Question

Discuss why a Neutron Star has a stable (constant) radius. What supports it against gravitational collapse?

Answer #1

Neutron Star Physics
Under some circumstances, an ordinary star can undergo
gravitational collapse into an extremely dense object made mostly
of neutrons. This type of star is called a "neutron star". A
neutron star has a mass density roughly 1014 times
larger than that of ordinary solid matter.
Suppose we represent an ordinary star as a uniform solid rigid
sphere, both before and after the collapse. The original star's
initial radius is 7.0 x 105 km (comparable to the size...

A star may collapse into an extremely dense body (called neutron
star ) composed predominantly of neutrons. This can happen when
massive stars die in supernovas and their cores collapse. Represent
the star as a uniform solid sphere both before and after the
collpase. Assume no astronomical bodies are in the vicinity of the
star, so no forces or torques are exerted on the star. The star’s
initial radius was 9.45 × 108 m, its final radius is 15200 m,...

Suppose that a neutron star has a radius of 14 km and a
temperature of 1,000,000 K. How luminous is it?

A typical neutron star may have a mass equal to that of the Sun
but a radius of only 12 km. (a) What is the gravitational
acceleration at the surface of such a star? (b) How fast would an
object be moving if it fell from rest through a distance of 1.5 m
on such a star? (Assume the star does not rotate.)

Neutron stars are one of the possible “final states” of a star.
The idea is that for a sufficiently massive star, the gravitational
pressure is enough to overcome the outward pressure (that comes
from essentially the Pauli exclusion principle) that keeps fermions
from coinciding with each other.
Part A) According to quantum statistics, the OUTWARD pressure of
a (neutron) fermionic gas is given by P=[(3.9?^2)/(2m)](N/V)^(5/3),
where m is the mass of a neutron, and N/V is the number density of...

Consider a neutron star with a mass equal to 0.9 times the mass
of the Sun, a radius of 15 km, and a rotation period of 1.3 s. What
is the speed of a point on the equator of this neutron star? What
is gg at the surface of this neutron star? A stationary 1.0 kg mass
has a weight of 9.8 N on Earth. What would be its weight on the
neutron star? How many revolutions per second are...

A certain star of radius 6.34 million meters, rotates twice
around its axis in one earth day. Find its angular frequency. This
star has a mass of 1.00x1032 kg. When this star collapses to a
neutron star, its radius shrinks by a factor of 104 while it loses
30% of its mass. Find the angular velocity of this star after the
collapse. Assume that the spherical shape and density of the star
remain unchanged . Find the speed and centripetal...

In an X-ray burster, the surface of a neutron star 10 km in
radius is heated to a temperature of 3 ×
107 K. (a) Determine the wavelength of maximum
emission of the heated surface, assuming it radiates as a
blackbody. In what part of the electromagnetic spectrum does this
lie? (b) Find the luminosity of the heated neutron star. Give your
answer in watts and in terms of the luminosity of the Sun. How does
this compare with the...

Suppose a star the size of our Sun, but of mass 8.0 times as
great, was rotating at a speed of 1.0 revolution every 21 days. If
it were to undergo gravitational collapse to a neutron star of
radius 20 km, losing three quarters of its mass in the process,
what would its rotation speed be? Assume that the star is a uniform
sphere at all times and that the lost mass carries off no angular
momentum.
Answer in rev/day

Why can emission of gravitational waves lead to mergers of white
dwarfs, neutron stars, and black holes?
A) Binary systems of compact objects experience the rapid
pulsations of the radiation, known as pulsars. The variability of
the light corresponds to the emission of the gravitational waves.
The merging corresponds to the rapid decreasing of the radius, i.e.
the merger of the compact object.
B) Compact objects have very large densities. When the compact
objects are very close, the matter falls...

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