Supermassive black holes occupy the centers of many, possibly most galaxies. The accretion process by which active galactic nuclei (AGN) "feed" on matter is often messy and dramatic, such that it can have a major impact on the black hole's surroundings, even its whole host galaxy.
The process by which feeding black holes affect their surroundings is called "feedback" because it is a self-regulating process, like sticking a microphone in front of its own speaker: a galaxy provides gas and stars on which the black hole feeds. As the black hole feeds, its accretion disk can emit radiation and a disk wind (at large accretion rates), or jets which can reach speeds of a significant fraction of the speed of light.
These feedback processes can compress gas in the host galaxy, encouraging star formation (positive feedback) or heat and ionize gas in the host galaxy, stifling star formation and reducing the supply of cool gas needed for the black hole to feed (negative feedback). Negative feedback can change the host galaxy from a blue galaxy with hot young stars to a "red and dead" galaxy with an old and passive stellar population.
This feedback process can be complicated, which is why it's important to have multiwavelength high-resolution images of AGN hosts which allow us to study the feedback process in detail.
I am involved with CHEERS, the ultimate Chandra feedback survey. With deep observations of nearby AGN, we can actually see where and how each kind of feedback impacts its host galaxy. X-rays are necessary because the characteristic temperatures and energies of feedback are about 1 keV, i.e. in the X-ray band!
Chandra can resolve X-ray emission lines like O VII, O VIII and Ne IX, which powerful powerful diagnostics between shocks and photoionization. If we know where the shocks are, we can see where kinematic feedback (from jets and winds) is important! Such diagnostics can be more efficient than full-spectrum fitting, which require very large observation times due to the intrinsic difficulty of collecting large numbers of X-ray photons. My current favorite target for this study is NGC 3393, which demonstrates all three kinds of feedback: radiative, jet-based and wind-based!
When we combine these Chandra data with narrow emission line images (e.g. [O III] and [S II]) and spectroscopy from Hubble or ground-based IFUs, and radio data, we get a complete picture of where shocks are important for feedback and how powerful they are.
The Voorwerpjes provide particularly interesting examples of AGN feedback, since as an AGN shuts down, it may transition between a radiative (high accretion) mode to a kinematic (low-accretion) mode, and it looks like many of these fading AGN are doing just that!
The James Webb Space Telescope will soon be a powerful tool for studying feedback using narrow-line emission in the infrared, which is unobscured by the dust and gas which typically dominates galactic nuclei. ATHENA+ will provide many improvements over current X-ray observatories, but Lynx is necessary to study feedback at Chandra's spatial resolution, but with enough energy resolution and collecting area to take advantage of this capability. Chandra is powerful, but making the most of its angular resolution could take weeks of observing time for a single galaxy!