We are sure that at least two kinds of astrophysical black holes exist, one kind correspond to black holes of stellar mass (around 8 times the mass of the sun or bigger) and the black holes at the centers of galaxies with millions of solar masses. For some time there was speculation about the existence of some intermediate mass black holes with masses around few thousands the mass of the Sun, evidence from the rotation of stars in globular clusters gave the first evidence for the existence of intermediate mass black holes.
Despite evidence from the rotation of stars around the centers of globular clusters, the case is far from closed, the centers of globular clusters are regions of high density, filled with degenerate stars (mostly white dwarves) and maybe the rotation speeds can be explained by an overabundance of stars. A new paper (available here) by Stephan Rosswog, Enrico Ramirez-Ruiz, and William R. Hix proposes a radically new method for searching this black holes.
In close binary systems composed by a red giant and a white dwarf, the white dwarf can steal some matter from the red giant star (which has a low surface gravity), matter falling into the white dwarf has angular momentum and as a result of that an accretion disk is formed, white dwarves are supported against gravitational collapse by electron degeneracy (essentially if you try to pack electrons too closely they will start to move faster as a consequence of the uncertainty principle), this degeneracy can only support a mass of about 1.4 solar masses (otherwise the electrons would move faster than light), this is known as the Chandrasekhar limit, so when the white dwarf has "stealed" enough mass from its companion it will eventually surpass this limit, in this case the star is reignited by a mechanism known as carbon deflagration, creating a supernova explosion of the IA type.
Now, enter intermediate mass black holes. Computer simulations including gravity, hydrodynamics and nuclear physics show the effects of a close interaction between a white dwarf and an intermediate mass black holes. The star is heavily disrupted by tidal effects and acquires a pancake-like form, as the star is squeezed there is a dramatic increase in pressure and the star is reignited and creates a new kind of supernova, around half of the mass is ejected and the other half falls into the black hole creating an accretion disk that should emit x-rays.
This image shows the interaction of a white dwarf and a black hole, the star is heavily deformed in the first two frame, in the intermediate frames the star reignites and explodes, the "bubble" is the ejected material and at the bottom left corner an accretion disk is formed, the last two frames follow the evolution of this disk.
While this supernovas should be much scarcer than usual IA supernovas, new surveys like the LSST should detect enough supernovae to have a good chance of detecting this events, and x-ray emission should be detectable by the Chandra Space Telescope. The light curve should be different, although I haven't seen any detailed model. Considering that globular clusters are composed mostly of old stars and large populations of white dwarves this events should be happening relatively frequently around the universe and might give us unequivocal evidence of intermediate mass black holes.