Supermassive black holes occupy the centers of many, possibly most galaxies. Sometimes they are active, accreting matter rapidly and giving off lots of radiation as active galactic nuclei (AGN). In the local universe, however, they're mostly faint and relatively starved.
But we know they're there! We can see the supermassive black hole at the center of the Milky Way (Saggitarius A* or Sgr A*) is surrounded by a dense cluster of stars. Each star moves as if pulled by an immense mass at the galactic center. And in very nearby galaxies, we can't resolve individual stars but we can measure the statistical effects of their motion.
Further away, however, it becomes harder to measure the signatures of stellar motion. This is a problem because we know that black holes and galaxies form and evolve together. Their stories are intrinsically linked.
When one of those stars wanders by a supermassive black hole, however, gravity can be so much stronger on one side of the star than the other that the star is ripped appart or tidally disrupted.
While this is very unfortunate for the star, it's great for astronomers! The black hole devours enormous quantities of stellar debris very quickly, creating a flare of X-rays, ultraviolet, optical light and more that gives away the location of the black hole. It also tells us about the black hole, the unfortunate star, and potentially the innermost regions of the host galaxy.
Tidal disruption events provide an exciting way to find and study intermediate mass black holes. We see plenty of small black holes (stellar-mass, a few suns' worth) in our own Milky Way, and black holes more massive than about one million suns are easy to find in other galaxies, but the ones in between are very hard to find... unless (for example) they swallow a star!
Tidal disruption events also help us study how massive black holes swallow matter at a variety of rates. AGN change their accretion rates in ways that appear somewhat random, but we have a very good idea of how a disrupted star falls into a black hole! As a result, we can follow very different accretion rates from super-Eddington (too much for the black hole to swallow!) to very small rates years later. Such large changes happen all the time with stellar-mass black holes, but for more massive ones are usually hard to study within a human lifespan.
Tidal disruption events allow us to study how rapidly accreting massive black holes produce winds, or turn jets on and off! Currently, I am involved in a large observational campaign to study a ASASSN-14li, a tidal disruption event discovered by ASAS-SN at only 90 megaparsecs! This is pretty far even by extragalactic standards, but these events are so rare, it's very unusual to catch them at such close distances. That makes ASASSN-14li very exciting, because it was detected relatively early and we can study it very well. X-ray spectroscopy, for example, requires very close, very bright objects which can produce lots of photons to analyze!
Currently I am studying ASASSN-14li using X-rays (Chandra and XMM-Newton), ultraviolet light (Hubble), and radio waves (the JVLA).
In the future, the Large Synoptic Survey Telescope (LSST) will identify many of these rare events. The James Webb Space Telescope will be key to studying how they illuminate the nuclei of their host galaxies, as well as other properties of the galaxies themselves (particularly very distant ones!). ATHENA+ and the X-ray Surveyor will be key to understanding the physics of tidal disruption events, which is critical for studying the statistical properties of the many events which LSST will discover.