Radius Of Star Research Articles

HAZMAT. IX. An Analysis of the UV and X-Ray Evolution of Low-mass Stars in the Era of Gaia

Low-mass stars (≤1 M ⊙) are some of the best candidates for hosting planets with detectable life because of these stars’ long lifetimes and relative ratios of planet to star mass and radius. An important aspect of these stars to consider is the amount of ultraviolet (UV) and X-ray radiation incident on planets in the habitable zones due to the ability of UV and X-ray radiation to alter the chemistry and evolution of planetary atmospheres. In this work, we build on the results of the HAZMAT I and HAZMAT III M-star studies to determine the intrinsic UV and X-ray flux evolution with age for M stars using Gaia parallactic distances. We then compare these results to the intrinsic fluxes of K stars adapted from HAZMAT V. We find that although the intrinsic M-star UV flux is 10–100 times lower than that of K stars, the UV fluxes in their respective habitable zone are similar. However, the habitable zone X-ray flux evolutions are slightly more distinguishable with a factor of 3–15 times larger X-ray flux for late M stars than for K stars. These results suggest that there may not be a K-dwarf advantage compared to M stars in the UV, but one may still exist in the X-ray.

Shear and interface modes in neutron stars with pasta structures

We carefully examine the shear and interface modes, which are excited due to the presence of crust elasticity, in neutron stars with pasta structures, adopting the relativistic Cowling approximation. We find that the shear modes are independent of the presence of the cylindrical-hole and spherical-hole nuclei at least up to a few kilohertz, while the interface modes strongly depend on the presence of the cylindrical-hole and spherical-hole nuclei. In addition, we find empirical relations for the interface mode frequencies multiplied by the stellar mass and for the shear mode frequencies multiplied by the stellar radius. These relations are expressed as a function of the stellar compactness almost independently of the stiffness in a higher-density region inside the neutron star, once one selects the crust equation of state. Thus, if one would simultaneously observe the shear and interface modes from a neutron star, one might extract the neutron star mass and radius with the help of the constraint on the crust stiffness obtained from terrestrial experiments.

Compact Stars in the vBag Model and Its f-Mode Oscillations

Electromagnetic (EM) observations and gravitational wave (GW) measurements enable us to determine the mass and radius of neutron stars (NSs) and their tidal deformability, respectively. These parameters offer valuable insights into the properties of dense matter in NSs. In this study, the vector-interaction-enhanced bag model (vBag model) is employed to investigate strange and hybrid stars’ properties. The parameters of the vBag model are constrained using multi-messenger observations, revealing that strange stars are incompatible with current observations. In contrast, hybrid stars can exhibit a substantial mixed phase region and a thin hadronic shell. Furthermore, we present the frequencies and damping time of fundamental mode (f-mode) oscillations of hybrid stars and test their universal relations with compactness and tidal deformability. The findings indicate that the presence of mixed phase components leads to larger frequencies and shorter damping time of the f-mode oscillation of hybrid stars, and the softer equation of state (EoS) affects this behavior more significantly. The universal relations of hybrid stars in the vBag model can be described by fourth-order/seventh-order polynomials, which do not break the previous results.

Constraints on the Nuclear Symmetry Energy from Experiments, Theory and Observations

Nuclear mass measurements and neutron matter theory tightly constrain the nuclear symmetry energy parameters J, L, Ksym and Qsym . Corroboration of these constraints on J and L can be found from measurements of the neutron skin thicknesses and dipole polarizabilities of neutron-rich nuclei. The experimental constraints on these parameters are compared with those obtained from consideration of astrophysical measurements of the neutron star radius, which we show is highly correlated with L. Attention is aimed at the recent PREX and CREX neutron skin measurements from Jefferson Lab, NICER neutron star radius measurements, and a new interpretation of the GW170817 tidal deformability measurement. We find joint satisfaction of PREX and CREX gives J = 32.2 ± 1.7 MeV and L = 52.9 ± 13.2 MeV, in excellent agreement with neutron matter predictions of J = 32.0±1.1 MeV and L = 51.9±7.9 MeV.

The value-added catalogue of ASAS-SN eclipsing binaries – III. Masses and radii of Gaia spectroscopic binaries

ABSTRACT Masses and radii of stars can be derived by combining eclipsing binary light curves with spectroscopic orbits. In our previous work, we modelled the All-Sky Automated Survey for Supernovae (ASAS-SN) light curves of more than 30 000 detached eclipsing binaries using phoebe. Here, we combine our results with 128 double-lined spectroscopic orbits from Gaia Data Release 3. We also visually inspect ASAS-SN light curves of the Gaia double-lined spectroscopic binaries on the lower main sequence and the giant branch, adding 11 binaries to our sample. We find that only 50 per cent of systems have Gaia periods and eccentricities consistent with the ASAS-SN values. We use emcee and phoebe to determine masses and radii for a total of 122 stars with median fractional uncertainties of 7.9 per cent and 6.3 per cent, respectively.

Properties of quark-matter cores in massive hybrid stars

Using the constraints from astrophysical observations and heavy-ion experiments, we investigate the equation of state (EOS) of hybrid star matter and the properties of quark-matter cores in hybrid stars. The quark matter interactions in hybrid stars are described based on 3-flavor Nambu-Jona-Lasinio model with various vector and vector-isovector coupling constants. In this work, we find that the hybrid star matter EOS is more sensitive to the strength of the vector interaction, and the EOS becomes stiffer with increasing vector strength $R_V$. The vector-isovector interaction characterized by the coupling constant $R_{IV}$ make main contribution to the hadron-quark mixed phase. Meanwhile, we note that a step change of both the sound velocity and the polytropic index $\gamma$ occurs in the hadron-quark phase transition, and it is restored with the decrease of nucleon and lepton degrees of freedom in the high density quark phase. Although the coupling constants increase the hybrid star maximum mass up to $2.08M_{\odot}$, they also decrease the mass and radius of the quark core and the mixed core. With different quark coupling constants, we also find that the maximum mass and radius of the quark matter core in a stable hybrid star can reach $0.80M_{\odot}$ and 6.95 km, which are close to half of the maximum mass and radius of the complete star. However, properties of quark matter have no effect on the $M = 1.4M_{\odot}$ hybrid star as a result of no quark matter inner core, which can also be confirmed by the criterion of the polytropic index, and thus our results also indicate that the quark interactions have no effect on the tidal deformability $\Lambda_{1.4}$ of hybrid stars.

A Deep Learning Approach to Extracting Nuclear Matter Properties from Neutron Star Observations

Understanding the equation of state of dense neutron-rich matter remains a major challenge in modern physics and astrophysics. Neutron star observations from electromagnetic and gravitational wave spectra provide critical insights into the behavior of dense neutron-rich matter. The next generation of telescopes and gravitational wave detectors will offer even more detailed neutron-star observations. Employing deep learning techniques to map neutron star mass and radius observations to the equation of state allows for its accurate and reliable determination. This work demonstrates the feasibility of using deep learning to extract the equation of state directly from observations of neutron stars, and to also obtain related nuclear matter properties such as the slope, curvature, and skewness of nuclear symmetry energy at saturation density. Most importantly, it shows that this deep learning approach is able to reconstruct realistic equations of state and deduce realistic nuclear matter properties. This highlights the potential of artificial neural networks in providing a reliable and efficient means to extract crucial information about the equation of state and related properties of dense neutron-rich matter in the era of multi-messenger astrophysics.

Systematic analysis of the impacts of symmetry energy parameters on neutron star properties

The impacts of various symmetry energy parameters on the properties of neutron stars (NSs) have been recently investigated, and the outcomes are at variance, as summarized in Table III of Phys. Rev. D 106, 063005 (2022). We have systematically analyzed the correlations of slope and curvature parameters of symmetry energy at the saturation density ($\rho_0=0.16 \text{fm}^{-3}$) with the tidal deformability and stellar radius of non-spinning neutron stars in the mass range of $1.2 - 1.6 M_\odot$ using a large set of minimally constrained equations of state (EoSs). The EoSs at low densities correspond to the nucleonic matter and are constrained by empirical ranges of a few low-order nuclear matter parameters from the finite nuclei data and the pure neutron matter EoS from chiral effective field theory. The EoSs at high densities ($\rho > 1.5 - 2\rho_0$) are obtained by a parametric form for the speed of sound that satisfies the causality condition. Several factors affecting the correlations between the NS properties and the individual symmetry energy parameters usually encountered in the literature are considered. These correlations are quite sensitive to the choice of the distributions of symmetry energy parameters and their interdependence. But, variations of NS properties with the pressure of $\beta -$ equilibrated matter at twice the saturation density remain quite robust which maybe due to the fact that the pressure depends on the combination of multiple nuclear matter parameters that describe the symmetric nuclear matter as well as the density dependence of the symmetry energy. Our results are practically insensitive to the behavior of EoS at high densities.

Bayesian inference of neutron-star observables based on effective nuclear interactions

Based on the Skyrme-Hartree-Fock model (SHF) as well as its extension [the Korea-IBS-Daegu-SKKU (KIDS) model] and the relativistic mean-field (RMF) model, we have studied the constraints on the parameters of the nuclear matter equation of state (EOS) from adopted astrophysical observables using a Bayesian approach. While the masses and radii of neutron stars generally favor a stiff isoscalar EOS and a moderately soft nuclear symmetry energy, model dependence on the constraints is observed and mostly originates from the incorporation of higher-order EOS parameters and differences between relativistic and nonrelativistic models. At twice saturation density, the value of the symmetry energy is constrained to be ${48}_{\ensuremath{-}11}^{+15}\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ in the standard SHF model, ${48}_{\ensuremath{-}15}^{+8}\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ in the KIDS model, and ${48}_{\ensuremath{-}6}^{+5}\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ in the RMF model, around their maximum a posteriori values within $68%$ confidence intervals. Our study helps to obtain a robust constraint on nuclear matter EOS, and, meanwhile, to understand the model dependence of the results.

Nuclear Physics with Gravitational Waves from Neutron Stars Disrupted by Black Holes

Gravitational waves from neutron star–black hole (NSBH) mergers that undergo tidal disruption provide a potential avenue to study the equation of state of neutron stars and hence the behavior of matter at its most extreme densities. We present a phenomenological model for the gravitational-wave signature of tidal disruption, which allows us to measure the disruption time. We carry out a study with mock data, assuming an optimistically nearby NSBH event with parameters tuned for measuring the tidal disruption. We show that a two-detector network of 40 km Cosmic Explorer instruments can measure the time of disruption with a precision of ≈0.5 ms, which corresponds to a constraint on the neutron star radius of ≈0.7 km (90% credibility). This radius constraint is wider than the constraint obtained by measuring the tidal deformability of the neutron star of the same system during the inspiral. Moreover, the neutron star radius is likely to be more tightly constrained using binary neutron star mergers. While NSBH mergers are important for the information they provide about stellar and binary astrophysics, they are unlikely to provide insights into nuclear physics beyond what we will already know from binary neutron star mergers.

Structural properties of anisotropic stars in modified teleparallel gravity: a brief study via an embedding approach

In this paper, we attempt to construct the anisotropic solution for compact stellar configurations using the observed mass and radius of compact stars from the literature under the influence of Rastall Teleparallel gravity. To investigate the crucial elements of spherically symmetric metric space, we employed the embedding class one spacetime paradigm with Karmarkar’s condition. The field equations have been computed under the gravitational action of Rastall Teleparallel gravity. However, the unknown constants were evaluated via junction conditions using the Schwarzschild metric as the outer geometry. The compact stars analysis’s crucial physical and mathematical requirements are all admitted and shared by the model, which is physically viable and supports the emergence of novel realistic stellar configurations in Rastall Teleparallel gravity. We fix the parameters of our model to compare with three compact stars (LMC X-4, Cen X-3, and EXO 1785-248) and find that it can be regular, robust, and stable.

Relativistic X-ray reflection and photoionized absorption in the neutron star low-mass X-ray binary GX 13+1

ABSTRACT We analysed a dedicated NuSTAR observation of the neutron star low-mass X-ray binary Z-source GX 13+1 to study the timing and spectral properties of the source. From the colour–colour diagram, we conclude that during that observation the source transitioned from the normal branch to the flaring branch. We fitted the spectra of the source in each branch with a model consisting of an accretion disc, a Comptonized blackbody, relativistic reflection (relxillNS), and photoionized absorption (warmabs). Thanks to the combination of the large effective area and good energy resolution of NuSTAR at high energies, we found evidence of relativistic reflection in both the Fe K line profile and the Compton hump present in the 10–25 keV energy range. The inner disc radius is Rin ≲ 9.6 rg , which allowed us to further constrain the magnetic field strength to B ≲ 1.8 × 108 G. We also found evidence for the presence of a hot wind leading to photoionized absorption of Fe and Ni, with a Ni overabundance of ∼6 times solar. From the spectral fits, we find that the distance between the ionizing source and the slab of ionized absorbing material is ∼4–40 × 105 km. We also found that the width of the boundary layer extends ∼3 km above the surface of a neutron star, which yielded a neutron star radius RNS ≲ 16 km. The scenario inferred from the spectral modelling becomes self-consistent only for high electron densities in the accretion disc, ne ∼ 1022 − 1023 cm−3, as expected for a Shakura–Sunyaev disc, and significantly above the densities provided by relxillNS models. These results have implications for our understanding of the physical conditions in GX 13+1.

Rapidly rotating neutron stars in f(R,T)=R+2 lambda T gravity

In this work, we study the influence of f(R, T) gravity on rapidly rotating neutron stars. First we discuss the main aspects of this modified theory of gravity where the gravitational Lagrangian is an arbitrary function of the Ricci scalar R and of the trace of the energy–momentum tensor T. Then we present the basic equations for neutron stars including the equations of state used in the present work to describe the hadronic matter. Some physical quantities of interest are calculated such as mass–radius relations, moments of inertia, angular momentum, and compactness. By considering four different rotation regimes, we obtain results that indicate substantial modifications in the physical properties of neutron stars in f(R, T) gravity when compared to those in the context of general relativity. In particular, the mass–radius relation for sequences of stars indicates that f(R, T) gravity increases the mass and the equatorial radius of the neutron stars for stars rotating with an angular velocity smaller than Kepler limit.

Physical Parameters of W UMa Type Contact Binaries and Their Stability of Mass Transfer

In this study, we determined the physical parameters of W UMa type contact binaries and their stability of mass transfer with different stellar mass ranges over a broad space by applying the basic dynamical evolution equations of the W UMa type contact binaries using accretor and donor masses between 0.079 and 2.79 M ⊙. In these systems, we have studied the three subclasses of W UMa systems of A-, B- and W-type contact binaries using the initial and final mass ranges and we investigated different stellar and orbital parameters for the subclasses of W UMa systems. We examined the stability of the W UMa type contact binaries using the orbital parameters such as critical mass ratio, Roche lobe radius of the donor star and mass ratio of these systems. Thus, we computed the observed and calculated physical parameters of A-, B- and W-type W UMa systems. Moreover, we determined the combined and color temperatures to classify the three subclasses of the systems. Also, we presented the result of the internal stellar structure and evolution of W UMa type contact binaries by using the polytropic model.

Low-energy nuclear physics and global neutron star properties

We address the question of the role of low-energy nuclear physics data in constraining neutron star global properties, e.g., masses, radii, angular momentum, and tidal deformability, in the absence of a phase transition in dense matter. To do so, we assess the capacity of 415 relativistic mean field and nonrelativistic Skyrme-type interactions to reproduce the ground state binding energies, the charge radii, and the giant monopole resonances of a set of spherical nuclei. The interactions are classified according to their ability to describe these characteristics, and we show that a tight correlation between the symmetry energy and its slope is obtained provided that $N=Z$ and $N\ensuremath{\ne}Z$ nuclei are described with the same accuracy (mainly driven by the charge radius data). By additionally imposing the constraints from isobaric analog states and neutron skin radius in $^{208}\mathrm{Pb}$, we obtain the following estimates: ${E}_{\mathrm{sym},2}=31.8\ifmmode\pm\else\textpm\fi{}0.7$ MeV and ${L}_{\mathrm{sym},2}=58.1\ifmmode\pm\else\textpm\fi{}9.0$ MeV. We then analyze predictions of neutron star properties and we find that the $1.4{M}_{\ensuremath{\bigodot}}$ neutron star (NS) radius lies between 12 and 14 km for the ``better'' nuclear interactions. We show that (i) the better reproduction of low-energy nuclear physics data by the nuclear models only weakly impacts the global properties of canonical mass neutron stars and (ii) the experimental constraint on the symmetry energy is the most effective one for reducing the uncertainties in NS matter. However, since the density region where constraints are required are well above densities in finite nuclei, the largest uncertainty originates from the density dependence of the energy density functional (EDF), which remains largely unknown.

Analogy of the interior Schwarzschild metric from transformation optics.

In this paper, we make an analogy of the interior Schwarzschild metric from transformation optics (we call the method transformation cosmology). It is shown that a simple refractive index profile is sufficient to capture the behavior of the metric to bend light. There is a critical value of the ratio of the radius of the massive star to the Schwarzschild radius, which is exactly related to the condition of collapsing into a black hole. We demonstrate the light bending effect for three cases from numerical simulations as well. Especially, we find that a point source at the photon sphere will form an image inside the star approximately, and the equivalent lens is like Maxwell's fish-eye lens. This work will help us to explore the phenomena of massive stars with laboratory optical tools.

Static neutron stars perspective of quadratic and induced inflationary attractor scalar-tensor theories

This study focuses on the static neutron star perspective for two types of cosmological inflationary attractor theories, namely the induced inflationary attractors and the quadratic inflationary attractors. The two cosmological models can be discriminated cosmologically, since one of the two does not provide a viable inflationary phenomenology, thus in this paper we investigate the predictions of these theories for static neutron stars, mainly focusing on the mass and radii of neutron stars. We aim to demonstrate that although the models have different inflationary phenomenology, the neutron star phenomenology predictions of the two models are quite similar. We solve numerically the Tolman–Oppenheimer–Volkoff equations in the Einstein frame using a powerful double shooting numerical technique, and after deriving the mass-radius graphs for three types of polytropic equations of state, we derive the Jordan frame mass and radii. With regard the equations of state we use polytropic equation of state with the small density part being either the Wiringa–Fiks–Fabrocini, the Akmal–Pandharipande–Ravenhall or the intermediate stiffness equation of state Skyrme–Lyon (SLy). The results of our models will be confronted with quite stringent recently developed constraints on the radius of neutron stars with specific mass. As we show, the only equation of state which provides results compatible with the constraints is the SLy, for both the quadratic and induced inflation attractors. Thus nowadays, scalar-tensor descriptions of neutron stars are quite scrutinized due to the growing number of constraining observations, which eventually may also constrain theories of inflation.

Empirical neutron star mass formula based on experimental observables

We derive the empirical formulae expressing the mass and gravitational redshift of a neutron star, whose central density is less than threefold the nuclear saturation density, as a function of the neutron-skin thickness or the dipole polarizability of $ {}^{208} \mathrm{Pb} $ or $ {}^{132} \mathrm{Sn} $, especially focusing on the 8 Skyrme-type effective interactions. The neutron star mass and its gravitational redshift can be estimated within $ \approx 10 \, \% $ errors with our formulae, while the neutron star radius is also expected within a few $\%$ errors by combining the derived formulae. Owing to the resultant empirical formulae, we find that the neutron star mass and radius are more sensitive to the neutron-skin thickness of $ {}^{208} \mathrm{Pb} $ than the dipole polarizability of $ {}^{208} \mathrm{Pb} $ or $ {}^{132} \mathrm{Sn} $.

Constraining free parameters of a color superconducting nonlocal Nambu–Jona-Lasinio model using Bayesian analysis of neutron stars mass and radius measurements

We provide a systematic study of hybrid neutron star equations of state (EOS) consisting of a relativistic density functional for the hadronic phase and a covariant nonlocal Nambu--Jona-Lasinio (nlNJL) model to describe the color superconducting quark matter phase. Changing the values of the two free parameters, the dimensionless vector and diquark coupling strengths ${\ensuremath{\eta}}_{V}$ and ${\ensuremath{\eta}}_{D}$ results in a set of EOS with varying stiffness and deconfinement onset. The favorable parameters are obtained from a systematic Bayesian analysis for which the multimessenger constraint on the neutron star radius at $14{M}_{\ensuremath{\bigodot}}$ and the combined mass-radius constraint for PSR $\mathrm{J}0740+6620$ from NICER experiment are used as the constraints. Additionally, the transition from hadronic matter to deconfined quark matter is constrained to occur above nuclear saturation density. Hybrid stars modeled with these favorable parameters are compatible with the NICER results for the radius of the highest known mass neutron star, PSR $\mathrm{J}0740+6620$. Three new observations interesting for neutron star phenomenology are reported: (i) we show that the constant sound speed (CSS) EOS provides an excellent fit to that of the nlNJL model which implies the squared speed of sound at high densities to be about 0.5 for the optimized parameters; (ii) we give a simple functional form for the mapping between the parameter spaces of these two models valid for the whole range of relevant chemical potentials and (iii) we observe that the special point property of hybrid EOS based on CSS quark matter generalizes to a set of lines consisting of special points when two EOS parameters are varied instead of one. A lower limit for the maximum mass of hybrid stars as a function of the vector coupling strength is obtained.

Strange quark star models from Rastall gravity

We study the possible existence of strange matter in the interior of compact stars in Rastall gravity. The main feature of the Rastall gravity is the covariant derivative of the energy–momentum tensor does not vanish and depends on the curvature R and a free parameter η. We consider the MIT bag model in the present work and numerically solve the modified Tolman–Oppenheimer–Volkoff (TOV) equations. We investigate the effect of the Rastall parameter η on the mass–radius and the mass-central energy density relation of quark stars. From the quark star masses and radii obtained, we conclude that η has significant consequences on the structure of stellar objects.