# Ask an Astronomer - Black Holes

## Light escaping from black holes

Published on 21/02/2013
Question:

Why can't light escape from black holes?

Nothing, not even light can escape a black hole if it gets too close. This is why they are called black holes. It is difficult to explain precisely without introducing some complicated ideas.

The simplest analogy is to consider throwing a ball up in the air: if you throw it fast enough it can escape off into space, but if not gravity will pull it back down to Earth. If we were to increase the gravity you would need to throw the ball faster and faster. Eventually there would come a point when you would have to throw the ball at the speed of light, which is the maximum speed anything can travel. At this point we have a black hole, and nothing will be able to escape. This is quite easy to understand, but has a number of flaws. For example, in this picture light would slow down, then stop, and then fall back towards a black hole: this isn't right, as light always travels at the speed of light.

A slightly more accurate but complicated picture is to think about gravity as the effect of the bending of space. In general relativity, which is our best theory of gravitation, mass bends space. This is often visualised as a rubber sheet being stretched by something heavy. Particles (whether light or matter) want to travel along straight lines, but when space is curved these become bent: they instead follow curving paths which we describe as the effect of gravity. Black holes have very high curvature, beyond a certain point (known as the event horizon), all straight lines are curved such that they point inwards towards the black hole. There is no direction you can go that will take you outside the event horizon! That might sound a little odd, but black holes are strange places. It's best to keep a safe distance.

## Stellar mass and supermassive black holes

Published on 21/02/2013
Question:

What is the difference between a stellar mass black hole and a super massive black hole?

In terms of physical properties, the difference between stellar mass black holes is their mass: stellar mass black holes are around 3-10 times the mass of the Sun, whilst supermassive black holes are 105-1010 times the mass of Sun. Supermassive black holes are just bigger versions of stellar mass black holes, but behave in the same way (just scaled up).

There are other differences, which are related to their formation. Stellar mass black holes form from the collapse of massive stars at the end of their lives. You can then find them scattered throughout galaxies, just like you find massive stars.

Supermassive black holes are found at the centres of galaxies. We are not exactly sure how they form, although we do have a number of ideas. They are too big to have formed from a collapsing star. We believe that quasars are powered by matter accreting onto supermassive black holes, and measurements of these show that these can grow to a billion solar masses in less than a billion years from the big bang. This means will need a highly efficient way for them to gain mass. We also observe that the properties of the surrounding galaxies are correlated to their central black hole's mass (this is most famously known as the M-σ relationship in astronomy, as we use M for the black hole mass and the Greek letter sigma for the velocity dispersion, a speed characterising how fast stars are moving). This correlation indicates that the growth of the black hole and galaxy are probably linked somehow.

## About the properties of black holes

Published on 09/02/2013
Question:

I have two questions in regards to black holes:

1. What is the relationship between the size of the star, the size of the black hole, the size of the event horizon, and the size of the general field of influence(area where there is a possibility of being sucked in)? Is there a formula, say, for example, star with mass of 10 tons = black hole with radius of 10 cm = event horizon with radius of 10 kilometers = field of influence with radius of 100 kilometers?
2. What is the relationship between the size of the black hole and its life span? For example, radius of 10 cm = dissolves in 10 years?

Thank you for your questions about black holes. Some are easier to answer than others. Black holes are described by a mass that is equivalent to the mass of the object from which they formed, so a 10 ton star (which is too light to really exist) would form a 10 ton black hole. Actually, it's not quite that simple, as when a star collapses some of the outer layers could be blown off and escape, but the important point is that the mass of the black hole is determined by the mass of the material that fell into it.

It is difficult to give a size to a black hole, as the theory says that everything is crushed down to an infinitesimally small point. (Some people argue that this is a reason to improving our theory, but the general consensus is still that everything would be crushed down to something so small that it might as well be infinitesimal: about the size of the Planck length, which is about 10-35 m).

We usually define the size of black holes by their event horizon, which is the point of no return: nothing, not even light, can escape from that point. (This is why they are called black holes). The size of the event horizon for a non-spinning black hole is

r = 2GM/c2,

where G is the universal gravitational constant, M is the mass and c is the speed of light. For our 10 ton black hole, that would give r = 1.5 × 10-24 m (depending exactly on your definition of the ton, I've actually used the metric tonne). For a black hole the same mass as the Sun r = 3 km.

Rotating black holes are slightly more complicated, but the numbers are similar, perhaps a factor of two smaller.

Gravity behaves the same for all objects. It gets weaker the further you are away, but there is no clear cut-off point. Therefore, it is difficult to define a field of influence. You will be able to pass closer to black hole and still escape if you are travelling faster. I would suggest that the event horizon is a suitable distance to consider, as this is the point at which there is absolutely no chance of avoiding getting sucked in.

The lifetime of black holes is an interesting questions. We believe that they should lose energy via Hawking radiation. If left on their own, they would eventually radiate away all of their energy and dissipate. The time taken to evaporate is

t = 5120πG2M3/(ħc4),

where π is the mathematical constant, M is the initial mass and ħ is the reduced Planck's constant (often called h-bar). However, in reality astrophysical black holes are not left on their own; they are constantly absorbing background radiation (as well as any gas or other material that gets too close). This means that they gain mass quicker than they radiate it away, so they will live much longer! No black hole that formed from a collapsing star should have evaporated yet, and none will until the Universe is much older. Some may last effectively forever.

## Falling into a Black Hole

Published on 15/02/2012
Question:

Could a black hole swallow a star or galaxy?

Galaxies tend to me millions of times more massive than black holes though, so the separation and speed of all the stars within a galaxy means that a whole galaxy is not going to get pulled into a black hole!

Material from stars can, however, be pulled into a black  hole. We can observe this when a star is in orbit around a black hole companion. The gravity of the black hole pulls (or "accretes") material from the surface of the star into the black hole, releasing enormous amounts of energy as it does so

## Black Hole Formation

Published on 02/04/2011
Question:

Are all black holes formed after the death of a massive star? If not, how are these non stellar black holes formed?

Black holes fall broadly into two categories. Firstly there are galactic, stellar mass black holes, which as the name suggests are found throughout galaxies and have masses similar to that of stars (of order 10 times the mass of the Sun). These form at the end of the lives of stars that are too massive to become white dwarfs or neutron stars. This occurs when they are still greater than two or three times the mass of the Sun by the time they have shed material through stellar winds or supernova explosions during their death. The gravitational force causing them to collapse is too strong for the pressure of electrons or neutrons to support the star as in the case of white dwarfs and neutron stars, so it keeps collapsing down to a black hole.

Secondly, there are so-called supermassive black holes, which tend to be around 100 million times as massive as the Sun. These are believed to be found at the centre of most galaxies about which the stars in that galaxy orbit (in fact our own galaxy, the Milky Way, has a black hole 4 million times the mass of the Sun at its centre). While the exact mechanism of their formation is still unknown, it is believed they form when a large gas cloud collapses to the centre of the large gravitational 'well' in the centre of a galaxy as it forms.

In addition there may be 'intermediate mass black holes' which could explain a number of observed phenomena such as 'ultraluminous X-ray sources.' When matter falls into a black hole, it emits radiation, part of which is seen as X-rays. These appear much brighter than stellar mass black holes, implying their mass is around 1000 times that of the Sun, but they are not at the centre of galaxies. Their formation is a mystery. They are too massive to form from a single star, but they could be formed when multiple stars or stellar mass black holes are pulled together by gravity and merge. Alternatively, they could be the central black hole from a smaller galaxy that has merged with the galaxy in which they are found and in the process, were thrown out from the centre.