## Do supermassive black holes cause galaxy rotation? (Advanced)

If a black hole is in the center of our galaxy, could it be the source of the rotation of the galaxy and if so, if it is acreeting matter could this mean that it is getting more and more massive? whouldn't this imply that the rotation is getting faster and finally could this mean that a galaxy year is getting shorter even if it's just a little bit?

The nice thing about black holes is that although they distort space and time quite severely in their vicinity, their gravitational influence on distant objects is just as we would expect for "normal matter". How far away is "distant" for black holes? We characterize the size of a black hole in terms of its Schwarzchild Radius, or the radius within which gravity is so strong that not even light can escape. A good rule to remember is this: for a black hole of mass "M" times the mass of the Sun, its size is 3xM measured in kilometres (km). So, a solar mass black hole has a Schwarzchild Radius of about 3 km. As a rough estimate, let's say that the general relativistic effects of a black hole become insignificant at about 1000 times the Schwarzchild radius. For a solar mass black hole, then, its gravitational effects are identical to the Sun (a solar mass star) once you're about 3x1000 km = 3000 km away from it. This is a much smaller distance than that between the Earth and the Sun, for instance, and it means that if the Sun were a black hole, the Earth would not change its orbit.

Let's run through the same exercise for a supermassive black hole at the centre of our galaxy. It has a mass of about 10 million solar masses, and so from the formula above it has a Schwarzchild radius of about 30 million kilometres. General relativistic effects are then only important within 1000x30 million kilometres, or in the inner 30 billion km of the Milky Way. Now, the solar system is about 6 billion km across, so you could fit 5 "solar systems" in the region around a supermassive black hole that general relativity must be accounted for. However, there are ~200 billion stars like our own in the galaxy, and they are light-years apart! Suffice it to say that the region in our galaxy in which you have to worry about the effects of a supermassive black hole is very small indeed. Now, the galaxy itself weighs about 100 billion solar masses, which is much greater than the 10 million inside the supermassive black hole. So, unless you are very close to it (ie where general relativity is important), a supermassive black hole contributes, in the mean, an insignificant amount of gravitational pull at a given point in a galaxy.

So black holes cannot be the source of galaxy rotation: they are simply too small, and too far away from most of the galaxy to do it. We think that the rotation in spiral galaxies stems from the law of conservation of angular momentum: this says that big things that spin a little bit and which turn into little things, must in fact turn into little things which spin rather rapidly.

The black hole at the centre of the galaxy is accreting matter (at an unknown rate), which means that it is getting more massive as time goes on. From the above arguments, however, this does not imply that the rotation rate of the galaxy is increasing. This means that a galaxy "year", or the time it takes a star near the middle of the galaxy to circle around the galactic centre once, is not affected by the presence of the black hole.

All of this is rather unfortunate for us, in fact: if the rotation rates of galaxies did increase because of supermassive black holes, then we could look for this increase and use it to hunt down the black holes. As it is, however, black holes are rather hard to identify in galaxy centres, because their effects are so localized.