Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of using observations of such compact ...objects to probe some of the most intriguing general relativistic predictions in the strong-field regime: the absence of stable circular orbits near a compact object and the presence of event horizons around black-hole singularities. I discuss the need for a theoretical framework, within which future experiments will provide detailed, quantitative tests of gravity theories. Finally, I summarize the constraints imposed by current observations of neutron stars on potential deviations from general relativity.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
Abstract
The images of supermassive black holes surrounded by optically thin, radiatively inefficient accretion flows, like those observed with the Event Horizon Telescope, are characterized by a ...bright ring of emission surrounding the black hole shadow. In the Kerr spacetime, this bright ring, when narrow, closely traces the boundary of the shadow and can, with appropriate calibration, serve as its proxy. The present paper expands the validity of this statement by considering two particular spacetime geometries: a solution to the field equations of a modified gravity theory and another that parametrically deviates from Kerr but recovers the Kerr spacetime when its deviation parameters vanish. A covariant, axisymmetric analytic model of the accretion flow based on conservation laws and spanning a broad range of plasma conditions is utilized to calculate synthetic non-Kerr black hole images, which are then analyzed and characterized. We find that in all spacetimes: (i) it is the gravitationally lensed unstable photon orbit that plays the critical role in establishing the diameter of the rings observed in black hole images, not the event horizon or the innermost stable circular orbit, (ii) bright rings in these images scale in size with, and encompass, the boundaries of the black hole shadows, even when deviating significantly from Kerr, and (iii) uncertainties in the physical properties of the accreting plasma introduce subdominant corrections to the relation between the diameter of the image and the diameter of the black hole shadow. These results provide important new theoretical justification for using black hole images to probe and test the spacetimes of supermassive black holes.
The Event Horizon Telescope (EHT) is taking the first images of black holes resolved at horizon scales to measure their shadows and probe accretion physics. A promising avenue for testing the ...hypothesis that astrophysical black holes are described by the Kerr solution to Einstein's equations is to compare the size and shape of the shadow a black hole casts on the surrounding emission to the predictions of the Kerr metric. We develop here an efficient parametric framework to perform this test. We carry out ray-tracing simulations for several parameterized non-Kerr metrics to create a large data set of non-Kerr shadows that probe the allowed parameter space for the free parameters of each metric. We then perform principal components analysis (PCA) on this set of shadows and show that only a small number of components are needed to accurately reconstruct all shadows within the set. We further show that the amplitude of the PCA components are smoothly related to the free parameters in the metrics and, therefore, that these PCA components can be fit to EHT observations in order to place constraints on the free parameters of these metrics that will help quantify any potential deviations from the Kerr solution.
Gravitational waves from the coalescence of two neutron stars were recently detected for the first time by the LIGO-Virgo Collaboration, in event GW170817. This detection placed an upper limit on the ...effective tidal deformability of the two neutron stars and tightly constrained the chirp mass of the system. We report here on a new simplification that arises in the effective tidal deformability of the binary, when the chirp mass is specified. We find that, in this case, the effective tidal deformability of the binary is surprisingly independent of the component masses of the individual neutron stars, and instead depends primarily on the ratio of the chirp mass to the neutron star radius. Thus, a measurement of the effective tidal deformability can be used to directly measure the neutron star radius. We find that the upper limit on the effective tidal deformability from GW170817 implies that the radius cannot be larger than ∼13 km, at the 90% level, independent of the assumed masses for the component stars. The result can be applied generally, to probe the stellar radii in any neutron star-neutron star merger with a measured chirp mass. The approximate mass independence disappears for neutron star-black hole mergers. Finally, we discuss a Bayesian inference of the equation of state that uses the measured chirp mass and tidal deformability from GW170817 combined with nuclear and astrophysical priors and discuss possible statistical biases in this inference.
The need for a consistent quantum evolution for black holes has led to proposals that their semiclassical description is modified not just near the singularity, but at horizon or larger scales. If ...such modifications extend beyond the horizon, they influence regions accessible to distant observation. Natural candidates for these modifications behave like metric fluctuations, with characteristic length scales and timescales set by the horizon radius. We investigate the possibility of using the Event Horizon Telescope to observe these effects, if they have a strength sufficient to make quantum evolution consistent with unitarity, without introducing new scales. We find that such quantum fluctuations can introduce a strong time dependence for the shape and size of the shadow that a black hole casts on its surrounding emission. For the black hole in the center of the Milky Way, detecting the rapid time variability of its shadow will require nonimaging timing techniques. However, for the much larger black hole in the center of the M87 galaxy, a variable black-hole shadow, if present with these parameters, would be readily observable in the individual snapshots that will be obtained by the Event Horizon Telescope.
In general relativity, the spacetimes of black holes have three fundamental properties: (i) they are the same, to the lowest order in spin, as the metrics of stellar objects; (ii) they are ...independent of mass when expressed in geometric units; and (iii) they are described by the Kerr metric. In this paper, we quantify the upper bounds on potential black-hole metric deviations imposed by observations of black-hole shadows and of binary black-hole inspirals in order to explore the current experimental limits on possible violations of the last two predictions. We find that both types of experiments provide correlated constraints on deviation parameters that are primarily in the t t components of the spacetimes when expressed in areal coordinates. We conclude that, currently, there is no evidence for deviations from the Kerr metric across the 8 orders of magnitude in mass and 16 orders in curvature spanned by the two types of black holes. Moreover, because of the particular masses of black holes in the current sample of gravitational-wave sources, the correlations imposed by the two experiments are aligned and of similar magnitudes when expressed in terms of the far-field, post-Newtonian predictions of the metrics. If a future coalescing black-hole binary with two low-mass (e.g., ∼ 3 M⊙) components is discovered, the degeneracy between the deviation parameters can be broken by combining the inspiral constraints with those from the black-hole shadow measurements.
ABSTRACT 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 (EOS). One way to facilitate the mapping of observables to the EOS 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 EOS 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 of 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 EOS and to within less than 0.12 km for 95% of a sample of 42 proposed, physically motivated EOS. Such a parametrization is also able to reproduce the maximum mass to within 0.04 and the moment of inertia of a 1.338 neutron star to within less than 10% for 95% of the proposed sample of EOS.
One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. Here, we present a Bayesian statistical method of inferring ...the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parameterized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, , can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ∼30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, toward larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.
ABSTRACT We present a comprehensive study of spectroscopic radius measurements of twelve neutron stars obtained during thermonuclear bursts or in quiescence. We incorporate, for the first time, a ...large number of systematic uncertainties in the measurement of the apparent angular sizes, Eddington fluxes, and distances, in the composition of the interstellar medium, and in the flux calibration of X-ray detectors. We also take into account the results of recent theoretical calculations of rotational effects on neutron star radii, of atmospheric effects on surface spectra, and of relativistic corrections to the Eddington critical flux. We employ Bayesian statistical frameworks to obtain neutron star radii from the spectroscopic measurements as well as to infer the equation of state from the radius measurements. Combining these with the results of experiments in the vicinity of nuclear saturation density and the observations of neutron stars, we place strong and quantitative constraints on the properties of the equation of state between times the nuclear saturation density. We find that around the preferred equation of state predicts radii between 10.1 and 11.1 km. When interpreting the pressure constraints in the context of high density equations of state based on interacting nucleons, our results suggest a relatively weak contribution of the three-body interaction potential.
Observations of isolated neutron stars place constraints on the equation of state (EOS) of cold, neutron-rich matter, while nuclear physics experiments probe the EOS of hot, symmetric matter. Many ...dynamical phenomena, such as core-collapse supernovae, the formation and cooling of proto-neutron stars, and neutron star mergers, lie between these two regimes and depend on the EOS at finite temperatures for matter with varying proton fractions. In this paper, we introduce a new framework to accurately calculate the thermal pressure of neutron-proton-electron matter at arbitrary density, temperature, and proton fraction. This framework can be expressed using a set of five physically motivated parameters that span a narrow range of values for realistic EOS and are able to capture the leading-order effects of degenerate matter on the thermal pressure. We base two of these parameters on a new approximation of the Dirac effective mass, with which we reproduce the thermal pressure to within 30% for a variety of realistic EOS at densities of interest. Three additional parameters, which are based on the behavior of the symmetry energy near the nuclear saturation density, allow us to extrapolate any cold EOS in β-equilibrium to arbitrary proton fractions. Our model thus allows a user to extend any cold nucleonic EOS, including piecewise polytropes, to arbitrary temperature and proton fraction for use in calculations and numerical simulations of astrophysical phenomena. We find that our formalism is able to reproduce realistic finite-temperature EOS with errors of 20% and offers a 1-3 orders-of-magnitude improvement over existing ideal-fluid models.
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