Stellar Core Research Articles

Can Protostellar Outflows Set Stellar Masses?

The opening angles of some protostellar outflows appear too narrow to match the expected core–star mass efficiency (SFE) = 0.3–0.5, if the outflow cavity volume traces outflow mass, with a conical shape and a maximum opening angle near 90°. However, outflow cavities with a paraboloidal shape and wider angles are more consistent with observed estimates of the SFE. This paper presents a model of infall and outflow evolution based on these properties. The initial state is a truncated singular isothermal sphere which has mass ≈ 1 M ⊙, freefall time ≈ 80 kyr, and small fractions of magnetic, rotational, and turbulent energy. The core collapses pressure free as its protostar and disk launch a paraboloidal wide-angle wind. The cavity walls expand radially and entrain envelope gas into the outflow. The model matches the SFE values when the outflow mass increases faster than the protostar mass by a factor 1–2, yielding protostar masses typical of the IMF. It matches the observed outflow angles if the outflow mass increases at nearly the same rate as the cavity volume. The predicted outflow angles are then typically ∼50° as they increase rapidly through the stage 0 duration of ∼40 kyr. They increase more slowly up to ∼110° during their stage I duration of ∼70 kyr. With these outflow rates and shapes, the model predictions appear consistent with observational estimates of the typical stellar masses, SFEs, stage durations, and outflow angles, with no need for external mechanisms of core dispersal.

Building an Equation of State Density Ladder

The confluence of major theoretical, experimental, and observational advances are providing a unique perspective on the equation of state of dense neutron-rich matter—particularly its symmetry energy—and its imprint on the mass-radius relation for neutron stars. In this contribution, we organize these developments in an equation of the state density ladder. Of particular relevance to this discussion are the impact of the various rungs on the equation of state and the identification of possible discrepancies among the various methods. A preliminary analysis identifies possible tension between laboratory measurements and gravitational-wave detections that could indicate the emergence of a phase transition in the stellar core.

Opacities and Atomic Diffusion

Opacity is a fundamental quantity for stellar modeling, and it plays an essential role throughout the life of stars. After gravity drives the collapse of interstellar matter into a protostar, the opacity determines how this matter is structured around the stellar core. The opacity explains how the radiation field interacts with the matter and how a major part of the energy flows through the star. It results from all the microscopic interactions of photons with atoms. Part of the momentum exchange between photons and atoms gives rise to radiative accelerations (specific to each type of atom), which are strongly involved in a second-order process: atomic diffusion. Although this process is a slow one, it can have a significant impact on stellar structure and chemical composition measurements. In this review, we discuss the way opacities are presently computed and used in numerical codes. Atomic diffusion is described, and the current status of the consideration of this process is presented.

Impact of symmetry energy on sound speed and spinodal decomposition in dense neutron-rich matter

Using a meta model for nuclear Equation of State (EOS) with its parameters constrained by astrophysical observations and terrestrial nuclear experiments, we examine effects of nuclear EOS especially its symmetry energy \esym term on the speed of sound squared $C^2_s(\rho)$ and the critical density $\rho_t$ where $C^2_s(\rho_t)$ vanishes (indicating the onset of spinodal decomposition) in both dense neutron-rich nucleonic matter relevant for relativistic heavy-ion collisions and the cold $n+p+e+\mu$ matter in neutron stars at $\beta$-equilibrium. Unlike in nucleonic matter with fixed values of the isospin asymmetry $\delta$, in neutron stars with a density dependent isospin profile $\delta(\rho)$ determined consistently by the $\beta$ equilibrium and charge neutrality conditions, the $C^2_s(\rho)$ almost always show a peak and then vanishes at $\rho_t$. The latter strongly depends on the high-density behavior of \esym if the skewness parameter $J_0$ characterizing the stiffness of high-density symmetric nuclear matter (SNM) EOS is not too far above its currently known most probable value of about $-190$ MeV inferred from recent Bayesian analyses of neutron star observables. Moreover, in the case of having a super-soft \esym that is decreasing with increasing density above about twice the saturation density of nuclear matter, the $\rho_t$ is significantly lower than the density where the \esym vanishes (indicating the onset of isospin-separation instability and pure neutron matter formation) in neutron star cores.

Universality and Nonuniversality in Distributed Nuclear Burning in Homogeneous Isotropic Turbulence.

Nuclear burning plays a key role in a wide range of astrophysical stellar transients, including thermonuclear, pair instability, and core collapse supernovae, as well as kilonovae and collapsars. Turbulence is now understood to also play a key role in these astrophysical transients. Here, we demonstrate that turbulent nuclear burning may lead to large enhancements above the uniform background burning rate, since turbulent dissipation gives rise to temperature fluctuations, and in general the nuclear burning rates are highly sensitive to temperature. We derive results for the turbulent enhancement of the nuclear burning rate under the influence of strong turbulence in the distributed burning regime in homogeneous isotropic turbulence, using probability distribution function methods. We demonstrate that the turbulent enhancement obeys a universal scaling law in the limit of weak turbulence. We further demonstrate that, for a wide range of key nuclear reactions, such as C^{12}(O^{16},α)Mg^{24} and 3-α, even relatively modest temperature fluctuations, of the order of 10%, can lead to enhancements of 1-3 orders of magnitude in the turbulent nuclear burning rate. We verify the predicted turbulent enhancement directly against numerical simulations, and find very good agreement. We also present an estimation for the onset of turbulent detonation initiation, and discuss implications of our results for stellar transients.

Strong magnetic fields and pasta phases reexamined

In this work, we compute the structure and composition of the inner crust of a neutron star in the presence of a strong magnetic field, such as it can be found in magnetars. To determine the geometry and characteristics of the crust inhomogeneities, we consider the compressible liquid drop model, where surface and Coulomb terms are included in the variational equations, and we compare our results with previous calculations based on more approximate treatments. For the equation of state (EoS), we consider two non-linear relativistic mean-field models with different slopes of the symmetry energy, and we show that the extension of the inhomogeneous region inside the star core due to the magnetic field strongly depends on the behavior of the symmetry energy in the crustal EoS. Finally, we argue that the extended spinodal instability observed in previous calculations can be related to the presence of small amplitude density fluctuations in the magnetar outer core, rather than to a thicker solid crust. The compressible liquid drop model formalism, while in overall agreement with the previous calculations, leads to a systematic suppression of the metastable solutions, thus allowing a more precise estimation of the crust-core transition density and pressure, and therefore a better estimation of the crustal radius.

Kaon condensation in skyrmion matter and compact stars

We address the possibility of the appearance of a charged kaon condensate in neutron star cores described within a generalized Skyrme model. Our treatment of strange degrees of freedom is based on the Bound State Approach by Callan and Klebanov, which allows to obtain an in-medium effective potential for the $s$-wave kaon condensate. We predict the onset of kaon condensation at a certain threshold density - whose value depends on the parameters of the model, and ranges between 1.5 and 2.5 times saturation density -, and obtain both the particle fractions and equation of state for dense matter in the kaon condensed phase. Finally, we discuss the effect of such condensates on the mass-radius curves and other observable properties of neutron stars with kaon condensed cores.

Proximity effects of vortices in neutron 3P2 superfluids in neutron stars: Vortex core transitions and covalent bonding of vortex molecules

Neutron $^{3}P_{2}$ superfluids consisting of neutron pairs with the total angular momentum $J=2$, spin-triplet, and $P$ wave are believed to be realized in neutron star cores. Within the Ginzburg-Landau theory it was previously found that a singly quantized vortex is split into two half-quantized non-Abelian vortices connected by one (or three) soliton(s) forming a vortex molecule with the soliton bond(s), in the absence (presence) of a magnetic field parallel to them. In this paper, we investigate proximity effects of two vortex molecules by exhausting all possible two vortex molecule states consisting of four half-quantized vortices and determine the phase diagram spanned by the magnetic field and rotation speed. As the rotation speed is increased, the distance between the two vortex molecules becomes shorter. In the magnetic field below the critical value, we find that as the rotation speed is increased, the two separated vortex molecules transit to a dimerized vortex molecule, where the two vortex molecules are bridged by two solitons that we call ``covalent bonds'' in analogy with chemical molecules. We also find that the orders of the constituent half-quantized vortex cores transit from a ferromagnetic order to a cyclic order as the vortex molecules come closer. On the other hand, no dimerization occurs in the magnetic field above the critical value. Instead, we find a transition for the polarization direction of the vortex molecules from a configuration parallel to the separation to one perpendicular to the separation as they come closer. We also show some examples of three, four, and many vortex molecule states.

Charged compact stars with color–flavor-locked strange quark matter in f(R,T) gravity

Due to the high density of neutron stars, there is still an open question on the complete structure of the inner core of compact object. It is a great challenge to propose a model describing the highly-dense matter of neutron stars since there are neither experimentally nor observationally adequate results. In theoretical physics, Quantum Chromodynamics (QCD) predicts that at high densities and low temperatures the inner core of neutron stars could be made of exotic quark matter in the color-flavor-locked (CFL) phase of color superconductivity. Regarding the equation-of-state, we predict the existence of electrically charged strange quark stars in the background of the modified theory of gravity f(R,T). In our discussion, we assume a linear relation between charge density and the fluid energy density, and also utilize the f(R,T)=R+2βT model to numerically compute the generalized Tolman–Oppenheimer–Volkoff (TOV) structure equations. In order to compute the properties of quark stars, we discuss the mass–radius profile, the effect of the charge in the stellar interior, factor of compactness, and mass-central energy density relation for stellar stability. Finally, we provide a set of basic differences between the standard Einstein-Maxwell gravity and the modified f(R,T) gravity theory.

Dark matter effects on hybrid star properties

In the present work, we investigate the effects of dark matter (DM) on hybrid star properties. We assume that dark matter is mixed with both hadronic and quark matter and interacts with them through the exchange of a Higgs boson. The hybrid star properties are obtained from equations of state calculated with a Maxwell prescription. For the hadronic matter, we use the NL3* parameter set, and for the quark matter, the MIT bag model with a vector interaction. We see that dark matter does not influence the phase transition points (pressure and chemical potential) but shifts the discontinuity on the energy density, which ultimately reduces the minimum mass star that contains a quark core. Moreover, it changes considerably the star family mass-radius diagrams and moves the merger polarizability curves inside the confidence lines. Another interesting feature is the influence of DM in the quark core of the hybrid stars constructed. Our results show an increase of the core radius for higher values of the dark particle Fermi momentum.

Core–EP Star and Star Core–EP Operators

In this paper, we will introduce two new classes of generalized Drazin invertible operators on Hilbert space, which are called core–EP star and star core–EP operators, using the core–EP inverse and the adjoint of a given operator. We also represent here a few characterizations of these new operators from two points of view, algebraic and geometrical, and make relations to some familiar inverses, which are studied before. Next, we will consider two decompositions of Hilbert space and give the matrix representations of these new operators, following the decompositions. As the special section, there is the case when the operator is Drazin invertible. By using a *core–EP inverse, instead of the core–EP inverse, we get another new classes called *core–EP star and star *core–EP operators.

(Anti)kaon condensation in strongly magnetized dense matter

Recent observations of several massive pulsars, with masses near and above $2~M_\odot$, point towards the existence of matter at very high densities, compared to normal matter that we are familiar with in our terrestrial world. This leads to the possibility of appearance of exotic degrees of freedom other than nucleons inside the core of the neutrons stars (NS). Another significant property of NSs is the presence of high surface magnetic field, with highest range of the order of $\sim~10^{16}$ G. We study the properties of highly dense matter with the possibility of appearance of heavier strange and non-strange baryons, and kaons in presence of strong magnetic field. We find that the presence of a strong magnetic field stiffens the matter at high density, delaying the kaon appearance and, hence, increasing the maximum attainable mass of NS family.

Gravitational wave emission from dynamical stellar interactions

We are witnessing the dawn of gravitational wave (GW) astronomy. With currently available detectors, observations are restricted to GW frequencies in the range between ∼10 Hz and 10 kHz, which covers the signals from mergers of compact objects. The launch of the space observatory LISA will open up a new frequency band for the detection of stellar interactions at lower frequencies. In this work, we predict the shape and strength of the GW signals associated with common-envelope interaction and merger events in binary stars, and we discuss their detectability. Previous studies estimated these characteristics based on semi-analytical models. In contrast, we used detailed three-dimensional magnetohydrodynamic simulations to compute the GW signals. We show that for the studied models, the dynamical phase of common-envelope events and mergers between main-sequence stars lies outside of the detectability band of the LISA mission. We find, however, that the final stages of common-envelope interactions leading to mergers of the stellar cores fall into the frequency band in which the sensitivity of LISA peaks, making them promising candidates for detection. These detections can constrain the enigmatic common-envelope dynamics. Furthermore, future decihertz observatories such as DECIGO or BBO would also be able to observe this final stage and the post-merger signal, through which we might be able to detect the formation of Thorne-Żytkow objects.

Topology and Emergent Symmetries in Dense Compact Star Matter

It has been found that the topology effect and the possible emergent hidden scale and hidden local flavor symmetries at high density reveal a novel structure of compact star matter. When Nf≥2, baryons can be described by skyrmions when the number of color Nc is regarded as a large parameter and there is a robust topology change—the transition from skyrmion to half-skyrmion—in the skyrmion matter approach to dense nuclear matter. The hidden scale and local flavor symmetries, which are sources introducing the scalar meson and vector mesons, are significant elements for understanding the nuclear force in nonlinear chiral effective theories. We review in this paper how the robust conclusions from the topology approach to dense matter and emergent hidden scale and hidden local flavor symmetries figure in generalized nuclear effective field theory (GnEFT), which is applicable to nuclear matter from low density to compact star density. The topology change encoded in the parameters of the effective field theory is interpreted as the hadron-quark continuity in the sense of the Cheshire Cat Principle. A novel feature predicted in this theory that has not been found before is the precocious appearance of the conformal sound velocity in the cores of massive stars, although the trace of the energy-momentum tensor of the system is not zero. That is, there is a pseudoconformal structure in the compact star matter and, in contrast to the usual picture, the matter is made of colorless quasiparticles of fractional baryon charges. A possible resolution of the longstanding gA quench problem in nuclei transition and the compatibility of the predictions of the GnEFT with the global properties of neutron star and the data from gravitational wave detections are also discussed.

Standing accretion shock instability in the collapse of a rotating stellar core

Hydrodynamical instabilities, such as the standing accretion shock instability (SASI), play an essential role in the dynamics of core-collapse supernovae, with observable imprints in the neutrino and gravitational wave signals. Yet, the impact of stellar rotation on the development of SASI is poorly explored. We investigate the conditions favoring the growth of SASI in the presence of rotation through a perturbative analysis. The properties of SASI are compared in two stationary configurations, cylindrical and spherical equatorial, which mainly differ by their advection timescales from the shock to the proto-neutron star surface. Without rotation, the mode $m=1$, corresponding to a one-armed spiral SASI deformation, can be significantly more unstable in the spherical equatorial configuration. In fact, the shorter advection time in the spherical equatorial geometry allows for a larger contribution of the entropic-acoustic coupling from the region of adiabatic compression near the surface of the proto-neutron star. The angular momentum of the collapsing core favors the growth of prograde spiral modes $m=1$ and $m=2$ in both geometries. Although the growth rate of the spiral instability is systematically faster in spherical geometry, its oscillation frequency is remarkably insensitive to the geometry. Such a contrast with nonrotating flows calls for a deeper understanding of the role of advection in the mechanism of spiral SASI. Our findings suggest that the resonant coupling of acoustic waves with their corotation radius may play a major role in the instability mechanism of collapsing cores with rotation. Elucidating this physical mechanism is essential to interpret the signal from future multimessenger supernova observations.

Energy-Density Modeling of Strongly Interacting Matter: Atomic Nuclei and Dense Stars

We seek a simple but physically motivated model of strongly interacting matter applicable in atomic nuclei and the dense matter in the core of neutron stars. For densities below and somewhat above normal nuclear density, energy density functional (EDF) theory based on nucleonic degrees of freedom is the ideal candidate. We have explored that direction within the KIDS (Korea-IBS-Daegu-SKKU) framework, which we review in this contribution. The formalism for the KIDS-EoS and microscopic KIDS-EDF and optimization options for the EDF are described in a practical way to facilitate further applications. At densities higher than one nucleon per single-nucleon volume, i.e., roughly 0.4 fm−3, nucleonic degrees of freedom are no longer appropriate. The pseudo-conformal symmetry emergent in dense, topologically altered nuclear matter provides a simple expression for the energy per baryon in terms of the baryonic density. Besides resembling a simple EDF for dense matter, the expression has the appeal that it predicts a converged speed of sound at high densities. It can thus be implemented as a special case of the constant speed of sound (CSS) model. Here we consider a matching between representative nucleonic KIDS-EoSs and the CSS model, including the pseudo-conformal EoS, and apply the unified model to describe the mass–radius relation of neutron stars and examine the compatibility of CSS cores with heavy neutron stars. Although an abrupt transition to the pseudo-conformal regime at low densities does not favor heavy neutron stars, intermediate scenarios including a cusp in the speed of sound are not ruled out, while some appear more favorable to heavy stars than purely nucleonic matter.

Gravitational Wave Signal for Quark Matter with Realistic Phase Transition.

The cores of neutron stars (NSs) near the maximum mass can realize a transitional change to quark matter (QM). Gravitational waves from binary NS mergers are expected to convey information about the equation of state (EOS) sensitive to the QM transition. Here, we present the first results of gravitational wave simulation with the realistic EOS that is consistent with abinitio approaches of χEFT and pQCD and is assumed to go through smooth crossover. We compare them to results obtained with another EOS with a first-order hadron-quark phase transition. Our results suggest that early collapse to a black hole in the post-merger stage after NS merger robustly signifies softening of the EOS associated with the QM onset in the crossover scenario. The nature of the hadron-quark phase transition can be further constrained by the condition that electromagnetic counterparts should be energized by the material left outside the remnant black hole.

Monotonicity of the Cores of Massive Stars

Massive stars are linked to diverse astronomical processes and objects including star formation, supernovae and their remnants, cosmic rays, interstellar media, and galaxy evolution. Understanding their properties is of primary importance for modern astronomy, and finding simple rules that characterize them is especially useful. However, theoretical simulations have not yet realized such relations, instead finding that the late evolutionary phases are significantly affected by a complicated interplay between nuclear reactions, chemical mixing, and neutrino radiation, leading to nonmonotonic initial-mass dependencies of the iron core mass and the compactness parameter. We conduct a set of stellar evolution simulations, in which evolutions of He star models are followed until their central densities uniformly reach 1010 g cm−3, and analyze their final structures as well as their evolutionary properties, including the lifetime, surface radius change, and presumable fates after core collapse. Based on the homogeneous data set, we have found that monotonicity is inherent in the cores of massive stars. We show that not only the density, entropy, and chemical distributions, but also their lifetimes and explosion properties such as the proto-neutron-star mass and the explosion energy can be simultaneously ordered into a monotonic sequence. This monotonicity can be regarded as an empirical principle that characterizes the cores of massive stars.

Tidally excited gravity waves in the cores of solar-type stars: resonances and critical-layer formation

ABSTRACT We simulate the propagation and dissipation of tidally induced non-linear gravity waves in the cores of solar-type stars. We perform hydrodynamical simulations of a previously developed Boussinesq model using a spectral-element code to study the stellar core as a wave cavity that is periodically forced at the outer boundary with a given azimuthal wavenumber and an adjustable frequency. For low-amplitude forcing, the system exhibits resonances with standing g modes at particular frequencies, corresponding to a situation in which the tidal torque is highly frequency-dependent. For high-amplitude forcing, the excited waves break promptly near the centre and spin up the core so that subsequent waves are absorbed in an expanding critical layer (CL), as found in previous work, leading to a tidal torque with a smooth frequency-dependence. For intermediate-amplitude forcing, we find that linear damping of the waves gradually spins up the core such that the resonance condition can be altered drastically. The system can evolve towards or away from g-mode resonances, depending on the difference between the forcing frequency and the closest eigenfrequency. Eventually, a CL forms and absorbs the incoming waves, leading to a situation similar to the high-amplitude case in which the waves break promptly. We study the dependence of this process on the forcing amplitude and frequency, as well as on the diffusion coefficients. We emphasize that the small Prandtl number in the centre of solar-like stars facilitates the development of a differentially rotating core owing to the non-linear feedback of waves. Our simulations and analysis reveal that this important mechanism may drastically change the phase of gravity waves and thus the classical picture of resonance locking in solar-type stars needs to be revised.

Tidally perturbed gravity-mode pulsations in a sample of close eclipsing binaries

Context. Thanks to the high-precision photometry from space missions such as Kepler and TESS, tidal perturbations and tilting of pulsations have been detected in more than a dozen binary systems. However, only two of these were gravity-mode (g-mode) pulsators. Aims. We aim to detect tidally perturbed g modes in additional binary systems and characterise them observationally. Methods. We performed a custom data reduction of the available Kepler and TESS photometry of a well-studied, published sample of 35 binary systems with γ Doradus (γ Dor) pulsators. For each target, we modelled the binary signal using a sum of 100 sine waves with frequencies at orbital harmonics and measured significant pulsation frequencies in an iterative pre-whitening analysis of the residual light curve. Pulsations are labelled as tidally perturbed g modes if they are part of both period-spacing patterns and multiplets spaced by integer multiples of the orbital frequency. After visual inspection and confirmation, the properties of these targets and g modes were characterised. Results. We detect tidally perturbed g-mode pulsations for five short-period binaries that are circularised and (almost) synchronously rotating: KIC 3228863, KIC 3341457, KIC 4947528, KIC 9108579, and KIC 12785282. Tidally perturbed g modes that occur within the same star and have the same mode identification (k, m), are found to have near-identical relative amplitude and phase modulations, which are within their respective 1 − σ uncertainties and also identical for the Kepler and TESS photometric passbands. By contrast, pulsations with different mode identifications (k, m) are found to exhibit different modulations. Moreover, the observed amplitude and phase modulations are correlated, indicating that the binary tides primarily distort the g-mode amplitudes on the stellar surface. The phase modulations are then primarily a geometric effect of the integration of the stellar flux over the visible stellar surface. All selected binaries also exhibit signal that resembles rotational modulation in the Fourier domain. In the case of KIC 3228863, this is caused by the presence of the known tertiary component, and for the other systems we hypothesise that it is caused by temperature variations on the stellar surface. Alternatively, the signal can be made up of overstable convective modes in the stellar core or may belong to the non-pulsating companion. Conclusions. While g-mode pulsation periods are known to be a direct probe of the deep interior stellar structure, the binary tides that cause the pulsation modulations are dominant in the outer stellar layers. Hence, in the future, tidally perturbed g modes may allow us to carry out core-to-surface asteroseismic modelling of tidally distorted stars.