Expert: Jayendra Upadhye - 3/11/2008

Question
How many kg per sq metre of pressure exists at the centre of a neutron star?

Answer
Hi Jason,

refer to this link:-
http://en.wikipedia.org/wiki/Neutron_star

The answer is (approximate) 16 * 10 raised to 21 Newton.
this also will be the rate at which pressure will increase as that rate is a linear function of depth over relatively small depth ranges.

if you are interested in the "how" read on..

I am going to fire straight from the hip jason,
(doing some creative thinking for both of us),
and i am hoping you will agree to my line of thinking.

Sometimes even "experts" like me have to do this, mainly because
independent sources of verification are not to be easily found.

You see, i believe (and am most probably correct) that the general laws
of physics (not relativistic) continue to apply to larger and stranger bodies too.

For example, the law of conservation of momentum (translatory as well as angular)
applies to neutron stars as well as a simple humdrum table at which you sit and wr
ite.

Likewise, the law of hydrostatic pressure (as applied in gravitating bodies) will apply on a neutron star too.
if you look up the wiki site above, the star even has an "atomsophere"..a layer of about 1 km thickness where "non-degenerate" matter is still allowed,
albeit with some admixture of "all neutron" stuff.

Below that, we can presume that the law of hydrostatics will apply.
[Mind you even on earth, this "simple" law can be applied to only "simple conditions where:-
1 - average density of matter in question does not vary all the way "above" the point.
   This is almost true on earth where water density is invariant ove the full depth of the ocean.
2 - the gravitational intensity is invariant throughout the rigion considered.
   This is almost true on earth where water density is invariant ove the full depth of the ocean.
   
On a neutron star, both density and gravitational intensity will vary with radius.
density will increase with reducing radius, gravity will reduce (blame newton's calculus for that)
with reducing radius.

But at reasonably shallow depths from the surface, say upto a few 100 meters or so,
P = W*h where P is pressure/unit area, W is specific weight, h is depth.

based on the wiki figures,
the average density of a neutron star is say 1000000000 kg/met cubed. we take g at surface too.
g= 16000000000000 m/sec/sec.

P in Newton / met squared would be 16000000000000000000000 at a depth of 1 meter!!
ie 16 * 10 raised to 21 Newton.

This would increase linearly at above rate as long as surface gravity and density does not vary.
[which is say for a few 100 meters].

Both gradients are very strong in compact bodies such as neutron stars, and this "simple relationship will
be marred with integerals crreping into the equation beyond this range.

Hope that suffices.

kindly do rate the answer.
Jayen

further references..
ref:- http://tabitha.phas.ubc.ca/wiki/index.php/INT_-_Neutron_Star_Crust_and_Surface
for the overall star,
Neutron star pressure is approximately proportional to the density squared ..