The imprint of the equation of state on the axial w-modes of oscillating neutron stars

We discuss the dependence of the pulsation frequencies of the axial quasi-normal modes of a nonrotating neutron star upon the equation of state describing the star interior. The continued fraction method has been used to compute the complex frequencies for a set of equations of state based on different physical assumptions and spanning a wide range of stiffness. The numerical results show that the detection of axial gravitational waves would allow to discriminate between the models underlying the different equation of states, thus providing relevant information on both the structure of neutron star matter and the nature of the hadronic interactions.Comment: 9 pages, 7 figures, mn.st

Non-radial oscillation modes as a probe of density discontinuities in neutron stars

A phase transition occurring in the inner core of a neutron star could be associated to a density discontinuity that would affect the frequency spectrum of the non-radial oscillation modes in two ways. Firstly, it would produce a softening of the equation of state, leading to more compact equilibrium configurations and changing the frequency of the fundamental and pressure modes of the neutron star. Secondly, a new non-zero frequency g-- mode would appear, associated to each discontinuity. These discontinuity g--modes have typical frequencies larger than those of g--modes previously studied in the literature (thermal, core g-- modes, or g--modes due to chemical inhomogeneities in the outer layers), and smaller than that of the fundamental mode; therefore they should be distinguishable from the other modes of non radial oscillation. In this paper we investigate how high density discontinuities change the frequency spectrum of the non-radial oscillations, in the framework of the general relativistic theory of stellar perturbations. Our purpose is to understand whether a gravitational signal, emitted at the frequencies of the quasi normal modes, may give some clear information on the equation of state of the neutron star and, in particular, on the parameters that characterize the density discontinuity. We discuss some astrophysical processes that may be associated to the excitation of these modes, and estimate how much gravitational energy should the modes convey to produce a signal detectable by high frequency gravitational detectors.Comment: submitted to MNRA

Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity

We study the transition from inspiral to plunge in general relativity by computing gravitational waveforms of non-spinning, equal-mass black-hole binaries. We consider three sequences of simulations, starting with a quasi-circular inspiral completing 1.5, 2.3 and 9.6 orbits, respectively, prior to coalescence of the holes. For each sequence, the binding energy of the system is kept constant and the orbital angular momentum is progressively reduced, producing orbits of increasing eccentricity and eventually a head-on collision. We analyze in detail the radiation of energy and angular momentum in gravitational waves, the contribution of different multipolar components and the final spin of the remnant. We find that the motion transitions from inspiral to plunge when the orbital angular momentum L=L_crit is about 0.8M^2. For L<L_crit the radiated energy drops very rapidly. Orbits with L of about L_crit produce our largest dimensionless Kerr parameter for the remnant, j=J/M^2=0.724. Generalizing a model recently proposed by Buonanno, Kidder and Lehner to eccentric binaries, we conjecture that (1) j=0.724 is the maximal Kerr parameter that can be obtained by any merger of non-spinning holes, and (2) no binary merger (even if the binary members are extremal Kerr black holes with spins aligned to the orbital angular momentum, and the inspiral is highly eccentric) can violate the cosmic censorship conjecture.Comment: Added sequence of long inspirals to the study. To match published versio

Well-posedness for solid-liquid phase transitions with a forth-order nonlinearity

A phase-field system which describes the evolution of both the absolute temperature $\theta$ and the phase variable $f$ during first-order transitions in thermal insulators is considered. A thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law. By virtue of the special form of the internal energy, a third-order nonlinearity $G_2^\prime(f)$ appears into the energy balance in place of the (customary constant) latent-heat. As a consequence, the bounds $0\le f\le1$ hold true whenever $\theta$ is positive valued. In addition, a nonlinear Fourier law with conductivity proportional to temperature is assumed. Well-posedness for the resulting initial and boundary value problem are then established in a suitable setting

On a doubly nonlinear phase-field model for first-order transitions with memory

Solid-liquid transitions in thermal insulators and weakly conducting media are modeled through a phase-field system with memory. The evolution of the phase variable $\varphi$ is ruled by a balance law which takes the form of a Ginzburg-Landau equation. A thermodynamic approach is developed starting from a special form of the internal energy and a nonlinear hereditary heat conduction flow of Coleman-Gurtin type. After some approximation of the energy balance, the absolute temperature $\theta$ obeys a doubly nonlinear "heat equation" where a third-order nonlinearity in $\varphi$ appears in place of the (customarily constant) latent-heat. The related initial and boundary value problem is then formulated in a suitable setting and its well--posedness and stability is proved

A three-dimensional phase transition model in ferromagnetism: existence and uniqueness

We scrutinize both from the physical and the analytical viewpoint the equations ruling the paramagnetic-ferromagnetic phase transition in a rigid three dimensional body. Starting from the order structure balance, we propose a non-isothermal phase-field model which is thermodynamically consistent and accounts for variations in space and time of all fields (the temperature $\theta$, the magnetic field vector H and the magnetization vector M). In particular, we are able to establish a well-posedness result for the resulting coupled system

Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow

We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a transition from stationary to randomly fluctuating states, via periodic ones. The increasing complexity of the flow in both time and space at progressively higher values of elasticity accompanies the establishment of mixing features. The peculiar dynamical behavior observed in the simulations is found to be related to the appearance of filamental propagating patterns, which develop even in the limit of very small inertial non-linearities, thanks to the feedback of elastic forces on the flow.Comment: 10 pages, 14 figure

Gravity-dominated unequal-mass black hole collisions

We continue our series of studies of high-energy collisions of black holes investigating unequal-mass, boosted head-on collisions in four dimensions. We show that the fraction of the center-of-mass energy radiated as gravitational waves becomes independent of mass ratio and approximately equal to $13\%$ at large energies. We support this conclusion with calculations using black hole perturbation theory and Smarr's zero-frequency limit approximation. These results lend strong support to the conjecture that the detailed structure of the colliding objects is irrelevant at high energies.This work was supported by the H2020-MSCA-RISE-2015 Grant No. StronGrHEP- 690904, the SDSC Comet and TACC Stampede clusters through NSF-XSEDE Grant No. PHY-090003, STFC Consolidator Grant No. ST/L000636/1, and DiRAC’s Cosmos Shared Memory system through BIS Grant No. ST/J005673/1 and STFC Grant Nos. ST/H008586/1, ST/K00333X/1. E.B. is supported by NSF CAREER Grant No. PHY-1055103 and by FCT contract IF/00797/2014/CP1214/CT0012 under the IF2014 Programme. V.C. thanks the Departament de F´ısica Fonamental at Universitat de Barcelona for hospitality while this work was being completed. V.C. and U.S. acknowledge financial support provided under the European Union’s H2020 ERC Consolidator Grant “Matter and strong-field gravity: New frontiers in Einstein’s theory” grant agreement no. MaGRaTh–646597. V.C. also acknowledges financial support from FCT under Sabbatical Fellowship nr. SFRH/BSAB/105955/2014. F.P. acknowledges financial support from the Simons Foundation and NSF grant PHY-1305682. This research was supported in part by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation.This is the author accepted manuscript. The final version is available from APS Physics via http://dx.doi.org/10.1103/PhysRevD.93.04401