EVOLUTIONARY STATUS AND INTERNAL STRUCTURE OF μ CASSIOPEIAE

After publication of Miguel et al. (2016), we found an error in the calculation of Jupiter internal structure when using REOS3b-H and REOS3sc-H equations of state (EOSs). The lowest pressure in those tables (see appendix in Miguel et al. 2016) was P = 31.623 bars, while our calculations of Jupiter's internal structure started at P = 1 bar. This difference lead to an extrapo-lation of the EOS of hydrogen, which caused an overestimation of Jupiter's interior calculations. We fixed this problem by using the SCvH-H EOS (Saumon et al. 1995) for pressures lower than 6 kbar and merged it with REOS3b-H and REOS3sc-H (correspondingly) for higher pressures. There was also a small offset of ∼2% in the specific entropy at low pressures (P < 1 kbar) between the REOS3b and REOS3sc tables with respect to the SCvH table, caused by a small difference in the s 0 parameter chosen to calculate the specific entropy. In Miguel et al. (2016), this parameter was determined calculating s − s 0 from equation 14 at T = 29 500 K and ρ = 0.036 g cc −1 and then using the value of s in SCvH EOS at the same conditions. This temperature was much higher than the border condition in our interior models (at 165 K) and the intrinsic differences between the tables at those conditions lead to the offset in the specific entropy. In order to fix this issue, we performed new calculations at T = 150 K and ρ = 0.3 g cc −1 , which corrected the offset in S between the EOSs. We also improved our method for calculating the gravity harmonics. Following Nettelmann (2017) and using results calculated with the more accurate CMS method (Hubbard 2013) as a comparison, we corrected the coefficients of the theory of figures of fourth order and improved the numerical handling of density discontinuities. With these improvements, the results agree with Nettelmann et al. (2012) and Hubbard & Militzer (2016). The differences from previous calculations are of the Full appendix tables are only available at CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/618/C2 order of 6 × 10 −7 in J 2 , 1.4 × 10 −8 in J 4 , 2 × 10 −6 in J 6 and 6 × 10 −8 in J 8. We thus ran our simulations again and show the corrected figures below. We also include the corrected EOS tables (see Appendix A). For comparison purposes, the MH13+SCvH table for pure hydrogen was also recalculated by accounting for the entropy of mixing. Along a fixed adiabat, Jupiter's internal temperature is found to be 10% smaller with the new REOS3b table compared to the previous calculation. Nevertheless, the trend remains the same, with REOS3b models being the warmest and MH13 ones the coldest. The core masses found with REOS3b are now 5 < M core < 16 M Earth , i.e., the lower limit is about 2 M Earth smaller than previous calculations. The mass of heavy elements found with REOS3b is significantly lower than previously, being now 13 < M Z < 27 M Earth instead of 20 − 40 M Earth previously. The space of solutions of M core and M Z found with MH13 is almost the same as before with 1 < M Z < 8 M Earth and 10 < M core < 17 M Earth compared with our previous estimations 1-7 M Earth and 11-17 M Earth , correspondingly. Due to the changes in the calculation of gravity harmonics, the results using SCvH also changed. The core masses remain unchanged but M Z changed from 18-44 M Earth to 23-36 M Earth. The new results still show that the internal structure of Jupiter strongly depends on the accuracy of the EOSs. The differences between the MH13 and REOS3 solutions remain significant, in particular in terms of the total mass of heavy elements in the envelope. The location at which helium rain occurs still controls to a large extent the inferred core mass. The main conclusions of the paper therefore remain unchanged. We wish to apologise for this oversight. We thank Burkhard Militzer for noticing the EOS issue. We also thank William B. Hubbard and Nadine Nettelmann who shared codes and algorithms that allowed an accurate comparison of gravitational moments. Article published by EDP Sciences C2, page 1 of 6

view Abstract Citations (12) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Insensitivity of Solar p-Mode Frequencies to Changes in the Helium Abundance Guenther, D. B. ; Sarajedini, Ataollah Abstract P-mode oscillation spectra (l = 0-4; n = 12-30) were calculated for three solar models with helium mass fractions Y = 0.230, 0.235, and 0.240. The solar models were tuned to have the Sun's radius and luminosity by adjusting both the age and the ratio of the mixing length to pressure scale height parameter. The models were identically constrained in all other respects. A 4 percent change in the mass fraction of helium produces less than a 0.1 percent change in the frequencies of the low degree p-modes. This result implies that it will be very difficult to determine the helium abundance of the sun directly from the p-mode oscillation spectrum since the frequencies of the modes are relatively insensitive to changes in the helium abundance. Publication: The Astrophysical Journal Pub Date: April 1988 DOI: 10.1086/166256 Bibcode: 1988ApJ...327..993G Keywords: Abundance; Acoustic Velocity; Helium; Molecular Weight; Solar Interior; Solar Oscillations; Equations Of State; Heavy Elements; Perturbation Theory; Stellar Evolution; Vibrational Spectra; Solar Physics; SUN: ABUNDANCES; SUN: INTERIOR; SUN: OSCILLATIONS full text sources ADS |

Internal structure and macroscopic properties of neutron stars are strongly correlated with the equation of state (EOS) of dense matter, while the EOS remains exceedingly uncertain especially at high densities. The observed massive neutron star with gravitation mass of $\ensuremath{\approx}2\phantom{\rule{4pt}{0ex}}{M}_{\ensuremath{\bigodot}}$ have imposed strong constraints on the EOS of super-dense matter. The upper limit of the speed of sound, as a crucial quantity to characterize the stiffness of the EOS, has significant influence on the maximum mass of a neutron star. The main propose of this work is to probe the possible lower bound for the upper limit of the speed of sound, where being coincident with the observations for massive neutron stars is considered. By employing a set of heterogeneous EOSs and through a constructed EOS model to describe the high-density part of the employed EOSs, we conclude that the upper limit of the speed of sound can be as low as 0.5386 $c$ (where $c$ is the speed of light). Furthermore, to eliminate the effect of the model dependence for the EOSs, we adopt a set of parameterized and model-independent EOSs to investigate this problem. As a result, a lower bound 0.5749 $c$ of the upper limit of the speed of sound is obtained, which is very close to the free-quark-matter's speed of sound, $\frac{1}{\sqrt{3}}c$. In addition, we semiempirically analyze the characteristics of the profile of neutron star $M\text{\ensuremath{-}}R$ relations and find out that the profiles of $M\text{\ensuremath{-}}R$ relations mainly depend on the speed of sound of the central density of neutron star sequences in the mass range around $0.3\phantom{\rule{0.28em}{0ex}}\text{to}\phantom{\rule{0.28em}{0ex}}1\phantom{\rule{0.16em}{0ex}}{M}_{\ensuremath{\bigodot}}$. However, the $M\text{\ensuremath{-}}R$ profile also can be explained by the universal relation proposed by Lattimer et al. Astroph. J. 550, 426 (2001), where the case with extremely soft EOS in ${\ensuremath{\rho}}_{0}\phantom{\rule{0.28em}{0ex}}\text{to}\phantom{\rule{0.28em}{0ex}}2{\ensuremath{\rho}}_{0}$ should be excluded.

Saturn layered structure and homogeneous evolution models with different EOSs

We consider the internal structure and the physical properties of specific\nclasses of neutron, quark and Bose-Einstein Condensate stars in the hybrid\nmetric-Palatini gravity theory, which is a combination of the metric and\nPalatini $f(R)$ formalisms. The theory is very successful in accounting for the\nobserved phenomenology, since it unifies local constraints at the Solar System\nlevel and the late-time cosmic acceleration, even if the scalar field is very\nlight. We derive the equilibrium equations for a spherically symmetric\nconfiguration (mass continuity and Tolman-Oppenheimer-Volkoff) in the framework\nof hybrid metric-Palatini theory, and we investigate their solutions\nnumerically for different equations of state of neutron and quark matter, by\nadopting for the scalar field potential a Higgs-type form. Stellar models,\ndescribed by the stiff fluid, radiation-like, the bag model and the\nBose-Einstein Condensate equations of state are explicitly constructed in both\nGeneral Relativity and hybrid metric-Palatini gravity, thus allowing an in\ndepth comparison between the predictions of these two gravitational theories.\nAs a general result it turns out that for all the considered equations of\nstate, hybrid metric-Palatini gravity stars are more massive than their general\nrelativistic counterparts. Furthermore, two classes of stellar models\ncorresponding to fixed forms of the scalar field are also investigated.\nInterestingly enough, in the case of a constant scalar field the equation of\nstate of the matter takes the form of the bag model equation of state\ndescribing quark matter. As a possible astrophysical application of the\nobtained results we suggest that stellar mass black holes, with masses in the\nrange of $3.8M_{\\odot}$ and $6M_{\\odot}$, respectively, could be in fact hybrid\nmetric-Palatini gravity neutron or quark stars.\n

Planetary interior models rely on the thermodynamic properties of the used materials. Equations of states (EOSs) are key ingredients to compute internal structures, as they link the pressure and density profiles, and leave a unique solution satisfying all equations describing the interior of the planet. Often, when thermodynamic data are lacking, the formulation of EOSs allow extrapolation in both pressure and temperature. The effect of temperature on EOSs is often minor, implying that models of isothermal planets provide consistent results. This approach meets limitations in the case of fluids (liquids, gases and supercritical fluids), whose properties are very sensitive to variations in temperature. Here we propose a way to compute the relevant thermodynamic parameters in supercritical water from the most recent EOSs, in order to compute the internal structures of irradiated ocean planets, coupled with a 1D convective-radiative atmospheric model. Our results allow a better understanding of the diversity of observed sub-Neptunes, linking their internal structure to formation conditions.

A novel approach is proposed for solving the problem of the overestimation of the liquid–liquid equilibrium (LLE) range in mixtures typically associated with the use of equations of state (EOS) of the van der Waals type. This approach modifies the internal EOS structure by combining the van der Waals and the Dieterici forms. It advantageously uses the drawback of the Dieterici form, which strongly underestimates the LLE range. Thus, the new EOS is capable of generating an appropriate balance for the representation of vapor–liquid equilibria (VLE) and LLE critical data and therefore represents a major improvement in comparison with typical van der Waals–type EOSs. In addition, it gives accurate representation of the Joule–Thomson inversion curve and predicts critical data for nonpolar mixtures without any binary parameters. For polar systems, the novel EOS predicts critical data for complete homologous series of mixtures using a pair of binary parameters evaluated from a single system. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Context. The interpretation of stellar pulsations in terms of internal structure depends on the knowledge of the fundamental stellar parameters. Long-base interferometers permit us to determine very accurate stellar radii, which are independent constraints for stellar models that help us to locate the star in the HR diagram. Aims: Using a direct interferometric determination of the angular diameter and advanced three-dimensional (3D) modeling, we derive the radius of the CoRoT target HD 49933 and reduce the global stellar parameter space compatible with seismic data. Methods: The VEGA/CHARA spectro-interferometer is used to measure the angular diameter of the star. A 3D radiative hydrodynamical simulation of the surface is performed to compute the limb darkening and derive a reliable diameter from visibility curves. The other fundamental stellar parameters (mass, age, and Teff) are found by fitting the large and small p-mode frequency separations using a stellar evolution model that includes microscopic diffusion. Results: We obtain a limb-darkened angular diameter of {\theta}LD = 0.445 \pm 0.012 mas. With the Hipparcos parallax, we obtain a radius of R = 1.42 \pm 0.04 Rsun. The corresponding stellar evolution model that fits both large and small frequency separations has a mass of 1.20 \pm 0.08 Msun and an age of 2.7 Gy. The atmospheric parameters are Teff = 6640 \pm 100 K, log g = 4.21 \pm 0.14, and [Fe/H] = -0.38.

A systematic approach to high-fidelity modeling and efficient simulation of supercritical fluid mixing and combustion

Mass–radius curve for extrasolar Earth-like planets and ocean planets

We contrast the possibility of inflation starting (a) from the universe's inception or (b) from an earlier noninflationary state. Neither case is ideal since (a) assumes that quantum mechanical reasoning is straightforwardly applicable to the early universe, while case (b) requires that a singularity still be present. Further, in agreement with Vachaspati and Trodden case (b) can only solve the horizon problem if the noninflationary phase has an equation of state $\ensuremath{\gamma}&lt;4/3,$ thereby excluding radiation or massless scalar field dominated cases. Other alternative models, such as the smooth branch change in the pre-big-bang model, have related problems of requiring homogeneity over noncausally connected large scales.

The structure of neutron stars is investigated in the context of a scalar-tensor theory of gravity with variable Brans-Dicke parameter ω(Φ). Neutron star models are constructed using the Pandharipande (hyperon) equation of state and an equation of state that maximizes the mass for various values of the variability parameter α= 2ω'(Φ)/[3+2ω(Φ)] 2 . It is shown that the neutron stars are more compact and less massive than their counterparts in general relativity and standard Brans-Dicke theory

Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of general relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO–Virgo–KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering single-harmonic and dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the single-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical spin-down limit. The lowest upper limit on the amplitude is 6.4 × 10 −27 for the young energetic pulsar J0537−6910, while the lowest constraint on the ellipticity is 8.8 × 10 −9 for the bright nearby millisecond pulsar J0437−4715. Additionally, for a subset of 16 targets, we performed a narrowband search that is more robust regarding the emission model, with no evidence of a signal. We also found no evidence of nonstandard polarizations as predicted by the Brans–Dicke theory.

Ganymede׳s internal structure including thermodynamics of magnesium sulfate oceans in contact with ice

To study properties of magnetohydrodynamic (MHD) convection and resultant dynamo activities in proto-neutron stars (PNSs), we construct a “PNS in a box” simulation model and solve the compressible MHD equation coupled with a nuclear equation of state (EOS) and simplified leptonic transport. As a demonstration, we apply it to two types of PNS model with different internal structures: a fully convective model and a spherical-shell convection model. By varying the spin rate of the models, the rotational dependence of convection and the dynamo that operate inside the PNS is investigated. We find that, as a consequence of turbulent transport by rotating stratified convection, large-scale structures of flow and thermodynamic fields are developed in all models. Depending on the spin rate and the depth of the convection zone, various profiles of the large-scale structures are obtained, which can be physically understood as steady-state solutions to the “mean-field” equation of motion. Additionally to those hydrodynamic structures, a large-scale magnetic component of  ( 10 15 ) G is also spontaneously organized in disordered tangled magnetic fields in all models. The higher the spin rate, the stronger the large-scale magnetic component grows. Intriguingly, as an overall trend, the fully convective models have a stronger large-scale magnetic component than that in the spherical-shell convection models. The deeper the convection zone extends, the larger the size of the convective eddies becomes. As a result, rotationally constrained convection seems to be more easily achieved in the fully convective model, resulting in a higher efficiency of the large-scale dynamo there. To gain a better understanding of the origin of the diversity of a neutron star’s magnetic field, we need to study the PNS dynamo in a wider parameter range.