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Register a new userA reliable description of the radial oscillations of compact stars
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We develop a numerical algorithm for the solution of the Sturm-Liouville differential equation governing the stationary radial oscillations of nonrotating compact stars. Our method is based on the Numerovs method that turns the Sturm-Liouville differential equation in an eigenvalue problem. In our development we provide a strategy to correctly deal with the star boundaries and the interfaces between layers with different mechanical properties. Assuming that the fluctuations obey the same equation of state of the background, we analyze various different stellar models and we precisely determine hundreds of eigenfrequencies and of eigenmodes. If the equation of state does not present an interface discontinuity, the fundamental radial eigenmode becomes unstable exactly at the critical central energy density corresponding to the largest gravitational mass. However, in the presence of an interface discontinuity, there exist stable configurations with a central density exceeding the critical one and with a smaller gravitational mass.
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We investigate the properties of relativistic stars made of dark energy. We model stellar structure assuming i) isotropic perfect fluid and ii) a dark energy inspired equation of state, the generalized equation of state of Chaplygin gas, as we will be calling it. The mass-to-radius profiles, the tidal Love numbers as well as the ten lowest radial oscillation modes are computed. Causality, stability and energy conditions are also discussed.
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise, which accounts for the general memory and retarded effects of the frictional force, and on the fluctuation-dissipation theorem. The presence of the memory effects influences the response of the disk to external random interactions, and modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution (PSD) of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the Intra Day Variability (IDV) of the Active Galactic Nuclei (AGN) may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.
The stability properties of relativistic stars against gravitational collapse to black hole is a classical problem in general relativity. A sufficient criterion for secular instability was established by Friedman, Ipser and Sorkin (1988), who proved that a sequence of uniformly rotating barotropic stars is secularly unstable on one side of a turning point and then argued that a stronger result should hold: that the sequence should be stable on the opposite side, with the turning point marking the onset of secular instability. We show here that this expectation is not met. By computing in full general relativity the $F$-mode frequency for a large number of rotating stars, we show that the neutral-stability point, i.e., where the frequency becomes zero, differs from the turning point for rotating stars. Using numerical simulations we validate that the new criterion can be used to assess the dynamical stability of relativistic rotating stars.
According to the braneworld idea, ordinary matter is confined on a 3-dimensional space (brane) that is embedded in a higher-dimensional space-time where gravity propagates. In this work, after reviewing the limits coming from general relativity, finiteness of pressure and causality on the brane, we derive observational constraints on the braneworld parameters from the existence of stable compact stars. The analysis is carried out by solving numerically the brane-modified Tolman-Oppenheimer-Volkoff equations, using different representative equations of state to describe matter in the star interior. The cases of normal dense matter, pure quark matter and hybrid matter are considered.
We develop a theoretical framework to study slowly rotating compact stars in a rather general class of alternative theories of gravity, with the ultimate goal of investigating constraints on alternative theories from electromagnetic and gravitational-wave observations of compact stars. Our Lagrangian includes as special cases scalar-tensor theories (and indirectly f(R) theories) as well as models with a scalar field coupled to quadratic curvature invariants. As a first application of the formalism, we discuss (for the first time in the literature) compact stars in Einstein-Dilaton-Gauss-Bonnet gravity. We show that compact objects with central densities typical of neutron stars cannot exist for certain values of the coupling constants of the theory. In fact, the existence and stability of compact stars sets more stringent constraints on the theory than the existence of black hole solutions. This work is a first step in a program to systematically rule out (possibly using Bayesian model selection) theories that are incompatible with astrophysical observations of compact stars.
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