Schutz, page 226 - Black hole formation

[Jimmy Snyder]

This question involves the following statement in Schutz, A First Course in GR, but you don't need to have a copy to answer it.

He says that in the formation of a black hole from a supernova explosion, we should expect gravity waves of amplitude M/R, where M is the mass and R is the distance to the explosion. He goes on to say that for a black hole of 10 solar masses, whose distance is [itex]10^{23}m[/itex], this is about [itex]10^{-17}[/itex]. Since 1 solar mass is roughly [itex]10^3m[/itex], M/R for the black hole itself would be [itex]10^{-19}[/itex]. This seems to imply that it would take the supernova explosion of a star of 1000 solar masses to create a black hole of 10 solar masses. Is this correct?

 

[pmb_phy]

This question involves the following statement in Schutz, A First Course in GR, but you don't need to have a copy to answer it.
He says that in the formation of a black hole from a supernova explosion, we should expect waves of amplitude M/R, where M is the mass and R is the distance to the explosion. He goes on to say that for a black hole of 10 solar masses, whose distance is [itex]10^{23}m[/itex], this is about [itex]10^{-17}[/itex]. Since 1 solar mass is roughly [itex]10^3m[/itex], M/R for the black hole itself would be [itex]10^{-19}[/itex]. This seems to imply that it would take the supernova explosion of a star of 1000 solar masses to create a black hole of 10 solar masses. Is this correct?

What's going on with latex lately? The syntax here seems perfect an it can't be.

Pete

 

[Jimmy Snyder]

What's going on with latex lately? The syntax here seems perfect an it can't be.
Pete

Can you be more specific. On my screen my posts appear as I intend them to appear on your screen. Also, please note that I just edited my first post to add the word gravity so we know what kind of waves Schutz is talking about.

 

[pervect]

This question involves the following statement in Schutz, A First Course in GR, but you don't need to have a copy to answer it.
He says that in the formation of a black hole from a supernova explosion, we should expect gravity waves of amplitude M/R, where M is the mass and R is the distance to the explosion. He goes on to say that for a black hole of 10 solar masses, whose distance is [itex]10^{23}m[/itex], this is about [itex]10^{-17}[/itex]. Since 1 solar mass is roughly [itex]10^3m[/itex], M/R for the black hole itself would be [itex]10^{-19}[/itex]. This seems to imply that it would take the supernova explosion of a star of 1000 solar masses to create a black hole of 10 solar masses. Is this correct?

I assume this is all in geometric units.

M/r is a dimensionless number (in geometric units, which I've assumed). So when Schutz is talking about the amplitude of gravity waves, I assume he is talking about the power. (Power is another dimensionless number in geometric units). Energy is not dimensionless in geometric units.

(I suppose I don't have to assume - I'll have to refresh my memory on the emission of gravitational waves from MTW before I can verify this. More later after breakfast).

I don't see how you go from a statement about the power emitted in gravity waves to a statement about the final masses.

 

[Jimmy Snyder]

in geometric units, which I've assumed.

Thanks for taking a look at this pervect. Yes, mass is given in geometric units. The book gives a figure of [itex]1.477[/itex] x [itex]10^{3}m[/itex] for the mass of the sun. So the figures are rounded off severely.

As for the amplitude of the gravitational wave, you don't really need to concentrate on that to answer the question. The real question may not have been totally clear so I repeat it:

When a supernova creates a black hole, does it take a 1000 solar mass star to make a 10 solar mass black hole?

The rest of that post was simply to justify why I was asking the question. Schutz's text seems to imply that the answer is yes.

But if the answer is yes, then there are other questions that come to my mind. A star of that mass burns so quickly, can the protostellar material have had time to clear away? But if the material is still there when the supernova occurs, wouldn't it slow down the dispersion of the ejecta? If it does, might not the ejecta fail to reach escape velocity and come crashing back to the black hole? But if it does then won't it add to the 10 solar mass of the black hole?

 

[pervect]

As for the amplitude of the gravitational wave, you don't really need to concentrate on that to answer the question. The real question may not have been totally clear so I repeat it:
When a supernova creates a black hole, does it take a 1000 solar mass star to make a 10 solar mass black hole?
The rest of that post was simply to justify why I was asking the question. Schutz's text seems to imply that the answer is yes.
But if the answer is yes, then there are other questions that come to my mind. A star of that mass burns so quickly, can the protostellar material have had time to clear away? But if the material is still there when the supernova occurs, wouldn't it slow down the dispersion of the ejecta? If it does, might not the ejecta fail to reach escape velocity and come crashing back to the black hole? But if it does then won't it add to the 10 solar mass of the black hole?

I don't know the answer to your question. MTW appears to be very dated on this point, so I won't repeat what they have to say here.
A couple of interesting links I stumbled across are:
http://www.ligo.caltech.edu/docs/G/G020075-00.pdf
http://arxiv.org/abs/astro-ph/0409035
The second mainly for the following very short quote

We do not yet have an agreed-upon explanation for the mechanism of corecollapse
supernovae, nor for the related phenomena of neutron star kicks and
blast debris morphology.

Space Tiger might know more, he usually posts in the general astronomy and cosmology forum, so I'm not sure if he's seen your question here.
I would tend to trust observational evidence more than theory - as the second paper points out, there appear to be a lot of elements that have to be modeled properly to explain supernova.

 

[pmb_phy]

Can you be more specific. On my screen my posts appear as I intend them to appear on your screen. Also, please note that I just edited my first post to add the word gravity so we know what kind of waves Schutz is talking about.

I dunno. Sometimes the Latex appears all messed up and then at other times it appears perfect.

It is a puzzlement!

Pete

 

[George Jones]

With respect to the original post, I have a hunch that Schutz used the value of the Sun's mass given inside the back cover of MTW, i.e., Schutz forgot to convert centimetres to metres. This would account for the missing factor of 100.

Regards,
George

 

[Jimmy Snyder]

Schutz forgot to convert centimetres to metres. This would account for the missing factor of 100.

Thanks George.