Mass of the dynamically hot inner stellar halo predicts the ancient
  accreted stellar mass
  Galactic dynamical structures are fossil records of the assembly histories of
galaxies. By analyzing the cosmological hydrodynamical simulation TNG50, we
find that a dynamical structure that we call the "hot inner stellar halo,"
defined by stars on dynamically hot orbits with circularity $\lambda_z < 0.5$
at $3.5\,{\rm kpc}<r \lesssim 2\,R_e$, is a strong indicator of the mass of
accreted satellite galaxies. We find a strong correlation between the mass of
this hot inner stellar halo and the total ex situ stellar mass. There is a
similarly strong correlation with the stellar mass of the most massive
secondary galaxy ever merged. These TNG50 correlations are compatible with
those predicted by other simulations, for example by TNG100 across the whole
mass range under study (galaxy stellar masses, $M_*$, in the
$10^{10.3-11.6}$\,\Msun\, range) and by EAGLE for $M_* \gtrsim 10^{10.6}
$\,\Msun\, galaxies.\ This shows that our predictions are robust across
different galaxy formation and feedback models and hold across a wide range of
numerical resolution. The hot inner stellar halo is a product of massive and
typically ancient mergers, with inner-halo stars exhibiting three main physical
origins: accreted and stripped from massive satellites, dynamically heated by
mergers from the bulge and/or disk in the main progenitor, and formed from star
formation triggered during mergers. The mass of the hot inner stellar halo
defined in this paper is a quantity that can be robustly obtained for real
galaxies by applying a population-orbit superposition method to
integral-field-unit spectroscopy data, out to a distance of $\sim2\,R_e$, which
is possible with current observations. Hence, this paper shows that
integral-field-unit observations and dynamical models of the inner regions of
galaxies provide a way to quantitatively determine the mass of ancient accreted
satellites.
