Stability analysis of orbital modes for a generalized Lane-Emden equation

We present a stability analysis of the standard nonautonomous systems type for a recently introduced generalized Lane-Emden equation which is shown to explain the presence of some of the structures observed in the atomic spatial distributions of magnetically-trapped ultracold atomic clouds. A Lyapunov function is defined which helps us to prove that stable spatial structures in the atomic clouds exist only for the adiabatic index $\gamma=1+1/n$ with even $n$. In the case when $n$ is odd we provide an instability result indicating the divergence of the density function for the atoms. Several numerical solutions, which according to our stability analysis are stable, are also presented.Comment: 11 pages, 4 figure

Approximate Universal Relations for Neutron Stars and Quark Stars

Neutron stars and quark stars are ideal laboratories to study fundamental physics at supra nuclear densities and strong gravitational fields. Astrophysical observables, however, depend strongly on the star's internal structure, which is currently unknown due to uncertainties in the equation of state. Universal relations, however, exist among certain stellar observables that do not depend sensitively on the star's internal structure. One such set of relations is between the star's moment of inertia ($I$), its tidal Love number (Love) and its quadrupole moment ($Q$), the so-called I-Love-Q relations. Similar relations hold among the star's multipole moments, which resemble the well-known black hole no-hair theorems. Universal relations break degeneracies among astrophysical observables, leading to a variety of applications: (i) X-ray measurements of the nuclear matter equation of state, (ii) gravitational wave measurements of the intrinsic spin of inspiraling compact objects, and (iii) gravitational and astrophysical tests of General Relativity that are independent of the equation of state. We here review how the universal relations come about and all the applications that have been devised to date.Comment: 89 pages, 38 figures; review article submitted to Physics Report

Halted-Pendulum Relaxation: Application to White Dwarf Binary Initial Data

Studying compact star binaries and their mergers is integral to modern astrophysics. In particular, binary white dwarfs are associated with Type Ia supernovae, used as standard candles to measure the expansion of the Universe. Today, compact-star mergers are typically studied via state-of-the-art computational fluid dynamics codes. One such numerical techniques, Smoothed Particle Hydrodynamics (SPH), is frequently chosen for its excellent mass, energy, and momentum conservation. Furthermore, the natural treatment of vacuum and the ability to represent highly irregular morphologies make SPH an excellent tool for the numerical study of compact-star binaries and mergers. However, for many scenarios, including binary systems, the outcome simulations are only as accurate as the initial conditions. For SPH, it is essential to ensure that particles are distributed semi-regularly, correctly representing the initial density profile. Additionally, particle noise in the form of high-frequency local motion and low-frequency global dynamics must be damped out. Damping the latter can be as computationally intensive as the actual simulation. Here, we discuss a new and straightforward relaxation method, Halted-Pendulum Relaxation (HPR), to remove the global oscillation modes of SPH particle configurations. In combination with effective external potentials representing gravitational and orbital forces, we show that HPR has an excellent performance in efficiently relaxing SPH particles to the desired density distribution and removing global oscillation modes. We compare the method to frequently used relaxation approaches such as gravitational glass, increased artificial viscosity, and Weighted Voronoi Tesselations, and test it on a white dwarf binary model at its Roche lobe overflow limit

Equation of state of a laser-cooled gas

We experimentally determine the equation of state of a laser-cooled gas. By employing the Lane-Emden formalism, widely used in astrophysics, we derive the equilibrium atomic profiles in large magneto-optical traps where the thermodynamic effects are cast in a polytropic equation of state. The effects of multiple scattering of light are included, which results in a generalized Lane-Emden equation for the atomic profiles. A detailed experimental investigation reveals an excellent agreement with the model, with a twofold significance. On one hand, we can infer the details of the equation of state of the system, from an ideal gas to a correlated phase due to an effective electrical charge for the atoms, which is accurately described by a microscopical description of the effective electrostatic interaction. On the other hand, we are able map the effects of multiple scattering onto directly controllable experimental variables, which paves the way to subsequent experimental investigations of this collective interaction

Stellar structure models in modified theories of gravity: lessons and challenges.

The understanding of stellar structure represents the crossroads of our theories of the nuclear force and the gravitational interaction under the most extreme conditions observably accessible. It provides a powerful probe of the strong field regime of General Relativity, and opens fruitful avenues for the exploration of new gravitational physics. The latter can be captured via modified theories of gravity, which modify the Einstein-Hilbert action of General Relativity and/or some of its principles. These theories typically change the Tolman-Oppenheimer-Volkoff equations of stellar's hydrostatic equilibrium, thus having a large impact on the astrophysical properties of the corresponding stars and opening a new window to constrain these theories with present and future observations of different types of stars. For relativistic stars, such as neutron stars, the uncertainty on the equation of state of matter at supranuclear densities intertwines with the new parameters coming from the modified gravity side, providing a whole new phenomenology for the typical predictions of stellar structure models, such as mass-radius relations, maximum masses, or moment of inertia. For non-relativistic stars, such as white, brown and red dwarfs, the weakening/strengthening of the gravitational force inside astrophysical bodies via the modified Newtonian (Poisson) equation may induce changes on the star's mass, radius, central density or luminosity, having an impact, for instance, in the Chandrasekhar's limit for white dwarfs, or in the minimum mass for stable hydrogen burning in high-mass brown dwarfs. This work aims to provide a broad overview of the main such results achieved in the recent literature for many such modified theories of gravity, by combining the results and constraints obtained from the analysis of relativistic and non-relativistic stars in different scenarios. Moreover, we will build a bridge between the efforts of the community working on different theories, formulations, types of stars, theoretical modelings, and observational aspects, highlighting some of the most promising opportunities in the field. (C) 2020 Elsevier B.V. All rights reserved