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Register a new userDiscretization and Filtering Effects on Black Hole Images Obtained with the Event Horizon Telescope
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Interferometers, such as the Event Horizon Telescope (EHT), do not directly observe the images of sources but rather measure their Fourier components at discrete spatial frequencies up to a maximum value set by the longest baseline in the array. Construction of images from the Fourier components or analysis of them with high-resolution models requires careful treatment of fine source structure nominally beyond the array resolution. The primary EHT targets, Sgr A* and M87, are expected to have black-hole shadows with sharp edges and strongly filamentary emission from the surrounding plasma on scales much smaller than those probed by the currently largest baselines. We show that for aliasing not to affect images reconstructed with regularized maximum likelihood methods and model images that are directly compared to the data, the sampling of these images (i.e., their pixel spacing) needs to be significantly finer than the scale probed by the largest baseline in the array. Using GRMHD simulations of black-hole images, we estimate the maximum allowable pixel spacing to be approximately equal to (1/8)GM/c^2; for both of the primary EHT targets, this corresponds to an angular pixel size of <0.5 microarcseconds. With aliasing under control, we then advocate use of the second-order Butterworth filter with a cut-off scale equal to the maximum array baseline as optimal for visualizing the reconstructed images. In contrast to the traditional Gaussian filters, this Butterworth filter retains most of the power at the scales probed by the array while suppressing the fine image details for which no data exist.
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A fundamental difference between a neutron star (NS) and a black hole (BH) is the absence of a physical surface in the latter. For this reason, any remaining kinetic energy of the matter accreting onto a BH is advected inside its event horizon. In the case of an NS, on the contrary, accreting material is decelerated on the NS surface, and its kinetic energy is eventually radiated away. Copious soft photons produced by the NS surface will affect the properties of the Comptonised component dominating spectra of X-ray binaries in the hard state. Thus, parameters of the Comptonised spectra -- the electron temperature $kT_{rm e}$ and the Compton $y$-parameter, could serve as an important tool for distinguishing BHs from NSs. In this paper, we systematically analyse heretofore the largest sample of spectra from the BH and NS X-ray binaries in the hard state for this purpose, using archival RXTE/PCA and RXTE/HEXTE observations. We find that the BHs and NSs occupy distinctly different regions in the $y-kT_{rm e}$ plane with NSs being characterised by systematically lower values of $y$-parameter and electron temperature. Due to the shape of the boundary between BHs and NSs on the $y-kT_{rm e}$ plane, their one-dimensional $y$ and $kT_{rm e}$ distributions have some overlap. A cleaner one parameter diagnostic of the nature of the compact object in X-ray binaries is provided by the Compton amplification factor $A$, with the boundary between BHs and NSs lying at $Aapprox 3.5-4$. This is by far the most significant detection of the imprint of the event horizon on the X-ray spectra for stable stellar-mass BHs.
We have now entered the new era of high-resolution imaging astronomy with the beginning of the Event Horizon Telescope (EHT). The EHT can resolve the dynamics of matter in the immediate vicinity around black holes at and below the horizon scale. One of the candidate black holes, Sagittarius A* flares 1-4 times a day depending on the wavelength. A possible interpretation of these flares could be hotspots generated through magnetic reconnection events in the accretion flow. In this paper, we construct a semi-analytical model for hotspots that include the effects of shearing as a spot moves along the accretion flow. We then explore the ability of the EHT to recover these hotspots. Even including significant systematic uncertainties, such as thermal noise, diffractive scattering, and background emission due to an accretion disk, we were able to recover the hotspots and spacetime structure to sub-percent precision. Moreover, by observing multiple flaring events we show how the EHT could be used to tomographically map spacetime. This provides new avenues for testing relativistic fluid dynamics and general relativity near the event horizon of supermassive black holes.
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 observeration. Natural candidates for these modifications behave like metric fluctuations, with characteristic length and time scales 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. 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 non-imaging 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.
Simulated images of a black hole surrounded by optically thin emission typically display two main features: a central brightness depression and a narrow, bright photon ring consisting of strongly lensed images superposed on top of the direct emission. The photon ring closely tracks a theoretical curve on the image plane corresponding to light rays that asymptote to unstably bound photon orbits around the black hole. This critical curve has a size and shape that are purely governed by the Kerr geometry; in contrast, the size, shape, and depth of the observed brightness depression all depend on the details of the emission region. For instance, images of spherical accretion models display a distinctive dark region -- the black hole shadow -- that completely fills the photon ring. By contrast, in models of equatorial disks extending to the black holes event horizon, the darkest region in the image is restricted to a much smaller area -- an inner shadow -- whose edge lies near the direct lensed image of the equatorial horizon. Using both semi-analytic models and general relativistic magnetohydrodynamic (GRMHD) simulations, we demonstrate that the photon ring and inner shadow may be simultaneously visible in submillimeter images of M87*, where magnetically arrested disk (MAD) simulations predict that the emission arises in a thin region near the equatorial plane. We show that the relative size, shape, and centroid of the photon ring and inner shadow can be used to estimate the black hole mass and spin, breaking degeneracies in measurements of these quantities that rely on the photon ring alone. Both features may be accessible to direct observation via high-dynamic-range images with a next-generation Event Horizon Telescope.
The advent of the Event Horizon Telescope (EHT), a millimeter-wave very-long baseline interferometric array, has enabled spatially-resolved studies of the sub-horizon-scale structure for a handful of supermassive black holes. Among these, the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), presents the largest angular cross section. Thus far, these studies have focused upon measurements of the black hole spin and the validation of low-luminosity accretion models. However, a critical input into the analysis of EHT data is the structure of the black hole spacetime, and thus these observations provide the novel opportunity to test the applicability of the Kerr metric to astrophysical black holes. Here we present the first simulated images of a radiatively inefficient accretion flow (RIAF) around Sgr A* employing a quasi-Kerr metric that contains an independent quadrupole moment in addition to the mass and spin that fully characterize a black hole in general relativity. We show that these images can be significantly different from the images of a RIAF around a Kerr black hole with the same spin and demonstrate the feasibility of testing the no-hair theorem by constraining the quadrupolar deviation from the Kerr metric with existing EHT data. Equally important, we find that the disk inclination and spin orientation angles are robust to the inclusion of additional parameters, providing confidence in previous estimations assuming the Kerr metric based upon EHT observations. However, at present the limits upon potential modifications of the Kerr metric remain weak.
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