The half opening angle of a Kerr black-hole shadow is always equal to (5+-0.2)GM/Dc^2, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% ra
nge constitutes a null hypothesis test of General Relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope. We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of +-4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A and the Earth, the effects of which will need to be corrected for in order for the black-hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ~9%. All these results suggest that our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this General Relativistic null hypothesis test with Event Horizon Telescope observations of Sgr A* to 10%.
Observations of the black hole in the center of the Milky Way with the Event Horizon Telescope at 1.3 mm have revealed a size of the emitting region that is smaller than the size of the black-hole shadow. This can be reconciled with the spectral prop
erties of the source, if the accretion flow is seen at a relatively high inclination (50-60 degrees). Such an inclination makes the angular momentum of the flow, and perhaps of the black hole, nearly aligned with the angular momenta of the orbits of stars that lie within 3 arcsec from the black hole. We discuss the implications of such an alignment for the properties of the black hole and of its accretion flow. We argue that future Event-Horizon-Telescope observations will not only refine the inclination of Sgr A* but also measure precisely its orientation on the plane of the sky.
We explore the evolution of the mass distribution of dust in collision-dominated debris disks, using the collisional code introduced in our previous paper. We analyze the equilibrium distribution and its dependence on model parameters by evolving ove
r 100 models to 10 Gyr. With our numerical models, we confirm that systems reach collisional equilibrium with a mass distribution that is steeper than the traditional solution by Dohnanyi (1969). Our model yields a quasi steady-state slope of n(m) ~ m^{-1.88} [n(a) ~ a^{-3.65}] as a robust solution for a wide range of possible model parameters. We also show that a simple power-law function can be an appropriate approximation for the mass distribution of particles in certain regimes. The steeper solution has observable effects in the submillimeter and millimeter wavelength regimes of the electromagnetic spectrum. We assemble data for nine debris disks that have been observed at these wavelengths and, using a simplified absorption efficiency model, show that the predicted slope of the particle mass distribution generates SEDs that are in agreement with the observed ones.
We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a
-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.
Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have been studied in great detail. When considered as complete theories of gravity they can gener
ate non-perturbative deviations from the general relativistic predictions in the solar system, and the simplest models show instabilites on cosmological scales. Here we show that it is possible to treat $f(R)=Rpmmu^4/R$ gravity in a perturbative fashion such that it shows no instabilities on cosmological scales and, in the solar system, is consistent with measurements of the PPN parameters. We show that such a theory produces a spatially flat, accelerating universe, even in the absence of dark energy and when the matter density is too small to close the universe in the general relativistic case.
The redshift evolution of the Tully-Fisher Relation probes gravitational dynamics that must be consistent with any modified gravity theory seeking to explain the galactic rotation curves without the need for dark matter. Within the context of non-rel
ativistic Modified Newtonian Dynamics (MOND), the characteristic acceleration scale of the theory appears to be related to the current value of either the Hubble constant, i.e., alpha ~ cH_0, or the dark energy density, i.e., alpha (8 pi G rho_lambda/3)^{1/2}. If these relations are the manifestation of a fundamental coupling of a_0 to either of the two cosmological parameters, the cosmological evolution would then dictate a particular dependence of the MOND acceleration scale with redshift that can be tested with Tully-Fisher relations of high-redshift galaxies. We compare this prediction to two sets of Tully-Fisher data with redshifts up to z=1.2. We find that both couplings are excluded within the formal uncertainties. However, when we take into account the potential systematic uncertainties in the data, we find that they marginally favor the coupling of the MOND acceleration scale to the density of dark energy.
Eddington-limited X-ray bursts from neutron stars can be used in conjunction with other spectroscopic observations to measure neutron star masses, radii, and distances. In order to quantify some of the uncertainties in the determination of the Edding
ton limit, we analysed a large sample of photospheric radius-expansion thermonuclear bursts observed with the Rossi X-ray Timing Explorer. We identified the instant at which the expanded photosphere touches down back onto the surface of the neutron star and compared the corresponding touchdown flux to the peak flux of each burst. We found that for the majority of sources, the ratio of these fluxes is smaller than 1.6, which is the maximum value expected from the changing gravitational redshift during the radius expansion episodes (for a 2M_sun neutron star). The only sources for which this ratio is larger than 1.6 are high inclination sources that include dippers and Cyg X-2. We discuss two possible geometric interpretations of this effect and show that the inferred masses and radii of neutron stars are not affected by this bias. On the other hand, systematic uncertainties as large as ~50% may be introduced to the distance determination.
Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this paper, we show that the black-hole solutions of these theories are essentia
lly indistinguishable from those of general relativity. Thus, we conclude that a potential observational verification of the Kerr metric around an astrophysical black hole cannot, in and of itself, be used to distinguish between these theories. On the other hand, it remains true that detection of deviations from the Kerr metric will signify the need for a major change in our understanding of gravitational physics.
