Gravitational Binding Energy Research Articles

Galaxy Groups as the Ultimate Probe of AGN Feedback

The co-evolution between supermassive black holes and their environment is most directly traced by the hot atmospheres of dark matter halos. The cooling of the hot atmosphere supplies the central regions with fresh gas, igniting active galactic nuclei (AGN) with long duty cycles. The outflows from the central engine tightly couple with the surrounding gaseous medium and provide the dominant heating source, preventing runaway cooling. Every major modern hydrodynamical simulation suite now includes a prescription for AGN feedback to reproduce the realistic populations of galaxies. However, the mechanisms governing the feeding/feedback cycle between the central black holes and their surrounding galaxies and halos are still poorly understood. Galaxy groups are uniquely suited to constrain the mechanisms governing the cooling–heating balance, as the energy supplied by the central AGN can exceed the gravitational binding energy of halo gas particles. Here, we provide a brief overview of our knowledge of the impact of AGN on the hot atmospheres of galaxy groups, with a specific focus on the thermodynamic profiles of the groups. We then present our on-going efforts to improve on the implementation of AGN feedback in galaxy evolution models by providing precise measurements of the properties of galaxy groups. We introduce the XMM-Newton Group AGN Project (X-GAP), a large program on XMM-Newton targeting a sample of 49 galaxy groups out to R500c.

Bulk Properties of PSR J0030+0451 Inferred with the Compactness Measurement of NICER

In 2019, the Neutron star Interior Composition ExploreR (NICER) mission released its findings on the mass and radius of the isolated neutron star (INS) PSR J0030+0451, revealing a mass of approximately 1.4 solar masses (M ⊙) and a radius near 13 km. However, the recent reanalysis by the NICER collaboration suggests that the available data primarily yield a precise inference of the compactness for this source while the resulting mass and radius are strongly model-dependent and diverse (the 68.3% credible regions just overlap slightly for the ST+PDT and PDT-U models). By integrating this compactness data with the equation of state (EOS) refined by our latest investigations, we have deduced the mass and radius for PSR J0030+0451, delivering estimates of M=1.48−0.10+0.09M⊙ and R=12.38−0.70+0.51km for the compactness found in the ST+PDT model, alongside M=1.47−0.20+0.14M⊙ and R=12.37−0.69+0.50km for the compactness in the PDT-U model. These two groups of results are well consistent with each other and the direct X-ray data inference within the ST+PDT model seems to be favored. Additionally, we have calculated the tidal deformability, moment of inertia, and gravitational binding energy for this neutron star. Furthermore, employing these refined EOS models, we have updated mass–radius estimates for three INSs with established gravitational redshifts.

Inertia, gravity and the meaning of mass

Our concept of mass has evolved considerably over the centuries, most notably from Newton to Einstein, and then even more vigorously with the establishment of the standard model and the subsequent discovery of the Higgs boson. Mass is now invoked in various guises depending on the circumstance: it is used to represent inertia, or as a coupling constant in Newton’s law of universal gravitation, and even as a repository of a mysterious form of energy associated with a particle at rest. But recent developments in cosmology have demonstrated that rest-mass energy is most likely the gravitational binding energy of a particle in causal contact with that portion of the Universe within our gravitational horizon. In this paper, we examine how all these variations on the concept of mass are actually interrelated via this new development and the recognition that the source of gravity in general relativity is ultimately the total energy in the system.

Exploring Neutrino Mass Orderings through Supernova Neutrino Detection

Core-collapse supernovae (SNe) are one of the most powerful cosmic sources of neutrinos, with energies of several MeV. The emission of neutrinos and antineutrinos of all flavors carries away the gravitational binding energy of the compact remnant and drives its evolution from the hot initial to the cold final states. Detecting these neutrinos from Earth and analyzing the emitted signals present a unique opportunity to explore the neutrino mass ordering problem. This research outlines the detection of neutrinos from SNe and their relevance in understanding the neutrino mass ordering. The focus is on developing a model-independent analysis strategy, achieved by comparing distinct detection channels in large underground detectors. The objective is to identify potential indicators of mass ordering within the neutrino sector. Additionally, a thorough statistical analysis is performed on the anticipated neutrino signals for both mass orderings. Despite uncertainties in supernova explosion parameters, an exploration of the parameter space reveals an extensive array of models with significant sensitivity to differentiate between mass orderings. The assessment of various observables and their combinations underscores the potential of forthcoming supernova observations in addressing the neutrino mass ordering problem.

Systematic correlation analysis between the nuclear matter parameters and neutron star properties within relativistic mean-field theory

Motivated by constraining the neutron star properties and eliminating their uncertainties based on the constraints on nuclear matter parameters extracted from the terrestrial experiments, the correlations between a mount of nuclear matter parameters and neutron star properties have been analyzed by the selected equation of states within the relativistic mean-field theory and used to constrain the neutron star properties. It is found that the radius $R$, tidal deformability $\mathrm{\ensuremath{\Lambda}}$, and other neutron star properties have a notable correlation with the slope of symmetry energy $L$ for the typical neutron stars, and the ${R}_{1.4}$ and ${\mathrm{\ensuremath{\Lambda}}}_{1.4}$ restricted by the constraint on $L=54\ifmmode\pm\else\textpm\fi{}8\text{ }\text{ }\mathrm{MeV}$ can be consistent with the GW170817 and NICER observation constraints. Furthermore, it is shown that $L$ also has a good correlation with the properties of low-mass neutron stars, such as the gravitational binding energy $|{E}_{g}|$. The $|{E}_{g}|$ of low-mass neutron stars can be theoretically well constrained with the constraint range of $L$.

Statistical properties and correlation length in star-forming molecular clouds

In the first article of this series, we have used the ergodic theory to assess the validity of a statistical approach to characterize various properties of star-forming molecular clouds (MCs) from a limited number of observations or simulations. This allows the proper determination of confidence intervals for various volumetric averages of statistical quantities obtained form observations or numerical simulations. We have shown that these confidence intervals, centered on the statistical average of the given quantity, decrease as the ratio of the correlation length to the size of the sample gets smaller. In this joint paper, we apply the same formalism to a different kind of (observational or numerical) study of MCs. Indeed, as observations cannot fully unravel the complexity of the inner density structure of star forming clouds, it is important to know whether global observable estimates, such as the total mass and size of the cloud, can give an accurate estimation of various key physical quantities that characterize the dynamics of the cloud. Of prime importance is the correct determination of the total gravitational (binding) energy and virial parameter of a cloud. We show that, whereas for clouds that are not in a too advanced stage of star formation, such as Polaris or Orion B, the knowledge of only their mass and size is sufficient to yield an accurate determination of the aforementioned quantities from observations (i.e. in real space). In contrast, we show that this is no longer true for numerical simulations in a periodic box. We derive a relationship for the ratio of the virial parameter in these two respective cases.

Cosmic vacuum energy with thermodynamic and gravodynamic action power

In this paper we investigate the suspected effect of cosmic vacuum energy on the dynamics of cosmic space, while nevertheless still now the phenomenon of vacuum energy is not yet physically settled in a rigorous form. In view of what one needs for general relativistic approaches, we start here with considerations of the specific energy-momentum tensor of cosmic vacuum energy in the standard hydrodynamical form, and derive relations between vacuum energy density and vacuum pressure. With the help of fundamental thermodynamic relations we then find relations of the two quantities, vacuum pressure and energy density, to the scale R of the universe. These, however, allow for a multitude of power exponents n , including the case of a constant vacuum energy density with n=0 and Rn=const. Then we argue that for spaces of cosmic dimensions not only thermodynamical relations have to be fulfilled, but also, as we call them "gravodynamical relations", meaning that vacuum pressure has to work against the inner gravitational binding of space, mostly due to the gravitating masses distributed in this cosmic space. When we include this effect in addition to the thermodynamics we find that the vacuum energy density ρΛ then can not anymore be considered as constant, but unavoidably as falling off with the scale of the universe according R−2 . At the end of this article we then suspect, since vacuum energy even nowadays is not yet a physically well founded and understood quantity, that the Hubble expansion of the present universe is not driven by vacuum pressure, but by the change of gravitational binding energy at the ongoing structure formation of cosmic matter during the Hubble expansion.

How much could gravitational binding energy act as hidden cosmic vacuum energy?

Confronted with recent microwave background observations by WMAP and with puzzling supernovae locations in the magnitude - redshift m-z-diagram the present-day cosmology seems to call for cosmic vacuum energy as a necessary, unavoidable cosmological ingredient to get a rhyme for the disjunctive cosmological facts. Most often nowadays this vacuum energy is associated with Einstein‘s cosmological constant Λ or with the so-called: ”dark energy” paradigm, both of which are conceptually not well determined or physically clearly handable. Hereby, a positive value of Λ describes an inflationary action on cosmic scale dynamics which in view of recent cosmological data appears as an absolute need. In this article, however, we shall at least question the hypothesis of a constant vacuum energy density, since it is not justifyable on physical grounds and inconsistent with the energy conservation principle. Instead we show here that changes in gravitational binding energy of cosmic matter - connected with structure formation during the cosmic expansion -mathematically acts in a way very similar to vacuum energy, since it reduces the effective proper mass density and thus reduces the net cosmological gravitational attraction. Thus one may feel encouraged to believe that actions of cosmic vacuum energy, gravitational binding energy and effective mass reduction - taken by their pure cosmological effects - are closely related to each other, perhaps in some respects even have identical cosmological roots. Based on the results presented here we propose that the action of vacuum energy on cosmic spacetime dynamics inevitably leads to a decay of vacuum energy density. Connected with this decay is an increase of negative cosmic binding energy and the diminution of effective mass in the universe. If this all is adequately taken into account by the energy-momentum tensor of the GR field equations, one is then led to non-standard cosmologies which for the first time at least can guarantee the conservation of the total, global energy, both in static and expanding universes showing that the action of so-called vacuum energy is nothing else but the increase of gravitational binding energy in an evolved self-structured universe with a correlation coefficient of α ≥ 1. 5.

Exploring the universal relations with the correlation analysis of neutron star properties

Motivated by finding a way to construct the universal relations between the neutron star properties and obtaining the application scope of the universal relations, the linear correlation properties between several properties of neutron stars are analyzed. Based on this, several existing universal relations are tested and several new universal relations are predicted. The results show that in the whole typical central density range of neutron stars, the better the linear correlation properties between the combinations of physical quantities are, the better the universality of the universal relations will be. It is shown that the quantities possessing desired linear correlation properties are the compactness $\ensuremath{\beta}$, moment of inertia $I$, gravitational redshift $z$ and gravitational binding energy ${E}_{g}$, etc. Based on the linear correlation analysis of the above acquired quantities, several existing universal relations about the dimensionless gravitational binding energy and several new universal relations about the dimensionless moment of inertia are tested and predicted respectively. Moreover, the moment of inertia of PSR $\mathrm{J}0030+0451$ can be constrained by the newly discovered universal relation. In conclusion, the linear correlation analysis of the neutron star properties is an effective and feasible method to explore the universal relations.

Inferring the gravitational binding energy and moment of inertia of PSR J0030 + 0451 and PSR J0740 + 6620 from new universal relations

The neutron star interior composition explorer (NICER) recently simultaneously measured the gravitational mass (M g) and radius (R) of PSR J0030 + 0451 and PSR J0740 + 6620, respectively. Inspired by the groundbreaking observations, we establish two high accuracy universal relations (with the relative error at 1% level) related to M g and R to infer the gravitational binding energy (BE) (E g) and moment of inertia (I) of the two pulsars. By combining these universal relations with the data of (M g, R) released by NICER collaboration, the gravitational BE and moment of inertia of PSR J0030 + 0451 can be constrained within and g cm2 at 68% credible level, respectively. The gravitational BE and moment of inertia of PSR J0740 + 6620 can be constrained within and g cm2 at 68% credible level, respectively.

Supermassive stars with random transverse magnetic fields

ABSTRACT Gravitational dynamic collapses of supermassive stars (SMSs) triggered at certain critical stages may give rise to black holes (BHs) in a broad mass range that populate the Universe including the early Universe. SMSs have been speculated as the progenitors or seeds of supermassive BHs that power quasars and active galactic nuclei. We study quasi-spherical magnetostatic equilibria and magnetohydrodynamic (MHD) radial pulsational (in)stability properties of non-rotating SMSs involving random transverse magnetic fields (RTMFs) using the general relativity (GR). With RTMFs, the maxima of the gravitational binding energy mark the GR MHD transition from stability to instability and the RTMF does not modify the GR stability criterion significantly when the ratio ${\cal M}/\left|\Omega \right|\lesssim0.1$, where $\cal M$ is the total magnetic energy and Ω is the total gravitational potential energy. When $0.1\lesssim{\cal M}/\left|\Omega \right|\lesssim1$, nevertheless, the critical GR magnetostatic equilibria on the verge of GR MHD collapses or explosions may change drastically, raising the upper mass limit at the onset of GR MHD instability from ∼105 to ∼106 M⊙ and even higher. For ${\cal M}/\left|\Omega \right|\sim 1$, the evolution track of magnetized SMS is shifted towards the redder part of the Hertzsprung–Russell diagram, featuring a sort of ‘magnetic reddening’ associated with the stellar ‘magnetized envelope inflation’. By estimates, the RTMF energy stored in an SMS can be as large as ∼1057 erg, enough to power gamma-ray bursts, fast radio bursts, or other forms of powerful electromagnetic wave bursts. It is possible for magnetized massive stars to dynamically form BHs in the mass range from several tens to thousands of solar masses without necessarily triggering the central electron-positron e± instability inside such stars – this fact is highly pertinent to the reports of LIGO-Virgo gravitational wave event scenario of binary BH mergers.

The origin of rest-mass energy

Today we have a solid, if incomplete, physical picture of how inertia is created in the standard model. We know that most of the visible baryonic ‘mass’ in the Universe is due to gluonic back-reaction on accelerated quarks, the latter of which attribute their own inertia to a coupling with the Higgs field – a process that elegantly and self-consistently also assigns inertia to several other particles. But we have never had a physically viable explanation for the origin of rest-mass energy, in spite of many attempts at understanding it towards the end of the nineteenth century, culminating with Einstein’s own landmark contribution in his Annus Mirabilis. Here, we introduce to this discussion some of the insights we have garnered from the latest cosmological observations and theoretical modeling to calculate our gravitational binding energy with that portion of the Universe to which we are causally connected, and demonstrate that this energy is indeed equal to mc^2 when the inertia m is viewed as a surrogate for gravitational mass.

Feedback from Active Galactic Nuclei in Galaxy Groups

The co-evolution between supermassive black holes and their environment is most directly traced by the hot atmospheres of dark matter halos. The cooling of the hot atmosphere supplies the central regions with fresh gas, igniting active galactic nuclei (AGN) with long duty cycles. Outflows from the central engine tightly couple with the surrounding gaseous medium and provide the dominant heating source preventing runaway cooling by carving cavities and driving shocks across the medium. The AGN feedback loop is a key feature of all modern galaxy evolution models. Here, we review our knowledge of the AGN feedback process in the specific context of galaxy groups. Galaxy groups are uniquely suited to constrain the mechanisms governing the cooling–heating balance. Unlike in more massive halos, the energy that is supplied by the central AGN to the hot intragroup medium can exceed the gravitational binding energy of halo gas particles. We report on the state-of-the-art in observations of the feedback phenomenon and in theoretical models of the heating-cooling balance in galaxy groups. We also describe how our knowledge of the AGN feedback process impacts galaxy evolution models and large-scale baryon distributions. Finally, we discuss how new instrumentation will answer key open questions on the topic.

Is the binding energy of galaxies related to their core black hole mass?

Most of the large galaxies host a supermassive black hole, but their origin is still not well understood. In this paper, we look at a possible connection between the gravitational binding energies of large galaxies, etc., and the masses of their central black holes. Using this relation (between the gravitational binding energy of the host structure and the black hole energy), we argue why globular clusters are unlikely to harbour large black holes and why dwarf galaxies, if they have to host black holes, should have observed mass-to-light ratios of ~100.

Conserved charges in general relativity

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved space–time with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner–Sharp mass in the Oppenheimer–Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.

CO Outflow Candidates toward the W3/4/5 Complex. II. Feedback from Candidate Outflows

Abstract To date, few studies have focused on protostellar outflow feedback at scales larger than several parsecs. To address this paucity of research, we investigate the effects of feedback from CO outflow candidates on their parent clouds over ∼110 deg2 toward the W3/4/5 complex and its surroundings. Our search identified 265 13CO clouds with radii being ∼0.04–17.12 pc. We estimate the turbulent support and potential disruptive effect of the outflow activities through analyzing physical properties of outflow candidates and their host clouds in terms of turbulence and gravitational binding energy. We find that (1) clouds of larger size might be less affected by feedback; (2) the possible scale break is ≳4.7 pc for both turbulent support and potential disruptive effect; (3) if outflows couple to dense gas where stars are forming, for clouds in the Perseus arm, a scale ≲0.2–0.4 pc is sufficient for the energy and momentum injected by outflow activity to maintain turbulence, while for clouds in the Local arm, the scale is ≲0.1–0.2 pc; and (4) for clouds in the Perseus arm, a scale ≲0.3–1.0 pc is needed for outflow activity to potentially disperse material away from the natal clouds, while for clouds in the Local arm, the scale is ≲0.2–0.6 pc. The strength of outflow activity may affect the values in points 3 and 4. Finally, we find that outflow feedback probably possesses the power to alter the line width–size relation.

Total energy in supernova neutrinos and the tidal deformability and binding energy of neutron stars

The energy radiated in supernova neutrinos is a fundamental quantity that is closely related to the gravitational binding energy of a neutron star. Recently the tidal deformability of neutron stars was constrained by gravitational wave observations. By considering several equations of state, we find a strong correlation between the tidal deformability and neutron star binding energy. We use this correlation to sharpen predictions of the binding energy of neutron stars and the total neutrino energy in supernovae. We find a minimum binding energy for a neutron star formed in a supernova of $\sim1.5\times 10^{53}$ ergs. Should the neutrino energy in a supernova be significantly below this value, it would strongly suggest new unobserved particles are carrying away some of the supernova energy. Alternatively, if the neutrino energy is observed above $\sim 6\times 10^{53}$ ergs, it would strongly imply the formation of a (perhaps surprisingly) massive neutron star.

Boson stars in f(T) extended theory of gravity

Spherically symmetric configurations of the non-interacting massive complex scalar field, representing non-rotating boson stars, are considered within the framework of the modified torsion based $f(T)$ gravity, with $f(T) = T + \alpha \, T^2/2$. We find that with sufficiently large negative value of $\alpha$ the mass of the boson stars can be made arbitrarily large. This is in contrast to General Relativity where an upper bound, $M_{max} \sim M_{Planck}^2/m$, to the mass of the boson stars built from the non-interacting scalar field exists and where the masses of boson stars in the astrophysical regime can be obtained only with the introduction of the scalar field self-interaction. With sufficiently large negative $\alpha$ we also find negative gravitational binding energy for all masses, which can be seen as an indication of the stability of such configurations. In its positive regime, $\alpha$ can not be made arbitrarily large as a phase transition in the stress--energy components of the $f(T)$-fluid develops. This phenomenon has already been reported to occur in polytropic stars constructed within the $f(T)$ gravity theory.

Detecting dark matter around black holes with gravitational waves: Effects of dark-matter dynamics on the gravitational waveform

A dark matter overdensity around a black hole may significantly alter the dynamics of the black hole's merger with another compact object. We consider here intermediate mass-ratio inspirals of stellar-mass compact objects with intermediate-mass black holes "dressed" with dark matter. We first demonstrate that previous estimates based on a fixed dark-matter dress are unphysical for a range of binaries and dark-matter distributions by showing that the total energy dissipated by the compact object through dynamical friction, as it inspirals through the dense dark matter environment towards the black hole, is larger than the gravitational binding energy of the dark-matter dress itself. We then introduce a new formalism that allows us to self-consistently follow the evolution of the dark-matter dress due to its gravitational interaction with the binary. We show that the dephasing of the gravitational waveform induced by dark matter is smaller than previously thought, but is still potentially detectable with the LISA space interferometer. The gravitational waves from such binaries could provide powerful diagnostics of the particle nature of dark matter.

Why can hadronic stars convert into strange quark stars with larger radii

The total binding energy of compact stars is the sum of the gravitational binding energy $(BE)_g$ and the nuclear binding energy $(BE)_n$, the last being related to the microphysics of the interactions. While the first is positive (binding) both for hadronic stars and for strange quark stars, the second is large and negative for hadronic stars (anti-binding) and either small and negative (anti-binding) or positive (binding) for strange quark stars. A hadronic star can convert into a strange quark star with a larger radius because the consequent reduction of $(BE)_g$ is over-compensated by the large increase in $(BE)_n$. Thus, the total binding energy increases due to the conversion and the process is exothermic. Depending on the equations of state of hadronic matter and quark matter and on the baryonic mass of the star, the contrary is obviously also possible, namely the conversion of hadronic stars into strange quark stars having smaller radii, a situation more often discussed in the literature. We provide a condition that is sufficient and in most of the phenomenologically relevant cases also necessary in order to form strange quark stars with larger radii while satisfying the exothermicity request. Finally, we compare the two schemes in which quark stars are produced (one having large quark stars and the other having small quark stars) among themselves and with the third-family scenario and we discuss how present and future data can discriminate among them.