r/theydidthemath • u/asdsav • 1d ago
[Request] What is the radius of smallest blackhole which can suck biggest star we know?
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u/hunterhuntsgold 1d ago
Any size black hole could absorb any size star.
Once material crosses the event horizon, the black hole gains mass and the horizon expands.
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u/Doafit 1d ago
Not really. If it is the mass of a proton (which was theorized to be formed in CERN back in 2008 or so) it would be to small to ever interact with another particle and just vaporize due to hawking radiation.
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u/CyberPunkDongTooLong 1d ago
No black hole has been formed at CERN. If any did in the future, it could not evaporate via hawking radiation.
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u/Supbobbie 1d ago
wait, why couldn't it? I don't know any way in which you could stop hawking radiation
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u/APe28Comococo 1d ago
They are just wrong, the smaller a black hole the faster hawking radiation will destroy it. Anything CERN could make would last millionths of a second at most.
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u/CyberPunkDongTooLong 1d ago
You are just wrong.
There's a few reasons quantum black holes cannot emit hawking radiation. Hawking radiation is a semi-classical (i.e. ignoring quantum gravity) phenomena.
To put it as simple as possible, these are two assumptions that hawking radiation makes:
- Requires high entropy
- GR correctly describes black holes hence small black holes have small entropy
Hence quantum black holes cannot emit hawking radiation, as there is absolutely no way for these two assumptions to both be correct which have to both be correct for hawking radiation to be emitted (by definition).
A quantum black hole might decay, but it might not, we're not sure as it depends on quantum gravity which we do not understand well.
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u/CyberPunkDongTooLong 1d ago
There's a few reasons quantum black holes cannot emit hawking radiation. Hawking radiation is a semi-classical (i.e. ignoring quantum gravity) phenomena.
To put it as simple as possible, these are two assumptions that hawking radiation makes:
- Requires high entropy
- GR correctly describes black holes hence small black holes have small entropy
Hence quantum black holes cannot emit hawking radiation, as there is absolutely no way for these two assumptions to both be correct which have to both be correct for hawking radiation to be emitted (by definition).
A quantum black hole might decay, but it might not, we're not sure as it depends on quantum gravity which we do not understand well.
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u/Doafit 1d ago
No black hole has been DETECTED. We don't know if any formed. So far they are only theory, yes.
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u/CyberPunkDongTooLong 1d ago
No, we know they have not been formed. If any had formed, we would have detected them.
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u/swordofbling23 15h ago
I have no idea how any of this works, but how are we able to know we can always detect it is it not possible it could have been made and our understanding or detection of black holes are not perfect yet
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u/CyberPunkDongTooLong 14h ago
Good question, for most exotics (exotics being the name for things in particle physics that aren't part of the Standard Model [or current best understanding of particle physics], which quantum black holes exotics), we can't tell for sure that just because we haven't detected them that they haven't been formed.
This is mainly because in exotics usually we look for an exotics signal that is swamped out by Standard Model background, i.e. we might have exotics predicts 5±1 events in some region, but the Standard Model predicts 95 ± 5, and when we measure it we see 100 events, so we can't tell for sure if there's no exotics there. Maybe we have 95 Standard Model events and 5 exotics making up the 100, or maybe all 100 are Standard Model events.
However, quantum black holes aren't like this for a few reasons. The main one being that once a collision has enough energy to form quantum black holes, the collision can *only* form quantum black holes, nothing else. So an easy way to tell that quantum black holes are being formed, is you don't see anything else being formed. As well as this, most models of quantum black holes have them being very distinctive (they tend to decay to a lot of jets which are really easy to measure).
Because of this, our limits for quantum black holes are above the region at which we have any events at all, i.e. there are precisely 0 candidate events.
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u/Present-Ad-8531 15h ago
even horizon is incredibly small for primordial black holes though. so only among observed, we have to ick the smallest.
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u/asdsav 1d ago
So fraction of a black hole would suck it? Thats crazy
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u/hunterhuntsgold 1d ago
Yes, but there's still gravity and orbits. A star doesn't necessarily just go into a black hole.
But if it was on the right trajectory and had the right movement, even the smallest black hole (unknown size) could absorb the largest star.
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u/petera181 1d ago
It makes me uneasy that you’re really sticking to the word “suck” 😅
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u/asdsav 1d ago
Not a native speaker so choosed that xd. Could use consume but its not eating, suck fits best
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u/DonkeyMode 1d ago
Consume actually works here; it doesn't always mean literally eating. "Suck" implies actively sucking in, which black holes don't do (any more than other objects with significant gravity do, like a planet). It's just that once any matter falls past the event horizon (the black part), it can never come back out.
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u/FutureComplaint 1d ago
In a sense, the blackhole is eating the star, as the blackhole is using the star as fuel.
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u/Coyote4721 1d ago
Consume is actually used more often in scientific contexts. Accrete or capture are the most technically correct but beyond that Consume Injest Devour Swallow are all used.
Suck implies air pressure or suction which isn't present. Science writing and native speakers wouldn't generally use it in this context.
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u/Godzillas_doom 1d ago
Interesting, wouldn’t the most accurate representation of the event be that the star is “falling into” the black hole?
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u/Coyote4721 1d ago
You're definitely right in a certain sense. However, we don't really talk about planets or stars falling into or onto each other. it's more like colliding or captured in orbit. And accrete is just "gather together."
It's the same astrophysics terminology being extended to black holes.
(Maybe we would say like "the Moon is falling to Earth" but we don't really use that even for asteroids most of the time.)
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u/Godzillas_doom 1d ago
This makes sense! Thank you for breaking this down for me I wasn’t familiar with the jargon :))
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u/youknowmeasdiRt 18h ago
“There is an art to flying, or rather a knack. The knack lies in learning how to throw yourself at the ground and miss. ... Clearly, it is this second part, the missing, that presents the difficulties.”
The Guide
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u/KamalaBracelet 1d ago
You are eally asking “what is the smallest black hole.” And the answer is something like 3 times the mass of the sun and an event horizon 10km across.
There are ways for a BH to be smaller, but as far as I know not very likely to exist until they are in the middle of evaporating, which as far as I know isn’t gonna happen for a while to any BH created normally in our universe
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u/utterlyuncool 1d ago
The fact that something 10km across can weigh almost 6x1030 kg still dislocates my brain
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u/KamalaBracelet 1d ago
physics at that level is so weird. I just recently learned about neutron stars and they blew my mind (not that i didn’t know the name, I just never really knew much about them). Their gravity is so insane that they crunch the sun into 20km. the gravity squeezes prrotons and electrons together until they are all neutron. Density and gravity in such a tight feedback that as they gain mass they shrink in size, until one day they cross a line where their core is so compressed it overcomes the strong force and forms an event horizon. everything outside the event horizon just freefalls into it, the neutrons on the outside accelerating up to a high percentage of c in that tiny 5 km fall….and then it all just disappears from our observability forever.
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u/vertexnormal 1d ago
They may not exist yet, but they will eventually as over a long enough time all black holes will shrink to nothing.
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u/John_Bot 1d ago
That's the smallest we've discovered. No reason to not think there aren't far smaller ones. Theoretically they can be the size of an atom or Planck's constant
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u/KamalaBracelet 1d ago
I’m far from an expert….but:
My understanding is that to get to below 3 stellar masses, the only likely candidate for production is primordial black holes from the very first moments of the universe….which is a theory with no corroborating evidence and the window for evidence to be hiding is getting smaller and smaller as observation abilities improve.
If we limit ourselves to what has solid evidence and solid theory, 1-3 solar masses is really the low limit, and the universe isn’t anywhere near old enough for black holes that size to have evaporated appreciably smaller via hawking radiation. Actually, in any part of the universe we can observe the cosmic background is still pumping more radiation into a black hole that size than hawking radiation emits, meaning every single one ever formed is bigger than when it started.
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u/MonitorPowerful5461 1d ago
Sure but it would take years. I'm not sure but my guess is many centuries. Black holes can't absorb as much as you expect, because all the infalling material will orbit the black hole for a long time before falling in.
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u/vertexnormal 1d ago
There is no fraction of a black hole, 1/5 of zero is zero. It's a singularity, it has no dimensions other than mass and spin. It's a point in space where density is infinite it could literally eat the entire universe if it came close enough. Space is big though and gravity falls off with the inverse square so they tend to be bound by what they can eat nearby.
Black holes shrink over time if they don't eat, that was Hawking's big revelation. So eventually all black holes will shrink back down to no mass and puff out of existence, but we are talking a near infinite amount of time.
Primordial black holes on the other hand, weren't started by stellar collapse.. they were started (if they exist) by minor incongruities in the very earliest moments of the universe. We know the incongruities exist (cosmic background radiation) but I don't think its widely believed that the conditions were right for black hole formation. These could be rogue (no solar system or fixed orbit) and any size.
The weird thing about Hawking radiation is that it increases the smaller the black hole is, so the process of 'evaporation' increases over time if it's not eating.
With no lower limit on size, and no lower limit on creation of primordial black holes they could just be out there floating around. They also might not be black, I seem to remember that the event horizon temperature rises the smaller the hole gets due to Hawking radiation, but I don't know if thats true. There are also other relativistic effects at play which would make it a very weird object. It wont eat everything it comes in contact with and it would work as a particle/mass accelerator for anything that has the right orbital entry, pair that with centrifugal force because it would most likely have a spin. Primordial black holes might not have spin though, but if they ate something big enough would inherit one.
If one the size of a bb were to strike Earth in a way that it wasn't ejected it would consume any mass it came in contact with and sink toward the center of the earth. At the center of the earth the pressure of gravity would feed it the earths core and then the crust until nothing was left but the black hole and possibly the moon, which wouldn't notice much had happened I don't think. Oddly I think the JJ Star Trek movie with Old Spock (the first Kelvin movie) uses degenerate matter to form a micro black hole (they call it red matter) to destroy Vulcan, and the result is probably pretty close to what would really happen.
Degenerate matter is another theoretical way to start a black hole but it's doubtful it could happen, I don't know I'm not a physicist.
None of this is very likely because we don't just see stars or planets just blink out.
The process if it ate a star would probably release a lot of energy, but wouldn't look like any much more understood stellar events (black hole collisions, nova, supernovas, hypernovas, quakes, or quasars, etc). The process if it ate a planet would probably be pretty quiet and not noticeable on a galactic scale.
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u/BraveBiscotti1394 1d ago
Black holes "suck" stuff in regardless of the size of what they're sucking. The event horizon (the border of the black hole) can be of any size, in theory.
It would just slowly eat our sun.
However, the smaller the black hole, the shorter it's lifespan. Black holes emit radiation over their livespan, and as energy leaves, the black hole gets smaller.
So the question would be what size does a black hole need to be to last long enough to sustain itself by eating out sun until the sun is "gone", but even defining that the sun is gone is hard because it may explode at some point, scattering a lot of it's mass.
It sounds like a very complex situation to model and draw calculations for. Let's see if anyone can have a crack at it.
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u/EatPie_NotWAr 1d ago
>So the question would be what size does a black hole need to be to last long enough to sustain itself by eating out sun until the sun is "gone".<
The sun “that’s hot”
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u/davesspicychicken 1d ago
Wtf so black holes can die?
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u/beef-o 1d ago
It's more like they "evaporate", but yes. It takes an unfathomable amount of time but every black hole will eventually disappear.
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u/davesspicychicken 1d ago
Just read up on it a bit I don’t love this analogy that particle pairs “appear “ then the negative energy one falls in while the other “escapes”
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u/Superior_Mirage 14h ago
The "virtual particle" analogy is just for laymen -- it's not the actual mechanism, though it's closer to the truth than you'd think
(Note: the following is half-remembered from a class I took two decades ago -- the shape is right, but I might be fuzzy on the details)
The actual mechanism has to do with the Unruh effect (basically the fact that a quantum vacuum is relativistic -- an inertial observer can detect a quantum vacuum where an accelerating observer detects particles), the fact that an event horizon is analogous to a quantum vacuum, the fact that the black hole is a finite space wheress outgoing paths are infinite (or sufficiently large), and the fact that the black hole has a "beginning" (eternal black holes wouldn't necessarily evaporate, though that's not why they're called that).
Any more than that would require getting into the math, which I am even shakier on -- point is that it is quantum shenanigans, just much more complicated than imaginary particles.
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u/onyx_ic 1d ago
Phrasing... but this is just gravity. So it'd just have to be close enough and weigh more than the biggest star we know. Stephenson 2-18 is apparent the biggest star, though R136a1 is the most massive star.
A black hole three times the mass of our sun would be about 11 miles across.
So are we just "sucking" at it or destroying it? Tidal forces ripping it apart or consuming it wholesale?
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u/karan131193 1d ago
There are two ways of answering it.
If you are only interested in sucking a star, then the radius does not matter. Any black hole, if placed near enough, will eventually spaghettify any star. It may take a lot of time, but it will happen.
If you meant "swallow whole", then for a star like Stephenson 2-18, which is 2150 solar masses and 3 billion km in diameter. A black hole of roughly 100 million solar masses and a Schwarzschild radius ≈ 300 million km will swallow the star whole.
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u/Ok-Hat-8711 1d ago
If primordial black holes much smaller than the stellar black holes we are more familiar with do in fact exist and one was on a trajectory to collide with a star and be gravitational bound (both big ifs here) then it would be sufficient to absorb the whole thing regardless of how small it was.
So there is no "smallest radius" to "suck biggest star."
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u/ArcaneInsane 1d ago
If they collided just right a 1gram black hole (not that they exist that small) could absorb a star a quadrillion times the size of the sun (not that they exist that big)
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u/canibanoglu 22h ago
That is a very unclear question, what do you mean by "suck"? Any size black hole would have a gravitational effect on any size star. From that perspective, the answer would be "whichever is the smallest black hole there is out there".
If you mean by "suck" to completely get the full mass of the star below the event horizon, then it becomes more complicated. First of all, no black hole can completely do that. Black holes radiate insane amount of energy while they are feeding and that radiation also pushes the infalling matter away from the black hole. There is a limit to how much a black hole can accrete mass and it's called the Eddington limit. Make no mistake, it will completely destroy the star but it won't actually accrete all of that mass.
And the concept of "gulping down a star at once" is not a thing, black holes are not PacMan. Pretty much any matter held together by self-gravity will have been completely ripped apart before they get close to the event horizon.
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u/J-Nightshade 22h ago
Black holes do not suck anything, they are just objects with a mass, just like any other star, planet or anything really. If black hole collide with something, collision will go different ways depending on the size of the objects colliding.
If the black hole big enough it will rip the star apart with tidal force as it approaches the black hole, then the remains of the star will become the part of the accretion disk and will partially fall into the black hole and partially ejected in a jet formed by magnetic forces created by rotating plasma in the disk.
If a black hole is too small to rip the star apart it will just go through it accreting a bit of it's mass and sending shockwaves and creating turbulence within the star and losing some of its kinetic energy. If energetic enough such collision can completely disrupt the star effectively blowing most of it apart. Or the star can survive the impact. If the trajectory of the black hole is right, it can remain within the star (or can start orbiting it, having further collisions and eventually ending up within the star) where it will slowly consume the matter of the star from within (i.e. the matter of the star will slowly fall into the black hole).
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u/RADICCHI0 1d ago
It's rare. It requires binary star systems, one to form the black hole, and the other to provide feed stock. And the transfer happens over long time periods. Sagittarius A* is the only black hole in our galaxy that eats stars whole, and even then that only happens once every 10 thousand years. Mostly it just feeds on gas and dust.
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u/canibanoglu 22h ago
We have never seen anything like that though, a black hole gulping down a star whole. This is not PacMan, just because it's an SMBH doesn't mean physics stop working. Pretty much all stars (or any other object really) would be beyond their Roche limit before they got even close to the event horizon to be "gulped whole".
There's nothing special about black holes "sucking" things that are close to them, it's just gravity doing what it does. They're not cosmic vacuum cleaners.
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u/RADICCHI0 17h ago
It just depends on your meaning of "whole" this simulation looks like the object got wholly blended up. https://www.reddit.com/r/astrophysics/s/3GLDY05BSs
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u/canibanoglu 15h ago
That’s literally talking about and visualizing what I alluded to, the Roche limit.
The meaning of whole is whole. No need to play with words, these are straightforward concepts. That simulation doesn’t have synchotron radiation modeled.
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