Ignoring where such a diamond came from, how massive could a diamond before gravity could overcome its atomic structure and crush it into a sphere. than the earth since the earth’s gravity
If we’re looking at “before gravity crushes it into a sphere”, then that’ll depend on what shape the diamond is. What if it’s already a sphere, or something very close to it?
You could also ask how big it’d be before the center would be forced by the pressure into having some other crystalline structure, how big it’d be before the center has no crystalline structure at all, and how big it’d be before the carbon atoms in the center started to fuse into other elements.
One problem is that the surface won’t deform until the gravity at the surface is capable of breaking the diamond’s structure. And then you will need to define how smooth a sphere is OK in order to get the answer. One risks getting to neutron star densities before the residual surface gets really smooth.
Related question:
Say pressure creates a “diamond as big as the moon” at the center of a gas giant. Will it be perfectly smooth, or will it have crystalline ravines and mountain ranges?
Yeah, I’m not sure if the question here is ‘how big a diamond before gravity/pressure turns it into something else?’ or if it’s just ‘how big can a faceted diamond be, before gravity interferes with the shape?’ They’re both quite interesting questions.
There are hypotheses that white dwarf stars may cool to become large, singular diamonds the size of Earth or larger.
To quote from the Wiki entry on diamond:
“Used in so-called diamond anvil experiments to create high-pressure environments, diamonds are able to withstand crushing pressures in excess of 600 gigapascals (6 million atmospheres)”
So someone can run the calcs and see how large a sphere would need to be to generate such pressures due to gravity. That would be the upper boundary, I guess, since most diamonds fail much sooner due to internal flaws in the crystalline structure.
Dennis
I have nothing to add, since studying art, music and literature didn’t give me a whole lot of time left over for physics, but this conversation is the tits. I’ma sit back and learn me some gigapascals. Thanks guys.
Ok, here’s what I get. Take a spherical diamond of radius R and mass M. I’ll assume the density is constant throughout the diamond, which probably isn’t realistic but otherwise we need to understand how diamond deforms with pressure and that seems like it could get complicated and the details may not even be known at such high pressures. So for constant density k, the pressure P at the center is 3GM[sup]2[/sup]/8πR[sup]4[/sup], where G is the gravitational constant. The mass M is the density k times the volume (4/3)πR[sup]3[/sup]. Substituting for M and simplifying, we get P = (2/3)πGk[sup]2[/sup]R[sup]2[/sup]. Solving for R, R=sqrt(P/(2/3)πGk[sup]2[/sup]). Plugging in the numbers for G and k (3.5 g/cc), and taking P = 600 GPa, I get R=18,725 km, so the diameter is 37,450 km or 23,270 miles.
One factor may be the carbon starting to fuse Carbon-burning process - Wikipedia
(Though I’m not sure what happens if the temps are cool but you still have 8x mass of sun in carbon)
ETA though that is LOT larger than markn+ calculates
Brian
White dwarves are cool. To an excellent approximation, they can be treated as having zero temperature.
White dwarves aren’t 8 solar masses.
This paper comes up with a formula for the “potato radius” of a body. It is (page 6):
R[sub]pot[/sub] = (2s / piG*p[sup]2[/sup])[sup]1/2[/sup]
Using your numbers of 600 GPa and 3.5 g/cc, I get a radius of 21,600 km. Not too far off from your estimate.
Most geologic materials are modeled with a strength that increases with confining pressure (up to a point). If the 600 GPa is an unconfined pressure, this might be pretty conservative.
OK, let me rephrase that, then: Any degenerate-matter celestial body is cool.
I think what he’s getting at and you’re overlooking is that an 8 solar mass celestial body is over the Chandrasekhar limit of 1.6 solar masses, and won’t be stable as a degenerate-matter celestial body. It will have to either collapse into a black hole or undergo some sort of violent reaction to shed mass, and will only be ‘cool’ after it sheds mass to go under the 1.6 solar mass limit.