Mass Radius Research Articles

An Updated Mass–Radius Analysis of the 2017–2018 NICER Data Set of PSR J0030+0451

In 2019 the NICER collaboration published the first mass and radius inferred for PSR J0030+0451, thanks to NICER observations, and consequent constraints on the equation of state characterizing dense matter. Two independent analyses found a mass of ∼1.3–1.4 M ⊙ and a radius of ∼13 km. They also both found that the hot spots were all located on the same hemisphere, opposite to the observer, and that at least one of them had a significantly elongated shape. Here we reanalyze, in greater detail, the same NICER data set, incorporating the effects of an updated NICER response matrix and using an upgraded analysis framework. We expand the adopted models and also jointly analyze XMM-Newton data, which enables us to better constrain the fraction of observed counts coming from PSR J0030+0451. Adopting the same models used in previous publications, we find consistent results, although with more stringent inference requirements. We also find a multimodal structure in the posterior surface. This becomes crucial when XMM-Newton data is accounted for. Including the corresponding constraints disfavors the main solutions found previously, in favor of the new and more complex models. These have inferred masses and radii of ∼[1.4 M ⊙, 11.5 km] and ∼[1.7 M ⊙, 14.5 km], depending on the assumed model. They display configurations that do not require the two hot spots generating the observed X-rays to be on the same hemisphere, nor to show very elongated features, and point instead to the presence of temperature gradients and the need to account for them.

Control of Robot Motion in Radial Mass Density Field

T In this article, a new approach to control of robot motion in the radial mass density field is presented. This field is between the maximal and the minimal radial mass density values. Between these two limited values, one can use n points (n = 1, 2, . . . nmax) that can be included in the related algorithm for control of the robot motion. The number of the points nstep can be calculated by using the relation nstep = nmax / nvar , where nvar is the control parameter. The radial mass density is maximal at the minimal gravitational radius and minimal at the maximal gravitational radius. This is valid for Planck scale and for the scales that are less or higher of that one. Using the ratio of Planck mass and Planck radius it is generated the energy conservation constant κ = 0.99993392118.

Ultra-low-mass and small-radius white dwarfs made of heavy elements

Seven possible ultra-low-mass and small-radius white dwarfs have been recently identified, with masses ranging from ∼0.02 M⊙ to ∼0.08 M⊙ and radii ranging from ∼ 4,270 km to 10670 km. The mass–radius measurements of these white dwarfs pose challenges to traditional white dwarf models, assuming they are mostly made of nuclei lighter than 56Fe. In this work, we consider the possibility that those white dwarfs are made of heavier elements. Due to the small charge-to-mass ratios in heavy elements, the electron number density in white dwarf matter is effectively reduced, which reduces the pressure with additional contributions of lattice energy and electron polarization corrections. This consequently leads to white dwarfs with much smaller masses and radii, which coincide with the seven ultra-low-mass and small-radius white dwarfs. The mass of the most massive white dwarfs is effectively reduced and could possibly account for the sub-Chandrasekhar progenitors in underluminous Type Ia supernovae. The corresponding equation of state and matter contents of dense stellar matter with and without reaching the cold-catalyzed ground state are presented, which are obtained using the latest Atomic Mass Evaluation (AME 2020). Further observations are necessary to unveil the actual matter contents in those white dwarfs via, e.g., spectroscopy, asteroseismology, and the discoveries of other ultra-low-mass and small-radius white dwarfs.

Oxygen Vacancy-Enriched Bi2SeO5 Nanosheets with Dual Mechanism for Ammonium-Ion Batteries.

Ammonium ions feature a light molar mass and small hydrated radius, and the interesting interaction between NH4+ and host materials has attracted widespread attention in aqueous energy storage, while few studies focus on high-performance NH4+ storage anodes. Herein, we present a high-performance inset-type anode for aqueous ammonium-ion batteries (AIBs) based on Bi2SeO5 nanosheets. A reversible NH4+/H+ co-intercalation/deintercalation accompanied by hydrogen bond formation/breaking and a conversion reaction mechanism in layered Bi2SeO5 is proposed according to ex situ characterizations. Accordingly, the optimized Bi2SeO5 anode has a high reversible capacity of 341.03 mAh g-1 at 0.3 A g-1 in 1 M NH4Cl electrolyte and an impressive capacity retention of 86.7% after 7000 cycles at 3 A g-1, which is related to the existence of oxygen vacancies that enhance ion/electron transfer and promote the formation of hydrogen bonds between NH4+ and the host material. When the rocking-chair ammonium-ion battery is assembled using a MnO2 cathode, the device delivers an ultrahigh capacity of 140.73 mAh g-1 at 0.15 A g-1 and energy density of 207.13 Wh kg-1 at the power density of 2985.07 W kg-1. This work provides a promising strategy for designing high-performance anodes for next-generation AIBs.

Tensor and isovector–isoscalar terms of relativistic mean field model: Impacts on neutron-skin thickness, charge radius, and nuclear matter

The origin of the neutron skin thickness, measured by the CREX and PREX collaborations as thin for 40Ca and thick for 28Pb, remains a mystery. We investigate the effects of tensor and nonlinear isovector–isoscalar terms in a relativistic mean-field model (RMF) on the properties of finite nuclei and nuclear matter. Tensor couplings are crucial for better quality binding energies of finite nuclei and charge radii for relatively heavy nuclei. However, for light nuclei, the tensor terms cannot improve the compatibility of charge radius predictions by the RMF model with experimental data. We find that parameter sets with a larger nonlinear isovector–isoscalar parameter, particularly η2ρ = 0.028, agree better with experimental data for Δrnp across light, medium, and heavy isotope chains. Using PT28, we calculate Δrnp for 208Pb as 0.214 fm, J as 33.078, and L as 58.426. Δrnp for 208Pb obtained using PT28 is consistent with the PREX-II data. Moreover, the corresponding values of J and L agree with the low L constraints. Meanwhile, the canonical mass radius predicted by PT28 aligns with the mass and radius data from the NICER collaboration. The combination of tensor and nonlinear isovector–isoscalar couplings in the RMF model provides accurate predictions for finite nuclei binding energies and relatively heavy nuclei charge radii, resulting in relatively thick Δrnp values for 208Pb without substantial L values.

Compact stars in scalar–tensor theories with a single-well potential and the corresponding [formula omitted] theory

The macroscopic properties of compact stars in modified gravity theories can be significantly different from the general relativistic (GR) predictions. Within the gravitational context of scalar–tensor theories, with a scalar field ϕ and coupling function Φ(ϕ)=exp[2ϕ/3], we investigate the hydrostatic equilibrium structure of neutron stars for the simple potential V(ϕ)=ωϕ2/2 defined in the Einstein frame (EF). From the scalar field in the EF, we also interpret such theories as f(R) gravity in the corresponding Jordan frame (JF). The mass–radius relations, proper mass, and binding energy are obtained for a polytropic equation of state (EoS) in the JF. Our results reveal that the maximum-mass values increase substantially as ω gets smaller, while the radius and mass decrease in the low-central-density region as we move further away from the pure GR scenario. Furthermore, a cusp is formed when the binding energy is plotted as a function of the proper mass, which indicates the appearance of instability. Specifically, we find that the central-density value where the binding energy is a minimum corresponds precisely to dM/dρcJ=0 on the M(ρcJ)-curve.

Impact of spacetime curvature on the physical behaviour of Vaidya and Tikekar (VT) type anisotropic compact objects

The Vaidya and Tikekar (1982) ansatz has so far provided numerous stellar solutions which are useful for the description of compact stars like neutron stars and quark stars. We re-examine the impacts of the spacetime curvature parameter of the Vaidya–Tikekar ansatz on the physical properties of the relativistic anisotropic star. For a spherically symmetric, static and anisotropic stellar configuration, in the Vaidya–Tikekar background spacetime, we develop new exact solutions by assuming a polytropic type equation of state pr=kρ1+1n−β. Recent data from observed pulsars are taken as input parameters to validate the developed model. We examine the impact of the spheroidal curvature parameter of the VT spacetime on the stellar behaviour and mass–radius (M–R) relationship. It is observed that with the increase in the departure from spherical geometry, values of physical quantities, such as density and pressure, increase.

The EBLM Project—From False Positives to Benchmark Stars and Circumbinary Exoplanets

The EBLM project aims to characterise very-low-mass stars that are companions to solar-type stars in eclipsing binaries. We describe the history and motivation for this project, the methodology we use to obtain the precise mass, radius, and effective temperature estimates for very-low-mass M dwarfs, and review the results of the EBLM study and those from related projects. We show that radius inflation in fully convective stars is a more subtle effect than what was previously thought based on less precise measurements, i.e., the mass–radius–effective temperature relations we observe for fully convective stars in single-line eclipsing binaries show reasonable agreement with the theoretical models, particularly if we account for the M-dwarf metallicity, as inferred from the analysis of the primary star spectrum.

Understanding the Predication Mechanism of Deep Learning through Error Propagation among Parameters in Strong Lensing Case

The error propagation among estimated parameters reflects the correlation among the parameters. We study the capability of machine learning of “learning” the correlation of estimated parameters. We show that machine learning can recover the relation between the uncertainties of different parameters, especially, as predicted by the error propagation formula. Gravitational lensing can be used to probe both astrophysics and cosmology. As a practical application, we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters (effective lens mass M L and Einstein radius θ E ) in accordance with the theoretical formula for the singular isothermal ellipse (SIE) lens model. The relation of errors of lens mass and Einstein radius, (e.g., the ratio of standard deviations ) predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model. As a proof-of-principle test, a toy model of linear relation with Gaussian noise is presented. We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise. Error propagation plays a crucial role in identifying the physical relation among parameters, rather than a coincidence relation, therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

A four parameters quark star in quadratic [formula omitted]action

In this collaborative work, we model charged compact objects within the framework of f(Q) gravity. We assume a quadratic form for the metricity function cast as f(Q)=Q+aQ2 where a can be thought of as a ‘switch’, regaining the classical general relativity limit when it vanishes. In order to close the system of governing equations, we adopt the Krori–Barua ansatz for the metric functions and the MIT bag model equation of state (EOS) determines the evolution of the electric field. The resulting models are singularity-free and describe physically realizable stellar structures such as neutron stars. We demonstrate that the physical attributes of our models are sensitive to four parameters, namely, the EOS, metricity, and charge parameters together with the bag constant. We observe that an increase in the quadratic contribution culminates in a decrease of the density, radial pressure, electric field, and sound speeds while ωr,ωt, anisotropy, and pt increase. The novelty in our work centers on a possible mechanism of increasing the anisotropy of the stellar interior without resorting to exotic fluids or anisotropisation via gravitational decoupling. The robustness of our models can account for observed mass–radius relations of well-known compact stars such as PSR J1614-2230, PSR J1903+6620, Cen X-3 and LMC X-4 and the secondary component of GW190814 event.

Asteroseismic Study of KUV03442+0719 with Parallax Constraints

Hydrogen atmosphere white dwarf KUV03442+0719 was first reported as a pulsator by Gianninas et al. in 2006. Follow-up campaigns by Su et al. revealed more periods. Some spectroscopic results suggest that KUV03442+0719 has a slightly below-average mass and an effective temperature of 11,000 K. However, Gaia data (parallax and magnitude) suggest that it may be a low-mass white dwarf. Such an object would have a helium core. We perform asteroseismic fitting of KUV03442+0719, modeling it both as a carbon/oxygen normal mass white dwarf, and a helium-core low-mass white dwarf. To perform the study, we perform a grid search with WDEC models, refined by simplex minimization of the best fits. Both analyses result in best-fit models that are comparable in terms of quality of fit. More pulsation data would be required to allow us to distinguish between the two scenarios. We present and contrast our results with expectations from stellar evolution. We also provide analytic formulae for a temperature-dependent mass–radius relationship for helium-core white dwarfs.

Spright: a probabilistic mass–density–radius relation for small planets

ABSTRACT We present spright, a python package that implements a fast and lightweight mass–density–radius relation for small planets. The relation represents the joint planetary radius and bulk density probability distribution as a mean posterior predictive distribution of an analytical three-component mixture model. The analytical model, in turn, represents the probability for the planetary bulk density as three generalized Student’s t-distributions with radius-dependent weights and means based on theoretical composition models. The approach is based on Bayesian inference and aims to overcome the rigidity of simple parametric mass–radius relations and the danger of overfitting of non-parametric mass–radius relations. The package includes a set of pre-trained and ready-to-use relations based on two M-dwarf catalogues, one catalogue containing stars of spectral types F, G, and K (FGK stars), and two theoretical composition models for water-rich planets. The inference of new models is easy and fast, and the package includes a command line tool that allows for coding-free use of the relation, including the creation of publication-quality plots. Additionally, we study whether the current mass and radius observations of small exoplanets support the presence of a population of water-rich planets positioned between rocky planets and sub-Neptunes. The study is based on Bayesian model comparison and shows somewhat strong support against the existence of a water-world population around M dwarfs. However, the results of the study depend on the chosen theoretical water-world density model. A more conclusive result requires a larger sample of precisely characterized planets and community consensus on a realistic water-world interior structure and atmospheric composition model.

The Effect of Gravitational Decoupling on Constraining the Mass and Radius for the Secondary Component of GW190814 and Other Self-bound Strange Stars in f(Q) Gravity Theory

Inspired by the conundrum of the gravitational event GW190814, which brings to light the coalescence of a 23 M ⊙ black hole with a yet-to-be-determined secondary component, we look to modeling compact objects within the framework of gravity by employing the method of gravitational decoupling. We impose a quadratic equation of state (EOS) for the interior matter distribution, which in the appropriate limit reduces to the MIT bag model. The governing field equations arising from gravitational decoupling bifurcate into the and sectors, leading to two distinct classes of solutions. Both families of solutions are subjected to rigorous tests, qualifying them to describe a plethora of compact objects, including neutron stars, strange stars, and the possible progenitor of the secondary component of GW190814. Using observational data of mass–radius relations for compact objects LMC X-4, Cen X-3, PSR J1614–2230, and PSR J0740+6620, we show that it is possible to generate stellar masses and radii beyond 2.0 M ⊙ for neutron stars. Our findings reveal that the most suitable and versatile model in this framework is the quadratic EOS, which accounts for a range of low-mass stars and typical stellar candidates describing the secondary component of GW190814.

Theory and prospects of the pulsar study

After the pulsar was discovered by Hewish, the relevant research has become one of the hottest research fields. Astronomers have noticed that pulsars are of great academic significance in the field of basic scientific research. Due to the large mass and small radius of pulsars, their surface gravitational field is very strong. The existence of general relativity effects cannot be ignored, making pulsars a natural laboratory for the study of strong gravitational fields. the strong magnetic field provides an identical place for the study of radio radiation process, magnetospheric particle acceleration mechanism and high energy radiation. Pulsar as the product of supernova burst after the collapse of massive stars, it is very important for the study of supernova burst theory and understand the formation mechanism of pulsars. In terms of application research, due to the high stability of its rotation period, it has significant applicating prospect in measuring time standard and X-ray pulsar navigation system. The Pulsar has made great remarkable achievements in the past 50 years since its discovery. In short, the discovery and research significance of pulsars are highly anticipated.

A method for establishing a bearing residual life prediction model for process enhancement equipment based on rotor imbalance response analysis

A rotating packed bed is a typical chemical process enhancement equipment that can strengthen micromixing and mass transfer. During the operation of the rotating packed bed, the nonreactants and products irregularly adhere to the wire mesh packing in the rotor, thus resulting in an imbalance in the vibration of the rotor, which may cause serious damage to the bearing and material leakage. This study proposes a model prediction for estimating the bearing residual life of a rotating packed bed based on rotor imbalance response analysis. This method is used to determine the influence of the mass on the imbalance in the vibration of the rotor on bearing damage. The major influence on rotor vibration was found to be exerted by the imbalanced mass and its distribution radius, as revealed by the results of orthogonal experiments. Through implementing finite element analysis, the imbalance response curve for the rotating packed bed rotor was obtained, and a correlation among rotor imbalance mass, distribution radius of imbalance mass, and bearing residue life was established via data fitting. The predicted value of the bearing life can be used as the reference basis for an early safety warning of a rotating packed bed to effectively avoid accidents.

Some new dark energy star models in Rastall gravity via Tolman–Kuchowicz potentials

In this paper, we are interested in modeling a new relativistic dark energy star by enforcing the static and anisotropic spherically symmetric fluid distribution in the realm of the Rastall theory of gravity. To do so, we have assumed a linear dark energy equation of state coupled with baryonic stellar matter: ρde=βρ, which has been used as a seed solution along with Tolman–Kuchowicz potentials to obtain the analytical solutions of the Rastall field equations. The stability of various physical attributes like matter variables, energy conditions, stability analysis, mass–radius relation, compactness and surface redshift have been examined corresponding to the observational data of the compact star PSRJ1614−2230 (R=9.69 km). Based on the evident results, for the small values of the Rastall parameter α, our proposed solutions are viable for a new stable relativistic dark energy star model in the realm of Rastall gravity, which comparatively seems to be more interesting than the results given in previous study (Saklany et al., 2022).

Early Planet Formation in Embedded Disks (eDisk). VIII. A Small Protostellar Disk around the Extremely Low Mass and Young Class 0 Protostar IRAS 15398–3359

Protostellar disks are an ubiquitous part of the star formation process and the future sites of planet formation. As part of the Early Planet Formation in Embedded Disks large program, we present high angular resolution dust continuum (∼40 mas) and molecular line (∼150 mas) observations of the Class 0 protostar IRAS 15398–3359. The dust continuum is small, compact, and centrally peaked, while more extended dust structures are found in the outflow directions. We perform a 2D Gaussian fitting and find the deconvolved size and 2σ radius of the dust disk to be 4.5 × 2.8 au and 3.8 au, respectively. We estimate the gas+dust disk mass assuming optically thin continuum emission to be 0.6M J–1.8M J, indicating a very low mass disk. The CO isotopologues trace components of the outflows and inner envelope, while SO traces a compact, rotating disk-like component. Using several rotation curve fittings on the position–velocity diagram of the SO emission, the lower limits of the protostellar mass and gas disk radius are 0.022 M ⊙ and 31.2 au, respectively, from our Modified 2 single power-law fitting. A conservative upper limit of the protostellar mass is inferred to be 0.1 M ⊙. The protostellar mass accretion rate and the specific angular momentum at the protostellar disk edge are found to be in the range of (1.3–6.1) × 10−6 M ⊙ yr−1 and (1.2–3.8) × 10−4 km s−1 pc, respectively, with an age estimated between 0.4 × 104 yr and 7.5 × 104 yr. At this young age with no clear substructures in the disk, planet formation would likely not yet have started. This study highlights the importance of high-resolution observations and systematic fitting procedures when deriving dynamical properties of deeply embedded Class 0 protostars.

What Is the Nature of the HESS J1731-347 Compact Object?

Once further confirmed in future analyses, the radius and mass measurement of HESS J1731-347 with and will be among the lightest and smallest compact objects ever detected. This raises many questions about its nature and opens up the window for different theories to explain such a measurement. In this article, we use the information from Doroshenko et al. on the mass, radius, and surface temperature together with the multimessenger observations of neutron stars to investigate the possibility that HESS J1731-347 is one of the lightest observed neutron star, a strange quark star, a hybrid star with an early deconfinement phase transition, or a dark matter–admixed neutron star. The nucleonic and quark matter are modeled within realistic equation of states (EOSs) with a self-consistent calculation of the pairing gaps in quark matter. By performing the joint analysis of the thermal evolution and mass–radius constraint, we find evidence that within a 1σ confidence level, HESS J1731-347 is consistent with the neutron star scenario with the soft EOS as well as with a strange and hybrid star with the early deconfinement phase transition with a strong quark pairing and neutron star admixed with dark matter.

Classify and Explore the Diversity of Planetary Population and Interior Properties

Classification is an essential method and has been developed widely in astronomy. However, planets still lack a universal classification framework, because the solar system planet sample is too small for statistical analysis. Fortunately, exoplanets supply large samples to help build up synthetic planetary populations then support a classification framework. In this study, we use synthetic populations to explore the diversity and evolution relations of planets. We detect six outstanding clusters in mass–radius space with the kernel density estimation and extract typical planets for each type. The first four types are gas-poor planets, and the last two are gas-rich. For an intermediate type, the light gas envelopes contribute to the observable radius but not the mass. Once the planet is massive enough (3.9 M J ), its size shrinks with increasing mass due to self-gravity. Based on the evolution tracks and the gas envelopes’ properties, the environment is linked strongly to the gas properties, and it controls which type can form at a specific location. The system with gas giants will be different from those without, including total planet mass and the number of planets in the system. Giant planets shape the whole system by orbital resonance. Each type of planets’ period ratios are different, and gas giants have the most outstanding accumulation peak at 2:1 resonance. In the future, the patterns of observed planets’ retrieved interior structures can help to confirm the suggested classification. However, the structure degeneracy induces high uncertainty, such that the framework will still profit from additional theoretical constraints.

Mechanism of heavy metal ion biosorption by microalgal cells: A mathematic approach

Microalgal biomasses have been established as promising biosorbents for biosorption to remove heavy metal ions (HMIs) from wastewaters and contaminated natural waterbodies. Understanding the mechanism is important for the development of cost-effective processes for large scale applications. In this paper, a simple mathematical model was proposed for the predication of biosorption capacity of HMI by microalgal cells based on single cell mass, cell size, and HMI radius. One fundamental assumption based on which this model was developed, i.e., the biosorption of HMI by microalgal cells is predominantly monolayer bio-adsorption, was established based on kinetic, isothermal, FTIR, and Pb(II) distribution data generated in this study and in literature. The model was validated using a combination of experimental and literature data as well, demonstrating its capability to provide reasonable estimations although with discrepancies. The biosorption capacities of HMIs (mmol/g) by Chlorella vulgaris were experimentally determined to be in the following order: Pb(II)(0.360)> Zn(II)(0.325)> Cu(II)(0.254)> Ni(II)(0.249)> Cd(II)(0.235)> Co(II)(0.182). We systematically investigated the deviations of the predicted biosorption capacities in term of the effects of a few important parameters that were unaccounted for in the model, including the nanostructures on cell surface, HMI electronegativity, and biosorption buffer pH. Results suggest that the nanostructures on cell wall, likely the hairlike fibers, might be the primary locations where the binding sites for HMI were housed. Furthermore, isothermal data, which is suported by the predictions of this model, indicate the each effective binding site on C. vulgaris cell surface could bind to more than one Co(II) in biosorption while each of the other five HMIs tested in this study required more than one binding sites.