Markarian 766 (which is also known as NGC 4253), is a relatively boring looking barred spiral galaxy located at a distance of about 200 light years (61 Mpc) from Earth [1] in the direction of Coma Berenices. Or, I should say, it's relatively boring looking if look at it in the visible part of the electromagnetic spectrum. Back in the 1960s, Beniamin Markarian looked at this galaxy in the ultraviolet part of the spectrum and found that it looked abnormally bright, so he added it to his catalog of bright ultraviolet sources. This is why the galaxy is named Markarian 766. However, while the galaxy looks somewhat interesting in ultraviolet images, it's really exciting-looking in X-ray images. Data published in 1980 from an X-ray telescope named the Einstein Observatory showed that Markarian 766 was an abnormally bright X-ray source [2].
Subsequent observations showed that the X-ray emission originates from an active galactic nucleus (AGN). To review, an AGN consists of a supermassive black hole millions or billions of times the mass of the Sun and a disk of gas and dust falling into the black hole that is commonly referred to as an accretion disk. Very often, AGN may have jets of gas that appear above one or both of the poles of the black hole and that originate from gas in the accretion disk that got very hot as it was falling into the black hole and expanded away from the disk instead of falling inwards, and magnetic fields not only help to deflect the gas away from the black hole but also collimate the gas into really narrow jets.
For reference, Markarian 766 appears to have one jet, and that jet is, to use the technical term, very dinky. Radio observations indicate that the jet is about 42 light years in size [3], which might sound like a lot, but given that some AGN have jets that are millions of light years in size, the jets in Markarian 766 really seem small in comparison.
Let's get back to the X-rays. The X-ray emission from Markarian 766 may originate from the really hot gas near the center of the accretion disk, the base of the jets near the black hole, or random clouds of gas just above the gas disk in an area called the corona that get superheated by all of the photons from everything else in the system. That X-ray emission is also variable [4]. The variations in the X-ray emission are almost certainly related in one way or another to variations in the rate at which mass is falling into the black hole.
Since this is a relatively nearby galaxy containing a black hole, astronomers have spent a lot of time trying to measure the mass of the black hole. This is in part just to understand the black hole itself as well as to relate the properties of the black hole to the rest of the galaxy, but astronomers also like to do this because it sounds really cool, which makes it easy to get science funding.
Anyway, one of the first techniques that was used to measure the mass of the black hole was based on observing the Doppler shifting of the gas emitting X-rays near the center of the accretion disk surrounding the black hole. The mass estimated from this technique is somewhere between 0.49 million and 45 million times the mass of the Sun [5].
Another technique used what is called reverberation mapping. This is based on some flash of electromagnetic radiation from some source outside the plane of the accretion disk being then reflected by the inner edges of the accretion disk. The delays between the initial flash, the reflection on the near side of the accretion disk, and the reflection on the far side of the accretion disk allow people to measure the size of the inner gap in the accretion disk and therefore infer how large the black hole is. Surprisingly, this technique has not been applied using X-ray emission but has instead been applied using light from ionized hydrogen gas in the visible part of the spectrum. That method gave a black hole mass somewhere between 1.7 million and 13.6 million times the mass of the Sun [6, 7].
A third technique used a relation between the frequency of the X-ray variability and the slope of the X-ray spectrum to estimate the central black hole mass at the center of the AGN. This technique is based on the assumption that these two quantities are directly related to each other in a way that depends on the mass of the black hole and that, if the relation is calibrated using an AGN where someone else has already measured the black hole mass very accurately, the relation can then be used to measure the mass of a black hole in another galaxy [8]. When this technique was applied to Markarian 766, it gave a black hole mass of 1.26 million times the mass of the Sun give or take a factor of 2 [9].
As you can tell, all of these techniques don't quite give very precise answers. It's quite apparent that more work is needed to try to better constrain the mass of the black hole in Markarian 766 as well as to understand the other aspects of the X-ray emission from the AGN, so you can expect to read many more scientific journal articles about this galaxy in the future. (That is, if you read scientific journal articles. If you don't, maybe you'll see a press release or something with a nice picture of X-ray emission at some point.)