Dark Stars ??

[beamish]

I've recently finished reading "Bang" and Universe In a Nutshell", having also recently viewed some of the You-Tube offerings regarding the scales of objects in the Universe it got me thinking(dangerous I know).

Q: Theoretically, how large can a star become without collapsing-there's bound to be a formula?

subsequent to this,

Q: Is it possible for a star to be so large that inspite of the radiation from the thermonuclear forces in the core working against gravity to prevent collapse, can the actual gravity of the star be so great so as to prevent light from escaping, hence a "Dark Star" ? (as opposed to the same effect from a Black

Hole)

Ta,

Karlo :scratch:

[Paxo]

Karlo,

estimates for largest size seems to be 150 - 200 solar masses - see here

http://www.astronomy.com/asy/default.aspx?c=a&id=2968

They appear to stop growing as the outer portions of the star become 'loosly' held by gravity and blow off into space, I guess this would greatly affect the answer to your second question.

Steve

[beamish]

Cheers Paxo. Nice read and fascinating.

Karlo

[ngc2403]

I would like to introduce a concept known as Radiation Pressure.

P_rad=aT^4 is the equation that you were searching for. Radiation pressure comes from photons transferring momenta to electrons. This bombardment creates the pressure to support againstg freefall collapse. The photons, as u know, come from thermonuclear fusion. The wonderful thing with radiation pressure is its steep temperature dependance..double the temp of a star and the rate of photon generation increases 16x.

On one scale, a star can be as light as around 0.01 solar masses. Any lower, and the star is not hot enough for fusion to kick in, and hence no radiation pressure is produced, andthe stable state for this object is a brown dwarf, not much bigger than jupiter, supported by quantum degeneracy pressure of electrons.

Above this limiting mass, fusion kicks in before degeneracy pressure does, and a star is born. To a good approximation, solar mass stars, spend their lives in hydrostaic equilibrium, where gravity and radiation pressure balance.

Moving on to massive stars around 10 solar masses, to balance their enormous gravity, these stars are hot (>15000K). Consequently, radiation pressure, now dominates over gravity, and material is forced off the star, and it ejects material into the surrounding neighbourhood.

The most dramatic of these massive stars has got to be the Wolf-rayet stars. These are exceptionally hot and massive (>25 solar masses). They loose around 0.0001 solar masses per year! This can be observed easily in the bubble nebula, or the crescent nebula.

Stars above this mass are rare, but eta carinae is one example around 100 solar masses, and will die soon...

There is a theoretical limit to the mass of stars, this is given by the Eddington Luminosity. It decribes the maximum luminosity for a given mass. Also known is a realtionship between luminosity and mass for the main sequence. It was derived empirically from observation. It says that L/L*=(M/M*)^3.5. On equating the two equations, one derive a theoretical limiting mass for stars before the blow themselves apart. This mass is around 100-150 solar masses depending on the mass luminosity relationship for MS stars.

So in answer to your question, large stars dont collapse they tear themselves apart. Should a massive star stop fusing then it would collapse into a Type II supernova, and create a Neutron Star or Black hole if massive enough...

Paul

[beamish]

Thanks Paul, good post!

I was simply wondering ,like one does, whether a star could attain such mass as to prevent the expulsion/escape of photons from the surface due to it's own gravity.

Karlo

[ngc2403]

Your question is plausible, but Im afraid you are wrong. A star cannot have such a mass as to prevent radiation from escaping.

You would require that for a star of mass M, it radius R<= Rs, its schwarzchild radius, where Rs= GM/C^2. This is also equivalent to Rs=3km*(M/Msun). So you would require a star to have a radius of the order of 10km. For a MS star, Radius is proportional to mass, and in fact for MS stars, the density falls as mass increases, so that heavy stars have gigantic radii, where R>>>Rs, so no freefall collapse would occur.

So a Main Sequence star cannot get heavy enough to initiate freefall collapse.

At the lower end of the mass scale, at 0.01 solar masses, we require a radius of around 30m. This radius is far too small. So we can conclude that all MS stars have R>>Rs.

Once stars stop fusing, interesting things start to happen.

White dwarfs are formed from solar mass stars. They have typically one solar mass, and the radius of the earth. For one solar mass, we require R<=Rs for collapse, ie R<=3km. The radius of the earth is 6,400km, over 2000Rs. The heaviest a white dwarf can be is 1.4 solar masses. Even allowing for the fact that as you pile mass onto a white dwarf, it shrinks, its radius is still >1000Rs. So we are getting closer...

The next candidate is the Neutron star, formed from a Type 1a, or Type II supernova. It is like a white dwarf, but it is supported by neutron degeneracy pressure rather than electron.

NS stars have a solar mass or 2 packed in a radius of 10km. So NS stars are very close to having R<=Rs. The limiting mass of NS is around 2.4 solar masses. As these stars have actually been observed, clearly light is able to escape the surface and reach us, and so NS stars have R>Rs.

The only object that has R<=Rs is a black hole, formed from the collapse of a NS, or very massive star. It is a black hole that has enough gravity to inhibit the escaping of photons

Even if there are stars out there that had R<=Rs, we could not see them (as in the case of a BH) as photons dont leave the surface

Paul

[beamish]

"Even if there are stars out there that had R<=Rs, we could not see them (as in the case of a BH) as photons dont leave the surface"

Exactly, thats why I'd asked if it was possible- many thanks for your explanation.

Karlo

[PhillyDee]

But how do we know . . Its not as if we could ever see them . . .

Sorry, I know you are correct though

[ngc2403]

but how do we know that there are blackholes?

nasa spent a long time looking for the tell tale sign that blackholes exist.

they wanted to catch the moment that a BH passed in front of a star and so made it disappear for a short time before reappearing

long shot but they got one after a few years of trying.

would you like a more detailed answer about the other evidence?

[PhillyDee]

but how do we know that there are blackholes?

nasa spent a long time looking for the tell tale sign that blackholes exist.

they wanted to catch the moment that a BH passed in front of a star and so made it disappear for a short time before reappearing

long shot but they got one after a few years of trying.

would you like a more detailed answer about the other evidence?

Nope, I believe you, I was just being awkward. It sounded better in my head.

[ngc2403]

no worries,

i am doing a degree in astronomy, it could be said that it is my duty to explain these things

[beamish]

So Paul, hypothetically speaking, "if" they existed, wouldn't they to all intents and purposes "appear" to an observer as a BH ?-may explain why they haven't been found ? As you say, it took NASA a long time to confirm the existence of a BH .

I'm not trying to be difficult, merely playing devil's advocate. As you mentioned the Wolf Rayet stars are stupendously huge and got me thinking. (too much time on my hands)

Karlo

[InvaderXan]

Actually, there is a theory that replaces Black Holes with what are termed "Gravastars". I forget the details, but it was proposed as an alternative concept to gravitational singularities.

A "classic" black hole is a gravitational singularity -- in other words, its mass in compressed into a point of negligible volume. This causes problems in quantum mechanics.

ngc2403 -- NASA recorded a black hole transit? That's cool, I hadn't heard about that! Do you have a link to anything they published about it?

[ngc2403]

no sorry,

i heard it two or so years ago on horizon, or something like that?? i had not heard of the other theory but i would suggest that the term black hole is more but the fact that the star's radius is smaller than it's schwarzchild radius.

as for the singularites, i don't like the idea of them. i think that it will be held up by Quarks or other smaller subatomic particles, follows the pattern really, white dwarfs-electrons, pulsar/neutron stars-neutrons, blackhole-???????

what about you?

[Paxo]

NASA recorded a black hole transit? That's cool, I hadn't heard about that! Do you have a link to anything they published about it?

I remember seeing something about it, it may have been the BBC 'Space' series or something like that, I don't think it was Horizon (as I haven't watched a Horizon programme for a few years now due to the BBC's attitude to science programmes in general).

Will keep an eye out for it though, it's something I've seen recently.

Steve..

[InvaderXan]

Cheers Steve.

I couldn't find an observation, but I found a theory paper about it.

My guess is that if they observed any transiting black hole, it would probably be Cygnus X-1...?

And no NGC2403, I don't much like the concept of a singularity. Partly because of the way seemingly everything else in nature obeys the Pauli Exclusion Principle. The concept of "quark stars", supported by quark degeneracy pressure seems like a logical progression. A quick Google search tells me that the 'neutron stars' RXJ1856.5-3754 and 3C58 are two suspected quark stars.

Beyond that, who knows? Superstring degeneracy? I'm not sure if we collectively understand enough about spacetime itself to be able to say what a black hole really is...

[acey]

A little remark on the "mass" required to form a black hole - remember it's density that counts, not mass. You could make a black hole out of sand if you had enough sand (I think you'd need a sphere of it with something like the radius of Saturn's orbit).

[ngc2403]

so sand is denser than a blackhole?

[thing]

If you mix it with water it is.

[ngc2403]

two parts sand one part concrete?

[acey]

From Schwarzschild radius r = 2Gm/c**2

and Volume of sphere V = 4/3pi*r**3

and density D = m/V

we get

r = 2c*sqrt(3/(32piGD)

(if my quick back-of-envelope algebra’s right)

where

c = 3x10**8 m/s (speed of light)

G = 6.67x10**-11 (grav. const. in appropriate units)

and D is the density of the required black-hole making substance.

Putting in the numbers I make this out to be

r = 1.269 x 10**18 / sqrtD

For dry sand D = 1600 kg/m**3.

This would give

r = 320 billion km

Pluto has a maximum distance of only about 7 billion km from Sun so I was wrong about Saturn (or, equally likely, I’ve messed up on my calculator).

If we take the volume of a black hole to be the volume enclosed inside the event horizon, then black hole densities decrease with size. I believe that supermassive black holes come out with densities less than water.

Not very practical, but fun.

[beamish]

If we take the volume of a black hole to be the volume enclosed inside the event horizon, then black hole densities decrease with size. I believe that supermassive black holes come out with densities less than water.

Well just seems to go against all common sense ! :scratch:

Karlo

[InvaderXan]

Just imagine a ball of sand with a radius of 2133AU. That's a lot of sand!

Though the silicon would begin fusing under gravitational pressure long before you amassed that much sand. I'm not sure though -- I don't have an envelope to calculate the Jeans Radius on.

But hang on... if density, rho = m/V, and a classical black hole has a volume approaching zero then surely it's density should tend towards infinity, regardless of mass...?

[beamish]

Exactly !

[Paxo]

Found it!

BBC series called SPACE, episode Black Holes showed the work of a Dr Tim Axelrod of the mt Stromio Observatory, who was the first to witness a black hole passing in front of a distant star. He used gravitational microlensing to directly show this. His original find was on a star on the very outskirts of the large magellenic cloud. It took him 8 years to find analysisng the data from over 20 million stars every night. Since this original find he has found many black holes wandering through our galaxy. They estimate that there is a suitable supernova producing a black hole in our galaxy every 1000 years, this gives the prospect of over 10,000,000 black holes wandering round our galaxy - and here was me worrying about when will I get a chance to cut the lawn!

Hope this information is useful.

I once thought that my car harboured a black hole in it. All the evidence was there:

1 high gravity caused cars to move closer to me in car parks making it oiften difficult for me to get into the car,

2 Gravitational lenses was making my car 'transparent' to other road users, especially at the wavelength used by taxi drivers,

and finally, the most compelling piece of evidence,

3 Dust accretion disc - my car is always getting filthy,

Keep the debate coming boys, but please remember one thing, there are lots of recreational (or unpaid professionals as I like to call them) astronomers who try and follow what's going on, please don't get too technical.

Edit: on reading this back I thought it may sound a little stroppy, it isn't meant to be, sorry if any offence caused.

Steve..