Testing General Relativity with the Black Hole Shadow Size and Asymmetry
  of Sagittarius A*: Limitations from Interstellar Scattering
  The Event Horizon Telescope (EHT), a global 230 GHz VLBI array, achieves an
angular resolution of ${\approx} 20\,\mu{\rm as}$, sufficient to resolve the
supermassive black hole Sagittarius A* (Sgr A*). This resolution may soon
enable measurement of the black hole "shadow" size and asymmetry, predicted to
be ${\approx}50\,\mu$as and ${\lesssim} 3\,\mu$as, respectively. Measurements
that depart from these values could indicate a violation of the "no-hair
theorem." However, refractive scattering by the turbulent ionized interstellar
medium distorts the image of Sgr A*, affecting its apparent size and asymmetry.
In this paper, we present a general analytic approach to quantify the expected
image wander, distortion, and asymmetry from refractive scattering. If the
turbulence in the scattering material of Sgr A* is close to Kolmogorov, we
estimate the mean refractive image wander, distortion, and asymmetry to be 0.53
$\mu$as, 0.72 $\mu$as, and 0.52 $\mu$as at 230 GHz. However, alternative
scattering models with flatter power spectra can yield larger values, up to 2.1
$\mu$as, 6.3 $\mu$as, and 5.0 $\mu$as, respectively. We demonstrate that these
effects can be reduced by averaging images over multiple observations. For a
small number of observations, the effects of scattering can be comparable to or
greater than those from black hole spin, and they determine a fundamental limit
for testing general relativity via images of Sgr A*.
