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The horizon-scale images of black holes obtained with the Event Horizon Telescope have provided new probes of their metrics and tests of General Relativity. The images are characterized by a bright, near circular ring from the gravitationally lensed emission from the hot plasma and a deep central depression cast by the black hole. The metric tests rely on fact that the bright ring closely traces the boundary of the black hole shadow with a small displacement that has been quantified using simulations. In this paper we develop a self-consistent covariant analytic model of the accretion flow that spans a broad range of plasma conditions and black-hole properties to explore the general validity of this result. We show that, for any physical model of the accretion flow, the ring always encompasses the outline of the shadow and is not displaced by it by more than half the ring width. This result is a consequence of conservation laws and basic thermodynamic considerations and does not depend on the microphysics of the plasma or the details of the numerical simulations. We also present a quantitative measurement of the bias between the bright ring and the shadow radius based on the analytical models.
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Black Hole Images as Tests of General Relativity: Effects of Spacetime Geometry
The image of a supermassive black hole surrounded by an optically-thin, radiatively-inefficient accretion flow, like that observed with the Event Horizon Telescope, is 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 analysed 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 theoretical justification for using black-hole images to probe and test the spacetimes of supermassive black holes.
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- Award ID(s):
- 1743747
- PAR ID:
- 10350547
- Date Published:
- Journal Name:
- ArXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Context. High-frequency very-long-baseline interferometry (VLBI) observations can now resolve the event-horizon-scale emission from sources in the immediate vicinity of nearby supermassive black holes. Future space-VLBI observations will access highly lensed features of black hole images – photon rings – that will provide particularly sharp probes of strong-field gravity. Aims. Focusing on the particular case of the supermassive black hole M 87*, our goal is to explore a wide variety of accretion flows onto a Kerr black hole and to understand their corresponding images and visibilities. We are particularly interested in the visibility on baselines to space, which encodes the photon ring shape and whose measurement could provide a stringent test of the Kerr hypothesis. Methods. We developed a fully analytical model of stationary, axisymmetric accretion flows with a variable disk thickness and a matter four-velocity that can smoothly interpolate between purely azimuthal rotation and purely radial infall. To determine the observational appearance of such flows, we numerically integrated the general-relativistic radiative transfer equation in the Kerr spacetime, taking care to include the effects of thermal synchrotron emission and absorption. We then Fourier transformed the resulting images and analyzed their visibility amplitudes along the directions parallel and orthogonal to the black hole spin projected on the observer sky. Results. Our images generically display a wedding cake structure composed of discrete, narrow photon rings ( n = 1, 2, …) stacked on top of broader primary emission that surrounds a central brightness depression of model-dependent size. At 230 GHz, the n = 1 ring is always visible, but the n = 2 ring is sometimes suppressed due to absorption. At 345 GHz, the medium is optically thinner and the n = 2 ring displays clear signatures in both the image and visibility domains. We also examine the thermal synchrotron emissivity in the equatorial plane and show that it exhibits an exponential dependence on the radius for the preferred M 87* parameters. Conclusions. The black hole shadow is a model-dependent phenomenon – even for diffuse, optically thin sources – and should not be regarded as a generic prediction of general relativity. Observations at 345 GHz are promising for future space-VLBI measurements of the photon ring shape, since at this frequency the signal of the n = 2 ring persists despite the disk thickness and nonzero absorption featured in our models. Future work is needed to investigate whether this conclusion holds in a larger variety of reasonable models.more » « less
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Abstract The Event Horizon Telescope (EHT) images of the supermassive black hole at the center of the galaxy M87 provided the first image of the accretion environment on horizon scales. General relativity (GR) predicts that the image of the shadow should be nearly circular given the inclination angle of the black hole M87*. A robust detection of ellipticity in image reconstructions of M87* could signal new gravitational physics on horizon scales. Here we analyze whether the imaging parameters used in EHT analyses are sensitive to ring ellipticity, and measure the constraints on the ellipticity of M87*. We find that the top set is unable to recover ellipticity. Even for simple geometric models, the true ellipticity is biased low, preferring circular rings. Therefore, to place a constraint on the ellipticity of M87*, we measure the ellipticity of 550 synthetic data sets produced from GRMHD simulations. We find that images with intrinsic axis ratios of 2:1 are consistent with the ellipticity seen from EHT image reconstructions.more » « less
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