation of the "stability peaks" which stabilize a star in the vicinity of these temperatures. We demonstrate that a NS in LMXB spends a substantial fraction of time on the stability peak, that is, in the region of stellar temperatures and spin frequencies, that has been previously thought to be CFS unstable with respect to excitation of \(r\)-modes. We also find that the spin frequencies of NSs are limited by the CFS instability of normal (octupole) \(m=3\) \(r\)-mode rather than by \(m=2\) \(r\)-mode. This result agrees with the predicted value of the cutoff spin frequency \(\sim 730\) Hz in the spin distribution of accreting millisecond X-ray pulsars. In addition, we analyze evolution of a NS after the end of the accretion phase and demonstrate that millisecond pulsars can be born in LMXBs within our scenario. Besides millisecond pulsars, our scenario also predicts a new class of LMXB descendants - hot and rapidly rotating nonaccreting NSs ("hot widows"/HOFNARs). Further comparison of the proposed theory with observations of rotating NSs can impose new important constraints on the properties of superdense matter.
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