Can Neutron Star Become Black Hole

[litespeed]

This is something of a trojan horse sort of post. Specifically, I already suspect the answer is no, but am not sure. However, assuming a Neutron star can not become a black hole through accretion of additional mass, that means Black Holes are generally created through momentum as the minimum mass needed accelerates in the initial collapse.

1) Does this mass accelerated by gravity increase as it approaches the speed of light, thus increasing the mass and gravity of the BH?

[Moontanman]

I think assuming a neutron star cannot become a black hole by accumulating mass is wrong. I see no reason a neutron star couldn't become a black hole by collecting mass. If a neutron star accumulated mass whether through collision with another neutron star or some other mass big enough to push it over the limit it should become a black hole. Even if it acquires this mass slowly over time it should become a black hole if it becomes massive enough.

[litespeed]

MT

I agree with you, but have never seen it stated elsewhere, and I will demure until more posters indulge us. In the mean time, I have another question about neutron stars. Are they entirely solid matter, or do they include space of any sort.

In elaboration, I have seen it said that an atom blown up to the size of a grape, and then blown up to the size of a NFL covered stadium, would have a nucleous the size of a grain of sand. I quess the various electrons would be even less cosequential. So an atom is almost entirely empty space.

I know that a neutron star is so dense it pushes electrons and protons together to form neutrons, and that only neutrons remain. However, I have yet to be informed if all these 'neutered' atoms are also squeezed together so that no empty space remains.

[freeztar]

Originally Posted by litespeed

This is something of a trojan horse sort of post. Specifically, I already suspect the answer is no, but am not sure. However, assuming a Neutron star can not become a black hole through accretion of additional mass, that means Black Holes are generally created through momentum as the minimum mass needed accelerates in the initial collapse.

From the wiki on neutron stars:

A typical neutron star has a mass between 1.35 and about 2.1 solar masses, with a corresponding radius of about 12 km if the Akmal-Pandharipande-Ravenhall (APR) Equation of state (EOS) is used.[1][2] In contrast, the Sun's radius is about 60,000 times that. Neutron stars have overall densities predicted by the APR EOS of 3.7 × 1017 (2.6 × 1014 times Solar density) to 5.9 × 1017 kg/m³ (4.1 × 1014 times Solar density),[3] which compares with the approximate density of an atomic nucleus of 3 × 1017 kg/m³.[4] The neutron star's density varies from below 1 × 109 kg/m³ in the crust increasing with depth to above 6 or 8 × 1017 kg/m³ deeper inside.[5]

In general, compact stars of less than 1.44 solar masses, the Chandrasekhar limit, are white dwarfs; above 2 to 3 solar masses (the Tolman-Oppenheimer-Volkoff limit), a quark star might be created, however this is uncertain. Gravitational collapse will always occur on any star over 5 solar masses, inevitably producing a black hole.

Originally Posted by litespeed

1) Does this mass accelerated by gravity increase as it approaches the speed of light, thus increasing the mass and gravity of the BH?

Originally Posted by wiki

The resulting force of gravity is so strong that if an object were to fall from just one meter high it would hit the surface of the neutron star at 2 thousand kilometers per second, or 4.3 million miles per hour

Since the speed of light is 670,616,629 mph, relativistic effects would be negligible.

[maddog]

Originally Posted by litespeed

This is something of a trojan horse sort of post. Specifically, I already suspect the answer is no, but am not sure. However, assuming a Neutron star can not become a black hole through accretion of additional mass, that means Black Holes are generally created through momentum as the minimum mass needed accelerates in the initial collapse.

1) Does this mass accelerated by gravity increase as it approaches the speed of light, thus increasing the mass and gravity of the BH?

Both Neutron Stars and Black Holes are both remnants of the explosion of a star once its fuel is exhausted. When the stars mass is sufficient to explode in a Supernovae event or a simple Novae, the latter producing White Dwarf stars.

What determines whether the remnant will be a Neutron Star or Black Hole is dependent upon the mass of the original star. If the original star is above about 2 solar masses (twice the size of our sun). Then then end product produces a Black Hole over Neutron Star. Once the end product is produced it is pretty much static.

There would be one exception where a Neutron Star could go black. That would be if a Neutron Star were part of a binary system where the Neutron Star could accrete material from the other star. Matter transfer is common with eclipsing binaries in close orbits. Were the Neutron Star to exceed 2 solar masses, it would become a Black Hole.

Note: This is the process I learned in Astrophysics when I was in school (and was the conventional wisdom, until the article I read in SciAm) -- this months issue on Naked Singularities.

I am not aware what are the defining rules (not even sure they are known yet) what makes a Naked Singularity over a Black Hole. From the article, they imply if creeping up to the limit allows an Event Horizon (Black) whereas if creation is abrupt (SuperNova) then maybe Naked (assuming pressure properly taken into account).

I know this muddies up the clarity. Well, that is science....



maddog

[freeztar]

Originally Posted by litespeed

I have yet to be informed if all these 'neutered' atoms are also squeezed together so that no empty space remains.

I believe that is the case. The wiki article mentions the Pauli Exclusion Principle which suggests to me that the neutrons are squeezed together up to the point of physical limitations.

[litespeed]

Free - You provided: "... fall from just one meter high it would hit the surface of the neutron star at 2 thousand kilometers per second, or 4.3 million miles per hour." Since the speed of light is 670,616,629 mph, relativistic effects would be negligible.

I invite a mathematician to calculate the impact velocity from one kilometer above the surface.

[freeztar]

Originally Posted by litespeed

Free - You provided: "... fall from just one meter high it would hit the surface of the neutron star at 2 thousand kilometers per second, or 4.3 million miles per hour." Since the speed of light is 670,616,629 mph, relativistic effects would be negligible.

I invite a mathematician to calculate the impact velocity from one kilometer above the surface.

I knew somebody was going to call me out on that.
I'm not sure how they came to that number really. Figuring it out using Newton's method seems fairly straightforward, but using GR to incorporate pressure is another story. I, too, will await someone with more math prowess than I have.

[CraigD]

Originally Posted by litespeed

I invite a mathematician to calculate the impact velocity from one kilometer above the surface [of a neutron star].

You can calculate this by calculating the change in gravitational potential energy for a test body at a radius 1 meter greater than vs. equal to the radius of the primary body, the neutron star.

GPE is given by

, where is the gravitational constant, the mass of the primary, the mass of the test body, the distance from the center of gravity of the system to the test body.

Change in GPE, then, is

, where is the test body’s initial distance, its distance at impact.

Taking an “average” neutron star of 1.5 solar masses and surface radius 12000 m, and for ease of calculation a test body massing 1 kg, this evaluates:



Suspecting that this is associated with a speed for which relativistic effects are slight, we can calculate impact velocity with the classical equation for kinetic energy,


getting



, close to wikipedia & freeztar’s example of

"... fall from just one meter high it would hit the surface of the neutron star at 2 thousand kilometers per second, or 4.3 million miles per hour."

which is indeed less than 1% of the speed of light.

More relevant than impact speed from 1 m above its surface, though, is impact speed from a great distance (it’s traditional in gravitational mechanics to assume “an infinite distance” to set an upper limit on such values). Recalculating with , , and .
This is high enough that we should use a relativistic calculation for kinetic energy,

, which gives an impact velocity of about 0.4 c, about 12000000 m/s.

Although a very high speed, this is still not enough to produce a dramatic mass dilation – a factor of about 1.19, (a 19% increase), so we can see that the original post’s question

Originally Posted by litespeed

1) Does this mass accelerated by gravity increase as it approaches the speed of light, thus increasing the mass and gravity of the BH?

incorrectly assumes that bodies falling toward the surfaces of compact bodies such as neutron stars or the event horizons of black holes (which requires a separate calculation, but one yielding a larger yet similar result) always reach high relativistic speeds.

It’s also necessary to realistically consider conditions around a star-mass body like a neutron star. Because our test body would not be alone, but part of a large accretion disk, it would almost certainly collide many times with similar bodies, preventing it from approaching this upper limit value of 0.4 c.

I think the answer to the title question “Can Neutron Star Become Black Hole”, is “yes, but before it became a black hole, it would cease being a neutron star. An explanation would require a separate, fairly lengthy post, which I’ll get to as time permits, and invite anyone who can spare the time now the pleasure of writing.

[maddog]

Originally Posted by freeztar

I believe that is the case. The wiki article mentions the Pauli Exclusion Principle which suggests to me that the neutrons are squeezed together up to the point of physical limitations.

As your Wiki link describes the Pauli Exclusion principle applies to all Fermions (spin 1/2 particles) and thus applies to Neutrons.

To get a sense of what a Neutron Star is like, the best example I know is a Sci Fi novel Dragon's Egg by Dr. Robert L. Forward. At first this may seem off topic, just hear me out. The novel is about creature that live on the Neutron Star. Dr. Forward is very descriptive about how a body of mass would behave on the surface of such an object.

maddog