Blackholes: Accretion Vs Expulsion

[Doum]

i understand chris. But if i calculate from a 1000 AU, i think that a certain amount of the escape velocity is already include in the 4000 km/s initial speed.
Bruce i have 2.97E-8 m/s2 for the sun acceleration and 5.95E-9 m/s2 for the black hole acceleration at t0.
I slice the 150E14 meter distance at t0 (1000 AU).(Number of slice= 42800 ) As the 2 mass get closer, the distance each slice have is diminish because the gravity force is getting stronger. Did it untill the 2 mass are at 7E8 meter distance. Wich is the surface of the sun( i suppose). Then i did continue after that untill the balck hole is a third inside the sun. just to see how much speed it add up.
For each distance, excel recalculate the Force, the Acceleration and the Speed. i use the new final speed of that calcul and add it to the one before to estimate the time it took for the next slice of distance to be cross. i also add the speed of the sun for each slice to the BH speed wich include the initial speed of 4E6 m/s. With that new time for crossing the next slice excel repeat all calculs.
PS: (The post before, i calculate the acceleration with the 2 mass body. Now i calculate the sun and the black hole acceleration separately and take them together as i go down in each distance.) Thanks for reminding me to do so.
So, at sun surface i get 4276 km/s.
A third Inside the sun i get 4422 km/s. Using the time to get a third Inside the sun ( as if acceleration continue) and the rest distance being cross at 4422 km/s i got 5 minutes and 19 seconde to cross it.
At the sun surface speed of 4276 km/s it take 5 minutes 27 secondes to cross the sun. Not much difference.
Question:
If the sun (G0 star) survive that encounter, will it become a k9 or k8 star or smaller? I wont try to calculate that

[Chris Peterson]

But if i calculate from a 1000 AU, i think that a certain amount of the escape velocity is already include in the 4000 km/s initial speed.

It's not an issue of escape velocity. It's just an issue of the minimum collision velocity (which happens to be equal to the escape velocity if you reversed the direction of time). So you just use the formula for speed, and add any reasonable initial velocity you want- somewhere between a few hundred and a few thousand kilometers per second, I would think.

[Doum]

ok

Sun escape velocity is 617.55 km/s and black hole escape velocity at 7E8 meter from the sun center (surface) is 1380km/s. So the final speed of impact at sun surface is 1998 km/s. let say 2000 km/s.
With an initial speed of 4000 km/s we have 6000 km/s final speed. And it take 4 minutes 26 seconds to cross the sun.

There is probably a bit more speed to that as the black hole and the sun still accelerate toward each other while the black hole is inside the sun.

Estimate final speed when the black hole is a third Inside the sun: 6500 km/s and 4 minutes 6 seconds to cross.

My excel table worth nothing.

ohhh, i'm hurt somewhere above my shoulder. is that a black hole.
Yea, information do get lost in a black hole.

thanks Chris.

[neufer]

[b][color=#0000FF]Transient Solar Oscillations Driven By Primordial Black Holes Ref: arxiv.org/abs/1106.0011:[/color][/b]

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If A Primordial Black Hole Hits The Sun...
M.I.T. Technology Review, June 3, 2011

<<Michael Kesden at New York University and Shravan Hanasoge at Princeton University in New Jersey say that the effect of a primordial black hole hitting the Sun ought to be easily observable.

Such an event wouldn’t be as catastrophic as it sounds. The likelihood is that a primordial black hole with mass of an asteroid or comet (about 10²¹ g) would pass straight through the Sun, generating a small puff of X-rays in the process. Such a burst would be less even than the background rate of X-rays, so it would be impossible for astronomers to see.

Instead, Kesden and Hanasoge say that the collision would generate supersonic turbulence that would set the Sun ringing like a bell. Today, they calculate what these oscillations would look like.

Their conclusion is that the oscillations ought to be visible with today’s solar observatories as a kind of solar hiccup. So we might have seen them already.

That should generate a scramble. You can bet that solar scientists will be pouring over their data right now to see if they’ve missed the telltale signs of a black hole collision. If they find any, we should hear soon. However, primordial black holes are likely to be rare, which means that collisions with Sun will be few and far between. So a more promising approach, say Kesden and Hanasoge, is to look at the way other stars oscillate. And as luck would have it, astroseismology is an infant science that is rapidly maturing thanks to the observations being made by spacecraft such as CoRot and Kepler which can see other stars oscillating. One way or another, we’re going to learn a lot more about the way stars vibrate.>>

[Chris Peterson]

Sun escape velocity is 617.55 km/s and black hole escape velocity at 7E8 meter from the sun center (surface) is 1380km/s. So the final speed of impact at sun surface is 1998 km/s. let say 2000 km/s.

Not quite. The formula simply provides the relative velocity between two masses that are falling towards each other under the influence of their own gravity. While the derivation of the formula is the same as that for escape velocity, we're not really talking about escape velocities here. What the escape velocity is at the surface of the Sun, or for some mass at a certain distance, isn't important. Pick a distance, and calculate the velocity. Thus, a 5 solar mass black hole which is 7e8 meters from the Sun produces a relative velocity between the two of 1512 km/s. Add to this any initial velocity you like. But it only applies to that one distance. The problem is, once you're much less than 7e8 meters, the whole problem becomes very complex- insoluble except by some finite element simulation on a supercomputer.

With an initial speed of 4000 km/s we have 6000 km/s final speed. And it take 4 minutes 26 seconds to cross the sun.

There is probably a bit more speed to that as the black hole and the sun still accelerate toward each other while the black hole is inside the sun.

Estimate final speed when the black hole is a third Inside the sun: 6500 km/s and 4 minutes 6 seconds to cross.

What I did was look at the velocity profile as the BH passes through the Sun, assuming no drag and no significant transfer of mass (I don't know how realistic those assumptions are), and then integrated that to get a transit time of 610 seconds. I also capped the velocity very close to the center to avoid the infinite speed singularity that the equation produces there. The actual time would be less assuming some initial velocity greater than zero.

sun_bh_coll.gif (11.32 KiB) Viewed 1568 times

[BDanielMayfield]

What I did was look at the velocity profile as the BH passes through the Sun, assuming no drag and no significant transfer of mass (I don't know how realistic those assumptions are), and then integrated that to get a transit time of 610 seconds. I also capped the velocity very close to the center to avoid the infinite speed singularity that the equation produces there. The actual time would be less assuming some initial velocity greater than zero.

The no drag assumption seems very safe. A hot knife cutting though warm butter would see more frictional resistance than this scenario, as whatever the BH contacts just disappears down the hole.

The no significant mass transfer assumption is unrealistic, imo. It's not like this collision is happening at relativistic speeds where the BH can outrun the matter that is being drawn into it. Minutes of transit time through the Sun's interior seems like plenty of time for particles seeing accelerations approaching 300,000 km/s² to get sucked in. This then is a key question as to what happens to the Sun here: How fast can the BH accrete solar plasma during its passage? Is there something I'm not factoring in that is choking off the flow?

Once (or if) the question of rate of mass transfer is resolved the next important question is what is the maximum speed reached by the BH? The equations we've been using begin to break down once the BH passes inside the Sun because they treat both bodies as point sources, which the Sun obviously isn't. The deeper in the collision progresses, the more of the Sun is behind the BH, countering the pull of matter ahead of the hole. The maximum speed would be reached when the acceleration drops to zero, which would be at the point where Solar mass is balanced ahead of and behind the BH. This could even be past the Sun's center, depending upon how much of the Sun has already been swallowed.

After this point acceleration is negative, slowing the BH as it moves away from the Sun's center. On its way out the hole continues to accrete solar plasma, but at a somewhat greater rate than it did on the inward passage because it's now a more massive attractor. (If, as a handwaving guess the BH grew by 0.1 solar masses on the way in it might grow by another 0.12 on the way out. After the nova [with greatly increased solar wind] settles down the Sun is about 77% of its former mass.)

The BH will exit the Sun (and the system) with both more mass and a larger velocity, because there is less mass in the wreckage it leaves behind to slow it down. Black holes break for nobody.

Bruce

[rstevenson]

Nice analysis Bruce. I think we're closing in on something resembling a reasonable scenario.

As for the story I earlier mentioned I'd try to write, I've blocked out some key characters and laid out something vaguely resembling a plot line. I've even written a few short scenes to try to get a feel for the mood of the story, (rediscovering in the process how bad I am at dialog.). I was hoping to cram it all into a short story format, but that would not do justice to the concept. Whether I can write anything a reasonable person would call a novel remains to be seen. I seriously doubt it. (I wrote a couple of short children's stories a few decades ago, but nothing since. How long ago? I still have the original proofs, printed on a dot-matrix Apple ImageWriter!) Anyway, it's fun to give the typing fingers a workout.

Rob

[Chris Peterson]

What I did was look at the velocity profile as the BH passes through the Sun, assuming no drag and no significant transfer of mass (I don't know how realistic those assumptions are), and then integrated that to get a transit time of 610 seconds. I also capped the velocity very close to the center to avoid the infinite speed singularity that the equation produces there. The actual time would be less assuming some initial velocity greater than zero.

The no significant mass transfer assumption is unrealistic, imo. It's not like this collision is happening at relativistic speeds where the BH can outrun the matter that is being drawn into it. Minutes of transit time through the Sun's interior seems like plenty of time for particles seeing accelerations approaching 300,000 km/s² to get sucked in. This then is a key question as to what happens to the Sun here: How fast can the BH accrete solar plasma during its passage? Is there something I'm not factoring in that is choking off the flow?

I think so. The surface area of the black hole (that is, its event horizon) is very small. Furthermore, almost none of the attracted material is falling on a line towards the center. So virtually all of the material will be falling into an orbit, and the pressure from this material will be limiting other material from getting closer.

What I think is that an insignificant amount of solar material will fall into the black hole. What's very hard to figure is how much material will end up in a closed orbit around the black hole (that is, an accretion disk) and be carried away from the Sun after the black hole's passing.

The BH will exit the Sun (and the system) with both more mass and a larger velocity, because there is less mass in the wreckage it leaves behind to slow it down.

Or with less velocity because it's more massive. If it's more massive. You need to consider conservation of momentum here, as well as the location of the center of mass of the system.

[BDanielMayfield]

Nice analysis Bruce. I think we're closing in on something resembling a reasonable scenario.

As for the story I earlier mentioned I'd try to write, I've blocked out some key characters and laid out something vaguely resembling a plot line. I've even written a few short scenes to try to get a feel for the mood of the story, (rediscovering in the process how bad I am at dialog.). I was hoping to cram it all into a short story format, but that would not do justice to the concept. Whether I can write anything a reasonable person would call a novel remains to be seen. I seriously doubt it. (I wrote a couple of short children's stories a few decades ago, but nothing since. How long ago? I still have the original proofs, printed on a dot-matrix Apple ImageWriter!) Anyway, it's fun to give the typing fingers a workout.

Rob

Thanks Rob. We look forward to reading your story. Of course, I'm closer to being a farmer than an astrophysicist, so use these imaginings at your own risk. It could all be a load of cow manure.

There are such a broad range of possibilities with this; everything from little effect to complete destruction of the Sun. There are different conceivable modes for how the Sun could be destroyed too. It could all be sucked down, or a core collapse SN might be triggered. A less catastrophic, plausible outcome could also involve the inflation of the Sun into a short Red Giant phase, possibly with planetary neubula discharge before the Sun settles back onto the main sequence. Hay y'all, this could even have a bright side: If a reduced massed Sun survives it might stay on the MS for a few more billions of years! The Sun will have had a life extending makeover. Too bad for the hapless planets however.

Bruce

[neufer]

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On its way out the hole continues to accrete solar plasma, but at a somewhat greater rate than it did on the inward passage because it's now a more massive attractor. (If, as a handwaving guess the BH grew by 0.1 solar masses on the way in it might grow by another 0.12 on the way out. After the nova [with greatly increased solar wind] settles down the Sun is about 77% of its former mass.)

The BH will exit the Sun (and the system) with both more mass and a larger velocity, because there is less mass in the wreckage it leaves behind to slow it down. Black holes break for nobody.

A solar mass black hole has a tiny, tiny "mouth" which can devour food no faster than the speed of light.

Hence, in 610 seconds the BH's tiny, tiny "mouth" can devour no more than 20 billion cubic kilometers of Sun
and drill a hole through the Sun no wider than ~135 kilometers (corresponding to 1/70,000,000 of a solar mass).

The BH will exit the Sun virtually unchanged in size.

[Chris Peterson]

The BH will exit the Sun virtually unchanged in size.

I agree that the black hole itself will exit with almost the same mass it entered with. What I think is harder to figure (as in very hard) is how much solar material will be dragged into orbit around the black hole during the encounter (which starts before they intersect, of course).

[Doum]

What about solar flare. Do you think that giant solar flare might trow away a significant amount of matter from the sun after the passage of the black hole? As the black hole pass, the empty space it left behind in the sun will fill up. Will it increase the sun temperature and make giant solar flare?
Also Chris, is it possible that this accretion disc around the black hole will make powerfull jet inside the sun. That might add up to destabilising the sun.

If not much mass lost then the sun will stay a G0 star. But can it end up being a K8 or K9 or smaller?

[Doum]

Ohh by the way Chris,

i do get the same speed (1513 km/s) if i do the calcul the same way you did. i am trying not to think of all the attempt i make with excel to have the final speed of encounter between the 2 bodies.

So, with an initial speed of 4000 km/s + 1513 km/s we have 5513 km/s as final speed near the sun surface and it take 290 seconds for the black hole to go trough the sun.

[BDanielMayfield]

The no significant mass transfer assumption is unrealistic, imo. It's not like this collision is happening at relativistic speeds where the BH can outrun the matter that is being drawn into it. Minutes of transit time through the Sun's interior seems like plenty of time for particles seeing accelerations approaching 300,000 km/s² to get sucked in. This then is a key question as to what happens to the Sun here: How fast can the BH accrete solar plasma during its passage? Is there something I'm not factoring in that is choking off the flow?

I think so. The surface area of the black hole (that is, its event horizon) is very small. Furthermore, almost none of the attracted material is falling on a line towards the center. So virtually all of the material will be falling into an orbit, and the pressure from this material will be limiting other material from getting closer.

Ok, conservation of angular momentum is what I wasn't accounting for. Thanks.

What I think is that an insignificant amount of solar material will fall into the black hole. What's very hard to figure is how much material will end up in a closed orbit around the black hole (that is, an accretion disk) and be carried away from the Sun after the black hole's passing.

This is good, putting my opening question about accretion disks and jets back on the table.

The BH will exit the Sun (and the system) with both more mass and a larger velocity, because there is less mass in the wreckage it leaves behind to slow it down.

Or with less velocity because it's more massive. If it's more massive. You need to consider conservation of momentum here, as well as the location of the center of mass of the system.

Agreed, reluctantly. The BH leaving with both more mass and with more speed seemed too good to be true, like a violation of something fundamental. But I still think that significant mass transfer might be possible.

Bruce

[Chris Peterson]

What about solar flare. Do you think that giant solar flare might trow away a significant amount of matter from the sun after the passage of the black hole? As the black hole pass, the empty space it left behind in the sun will fill up. Will it increase the sun temperature and make giant solar flare?

Well, a solar flare is a magnetic phenomenon, and the largest ones ever observed have very low mass compared with the mass of the Sun. The volume of the hole drilled through the Sun is still incredibly tiny compared with the volume of the Sun itself. My feeling is that it's not going to matter. I think the major effect the BH will have is purely due to its mass being five times that of the Sun, and the consequent tidal effects before, during, and after the actual collision. And those effects might not be all that great on the Sun as a star. What's all but certain, however, is that the mass of the BH over a period of months or years before and after the collision will profoundly impact the orbits of all the planets in the Solar System.

Also Chris, is it possible that this accretion disc around the black hole will make powerfull jet inside the sun. That might add up to destabilising the sun.

Jets are also dependent on magnetic fields, and we haven't speculated on either the magnetic field of the BH, or its rotation, both of which are probably important to consider. But in any case, I don't think there's time during the actual collision for the accretion disk to do very much, or for jets to form.

[BDanielMayfield]

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On its way out the hole continues to accrete solar plasma, but at a somewhat greater rate than it did on the inward passage because it's now a more massive attractor. (If, as a handwaving guess the BH grew by 0.1 solar masses on the way in it might grow by another 0.12 on the way out. After the nova [with greatly increased solar wind] settles down the Sun is about 77% of its former mass.)

A solar mass black hole has a tiny, tiny "mouth" which can devour food no faster than the speed of light.

Hence, in 610 seconds the BH's tiny, tiny "mouth" can devour no more than 20 billion cubic kilometers of Sun
and drill a hole through the Sun no wider than ~135 kilometers (corresponding to 1/70,000,000 of a solar mass).

The BH will exit the Sun virtually unchanged in size.

Thanks for your valued input Art. How much more lunch could a five solar mass munch? Also, you can't "drill a hole through" a fluid. Does your 135 km figure allow for accretion all over the hole's entire surface? Secondly, does your core section through the sun accounting take into account that it includes the densest heart of the Sun?

[neufer]

Also Chris, is it possible that this accretion disc around the black hole will make powerfull jet inside the sun. That might add up to destabilising the sun.

Jets are also dependent on magnetic fields, and we haven't speculated on either the magnetic field of the BH, or its rotation, both of which are probably important to consider. But in any case, I don't think there's time during the actual collision for the accretion disk to do very much, or for jets to form.

The primary "jet" to consider is the one that shoots out the end of the drill hole created by the BH and chases the BH.

[Chris Peterson]

Also Chris, is it possible that this accretion disc around the black hole will make powerfull jet inside the sun. That might add up to destabilising the sun.

Jets are also dependent on magnetic fields, and we haven't speculated on either the magnetic field of the BH, or its rotation, both of which are probably important to consider. But in any case, I don't think there's time during the actual collision for the accretion disk to do very much, or for jets to form.

The primary "jet" to consider is the one that shoots out the end of the drill hole created by the BH and chases the BH.

Which may be less a "jet" and more a "lobe".

[Fred the Cat]

Do you suppose jets emit their own photons or cause electro-magnetic radiation to be generated by striking matter in their path? It would seem to me that relics from many previous emissions would be somewhat prevalent throughout the universe.

[Chris Peterson]

Do you suppose jets emit their own photons or cause electro-magnetic radiation to be generated by striking matter in their path? It would seem to me that relics from many previous emissions would be somewhat prevalent throughout the universe. :?

The only way we observe jets anywhere is by the photons they emit, either by thermal radiation, ionization relaxation, bremsstrahlung, or other processes.

[BDanielMayfield]

What about solar flare. Do you think that giant solar flare might trow away a significant amount of matter from the sun after the passage of the black hole? As the black hole pass, the empty space it left behind in the sun will fill up. Will it increase the sun temperature and make giant solar flare?
Also Chris, is it possible that this accretion disc around the black hole will make powerfull jet inside the sun. That might add up to destabilising the sun.

You're asking good questions Doum. I think that an event like this would greatly heat up stellar plasma via compression. Light element fusion would briefly add to the heat. The normal solar core temperature is already 1.57e7 degrees K, and it can only get hotter before it crosses the event horizon. All that rapidly rotating ionized matter must produce a powerful accretion disk magnetic field. Jets might indeed add to the mayhem, but they might not punch through the Sun's surface until the hole nears the exit point.

Bruce

P.S. The Sun is a G2 star.

[neufer]

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On its way out the hole continues to accrete solar plasma, but at a somewhat greater rate than it did on the inward passage because it's now a more massive attractor. (If, as a handwaving guess the BH grew by 0.1 solar masses on the way in it might grow by another 0.12 on the way out. After the nova [with greatly increased solar wind] settles down the Sun is about 77% of its former mass.)

A solar mass black hole has a tiny, tiny "mouth" which can devour food no faster than the speed of light.

Hence, in 610 seconds the BH's tiny, tiny "mouth" can devour no more than 20 billion cubic kilometers of Sun
and drill a hole through the Sun no wider than ~135 kilometers (corresponding to 1/70,000,000 of a solar mass).

The BH will exit the Sun virtually unchanged in size.

How much more lunch could a five solar mass munch?

A 5 solar mass BH would have 25 times the "mouth" area so:

• no more than 500 billion cubic kilometers of Sun (corresponding to 1/3,000,000 of a solar mass)
  
  and drill a hole through the Sun no wider than ~ 675 kilometers.

Also, you can't "drill a hole through" a fluid. Does your 135 km figure allow for accretion all over the hole's entire surface? Secondly, does your core section through the sun accounting take into account that it includes the densest heart of the Sun?

The heart of the Sun has very high temperatures & pressures but not necessarily high densities.

You are correct, however, that my so called "drill hole" is really a moving collapsing oval hardly longer than it is wide.

I am assuming that the one solar mass BH:

• devours matter at the speed of light over its entire 6 km wide spherical surface
  which is equivalent to ~600 km/s at its 135 km spherical surface.

But gas velocities are only ~250 km/s even at the heart of the Sun
so the Sun would be hard pressed to satiate the BH at its full capacity (except, perhaps, at its heart).

[Doum]

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How much more lunch could a five solar mass munch?

A 5 solar mass BH would have 25 times the "mouth" area so:

• no more than 500 billion cubic kilometers of Sun (corresponding to 1/3,000,000 of a solar mass)
  
  and drill a hole through the Sun no wider than ~ 675 kilometers.

So, If the 5 time sun mass black hole move trough the sun in 290 seconds instead of 610 seconds, is it ok to think it will take around 250 billion cubic kilometers of sun.

PS : Thanks Bruce for the correction for the sun to be a G2 star.

[BDanielMayfield]

A 5 solar mass BH would have 25 times the "mouth" area so:

• no more than 500 billion cubic kilometers of Sun (corresponding to 1/3,000,000 of a solar mass)
  
  and drill a hole through the Sun no wider than ~ 675 kilometers.

So, If the 5 time sun mass black hole move trough the sun in 290 seconds instead of 610 seconds, is it ok to think it will take around 250 billion cubic kilometers of sun.

PS : Thanks Bruce for the correction for the sun to be a G2 star.

This is a bit odd, but true, apparently: with ordinary objects, the larger the velocity of impact, the greater the damages, but if the objects are a star system and a black hole, the opposite is true.

Bruce

[BDanielMayfield]

But gas velocities are only ~250 km/s even at the heart of the Sun
so the Sun would be hard pressed to satiate the BH at its full capacity (except, perhaps, at its heart).

But that would be the Sun's normal internal state without a 5 solar mass BH plunging through its heart. During this period the whole internal physics of the Sun would be changed, because the whole Sun would briefly act as if it was a 6 solar mass star undergoing core collapse. This should be a real bear of a problem to model accurately, as Chris has pointed out.

Bruce