1,721,223 research outputs found
On the definition of substitution, replacement and allied notions in a abstract formal system
No full textCurry Haskell B. On the definition of substitution, replacement and allied notions in a abstract formal system. In: Revue Philosophique de Louvain. Troisième série, tome 50, n°26, 1952. pp. 251-269
Oscillations of rapidly rotating superfluid stars
No full textUsing time evolutions of the relevant linearized equations, we study non-axisymmetric oscillations of rapidly rotating and superfluid neutron stars. We consider perturbations of Newtonian axisymmetric background configurations and account for the presence of superfluid components via the standard two-fluid model. Within the Cowling approximation, we are able to carry out evolutions for uniformly rotating stars up to the mass-shedding limit. This leads to the first detailed analysis of superfluid neutron star oscillations in the fast rotation regime, where the star is significantly deformed by the centrifugal force. For simplicity, we focus on background models where the two fluids (superfluid neutrons and protons) corotate, are in ?-equilibrium and co-exist throughout the volume of the star. We construct sequences of rotating stars for two analytical model equations of state. These models represent relatively simple generalizations of single fluid, polytropic stars. We study the effects of entrainment, rotation and symmetry energy on non-radial oscillations of these models. Our results show that entrainment and symmetry energy can have a significant effect on the rotational splitting of non-axisymmetric modes. In particular, the symmetry energy modifies the inertial mode frequencies considerably in the regime of fast rotation
r modes and mutual friction in rapidly rotating superfluid neutron stars
No full textWe develop a new perturbative framework for studying the r modes of rotating superfluid neutron stars. Our analysis accounts for the centrifugal deformation of the star, and considers the two-fluid dynamics at linear order in the perturbed velocities. Our main focus is on a simple model system where the total density profile is that of an n= 1 polytrope. We derive a partially analytic solution for the superfluid analogue of the classical r mode. This solution is used to analyse the relevance of the vortex-mediated mutual friction damping, confirming that this dissipation mechanism is unlikely to suppress the gravitational-wave-driven instability in rapidly spinning superfluid neutron stars. Our calculation of the superfluid r modes is significantly simpler than previous approaches, because it decouples the r mode from all other inertial modes of the system. This leads to the results being clearer, but it also means that we cannot comment on the relevance of potential avoided crossings (and associated 'resonances') that may occur for particular parameter values. Our analysis of the mutual friction damping differs from previous studies in two important ways. First, we incorporate realistic pairing gaps which means that the regions of superfluidity in the star's core vary with temperature. Secondly, we allow the mutual friction parameters to take the whole range of permissible values rather than focusing on a particular mechanism. Thus, we consider not only the weak drag regime, but also the strong drag regime where the fluid dynamics are significantly different
Mountains on neutron stars: accreted versus non-accreted crusts
No full textThe aim of this paper is to compare the two cases of an isolated neutron star, with a non-accreted crust, and that of an accreting neutron star, with an accreted crust, and try to estimate which one of the two would make a better source of gravitational waves. In order to do this, we must evaluate the maximum 'mountain' that the crust can sustain in these two cases. We first do this using the formalism of Ushomirsky, Cutler & Bildsten and find that the maximum quadrupole is very similar in the two cases, with the non-accreted crust sustaining a slightly larger mountain. We then develop a perturbation formalism for the problem, that allows us to drop the Cowling approximation and have more control over the boundaries. The use of this formalism confirms that there is not much difference between the two cases, but leads to results approximately one order of magnitude larger than those we obtain with the formalism of Ushomirsky et al
Oscillations of dissipative superfluid neutron stars
No full textWe investigate the oscillations of slowly rotating superfluid stars, taking into account the vortex-mediated mutual friction force that is expected to be the main damping mechanism in mature neutron star cores. Working to linear order in the rotation of the star, we consider both the fundamental f-modes and the inertial r-modes. In the case of the (polar) f-modes, we work out an analytic approximation of the mode which allows us to write down a closed expression for the mutual friction damping time scale. The analytic result is in good agreement with previous numerical results obtained using an energy integral argument. We extend previous work by considering the full range of permissible values for the vortex drag, e.g. the friction between each individual vortex and the electron fluid. This leads to the first ever results for the f-mode in the strong drag regime. Our estimates provide useful insight into the dependence on, and relevance of, various equation of state parameters. In the case of the (axial) r-modes, we confirm the existence of two classes of modes. However, we demonstrate that only one of these sets remains purely axial in more realistic neutron star models. Our analysis lays the foundation for companion studies of the mutual friction damping of the r-modes at second order in the slow-rotation approximation, the first time evolutions for superfluid neutron star perturbations and also the first detailed attempt at studying the dynamics of superfluid neutron stars with both a relative rotation between the components and mutual friction
A new mechanism for saturating unstable r modes in neutron stars
Full text linkWe consider a new mechanism for damping the oscillations of a mature neutron star. The new dissipation channel arises if superfluid vortices are forced to cut through superconducting flux tubes. This mechanism is interesting because the oscillation modes need to exceed a critical amplitude in order for it to operate. Once it acts, the effect is very strong (and non-linear) leading to efficient damping. The upshot of this is that modes are unlikely to ever evolve far beyond the critical amplitude. We consider the effect of this new dissipation channel on the r modes, which may be driven unstable by the emission of gravitational waves. Our estimates show that the flux tube cutting leads to a saturation threshold for the instability that can be smaller than that of other proposed mechanisms. This suggests that the idea may be of direct astrophysical relevance
The dynamics of neutron star crusts: Lagrangian perturbation theory for a relativistic superfluid-elastic system
No full textThe inner crust of a mature neutron star is composed of an elastic lattice of neutron-rich nuclei penetrated by free neutrons. These neutrons can flow relative to the crust once the star cools below the superfluid transition temperature. In order to model the dynamics of this system, which is relevant for a range of problems from pulsar glitches to magnetar seismology and continuous gravitational-wave emission from rotating deformed neutron stars, we need to understand general relativistic Lagrangian perturbation theory for elastic matter coupled to a superfluid component. This paper develops the relevant formalism to the level required for astrophysical applications
Modelling magnetically deformed neutron stars
No full textRotating deformed neutron stars are important potential sources for ground-based gravitational wave interferometers such as LIGO, GEO600 and VIRGO. One mechanism that may lead to significant non-asymmetries is the internal magnetic field. It is well known that a magnetic star will not be spherical and, if the magnetic axis is not aligned with the spin axis, the deformation will lead to the emission of gravitational waves. The aim of this paper is to develop a formalism that would allow us to model magnetically deformed stars, using both realistic equations of state and field configurations. As a first step, we consider a set of simplified model problems. Focusing on dipolar fields, we determine the internal magnetic field which is consistent with a given neutron star model and calculate the associated deformation. We discuss the relevance of our results for current gravitational wave detectors and future prospects
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