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ENTER: a new frontier in physics
Abstract
Black hole (BH) formation via extreme star (ES, mean density comparable to or
larger than neutron mean density) instability, due to increasing mass, is
conceived as a phase transition from ordinary (energy + matter) to ENTER, an
indivisible ideal fluid. BHs and ESs are related to classical, heterogeneous
disks of equal mass, equatorial radius, moment of inertia, where surface
density distribution obeys a power law, by use of a principle of corresponding
states. With regard to static (TOV) and equatorial breackup (EQB)
configurations, ES reduced (dimensionless) parameters are inferred and
revised} from earlier results, and compared to the following BH relations:
(reduced moment of inertia)-(reduced angular momentum); (swivelness)-(reduced angular momentum); (angular momentum)-(mass)
in logarithmic plane for sequences of configurations where reduced
angular momentum remains unchanged. ES (reduced moment of
inertia)-(compactness) relation, inferred in earlier investigations for a large
number of equations of state (EOSs) and sequences of constant reduced
angular momentum, is extrapolated across the instability region,
and results are consistent with related BH
counterparts. Similarly to BHs, classical heterogeneous
disks associated via a principle of corresponding states exhibit surface
density distribution increasing with radial distance, contrary to TOV and EQB
configurations with assigned EOS, which allows the formulation of an empirical
criterion for ES stability.
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We describe the discovery of a solar neighborhood ( d = 468 pc) binary system with a main-sequence sunlike star and a massive noninteracting black hole candidate. The spectral energy distribution of the visible star is described by a single stellar model. We derive stellar parameters from a high signal-to-noise Magellan/MIKE spectrum, classifying the star as a main-sequence star with T eff = 5972 K, log g = 4.54 , and M = 0.91 M ⊙ . The spectrum shows no indication of a second luminous component. To determine the spectroscopic orbit of the binary, we measured the radial velocities of this system with the Automated Planet Finder, Magellan, and Keck over four months. We show that the velocity data are consistent with the Gaia astrometric orbit and provide independent evidence for a massive dark companion. From a combined fit of our spectroscopic data and the astrometry, we derive a companion mass of 11.39 − 1.31 + 1.51 M ⊙ . We conclude that this binary system harbors a massive black hole on an eccentric ( e = 0.46 ± 0.02), 185.4 ± 0.1 day orbit. These conclusions are independent of El-Badry et al., who recently reported the discovery of the same system. A joint fit to all available data yields a comparable period solution but a lower companion mass of 9.32 − 0.21 + 0.22 M ⊙ . Radial velocity fits to all available data produce a unimodal solution for the period that is not possible with either data set alone. The combination of both data sets yields the most accurate orbit currently available.
The generic properties of compact objects made of two different fluids of dark matter are studied in a scale-invariant approach. We investigate compact objects with a core–shell structure, where the two fluids are separated, and with mixed dark matter components, where both dark matter fluids are immersed within each other. The constellations considered are combinations of incompressible fluids, free and interacting Fermi gases, and equations of state with a vacuum term, i.e., self-bound dark matter. We find novel features in the mass–radius relations for combined dark matter compact objects, which distinguishes them from compact objects with a single dark matter fluid and compact stars made of ordinary baryonic matter, such as white dwarfs, neutron stars, and quark stars. The maximum compactness of certain combined dark matter stars can reach values up to the causality limit for compact stars but not beyond that limit if causality of the dark matter fluids is ensured.
The lack of objects between 2 and 5 M ⊙ in the joint mass distribution of compact objects has been termed the “mass gap,” and attributed mainly to the characteristics of the supernova mechanism precluding their birth. However, recent observations show that a number of candidates reported to lie inside the “gap” may fill it, suggesting instead a paucity that may be real or largely a result of small number statistics. We quantify in this work the individual candidates and evaluate the joint probability of a mass gap. Our results show that an absolute mass gap is not present, to a very high confidence level. It remains to be seen if a relative paucity of objects stands in the future, and how this population can be related to the formation processes, which may include neutron star mergers, the collapse of a neutron star to a black hole, and others.
In the past three decades, many stars orbiting about the supermassive black hole (SMBH) at the Galactic Centre (Sgr A*) were identified. Their orbital nature can give stringent constraints for the mass of the SMBH. In particular, the star S2 has completed at least one period since our first detection of its position, which can provide rich information to examine the properties of the SMBH, and the astrophysical environment surrounding the SMBH. Here, we report an interesting phenomenon that if a significant amount of dark matter or stellar mass is distributed around the SMBH, the precession speed of the S2 stellar orbit could be ‘slow down’ by at most 27% compared with that without dark matter surrounding the SMBH, assuming the optimal dark matter scenario. We anticipate that future high quality observational data of the S2 stellar orbit or other stellar orbits can help reveal the actual mass distribution near the SMBH and the nature of dark matter.
Context. Current wisdom suggests that the observed population of neutron stars are manifestations of their birth scenarios and their thermal and magnetic field evolution. Neutron stars can be observed at various wavebands as pulsars, and radio pulsars represent by far the largest population of neutron stars.
Aims. In this paper, we aim to constrain the observed population of the canonical neutron star period, its magnetic field, and its spatial distribution at birth in order to understand the radio and high-energy emission processes in a pulsar magnetosphere. For this purpose we design a population synthesis method, self-consistently taking into account the secular evolution of a force-free magnetosphere and the magnetic field decay.
Methods. We generated a population of pulsars and evolved them from their birth to the present time, using the force-free approximation. We assumed a given initial distribution for the spin period, surface magnetic field, and spatial Galactic location. Radio emission properties were accounted for by the polar cap geometry, whereas the gamma-ray emission was assumed to be produced within the striped wind model.
Results. We find that a decaying magnetic field gives better agreement with observations compared to a constant magnetic field model. Starting from an initial mean magnetic field strength of B = 2.5 × 10 ⁸ T with a characteristic decay timescale of 4.6 × 10 ⁵ yr, a neutron star birth rate of 1/70 yr and a mean initial spin period of 60 ms, we find that the force-free model satisfactorily reproduces the distribution of pulsars in the P − Ṗ diagram with simulated populations of radio-loud, radio-only, and radio quiet gamma-ray pulsars similar to the observed populations.
Dense nuclear matter is expected to be anisotropic due to effects such as solidification, superfluidity, strong magnetic fields, hyperons, pion-condensation. Therefore an anisotropic neutron star core seems more realistic than an ideally isotropic one. We model anisotropic neutron stars working in the Krori–Barua (KB) ansatz without preassuming an equation of state. We show that the physics of general KB solutions is encapsulated in the compactness. Imposing physical and stability requirements yields a maximum allowed compactness 2GM/Rc2<0.71 for a KB-spacetime. We further input observational data from numerous pulsars and calculate the boundary density. We focus especially on data from the LIGO/Virgo collaboration as well as recent independent measurements of mass and radius of miilisecond pulsars with white dwarf companions by the Neutron Star Interior Composition Explorer (NICER). For these data the KB-spacetime gives the same boundary density which surprisingly equals the nuclear saturation density within the data precision. Since this value designates the boundary of a neutron core, the KB-spacetime applies naturally to neutron stars. For this boundary condition we calculate a maximum mass of 4.1 solar masses.
Gravitational redshift in the Galactic Center
General relativity predicts that light emitted by an object in a strong gravitational field—for example, close to a black hole—should be shifted to longer wavelengths. This gravitational redshift does not exist in the Newtonian theory of gravity. Do et al. monitored the position and spectrum of the star S0-2 as it passed Sagittarius A*, the supermassive black hole at the center of the Milky Way. Around the closest part of S0-2's 16-year orbit, they detected the effect of gravitational redshift on its spectrum. These results are more consistent with general relativity than Newtonian gravity at the 5σ level.
Science , this issue p. 664
Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically different, and often conflicting, ways. All those ways, however, seem sound in the relevant contexts. After examining and comparing many of the definitions used in practice, I consider the problems that the lack of a universally accepted definition leads to, and discuss whether one is in fact needed for progress in the physics of black holes. I conclude that, within reasonable bounds, the profusion of different definitions is in fact a virtue, making the investigation of black holes possible and fruitful in all the many different kinds of problems about them that physicists consider, although one must take care in trying to translate results between fields.
We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be (68\%), (90\%), where this constraint is robust against the choice of model for the mass distribution and to removing the most extreme (highest mass) neutron stars from the dataset. If this sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts tight constraints on the equation of state. For a set of realistic equations of state that support neutron stars, our inference of is able to distinguish between models at odds ratios of up to 15:1, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at the nuclear saturation density by compared to simply requiring . We obtain a lower bound on the maximum sound speed attained inside the neutron star of (99.8\%), ruling out at high significance. Our constraints on the equation of state strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.
Within the context of Newton's theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable vortex-like surface, under the action of a tidal gravitational field along the symmetry axis. An interpretation is made in the light of a holographic principle, in the sense that motions in ordinary space are connected with motions on a selected surface and vice versa. Then ordinary space is conceived as a 3-hypersurface bounding a n-hypervolume where gravitation takes origin, within a n-hyperspace. The extension of the holographic principle to extra dimensions implies the existence of a minimum distance where test particles may still be considered as distinct from the central body. Below that threshold, it is inferred test particles lose theirs individuality and "glue" to the central body via unification of the four known interactions and, in addition, (i) particles can no longer be conceived as point-like but e.g., strings or membranes, and (ii) quantum effects are dominant and matter turns back to a pre-big bang state. A more detailed formulation including noncircular motions within the context of general relativity, together with further knowledge on neutron stars, quark stars and black holes, would provide further insight on the formulation of quantum gravity.
A set of theoretical mass-radius relations for rigidly rotating neutron stars
with exotic cores, obtained in various theories of dense matter, is reviewed.
Two basic observational constraints are used: the largest measured rotation
frequency is 716 Hz and the maximum measured mass is .
Present status of measuring the radii of neutron stars is described. The theory
of rigidly rotating stars in general relativity is reviewed and limitations of
the slow rotation approximation are pointed out. Mass-radius relations for
rotating neutron stars with hyperon and quark cores are illustrated using
several models. Problems related to the non-uniqueness of the crust-core
matching are mentioned. Limits on rigid rotation resulting from the
mass-shedding instability and the instability with respect to the axisymmetric
perturbations are summarized. The problem of instabilities and of the
back-bending phenomenon are discussed in detail. Metastability and instability
of a neutron star core in the case of a first-order phase transition, both
between pure phases, and into a mixed-phase state, are reviewed. The case of
two disjoint families (branches) of rotating neutron stars is discussed and
generic features of neutron-star families and of core-quakes triggered by the
instabilities are considered.
Black holes are said to have no hair because all of their multipole moments can be expressed in terms of just their mass, charge and spin angular momentum. The recent discovery of approximately equation-of-state-independent relations among certain multipole moments in neutron stars suggests that they are also approximately bald. We here explore the yet unknown origin for this universality. First, we investigate which region of the neutron star’s interior and of the equation of state is most responsible for the universality. We find that the universal relation between the moment of inertia and the quadrupole moment is dominated by the star’s outer core, a shell of width 50%–95% of the total radius, which corresponds to the density range 10^14–10^15 g/cm^3. In this range, realistic neutron star equations of state are not sufficiently similar to each other to explain the universality observed. Second, we study the impact on the universality of approximating stellar isodensity contours as self-similar ellipsoids. An analytical calculation in the nonrelativistic limit reveals that the shape of the ellipsoids per se does not affect the universal relations much, but relaxing the self-similarity assumption can completely destroy it. Third, we investigate the eccentricity profiles of rotating relativistic stars and find that the stellar eccentricity is roughly constant, with variations of roughly 20%–30% in the region that matters to the universal relations. Fourth, we repeat the above analysis for differentially rotating, noncompact, regular stars and find that this time the eccentricity is not constant, with variations that easily exceed 100%, and moreover universality is lost. These findings suggest that universality arises as an emergent approximate symmetry: as one flows in the stellar-structure phase space from noncompact star region to the relativistic star region, the eccentricity variation inside stars decreases, leading to approximate self-similarity in their isodensity contours, which then leads to the universal behavior observed in their exterior multipole moments.
Neutron stars and quark stars are not only characterized by their mass and radius but also by how fast they spin, through
their moment of inertia, and how much they can be deformed, through their Love number and quadrupole moment. These depend
sensitively on the star’s internal structure and thus on unknown nuclear physics. We find universal relations between the
moment of inertia, the Love number, and the quadrupole moment that are independent of the neutron and quark star’s internal
structure. These can be used to learn about neutron star deformability through observations of the moment of inertia, break
degeneracies in gravitational wave detection to measure spin in binary inspirals, distinguish neutron stars from quark stars,
and test general relativity in a nuclear structure–independent fashion.
Recent measurements of the velocities of stars near the centre of the Milky Way have provided the strongest evidence for the presence of a supermassive black hole in a galaxy, but the observational uncertainties poorly constrain many of the black hole's properties. Determining the accelerations of stars in their orbits around the centre provides much more precise information about the position and mass of the black hole. Here we report measurements of the accelerations of three stars located approximately 0.005 pc (projected on the sky) from the central radio source Sagittarius A* (Sgr A*); these accelerations are comparable to those experienced by the Earth as it orbits the Sun. These data increase the inferred minimum mass density in the central region of the Galaxy by an order of magnitude relative to previous results, and localize the dark mass to within 0.05 +/- 0.04 arcsec of the nominal position of Sgr A*. In addition, the orbital period of one of the observed stars could be as short as 15 years, allowing us the opportunity in the near future to observe an entire period.
We report discovery of a bright, nearby () Sun-like star orbiting a dark object. We identified the system as a black hole candidate via its astrometric orbital solution from the Gaia mission. Radial velocities validated and refined the Gaia solution, and spectroscopy ruled out significant light contributions from another star. Joint modeling of radial velocities and astrometry constrains the companion mass to M2 = 9.62 ± 0.18 M⊙. The spectroscopic orbit alone sets a minimum companion mass of M2 > 5 M⊙; if the companion were a 5 M⊙ star, it would be 500 times more luminous than the entire system. These constraints are insensitive to the mass of the luminous star, which appears as a slowly-rotating G dwarf (, log g = 4.5, M = 0.93 M⊙), with near-solar metallicity () and an unremarkable abundance pattern. We find no plausible astrophysical scenario that can explain the orbit and does not involve a black hole. The orbital period, Porb = 185.6 days, is longer than that of any known stellar-mass black hole binary. The system’s modest eccentricity (e = 0.45), high metallicity, and thin-disk Galactic orbit suggest that it was born in the Milky Way disk with at most a weak natal kick. How the system formed is uncertain. Common envelope evolution can only produce the system’s wide orbit under extreme and likely unphysical assumptions. Formation models involving triples or dynamical assembly in an open cluster may be more promising. This is the nearest known black hole by a factor of 3, and its discovery suggests the existence of a sizable population of dormant black holes in binaries. Future Gaia releases will likely facilitate the discovery of dozens more.
We perform a Bayesian analysis of neutrons star moment of inertia by utilizing the available gravitational-wave data from LIGO/Virgo (GW170817 and GW190425) and mass-radius measurements from the Neutron Star Interior Composition Explorer (PSR J0030+0415 and PSR J0740+6620), incorporating the possible phase transition in the pulsar inner core. We find that the moment of inertia of pulsar A in the double pulsar binary J0737-3039 is ∼1.30 × 1045 g cm2, which only slightly depends on the employed hadronic equation of states. We also demonstrate how a moment of inertia measurement would improve our knowledge of the equation of state and the mass-radius relation for neutron stars and discuss whether a quark deconfinement phase transition is supported by the available data and forthcoming data that could be consistent with this hypothesis. We find that if pulsar A is a quark star, that its moment of inertia is a large value of ∼1.55 × 1045 g cm2 suggesting the possibility of distinguishing it from (hybrid-)neutron stars with measurements of PSR J0737-3039A moment of inertia. We finally demonstrate the moment-of-inertia-compactness universal relations and provide analytical fits for both (hybrid-)neutron star and quark star results based on our analysis.
The occurrence of a desert between neutron star (NS) and black hole (BH)
remnants is reviewed using a set of well-determined masses from different
sources. The dependence of stellar remnants on the zero age main sequence
(ZAMS) progenitor mass for solar metallicity is taken from a recent
investigation and further effort is devoted to NS and BH remnants. In
particular, a density parameter is defined and related to NS mass and radius.
Spinning BHs in Kerr metrics are considered as infinitely thin, homogeneous,
rigidly rotating disks in Newtonian mechanics. Physical parameters for
nonrotating (TOV) and equatorial breakup (EQB) configurations are taken or
inferred from a recent investigation with regard to 4 NS and 3 quark star (QS)
physically motivated equation of state (EOS) kinds. A comparison is
performed with counterparts related to nonrotating and maximally rotating BHs.
The results are also considered in the light of empirical
relations present in literature. With regard to J-M relation, EQB
configurations are placed on a sequence of similar slope in comparison to
maximally rotating BHs, but shifted downwards due to lower angular momentum by
a factor of about 3.6. Under the assumption heavy baryons are NS
constituents and instantaneously undergo quark-level reactions, the energy
released (or adsorbed) is calculated using results from a recent
investigation. Even if NSs exclusively host heavy baryons of the kind
considered, the total amount cannot exceed about 10% of the binding energy,
which inhibits supernova explosions as in supramassive white dwarf (WD)
remnants or implosions into BH. Alternative channels for submassive
(2 <= M/m_sun <= 4) BH formation are shortly discussed. Whether
the desert between NS and BH remnants could be ascribed to biases and/or
selection effects, or related to lack of formation channels, still remains an
open question. To this respect, increasingly refined theoretical and
observational techniques are needed.
We study the innermost stable circular orbit (ISCO) of a test particle around rapidly rotating neutron stars. Based on 12 different nuclear-matter equations of state (EOS), we find numerically two approximately EOS-insensitive universal relations that connect the radius and orbital frequency of the ISCO to the spin frequency f and mass M of rotating neutron stars. The relations are EOS-insensitive to about the 2% level for a large range of Mf. We also find that the universal relation for the ISCO radius agrees with the corresponding relation for the Kerr black hole to within 6% up to Mf = 5000 M o Hz. Our relations can be applied to accreting neutron stars in low-mass X-ray binaries. Using the spin frequency f = 414 Hz and the highest kilohertz quasi-periodic oscillations (kHz QPOs) at 1220 Hz observed in the system 4U 0614+09, we determine the mass of the neutron star to be 2.0 M o. Our conclusion only makes a minimal assumption that the highest kHz QPO frequency is the ISCO frequency, bypassing the assumption of slow rotation and the uncertainty related to the dimensionless spin parameter, which are commonly required in the literature. © 2018. The American Astronomical Society. All rights reserved..
We estimate the accretion rates onto and spins of supermassive black holes (SMBH). Our results are based on the observed (rest frame) bolometric luminosities and luminosities at λ=5100Å, virial estimates of black hole masses, and scaling relations derived from the standard thin accretion disk model. We compare our results with BH spin measurements derived from relativistic reflection fitting of SMBH X-ray spectra. Obtained results confirm our conclusion on the efficiency of deriving SMBH spin values based on the model of standard (Shakura-Sunyaev) accretion disk. It is essential that polarimetric observations have a key role in determining spin values.
A supramassive, strongly-magnetized millisecond neutron star (NS) has been proposed to be the candidate central engine of at least some short gamma-ray bursts (SGRBs), based on the "internal plateau" commonly observed in the early X-ray afterglow. While a previous analysis shows a qualitative consistency between this suggestion and the Swift SGRB data, the distribution of observed break time is much narrower than the distribution of the collapse time of supramassive NSs for the several NS equations-of-state (EoSs) investigated. In this paper, we study four recently-constructed "unified" NS EoSs, as well as three developed strange quark star (QS) EoSs within the new confinement density-dependent mass model. All the EoSs chosen here satisfy the recent observational constraints of the two massive pulsars whose masses are precisely measured. We construct sequences of rigidly rotating NS/QS configurations with increasing spinning frequency f, from non-rotating () to the Keplerian frequency (), and provide convenient analytical parametrizations of the results. Assuming that the cosmological NS-NS merger systems have the same mass distribution as the Galactic NS-NS systems, we demonstrate that all except the BCPM NS EoS can reproduce the current supramassive NS/QS fraction constraint as derived from the SGRB data. We simultaneously simulate the observed quantities (the break time , the break time luminosity and the total energy in the electromagnetic channel ) of SGRBs, and find that while equally well reproducing other observational constraints, QS EoSs predict a much narrower distribution than that of the NS EoSs, better matching the data. We therefore suggest that the post-merger product of NS-NS mergers might be fast-rotating supramassive QSs rather than NSs.
The increasing number and precision of measurements of neutron star masses, radii, and, in the near future, moments of inertia offer the possibility of precisely determining the neutron star equation of state. One way to facilitate the mapping of observables to the equation of state is through a parametrization of the latter. We present here a generic method for optimizing the parametrization of any physically allowed EoS. We use mock equations of state that incorporate physically diverse and extreme behavior to test how well our parametrization reproduces the global properties of the stars, by minimizing the errors in the observables mass, radius, and the moment of inertia. We find that using piecewise polytropes and sampling the EoS with five fiducial densities between ~1-8 times the nuclear saturation density results in optimal errors for the smallest number of parameters. Specifically, it recreates the radii of the assumed EoS to within less than 0.5 km for the extreme mock equations of state and to within less than 0.12 km for 95% of a sample of 42 proposed, physically-motivated equations of state. Such a parametrization is also able to reproduce the maximum mass to within 0.04 M_sun and the moment of inertia of a 1.338 M_sun neutron star to within less than 10% for 95% of the proposed sample of equations of state.
We summarize our current knowledge of neutron star masses and radii. Recent instrumentation and computational advances have resulted in a rapid increase in the discovery rate and precise timing of radio pulsars in binaries in the last few years, leading to a large number of mass measurements. These discoveries show that the neutron star mass distribution is much wider than previously thought, with 3 known pulsars now firmly in the 1.9-2.0 Msun mass range. For radii, large, high quality datasets from X-ray satellites as well as significant progress in theoretical modeling led to considerable progress in the measurements, placing them in the 9.9-11.2 km range and shrinking their uncertainties due to a better understanding of the sources of systematic errors. The combination of the massive neutron star discoveries, the tighter radius measurements, and improved laboratory constraints of the properties of dense matter has already made a substantial impact on our understanding of the composition and bulk properties of cold nuclear matter at densities higher than that of the atomic nucleus, a major unsolved problem in modern physics.
A number of recent works have highlighted that it is possible to express the properties of general-relativistic stellar equilibrium
configurations in terms of functions that do not depend on the specific equation of state employed to describe matter at nuclear
densities. These functions are normally referred to as “universal relations” and have been found to apply, within limits,
both to static or stationary isolated stars, as well as to fully dynamical and merging binary systems. Further extending the
idea that universal relations can be valid also away from stability, we show that a universal relation is exhibited also by
equilibrium solutions that are not stable. In particular, the mass of rotating configurations on the turning-point line shows
a universal behaviour when expressed in terms of the normalised Keplerian angular momentum. In turn, this allows us to compute
the maximum mass allowed by uniform rotation, Mmax, simply in terms of the maximum mass of the nonrotating configuration, MTOV, finding that Mmax ≃ (1.203 ± 0.022) MTOV for all the equations of state we have considered. We further introduce an improvement to previously published universal
relations by Lattimer & Schutz (2005) between the dimensionless moment of inertia and the stellar compactness, which could
provide an accurate tool to constrain the equation of state of nuclear matter when measurements of the moment of inertia become
available.
The lowest neutron star masses currently measured are in the range 1.0 − 1.1~M⊙, but these measurement have either large uncertainties or refer to isolated neutron stars. The recent claim of a precisely
measured mass M/M⊙ = 1.174 ± 0.004 (Martinez et al. 2015) in a double neutron star system suggests that low-mass neutron stars may be an interesting
target for gravitational-wave detectors. Furthermore, Sotani et al. (2014) recently found empirical formulas relating the
mass and surface redshift of nonrotating neutron stars to the star’s central density and to the parameter η ≡ (K0L2)1/3, where K0 is the incompressibility of symmetric nuclear matter and L is the slope of the symmetry energy at saturation density. Motivated by these considerations, we extend the work by Sotani
et al. (2014) to slowly rotating and tidally deformed neutron stars. We compute the moment of inertia, quadrupole moment,
quadrupole ellipticity, tidal and rotational Love number and apsidal constant of slowly rotating neutron stars by integrating
the Hartle-Thorne equations at second order in rotation, and we fit all of these quantities as functions of η and of the central
density. These fits may be used to constrain η, either via observations of binary pulsars in the electromagnetic spectrum,
or via near-future observations of inspiralling compact binaries in the gravitational-wave spectrum.
We construct equilibrium configurations of uniformly rotating neutron stars
for selected relativistic mean-field nuclear matter equations of state (EOS).
We compute in particular the gravitational mass (M), equatorial () and polar () radii, eccentricity, angular momentum (J),
moment of inertia (I) and quadrupole moment () of neutron stars stable
against mass-shedding and secular axisymmetric instability. By constructing the
constant frequency sequence f=716 Hz of the fastest observed pulsar, PSR
J1748-2446ad, and constraining it to be within the stability region, we obtain
a lower mass bound for the pulsar, -, for the
EOS employed. Moreover we give a fitting formula relating the baryonic mass
() and gravitational mass of non-rotating neutron stars,
[or
], which is independent on the
EOS. We also obtain a fitting formula, although not EOS independent, relating
the gravitational mass and the angular momentum of neutron stars along the
secular axisymmetric instability line for each EOS. We compute the maximum
value of the dimensionless angular momentum, (or "Kerr
parameter"), , found to be also independent on the
EOS. We compare and contrast then the quadrupole moment of rotating neutron
stars with the one predicted by the Kerr exterior solution for the same values
of mass and angular momentum. Finally we show that, although the mass
quadrupole moment of realistic neutron stars never reaches the Kerr value, the
latter is closely approached from above at the maximum mass value, as
physically expected from the no-hair theorem. In particular the stiffer the EOS
is, the closer the Kerr solution is approached.
We discuss constraints on the properties and nature of the dark mass concentration at the core of the Milky Way. We present
0.15-arcsec astrometric K-band maps in five epochs beween 1992 and 1996. From these we derive imposed stellar proper motions within 3 arcsec of the
compact radio source Sgr A* whose infrared counterpart may have been detected, for the first time, in a deep image in 1996
June. We also report λ/Δλ ~ 35 speckle spectroscopy and show that several of the Sgr A* (infrared) cluster members are likely
early-type stars of mass ~ 15 to 20 M⊙. All available checks, including a first comparison with high-resolution maps that
are now becoming available from other groups, support our previous conclusion that there are several fast-moving stars ( ≥
103 km s−3) in the immediate vicinity (0.01 pc) of Sgr A*. From the stellar radial and proper motion data, we infer that a dark mass
of 2.61 (± 0.15stat)( ± 0.35stat+sys) × 106 M⊙ must reside within about one light-week of the compact radio source. Its density must be 2.2 × 1012 M° pc−3 or greater. There is no stable configuration of normal stars, stellar remnants or substellar entities at that density. From
an equipartition argument we infer that at least 5 per cent of the dark mass ( ≥ 105 M⊙) is associated with the compact radio source Sgr A* itself and is concentrated on a scale of less than 15 times the Schwarzschild
radius of a 2.6 × 106-M⊙ black hole. The corresponding density is 3 × 1020 M⊙ pc−3 or greater. if one accepts these arguments it is hard to escape the conclusion that there must be a massive black hole at
the core of the Milky Way.
A red giant orbiting a black hole
- K El-Badry
- H.-W Rix
- Y Cendes
- A C Rodriguez
- C Conroy
- E Quataert
- K Hawkins
- E Zari
- M Hobson
- K Breivik
- A Rau
- E Berger
- S Shahaf
- R Seeburger
K. El-Badry, H.-W. Rix, Y. Cendes, A.C. Rodriguez, C. Conroy, E.
Quataert, K. Hawkins, E. Zari, M. Hobson, K. Breivik, A. Rau, E. Berger,
S. Shahaf, R. Seeburger, et al., A red giant orbiting a black hole, Monthly
Notices of the Royal Astronomical Society, 521 (2023), 4323-4348.
https://doi.org/10.1093/mnras/stad799