Can a Star be Too Big to be Detected?

[Shirley]

Would it be possible for a star to be so large that the light emitting from it was redshifted beyond detection?

I had a question that I wanted to puzzle out in a research paper, but it seems easier to find questions than answers.

Anyway, thanks in advance,

John

 

[Shirley]

I think I may have answered my own question- y'all let me know, if not. A "dark star" cannot exist, because the amount of gravity required would mean that the star was immensely dense, and stars cannot reach that level of density while nuclear reactions are still producing outward force.

Right?

 

[Hurkyl]

You may be right, but there's an easier answer...

Would it be possible for a star to be so large that the light emitting from it was redshifted beyond detection?

If this were the case, then the star would be, almost by definition, a black hole.

 

[Shirley]

I suppose I assumed black holes to be "dead", but I see what you mean.

 

[jcsd]

Yes what you're describing is a black hole and funnily enough 'dark star'is the name that was first used to describe them. In a black hole the nuclear reactions can no longer produce the pressure required to resist the graviational pull of the stars mass and thus collapse.

 

[liujingshu]

There must be something has higher density than block hole. In the recent theory, we are sure that block hole has the highest density. But we know that theoretical physics is far away from its end.

 

[jcsd]

It depends what you mean by density, if you mean density within the event horzion, large black holes can have very small densities there, if you mean density of the singularity, well the density at the singularity is infinite.

 

[Shirley]

Thanks for the responses.

This is all theoretical, though, right? We can prove that something is refracting light in certain areas, but we can't actually "prove" a singularity? Because of the extreme forces involved, would be ever be able to prove what happened inside a singularity?

John

 

[marcus]

Originally posted by Shirley
Would it be possible for a star to be so large that the light emitting from it was redshifted beyond detection?

I had a question that I wanted to puzzle out in a research paper, but it seems easier to find questions than answers.

Anyway, thanks in advance,

John

It is clear from your other post that you are not talking about Hawking radiation from a black hole but conventional starlight from a dense cooling star.

"Beyond detection" depends on circumstances, such as distance to star etc.

Would you be satisfied with a gravitational redshift of 1000?

This is the redshift which the CMB has undergone so that instead of visible light it is called "microwave". If a factor of 1000 is not enough to make the light unrecognizable by your standards, then what is?

It seems to me to be a meaningful question. I urge you not to give up on it.


You are asking for something that let's light escape from its surface but that by the time the light has gotten clear of the star it is
extremely redshifted---say by a factor of 1000, to be definite.

Think about a neutron star that is still very hot and glowing.
Imagine that it is ALMOST but not quite massive enough to turn into a black hole.

I will look in Frank shu's astrophysics textbook and tell you the radius of this neutron star and you can see if its grav redshift far from the star is more than 1000.

It looks like this poster may have just come in, gotten the earlier answers, and is now gone for good, but I'll follow through anyway.

This is a good question. It is not automatic that you are talking about a black hole, what you said was it let's out its light but the light is strongly redshifted by the time it gets far away from the star.

 

[marcus]

If you think of "research questions" like this then you should have Frank Shu's astroph book "the physical universe". It has many thoughtprovoking questions and builds selfreliant calculation. It is a classic.
He teaches at UC berkeley.

On page 129 it says that if M is the mass of a neutron star
and R is the radius------in any system of units you wish-----
then the bigger the mass the smaller will be the radius
and

the radius is given by this formula, with Planck's h and the neutron mass m in it:

R = 0.114 M^-1/3 h²/Gm^8/3

You can use this formula to study the fate of a photon leaving the surface of the neutron star which is ALMOST BUT NOT QUITE massive enough to collapse into a black hole

You can learn even more from this formula. For any mass the Schw. radius is 2GM/c²

if you have a neutron star and you keep adding more and more material the star will get smaller and smaller and as it gets smaller its radius will approach its Schw. radius!
When it gets that small it will collapse to a BH

Therefore you can solve to estimate the critical M that will make the neutron star collapse.

For your redshift problem you must have a mass which is not quite that big.

Have fun and keep asking questions

 

[marcus]

the asker has checked out it seems

John, or Shirley, doesn't seem to be around but
I think its interesting so I'll finish
the star really doesn't have to be BH to have extreme redshift


the formula for grav redshift is

1+z = 1/sqrt( 1- R/r)

where R is the Schw. radius and r the actual radius

so you can easily solve for z = 1000 or z = 2000 or whatever
and estimate what the radius has to be relative to
the Schw. radius determined by the mass

and the neutron star formula then can tell the mass

it works out that the neutron star has to be right on the brink of collapse---its radius only like one ppm larger than its schwarzschild radius, and then its light will still get to the outside world but will be gravitationally redshifted almost beyond recognition, may not even be detectable depending on distance and background etc.

interesting thought. too bad the poster split

 

[Shirley]

marcus,
thanks for the in-depth and insightful reply. You did indeed understand exactly what I was asking. I'll have to get the book you reference, when I can (my life is pretty busy just now).

You can check posting date and time at the bottom of the messages.

Regards,

John Shirley

 

[marcus]

Originally posted by Shirley
marcus,
...I'll have to get the book you reference, when I can (my life is pretty busy just now).
...

Glad you are still around!
Trouble with buying textbooks is they are expensive and go out of date. If you are near a college or university library you may be able to check it out (or request interlibrary loan copy) and see if it would really be worth the money to you.

an amazing amount of decent textbook material is on web
and when talking at PF I try where possible to only refer to online stuff
because it is immediately available to whomever reads the post

but even though Shu is an old book (1982!) I keep having to consult it

if you stick around PF, maybe someone will come up with a good general purpose online entry-level astrophysics text that can serve as a replacement, and you won't ever have to buy or borrow "The Physical Universe"

How did you happen to choose the Chinese character for death
("szu" on the 3rd tone)? Did you pick it from some menu at PF or bring it with you from somewhere. I am not chinese but have studied and like them-----in classical mandarin I believe "szu(3)" can also mean "ultimate or extreme".

 

[Shirley]

Marcus,
I am leaving active Army service in the next two months, after which I will complete my schooling, so I will indeed have access to university libraries. The kanji was chosen for a few reasons, including the death of an old way, and the beginning (or renewal) of a different path. (Also, if said in Japanese, and written phonetically in English, it's the first three letters of my last name.) :)

John

 

[marcus]

Originally posted by Shirley
Marcus,
I am leaving active Army service in the next two months, after which I will complete my schooling, so I will indeed have access to university libraries. The kanji was chosen for a few reasons, including the death of an old way, and the beginning (or renewal) of a different path. (Also, if said in Japanese, and written phonetically in English, it's the first three letters of my last name.) :)

John

Ah! It is the Japanese kanji "shi" as well as being a classical chinese character "szu(3)". Forgive my one-track way of thinking. I am mostly ignorant about things Japanese.

To me, now, cosmology and astrophysics are the most exciting areas of research----there are fine new instruments and a lot of new observational data so that research is advancing at a surprising pace. I hope someone here at PF can suggest an introductory online astrophysics text which can be used as I have used Frank Shu's book. I will keep a look out for something like
that.

Let us try something. I will suggest online astronomy textbooks to you and you test them out. Tell me how accessible they are
and whether they have a good focus and style in your personal opinion. In this way you can help me evaluate online textbooks and I can help you get an early start on your post-military studies.

If I find an online beginning astronomy book this evening I will edit the link into this post. Other PFers may have suggestions too.


Have a look at this from the University of Rochester. I believe it is the course notes for an undergraduate general astro course by Jay Pasachoff or some associate of his

http://www.pas.rochester.edu/~dmw/ast142/Lectures/

What a bummer. I have just tried this link and failed to get the expected Astro 142 lecture notes----either a weakness of my computer or something wrong with the link. Will have to ask Labguy or Chroot---both knowledgeable about online astronomy source material.

 

[Shirley]

I definitely appreciate the input. Good to get the synapses firing again after the infantry lowest-common-denominator homogenization.

Thanks,

John