Radius Relation Research Articles

Role of Magma Oceans in Controlling Carbon and Oxygen of Sub-Neptune Atmospheres

Most exoplanets with a few Earth radii are more inflated than bare-rock planets with the same mass, indicating a substantial volatile amount. Neither the origin of the volatiles nor the planet’s bulk composition can be constrained from the mass–radius relation alone, and the spectral characterization of their atmospheres is needed to solve this degeneracy. Previous studies showed that chemical interaction between accreted volatile and possible molten rocky surface (i.e., magma ocean) can greatly affect the atmospheric composition. However, a variety in the atmospheric compositions of such planets with different properties remains elusive. In this work, we examine the dependence of atmospheric H, O, and C on planetary parameters (atmospheric thickness, planetary mass, equilibrium temperature, and magma properties such as redox state) assuming nebula gas accretion on an Earth-like core, using an atmosphere-magma chemical equilibrium model. Consistent with previous work, we show that atmospheric H2O fraction on a fully molten rocky interior with an Earth-like redox state is on the order of 10−2–10−1 regardless of other planetary parameters. Despite the solubility difference between H- and C-bearing species, C/H increases only a few times above the nebula value except for atmospheric pressure ≲1000 bar and H2O fraction ≳10%. This results in a negative O/H–C/O trend and depleted C/O below one-tenth of the nebula gas value under an oxidized atmosphere, which could provide a piece of evidence of rocky interior and endogenic water. We also highlight the importance of constraints on the high-pressure material properties for interpreting the magma–atmospheric interaction of inflated planets.

ATOMS: ALMA three-millimetre observations of massive star-forming regions–XVII. High-mass star-formation through a large-scale collapse in IRAS 15394-5358

ABSTRACT Hub-filament systems are considered as natural sites for high-mass star formation. Kinematic analysis of the surroundings of hub-filaments is essential to better understand high-mass star formation within such systems. In this work, we present a detailed study of the massive Galactic protocluster IRAS 15394$-$5358, using continuum and molecular line data from the ALMA three-millimetre observations of massive star-forming regions (ATOMS) survey. The 3 mm dust continuum map reveals the fragmentation of the massive ($\rm M=843~{\rm M}_{\odot }$) clump into six cores. The core C-1A is the largest (radius = 0.04 pc), the most massive ($\rm M=157~{\rm M}_{\odot }$), and lies within the dense central region, along with two smaller cores ($\rm M=7~and~3~{\rm M}_{\odot }$). The fragmentation process is consistent with the thermal Jeans fragmentation mechanism and virial analysis shows that all the cores have small virial parameter values ($\rm \alpha _{vir}\lt \lt 2$), suggesting that the cores are gravitationally bound. The mass versus radius relation indicates that three cores can potentially form at least a single massive star. The integrated intensity map of $\rm H^{13}CO^{+}$ shows that the massive clump is associated with a hub-filament system, where the central hub is linked with four filaments. A sharp velocity gradient is observed towards the hub, suggesting a global collapse where the filaments are actively feeding the hub. We discuss the role of global collapse and the possible driving mechanisms for the massive star formation activity in the protocluster.

Impact of charge on the stability of pulsar SAX J1748.9-2021 in modified symmetric teleparallel gravity

In this paper, we explore the effect of charge on the stability of pulsar star SAX J1748.9-2021 in f(Q) gravity, where Q represents non-metricity. For this purpose, we apply the Krori-Barua metric ansatz with anisotropic fluid and use a linear f(Q) model f(Q)=ζQ, where ζ is a non-zero constant. We derive exact relativistic solutions of the corresponding field equations. Furthermore, we study its geometric and physical properties through astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. We examine features like anisotropic pressure, the mass–radius relationship, redshift, the Zeldovich condition, energy and causality conditions, the adiabatic index, the Tolman–Oppenheimer–Volkoff equation, the equation of state parameter and compactness. Our findings align with the observational data which indicate that the pulsar SAX J1748.9-2021 is viable and stable under this modified theory of gravity.

Charged analog of anisotropic dark energy star in Rastall gravity

Dark energy is one of the potential strategies for preventing compact objects from gravitationally collapsing into singularities. Because it is the cause of the accelerated expansion of our universe, it has the greatest impact on the cosmos. Thus, it is plausible that dark energy will interact with any stellar object that is compact in the universe [Phys. Rev. D 103 (2021) 084042]. Our main goal in this work is to create a simplified model, in the Rastall gravitational framework, of a charged strange star coupled to anisotropic dark energy in Krori–Barua spacetime [J. Phys. A, Math. Gen. 8 (1975) 508]. Here, we consider a specific strange star object, Her [Formula: see text], with observed values of mass [Formula: see text] and radius [Formula: see text] km, so that we can develop our model. In this context, we began by modeling dark energy using the equation of state (EoS), in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The Darmois–Israel condition has been used to calculate the unknown constants that are present in the metric. We perform a detailed analysis of the model’s physical properties, including the mass–radius relation, pressure, density, metric function, and dark energy parameters for different Rastall coupling parameter values. We also examine the stability and force equilibrium of our proposed stellar configuration. Following a comprehensive theoretical analysis, we discovered that our suggested model is both singularity-free and meets all stability requirements needed to be a stable, physically reasonable stellar model.

Local charge radius relations based on neutron shell effects

Local charge radius relations based on neutron shell effects

Bose–Einstein Condensation dark matter models generated by gravitational decoupling

A study on massive compact objects influenced by Bose–Einstein condensation (BEC) dark matter (DM) with a gravitational decoupling approach is presented within the context of f(Q) gravity, assuming a linear form of f(Q). In order to obtain physically valid solutions to the basic field equations of the decoupled systems, we take the Tolman IV potential ansatz for the seed system and the BEC-DM density profile for the new source into consideration. After that, we apply the boundary conditions on the decoupled system with Schwarzschild-de Sitter spacetime as the exterior metric. Eventually, we obtain a complete non-singular solution to the decoupled system, consisting of a strange stellar configuration with a BEC-DM density profile. All the physical properties, such as the effective energy density, pressure along the radial as well as the tangential direction, and anisotropy in the system, are rigorously investigated. Analyzing the stability conditions of the decoupled stellar configuration, we study mass–radius (M−R) relations with observational constraints related to the supermassive compact stars, such as PSR J0740+6620, PSR J2215+5135, GW190814, and GW200210, with observed masses larger than or equal to 2 M⊙. Notably, we examine the influence of DM on constraining the M−R measurements of the observed stars, which satisfy the MIT bag model equation of state as well as the condition of mimicking, i.e., ρθ=ρDM, in the background of f(Q) gravity. Interestingly, any possible conversion of massive compact stars to smaller black holes can be restrained, as the presence of a DM halo in the strange stellar system reduces the maximum mass effectively, as indicated by the M−R curves. This result regarding the maximum mass of the compact star can be associated with the astrophysical data concerning the mass gap of the events GW190814 and GW200210. Specifically, the present model predicts the radius for PSR J0740+6620 as 13.69−0.10+0.09 km, which nearly matches the NICER and XMM-Newton data.

Stability and viability of charged anisotropic pulsar SAX J1748.9-2021 in extended symmetric teleparallel gravity

This manuscript aims to study the viability and stability of a pulsar SAX J1748.9-2021, containing a charged anisotropic matter configuration within the framework of f(Q,T) theory (Q and T are the non-metricity scalar and energy–momentum tensor, respectively). We employ a non-singular solution and a specific model of this gravitational theory and use junction conditions to determine the unknown constants in the metric coefficients. We explore different geometric and physical properties using astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. This framework establishes relationships between various physical quantities, including fluid parameters, anisotropy, mass–radius relation, redshift, the Zeldovich condition, energy conditions, causality conditions, adiabatic index, Tolman–Oppenheimer–Volkoff equation, equation of state parameter and compactness. Our findings affirm the feasibility and stability of the proposed charged pulsar within this theoretical framework.

Modeling Compact Object Mergers GW190814 and GW200210 and Other Self-bound Compact Stars with Dark Matter Induced by Gravitational Decoupling and Its Significance to the Mass Gap

We present a rigorous study of compact objects within f(Q) gravity where electrical fields and dark matter are studied and provide novel mass–radius relations with models falling in the mass gap of the events GW190814 and GW200210. After formulating the basic equations and finding their relevant solutions, we impose the boundary conditions on the system under treatment. The decoupled solution for the strange stellar model with the dark matter density profile is obtained. The distribution patterns of the effective energy density and the radial as well as the tangential pressure and anisotropy in the system are intensively examined. The stability properties of the stellar configuration and the influence of dark matter are studied. The recent observations of supermassive compact star candidates such as PSR J1614–2230 and PSR J0952–0607 with observed masses greater than or equal to 2 M ⊙ have been employed in our study. Interestingly, the present study predicts the constraints on mass–radius measurements of the observed stars satisfying the equation of state based on the MIT bag model and employing the condition of mimicking, i.e., ρ θ = χ1ρPI in f(Q) gravity. Our graphical results exhibit that for a particular M–R curve with fixed values of the parameters, neutron stars having mass less than M max exist with larger radii within the context of the f(Q) formalism.

Mardigras: A Visualization Tool of Theoretical Mass–Radius Relations in the Context of Planetary Science

Over the past two decades, mass–radius relations have become a crucial tool for inferring the bulk composition of exoplanets using only their measured masses and radii. These relations, often referred to as isocomposition curves, are derived from interior structure models by calculating the theoretical radius as a function of mass for a given fixed planetary composition. Each mass–radius curve can be influenced by a variety of parameters, such as planetary composition, age, and equilibrium temperature. Navigating this parameter space can be cumbersome, particularly when models or their results are not open-source. To address this challenge, I have developed MAss–Radius DIaGRAm with Sliders, a visualization tool that enables simple, fast, and interactive exploration of the parameter space that governs mass–radius relations for any given model.

Exploring the physical properties of anisotropic compact objects and constraining their mass–radius relations beyond standard limit in [formula omitted]-gravity

The progress in theoretical modeling of compact high-mass stars in the context of alternative gravity has become important in minimizing challenges associated with neutron star (NS) radius measurements. On this basis, we have presented a rigorous study of compact objects beyond the standard limit in gravity F(Q) in particular F(Q)=b1Q+b2 where b1 and b2 are constants. After formulating the basic equations and finding their relevant solutions by assuming a well-behaved ansatz for the metric potential as well as for anisotropy monitored by the parameters μ1,μ2,b1, along with imposing the boundary conditions on the system under treatment, we have developed a stellar model for anisotropic stars. Specifically, we explored the physical properties of these anisotropic stars and provided novel mass–radius (M−R) relations with models falling in the mass gap of the events GW190814 and GW200210, as well as the effects of slow rotation and moment of inertia on these findings. Interestingly, the behavior of the M−R curves represents a polytropic-type equation of state (EOS) for a negative Λ, while a positive Λ corresponds to a quark matter EOS. However, the analysis reveals that the predicted radii of the compact object observed in the GW190814 event, with a mass of 2.5–2.67 M⊙, is approximately 11.4 km for the de Sitter (dS) case and 11.8 km for the anti-de Sitter (AdS) case, assuming a specific value of the parameter b1=1.1. Furthermore, for b1>1.1, the model predicts the existence of more compact stars with a maximum mass of approximately 3M⊙, which is in good agreement with the R2 model of NSs maintaining the Sly EOS. From the I−M curves, it can be observed that higher values of b1 and μ1 in F(Q) gravity can sustain high moments of inertia (I) of stars with high masses. Interestingly, we obtained the range of I for the dS space as [1.92,3.92]×1045gcm2 and for the AdS space as [2.01,4.03]×1045gcm2 for 1.0≤b1≤1.2.

Self-bound isotropic models in [formula omitted] gravity and effect of [formula omitted] parameter on mass–radius relation and stability of compact objects

The present article investigates the effect of f(Q) parameters on two classes of exact spherically symmetric self-bound isotropic solutions for compact objects. The field equation in f(Q) gravity is solved using Korkina–Orlyanskii and Buchdahl models. The physical validity of both models has been verified using regularity, stability, and hydrostatic equilibrium tests. We have also shown the effect of f(Q) gravity parameter α on the stability and mass–radius relation. We predicted the radii of observable compact objects GW 190814, PSR J0740+6620 PSR J1614, 2230, Cen X-3, and LMC X-4. In the absence of β, the massive neutron star GW 190814 is detected at greater values of α=1.5 and 1.2 for models I and II respectively. The corresponding estimated radii for both models are 15.30−0.29+0.18km and 15.03−0.25+0.17km. Additionally, as the non-metricity scalar α increases, the mass–radius decreases, and when β increases with fix α, the reverse scenario arises. Our finding indicates that a lower mass−gap can be achieved in f(Q) gravity theory as compared to the standard theory of gravity.

Correction to: On the initial mass–radius relation of stellar clusters

Correction to: On the initial mass–radius relation of stellar clusters

Interacting quark star with pressure anisotropy and recent astrophysical observations

This paper investigates the internal structure and equation of state (EoS) of quark stars (QS) with pressure anisotropy, incorporating recent astrophysical observations. Utilizing perturbative QCD corrections and color superconductivity, the EoS is expressed as a dimensionless function dependent on a single parameter, providing a comprehensive exploration of strong interaction effects. By rescaling the EoS and introducing dimensionless variables, the study encompasses scenarios ranging from noninteracting quark matter to extreme stiffness characterized by a parameter, λ̄. Anisotropic QS configurations are constructed using a spherically symmetric metric, with locally anisotropic matter described by a generalized EoS for tangential pressure. The Tolman–Oppenheimer–Volkoff equations governing star structure are presented in dimensionless form, and numerical solutions explore the parameter space defined by effective bag constants and λ̄. Mass–radius relations and the compactness of anisotropic QSs are analyzed under various model parameter variations, considering constraints from pulsar masses and gravitational wave phenomena. The study highlights the influence of pressure anisotropy on the maximum mass of QSs and discusses the impact of model parameters on internal properties. Additionally, the paper considers static stability, adiabatic index, and sound velocity profiles, providing a comprehensive understanding of QS behavior. Overall, this investigation contributes valuable insights into the properties of QSs and their compatibility with observational constraints, offering a detailed exploration of their EoS and internal structure.

Theoretical and observational implications of Planck’s constant as a running fine structure constant

This paper explores how a reinterpretation of the generalized uncertainty principle as an effective variation of Planck’s constant provides a physical explanation for a number of fundamental quantities and couplings. In this context, a running fine structure constant is naturally emergent and the cosmological constant problem is solved, yielding a novel connection between gravitation and quantum field theories. The model could potentially clarify the recent experimental observations by the DESI Collaboration that could imply a fading of dark energy over time. When applied to quantum systems and their characteristic length scales, a simple geometric relationship between energy and entropy is disclosed. Lastly, a mass–radius relation for both quantum and classical systems reveals a phase transition-like behavior similar to thermodynamical systems, which we speculate to be a consequence of topological defects in the universe.

Impact of the hot inner crust on compact stars at finite temperature

We conducted a study on the thermal properties of stellar matter with the nuclear energy density functional BCPM. This functional is based on microscopic Brueckner–Hartree–Fock calculations and has demonstrated success in describing cold neutron stars. To enhance its applicability in astrophysics, we extended the BCPM equation of state to finite temperature for β-stable neutrino-free matter, taking into consideration the hot inner crust. Such an equation of state holds significant importance for hot compact objects, particularly those resulting from a binary neutron star merger event. Our exploration has shown that with increasing temperature, there is a fast decrease in the crust-core transition density, suggesting that for hot stars it is not realistic to assume a fixed value of this density. The microscopic calculations also reveal that the presence of nuclear clusters persists up to T = 7.21 MeV, identified as the limiting temperature of the crust. Above this threshold, the manifestation of clusters is not anticipated. Below this temperature, clusters within the inner crust are surrounded by uniform matter with varying densities, allowing for the distinction between the upper and lower transition density branches. Moreover, we computed mass–radius relations of neutron stars, assuming an isothermal profile for β-stable neutron star matter at various temperature values. Our findings highlight the significant influence of the hot inner crust on the mass–radius relationship, leading to the formation of larger and more inflated neutron stars. Consequently, under our prescription, the final outcome is a unified equation of state at finite temperature.

Constraints from Parallaxes and Average Period Spacings in the Asteroseismic Study of Eight Hydrogen-atmosphere Pulsating White Dwarfs

With space missions such as Kepler, TESS, and Gaia, we have a wealth of data on pulsating white dwarfs that can be leveraged in white dwarf asteroseismology. We address the question of the proportion of white dwarfs with thin hydrogen layers versus those with thick hydrogen layers. We also provide a mass–radius relation for carbon–oxygen-core, hydrogen-atmosphere white dwarfs. Such a relationship can be used in conjunction with magnitudes and distance measurements to constrain the mass and effective temperature of the white dwarfs. We select nine hydrogen-atmosphere pulsating white dwarfs for their rich pulsation spectra. From such pulsation spectra, we can derive the asymptotic period spacing, which in turn allows us to determine the thickness of the hydrogen and helium envelope of the models, without having to perform period-by-period fitting. We find that the majority of the white dwarfs have thicker hydrogen layers and we determine an upper limit of M r = 1–10−2.2 for the location of the base of the helium layer, in accordance with stellar evolution models. We confirm a finding from earlier studies that used a mass–radius relation and Gaia data to determine the effective temperatures of white dwarfs. The Gaia data systematically point to white dwarfs of lower effective temperature than indicated by the spectroscopy. Our results also support the hypothesis that white dwarfs with thicker hydrogen layers are more common than those with thinner layers.

Study of the effect of spark radius model upon the performance characteristics in EDM process

The evaluation of performance characteristics is of key importance to the EDM process technological reliability. By correctly estimating the power fraction and plasma flushing efficiency, it is possible to improve the accuracy of the surface integrity prediction of the EDM discharge models. In the present research, a combined computational and experimental approach is employed to study the effect of spark radius model upon the performance characteristics in EDM of Ti-6Al-4V alloy. Two famous spark radius relationships have been implemented and the effect on power fraction and removal efficiency was examined for a range of machining conditions. It has been found that the sparking radius relationship accounting for discharge current effect captures the essential dynamics of the EDM process and offers improved prediction accuracy. In such a case, the power fraction going to the cathode ranges from 8.5 to 24 %. When a cooper electrode is utilized, removal efficiency of up to 12 % was observed on the cathode surface. For specific machining conditions, an approximate constant ratio of 2.5 is seen between the power fractions transmitted to the cathode and tool-anode. Crater volume was computed and compared to the experiment to validate the proposed approach. The results of this comparison challenge the EDM model underlying assumption viability, which considers similarity between recast layer and electrode materials thermophysical proprieties when a hydrocarbon-based dielectric fluid is used. From a qualitative perspective, though, the outcomes are still encouraging and indicate that surface integrity in the EDM of Ti-6Al-4V alloy may be predicted using the performance characteristics found in this study.

Magnetic field breakout in ultramassive crystallizing white dwarfs

ABSTRACT Ultramassive white dwarfs with masses $M\gtrsim 1.1\, {\rm M}_{\odot }$ probe extreme physics near the Chandrasekhar limit. Despite the rapid increase in observations, it is still unclear how many harbour carbon–oxygen (CO) versus oxygen–neon (ONe) cores. The origin of these white dwarfs and their strong magnetic fields – single stellar evolution or a stellar merger – is another open question. The steep mass–radius relation of the relativistic ultramassive white dwarfs shortens their crystallization time $t_{\rm cryst}$, such that the recently proposed crystallization dynamo mechanism may present an alternative to mergers in explaining the early appearance of magnetism in the observed population. However, the magnetic diffusion time from the convective dynamo to the white dwarf’s surface delays the magnetic field’s breakout time $t_{\rm break}\gt t_{\rm cryst}$. We compute $t_{\rm break}(M)$ for CO and ONe ultramassive white dwarfs and compare it to the local 40 pc volume-limited sample. We find that the breakout time from CO cores is too long to account for the observations. ONe crystallization dynamos remain a viable option, but their surrounding non-convective envelopes comprise only a few per cent of the total mass, such that $t_{\rm break}$ is highly sensitive to the details of stellar evolution.

Mass–Radius Relationships and Contraction of Condensed Planets by Cooling or Despinning

Condensed planets contract or expand as their temperature changes. With the exception of the effect of phase changes, this phenomenon is generally interpreted as being solely related to the thermal expansivity of the planet’s components. However, changes in density affect pressure and gravity and, consequently, the planet’s compressibility. A planet’s radius is also linked to its rate of rotation. Here again, changes in pressure, gravity, and compressibility are coupled. In this article we clarify how the radius of a condensed planet changes with temperature and rotation, using a simple and rigorous thermodynamic model. We consider condensed materials to obey a simple equation of state which generalizes a polytopic EoS as temperature varies. Using this equation, we build simple models of condensed planet’s interiors including exoplanets, derive their mass–radius relationships, and study the dependence of their radius on temperature and rotation rate. We show that it depends crucially on the value of ρ s gR/K s (ρ s being surface density, g gravity, R radius, K s surface incompressibility). This nondimensional number is also the ratio of the dissipation number which appears in compressible convection and the Gruneïsen mineralogic parameter. While the radius of small planets depends on temperature, this is not the case for large planets with large dissipation numbers; Earth and a super-Earth like CoRoT-7b are in something of an intermediate state, with a moderately temperature-dependent radius. Similarly, while the radius of these two planets is a function of their rotation rates, this is not the case for smaller or larger planets.

The Discovery and Follow-up of Four Transiting Short-period Sub-Neptunes Orbiting M Dwarfs

Sub-Neptunes with radii of 2–3 R ⊕ are intermediate in size between rocky planets and Neptune-sized planets. The orbital properties and bulk compositions of transiting sub-Neptunes provide clues to the formation and evolution of close-in small planets. In this paper, we present the discovery and follow-up of four sub-Neptunes orbiting M dwarfs (TOI-782, TOI-1448, TOI-2120, and TOI-2406), three of which were newly validated by ground-based follow-up observations and statistical analyses. TOI-782 b, TOI-1448 b, TOI-2120 b, and TOI-2406 b have radii of Rp=2.740−0.079+0.082R⊕ , 2.769−0.068+0.073R⊕ , 2.120 ± 0.067 R ⊕, and 2.830−0.066+0.068R⊕ and orbital periods of P = 8.02, 8.11, 5.80, and 3.08 days, respectively. Doppler monitoring with the Subaru/InfraRed Doppler instrument led to 2σ upper limits on the masses of <19.1 M ⊕, <19.5 M ⊕, <6.8 M ⊕, and <15.6 M ⊕ for TOI-782 b, TOI-1448 b, TOI-2120 b, and TOI-2406 b, respectively. The mass–radius relationship of these four sub-Neptunes testifies to the existence of volatile material in their interiors. These four sub-Neptunes, which are located above the so-called “radius valley,” are likely to retain a significant atmosphere and/or an icy mantle on the core, such as a water world. We find that at least three of the four sub-Neptunes (TOI-782 b, TOI-2120 b, and TOI-2406 b), orbiting M dwarfs older than 1 Gyr, are likely to have eccentricities of e ∼ 0.2–0.3. The fact that tidal circularization of their orbits is not achieved over 1 Gyr suggests inefficient tidal dissipation in their interiors.