Expected intermediate-mass black holes in the Virgo cluster. I.
  Early-type galaxies
  We expand upon the AMUSE-Virgo survey which imaged 100 early-type Virgo
cluster galaxies with the Chandra X-ray Observatory, and we place an emphasis
on potential intermediate mass black holes (IMBHs). Virgo early-type galaxies
with absolute magnitudes $\mathfrak{M}_B\gtrsim-20.5$ mag have $B$-band
luminosities that scale with the square of the stellar velocity dispersion:
$L_B\propto\sigma^2$. We show that the non-linear `super-quadratic' relation
$M_{\rm bh}\propto L_B^2$-$L_B^{2.5}$ from Graham & Scott yields black hole
masses, $M_{\rm bh}$, that agree with the $M_{\rm bh}$-$\sigma$ relation down
to at least $M_{\rm bh}=10^4\,M_{\odot}$. We predict that 30 of the 100
galaxies have $M_{\rm bh}\le10^5\,M_{\odot}$, with IC3602 having $M_{\rm
bh}=10^4\,M_{\odot}$ and IC3633 having $M_{\rm
bh}=$(6-8)$\times10^3\,M_{\odot}$. We additionally revise the black hole
Eddington ratios and their scaling with black hole mass, and report a
point-like Chandra source at the nucleus of five additional galaxies (NGC4382,
NGC4387, NGC4417, NGC4467, and NGC4472). Moreover, three of the galaxies
predicted here to host an IMBH have a point-like Chandra source near their
nucleus: IC3442 ($M_{\rm bh}=2\times10^5\,M_{\odot}$); IC3492 ($M_{\rm
bh}=5\times10^4\,M_{\odot}$); and IC3292 ($M_{\rm bh}=6\times10^4\,M_{\odot}$).
Furthermore, IC3442 and IC3292 host a nuclear star cluster that is expected to
house an IMBH. Finally, we present the ($B-K$)-$\mathfrak{M}_K$
colour-magnitude diagram and discuss the implications for the $M_{\rm
bh}$-$L_K$ and $M_{\rm bh}$-$M_{\rm *,galaxy}$ relations, revealing why
stripped galaxies, especially rare compact elliptical galaxies, should be
excluded from $M_{\rm bh}$-$L$ and $M_{\rm bh}$-$M_{\rm *,galaxy}$ scaling
relations.
