Viewing the Shadow of the Black Hole at the Galactic Center

TL;DR

The paper addresses whether the shadow of a black hole at the Galactic Center can be imaged with sub-mm VLBI to provide direct evidence for an event horizon. It uses general-relativistic ray-tracing of optically thin near-horizon emission around Schwarzschild and Kerr black holes, including interstellar scatter and realistic VLBI resolution, to predict the observable shadow size. The results show a shadow of order 10 Rg (roughly 30 μas) largely independent of spin, with possible offsets up to about 2.5 Rg depending on spin and viewing angle; detectability improves at shorter sub-mm wavelengths where scatter is smaller. A detection would offer direct confirmation of the event horizon and the standard black-hole paradigm, while non-detection could challenge BH models and drive further development of sub-mm VLBI techniques.

Abstract

In recent years, the evidence for the existence of an ultra-compact concentration of dark mass associated with the radio source Sgr A* in the Galactic Center has become very strong. However, an unambiguous proof that this object is indeed a black hole is still lacking. A defining characteristic of a black hole is the event horizon. To a distant observer, the event horizon casts a relatively large ``shadow'' with an apparent diameter of ~10 gravitational radii due to bending of light by the black hole, nearly independent of the black hole spin or orientation. The predicted size (~30 micro-arcseconds) of this shadow for Sgr A* approaches the resolution of current radio-interferometers. If the black hole is maximally spinning and viewed edge-on, then the shadow will be offset by ~8 micro-arcseconds from the center of mass, and will be slightly flattened on one side. Taking into account scatter-broadening of the image in the interstellar medium and the finite achievable telescope resolution, we show that the shadow of Sgr A* may be observable with very long-baseline interferometry at sub-millimeter wavelengths, assuming that the accretion flow is optically thin in this region of the spectrum. Hence, there exists a realistic expectation of imaging the event horizon of a black hole within the next few years.

Figures (1)

• Figure 1: An image of an optically thin emission region surrounding a black hole with the characteristics of Sgr A* at the Galactic Center. The black hole is here either maximally rotating ($a_* = 0.998$, Figs. 1a-c) or non-rotating ($a_*=0$, Figs. 1d-f). The emitting gas is assumed to be in free fall with an emissivity $\propto r^{-2}$ (top) or on Keplerian shells (bottom) with a uniform emissivity (viewing angle $i=45^\circ$). Figs. 1a&d show the GR ray-tracing calculations, Figs. 1b&e are the images seen by an idealized VLBI array at 0.6 mm wavelength taking interstellar scattering into account, and Figs. 1c&f are those for a wavelength of 1.3 mm. The intensity variations along the $x$-axis (solid green curve) and the $y$-axis (dashed purple curve) are overlayed. The vertical axes show the intensity of the curves in arbitrary units and the horizontal axes shows the distance from the black hole in units of $R_{\rm g}$ which for Sgr A* is $3.9\times 10^{11}$ cm $\sim3\;\mu$arcseconds.