Estimating the EOS from the measurement of NS radii with 5% accuracy

Observations of heavy (${simeq}2,M_odot$) neutron stars in addition to the recent measurement of tidal deformability from the binary neutron-star merger GW170817, place interesting constraints on theories of dense matter. Current and future observatories, such as the NICER and ATHENA are expected to collect information on the global parameters of neutron stars, namely masses and radii, with the accuracy of a few percent. Such accuracy will allow for precise comparisons of measurements to models of compact objects. Here we investigate how the measurement accuracy of the NICER and ATHENA missions will improve our understanding of the dense-matter interior of neutron stars. We compare global parameters of stellar configurations obtained using three different equations of state: a reference (SLy4 EOS) and two piecewise polytropes manufactured to produce mass-radius relations indistinguishable from the observational point of view i.e. within the predicted error of the radius measurement. We assume observational errors on the radius determination corresponding to the expected accuracies. The effect of rotation is examined using high-precision numerical relativity computations. Due to the fact that masses and rotational frequencies might be determined very precisely in the most optimistic scenario, only the influence of observational errors on the radius measurements is investigated. We show that ${pm}5%$ errors in radius measurement lead to ${sim}10%$ and ${sim}40%$ accuracy in central parameter estimation, for low-mass and high-mass neutron stars, respectively. Global parameters, such as oblateness and surface area, can be established with $8-10%$ accuracy, even if only compactness (instead of mass and radius) is measured. We also report on the range of tidal deformabilities corresponding to the estimated masses of GW170817, for the assumed uncertainty in radius.

Accurate ray tracing of realistic neutron star atmospheres for constraining their parameters

Thermal dominated X-ray spectra of neutron stars in quiescent transient X-ray binaries and neutron stars that undergo thermonuclear bursts are sensitive to mass and radius. The mass-radius relation of neutron stars depends on the equation of state that governs their interior. Constraining this relation accurately is thus of fundamental importance to understand the nature of dense matter. In this context we introduce a pipeline to calculate realistic model spectra of rotating neutron stars with hydrogen and helium atmospheres. An arbitrarily fast rotating neutron star with a given equation of state generates the spacetime in which the atmosphere emits radiation. We use the Lorene/nrotstar code to compute the spacetime numerically and the ATM24 code to solve the radiative transfer equations self-consistently. Emerging specific intensity spectra are then ray-traced through the neutron stars spacetime from the atmosphere to a distant observer with the Gyoto code. Here, we present and test our fully relativistic numerical pipeline. To discuss and illustrate the importance of realistic atmosphere models we compare our model spectra to simpler models like the commonly used isotropic color-corrected blackbody emission. We highlight the importance of considering realistic model-atmosphere spectra together with relativistic ray tracing to obtain accurate predictions. We also insist on the crucial impact of the stars rotation on the observables. Finally, we close a controversy that has been appearing in the literature in the recent years regarding the validity of the ATM24 code.

Consequences of a strong phase transition in the dense matter equation of state for the rotational evolution of neutron stars

We explore the implications of a strong first-order phase transition region in the dense matter equation of state in the interiors of rotating neutron stars, and the resulting creation of two disjoint families of neutron-star configurations (the so-called high-mass twins). We numerically obtained rotating, axisymmetric, and stationary stellar configurations in the framework of general relativity, and studied their global parameters and stability. The instability induced by the equation of state divides stable neutron star configurations into two disjoint families: neutron stars (second family) and hybrid stars (third family), with an overlapping region in mass, the high-mass twin-star region. These two regions are divided by an instability strip. Its existence has interesting astrophysical consequences for rotating neutron stars. We note that it provides a natural explanation for the rotational frequency cutoff in the observed distribution of neutron star spins, and for the apparent lack of back-bending in pulsar timing. It also straightforwardly enables a substantial energy release in a mini-collapse to another neutron-star configuration (core quake), or to a black hole.

Searching for gravitational waves from known pulsars at once and twice the spin frequency

The existence of a superfluid core in the interior of a rotating neutron star may have an influence on its gravitational wave emission. In addition to the usually-assumed pure quadrupole radiation with the gravitational wave frequency at twice the spin frequency, a frequency of rotation itself may also be present in the gravitational wave spectrum. We study the parameters of a general model for such emission, compare it with previously proposed, simpler models, discuss the feasibility of the recovery of the stellar parameters and carry out the Monte Carlo simulations to test the performance of our estimation method.

Parameters of rotating neutron stars with and without hyperons

The discovery of a 2 Msun neutron star provided a robust constraint for the theory of exotic dense matter, bringing into question the existence of strange baryons in the interiors of neutron stars. Although many theories fail to reproduce this observational result, several equations of state containing hyperons are consistent with it. We study global properties of stars using equations of state containing hyperons, and compare them to those without hyperons to find similarities, differences, and limits that can be compared with the astrophysical observations. Rotating, axisymmetric, and stationary stellar configurations in general relativity are obtained, and their global parameters are studied. Approximate formulae describing the behavior of the maximum and minimum stellar mass, compactness, surface redshifts, and moments of inertia as functions of spin frequency are provided. We also study the thin disk accretion and compare the spin-up evolution of stars with different moments of inertia.

Formation of millisecond pulsars - NS initial mass and EOS constraints

Recent measurement of a high millisecond pulsar mass (PSR J1614-2230, 1.97+-0.04 Msun) compared with the low mass of PSR J0751+1807 (1.26+-0.14 Msun) indicates a large span of masses of recycled pulsars and suggests a broad range of neutron stars masses at birth. We aim at reconstructing the pre-accretion masses for these pulsars while taking into account interaction of the magnetic field with a thin accretion disk, magnetic field decay and relativistic 2D solutions for stellar configurations for a set of equations of state. We briefly discuss the evolutionary scenarios leading to the formation of these neutron stars and study the influence of the equation of state.

Keplerian frequency of uniformly rotating neutron stars and quark stars

We calculate Keplerian (mass shedding) configurations of rigidly rotating neutron stars and quark stars with crusts. We check the validity of empirical formula for Keplerian frequency, f_K, proposed by Lattimer & Prakash, f_K(M)=C (M/M_sun)^1/2 (R/10km)^-3/2, where M is the (gravitational) mass of Keplerian configuration, R is the (circumferential) radius of the non-rotating configuration of the same gravitational mass, and C = 1.04 kHz. Numerical calculations are performed using precise 2-D codes based on the multi-domain spectral methods. We use a representative set of equations of state (EOSs) of neutron stars and quark stars. We show that the empirical formula for f_K(M) holds within a few percent for neutron stars with realistic EOSs, provided 0.5 M_sun < M < 0.9 M_max,stat, where M_max,stat is the maximum allowable mass of non-rotating neutron stars for an EOS, and C=C_NS=1.08 kHz. Similar precision is obtained for quark stars with 0.5 M_sun < M < 0.9 M_max,stat. For maximal crust masses we obtain C_QS = 1.15 kHz, and the value of C_QS is not very sensitive to the crust mass. All our Cs are significantly larger than the analytic value from the relativistic Roche model, C_Roche = 1.00 kHz. For 0.5 M_sun < M < 0.9 M_max,stat, the equatorial radius of Keplerian configuration of mass M, R_K(M), is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, R_K(M) = aR(M), with a_NS approx a_QS approx 1.44. The value of a_QS is very weakly dependent on the mass of the crust of the quark star. Both as are smaller than the analytic value a_Roche = 1.5 from the relativistic Roche model.