Higher-order symmetry energy and neutron star core-crust transition with Gogny forces

We study the symmetry energy and the core-crust transition in neutron stars using the finite-range Gogny nuclear interaction and examine the deduced crustal thickness and crustal moment of inertia. We start by analyzing the second-, fourth- and sixth-order coefficients of the Taylor expansion of the energy per particle in powers of the isospin asymmetry for Gogny forces. These coefficients provide information about the departure of the symmetry energy from the widely used parabolic law. The neutron star core-crust transition is evaluated by looking at the onset of thermodynamical instability of the liquid core. The calculation is performed with the exact (i.e., without Taylor expansion) Gogny EoS for the core, and also with its Taylor expansion in order to assess the influence of isospin expansions on locating the inner edge of neutron star crusts. It is found that the properties of the core-crust transition derived from the exact EoS differ from the predictions of the Taylor expansion even when the expansion is carried through sixth order in the isospin asymmetry. Gogny forces, using the exact EoS, predict the ranges $0.094 \text{ fm}^{-3} \lesssim \rho_t \lesssim 0.118\text{ fm}^{-3}$ for the transition density and $0.339 \text{ MeV fm}^{-3} \lesssim P_t \lesssim 0.665 \text{ MeV fm}^{-3}$ for the transition pressure. The transition densities show an anticorrelation with the slope parameter $L$ of the symmetry energy. The transition pressures are not found to correlate with $L$. Neutron stars obtained with Gogny forces have maximum masses below $1.74M_\odot$ and relatively small moments of inertia. The crustal mass and moment of inertia are evaluated and comparisons are made with the constraints from observed glitches in pulsars.Comment: 24 pages, 15 figures, discussions and bibliography updated, to appear in Physical Review

Consistent Approximations for the Optimal Control of Constrained Switched Systems

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In this paper, we devise an algorithm for the computation of an optimal control of constrained nonlinear switched dynamical systems. The control parameter for such systems include a continuous-valued input and discrete-valued input, where the latter corresponds to the mode of the switched system that is active at a particular instance in time. Our approach, which we prove converges to local minimizers of the constrained optimal control problem, first relaxes the discrete-valued input, then performs traditional optimal control, and then projects the constructed relaxed discrete-valued input back to a pure discrete-valued input by employing an extension to the classical Chattering Lemma that we prove. We extend this algorithm by formulating a computationally implementable algorithm which works by discretizing the time interval over which the switched dynamical system is defined. Importantly, we prove that this implementable algorithm constructs a sequence of points by recursive application that converge to the local minimizers of the original constrained optimal control problem. Four simulation experiments are included to validate the theoretical developments

Metallicities of M Dwarf Planet Hosts from Spectral Synthesis

We present the first spectroscopic metallicities of three M dwarfs with known or candidate planetary mass companions. We have analyzed high resolution, high signal-to-noise spectra of these stars which we obtained at McDonald Observatory. Our analysis technique is based on spectral synthesis of atomic and molecular features using recently revised cool-star model atmospheres and spectrum synthesis code. The technique has been shown to yield results consistent with the analyses of solar-type stars and allows measurements of M dwarf [M/H] values to 0.12 dex precision. From our analysis, we find [M/H] = -0.12, -0.32, and -0.33 for GJ 876, GJ 436, and GJ 581 respectively. These three M dwarf planet hosts have sub-solar metallicities, a surprising departure from the trend observed in FGK-type stars. This study is the first part of our ongoing work to determine the metallicities of the M dwarfs included in the McDonald Observatory planet search program.Comment: 13 pages, 2 figures, accepted for publication in ApJ

On the origin of the X-ray emission from a narrow-line radioquasar at z>1

We present new XMM-Newton X-ray observations of the z=1.246 narrow-line radioquasar RX J1011.2+5545 serendipitously discovered by ROSAT. The flat X-ray spectrum previously measured by ROSAT and ASCA is shown to be the result of a steep Gamma~1.8 power law spectrum seen through a moderate intrinsic absorbing column NH~4E21 cm^-2. The position of the X-ray source is entirely coincident with the nucleus of the radio source that we have resolved in new sensitive VLA observations at 3.6 and 6 cm, implying that scattering in the radio lobes is not responsible for the bulk of X-ray emission. In the EPIC pn image, a faint patch of X-ray emission is apparent 14'' to the NE of the main X-ray source. The former is positionally coincident with an apparently extended optical object with R~21.9, but there is no associated radio emission, thus ruling out the possibility that this represents a hotspot in a jet emanating from the primary X-ray source. No reflection features are detected in the X-ray spectrum of the narrow-line radioquasar, although an Fe line with equivalent width of up to 600 eV cannot be ruled out.Comment: 7 pages, 6 figures, MNRAS in the pres

New Gogny interaction suitable for astrophysical applications

The D1 family of parametrizations of the Gogny interaction commonly suffers from a rather soft neutron matter equation of state that leads to maximal masses of neutron stars well below the observational value of two solar masses. We propose a reparametrization scheme that preserves the good properties of the Gogny force but allows one to tune the density dependence of the symmetry energy, which, in turn, modifies the predictions for the maximum stellar mass. The scheme works well for D1M, and leads to a new parameter set, dubbed D1M⁎. In the neutron-star domain, D1M⁎predicts a maximal mass of two solar masses and global properties of the star in harmony with those obtained with the SLy4 Skyrme interaction. By means of a set of selected calculations in finite nuclei, we check that D1M⁎performs comparably well to D1M in several aspects of nuclear structure in nucleiThe work of LMR was supported by Spanish Ministry of Economy and Competitiveness (MINECO) Grants No.FPA2015-65929-P and FIS2015-63770-P. C.G., M.C., and X.V. were partially sup-ported by Grant FIS2014-54672-P from MINECO and FEDER, Grant 2014SGR-401 from Generalitat de Catalunya, and Project MDM-2014-0369 of ICCUB (Unidad de Excelencia María de Maeztu) from MINECO. C.G. also acknowledges Grant BES-2015-074210 from MINEC