OAS NOVEMBER 20013 ASTRONOMY EZINE VOL 2 | Page 20

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is

, and we shall use the radius of the Earth that we used

above,

. These numbers give

us

which is 2% of the speed of light.

The escape velocity from a neutron star
A neutron star is the end produce of more massive stars. The Sun is not massive enough to become
a neutron star, but a star which is more than about 3 times the mass of the Sun is. In a neutron
star all the space that exits in atoms is squeezed out, so it is essentially a pure lump of nuclei. A
typical neutron star may have the mass of 2 Suns, but squeezed down into something the size of a
city! So, for our calculation, we are going to assume a 2 solar mass neutron
star,

. For the radius we will assume 10km,

so

. Plugging these values into the equation for the escape velocity

gives

which is 77% of the speed of light.

The event horizon of a black hole
The escape velocity from a neutron star is still below the speed of light. Pulsars are produced by
radiation from the surface of a neutron star being beamed past us as the neutron star rotates. So,
we have direct observational evidence that we can see radiation from neutron stars.
But, in the same way that a star which is a few times the mass of the Sun will end its life as a neutron star rather than a white dwarf; an even more massive star will not end as a neutron star. This
is because of something called theneutron degeneracy pressure. To put it simply, this is a physical
law which says that neutrons do not all want to be in the same place. They resist this through a resistive component in the strong nuclear force. But, if a neutron star were to have more than about
3 times the mass of the Sun, the gravity is strong enough to overcome this neutron degeneracy
pressure. There is no known force to stop the collapse of the neutron star, and this is what forms a
black hole.
We can work out the radius at which the escape velocity becomes equal to the speed of light for an
e.g. 2 solar mass black hole. This is the same mass as our neutron star example above. But, as we
shall see, it will need to be smaller than the 10km size of a neutron star. The radius at which the
escape velocity is equal to the speed of light is what we call the event horizon of black hole.
To do the calculation we just re-arrange our escape velocity equation to
find

when

For
event horizon to be

where

is the speed of light. The re-arrangement is that
, and

.

we find the radius of the
. Notice how close this is to the actual size of

a typical neutron star, just a little over half the size. It shows how little mass has to be added to a
neutron star to tip it over the edge into becoming a black hole.

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