The Correlation between Black Hole Mass and Stellar Mass for Classical
  Bulges and the Cores of Ellipticals
  The correlation between black hole mass and the stellar mass of the bulge of
the host galaxy has attracted much attention ever since its discovery. While
traditional investigations of this correlation have treated elliptical galaxies
as single, monolithic spheroids, the recent realization that massive elliptical
galaxies have undergone significant late-time ($z \lesssim 2$) dissipationless
assembly since their initially dense "red nugget" phase strongly suggests that
black holes in present-day ellipticals should be associated only with their
cores and not with their extended envelopes. We perform two-dimensional image
decomposition of Two Micron All Sky Survey $K_s$-band images to derive the
stellar mass of the cores of 35 nearby ellipticals with reliably measured black
hole masses. We revisit the relation between black hole mass and bulge stellar
mass by combining classical bulges with the cores of ellipticals. The new
relation exhibits nearly identical slope ($M_{\bullet} \propto
M_{\text{core}}^{1.2}$) as the conventional relation but a factor of $\sim2$
higher normalization and moderately larger intrinsic scatter (0.4 dex). At a
core mass of $10^{11}\,M_{\odot}$, $M_{\bullet}/M_{\text{core}} = 0.9\%$, but
it rises to $M_{\bullet}/M_{\text{core}}=1.5\%$ for the most massive cores with
mass $10^{12}\,M_{\odot}$. Fast and slow rotator ellipticals follow the same
correlation. The $M_{\bullet}-M_{\text{core}}$ relation provides a revised
benchmark for studies of black hole-galaxy coevolution in the high-redshift
Universe.
