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Old 05 Oct 2017, 02:07 PM   #677667 / #1
Roo St. Gallus
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Default Ejecta

Massive black hole 'ejected' from a galaxy by gravity waves.

I'm not sure if the descriptive language used to describe this is helpful or not. The description postulates two merging black holes, but implies that they become one black hole....and either it is ejected, or an another, somehow uncoalesced, black hole mass, not previously mentioned, is ejected.
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Old 05 Oct 2017, 10:58 PM   #677684 / #2
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I've wondered what would happen if two galactic black holes were to collide 'head on'- if their approach vectors were pointed so directly at each other that they never go into orbit about each other before merging. Wouldn't the kinetic energy of the more massive hole then propel the combination along approximately the same vector the larger one was traveling? Such a collision would be astonishingly rare, but in a universe with billions and billions of galaxies...
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Old 05 Oct 2017, 11:56 PM   #677687 / #3
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So, they state that there is a super dense black hole at the center of every galaxy.

They hypothesize that the perceived image was caused by two galaxies colliding and the two central massive black holes first circling each other, then coalescing in to a single, presumably even more massive black hole....but that black hole is ejected from the center of that galaxy by gravity waves generated by the black holes spinning around each other...

So. If the resultant black hole is ejected from the center of the galaxy, and seems to be hurtling away at an accelerated pace, then there is no longer a massive black hole at the center of that galaxy, right?

Or, do we have some kind of Schroedinger's Black Hole?
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Old 06 Oct 2017, 09:38 AM   #677715 / #4
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Here's a scenario where a black hole might kick itself out of a galaxy. That galaxy was formed by the merger of two other galaxies, each one with a central black hole. When they merge, the BH's have plenty of inertia, and they go back and forth in the core of the combined galaxy. Passing near stars slows them down and makes them orbit closer to the combined-galaxy center, but they still have elongated orbits. Eventually, they pass close enough to emit a burst of gravitational radiation. This slows them down enough to make them go into orbit around each other.

But they are in a very eccentric orbit, and the BH's radiate a burst of GW's when they are closest to each other. That makes them spiral inward, and it also reduces their orbit's eccentricity and causes their orbit to precess. But when they are close enough to touch, they emit a big burst and they merge, making a single new BH. But this burst carries enough momentum to give the merging BH's a big kick, enough of a kick to eject it from the galaxy.


That scenario might be somewhere in the professional literature, but I'd have to search for it.
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Old 06 Oct 2017, 01:34 PM   #677721 / #5
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That's the mechanism proposed by the researchers in that NASA article.

I'm not current enough on gravity-wave physics to be sure, but it seems to me that for the merged black hole to have sufficient velocity to escape the position at the center of the merged galaxies, one of the original holes must have considerably greater mass than the other, so that the emitted gravity waves are more powerful in one direction. Otherwise- if the holes were of roughly equal mass- the waves would be more evenly emitted, and the merged hole would stay centered in the merged galaxies.
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Old 06 Oct 2017, 07:02 PM   #677751 / #6
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Quote:
Originally Posted by lpetrich View Post
Here's a scenario where a black hole might kick itself out of a galaxy. That galaxy was formed by the merger of two other galaxies, each one with a central black hole. When they merge, the BH's have plenty of inertia, and they go back and forth in the core of the combined galaxy. Passing near stars slows them down and makes them orbit closer to the combined-galaxy center, but they still have elongated orbits. Eventually, they pass close enough to emit a burst of gravitational radiation. This slows them down enough to make them go into orbit around each other.

But they are in a very eccentric orbit, and the BH's radiate a burst of GW's when they are closest to each other. That makes them spiral inward, and it also reduces their orbit's eccentricity and causes their orbit to precess. But when they are close enough to touch, they emit a big burst and they merge, making a single new BH. But this burst carries enough momentum to give the merging BH's a big kick, enough of a kick to eject it from the galaxy.


That scenario might be somewhere in the professional literature, but I'd have to search for it.
But...Does that leave a galaxy without a BH center?
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Old 06 Oct 2017, 07:45 PM   #677753 / #7
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I'm not current enough on gravity-wave physics to be sure, but it seems to me that for the merged black hole to have sufficient velocity to escape the position at the center of the merged galaxies, one of the original holes must have considerably greater mass than the other, so that the emitted gravity waves are more powerful in one direction. Otherwise- if the holes were of roughly equal mass- the waves would be more evenly emitted, and the merged hole would stay centered in the merged galaxies.
Very good.

ESA Science & Technology: Gravitational waves eject black hole from galaxy -- describes that GW-kick scenario.

[0708.0771] Ejection of Supermassive Black Holes from Galaxy Cores is one of several papers that describe G-wave recoil effects. Quoting from its abstract, "Recent numerical relativity simulations have shown that the emission of gravitational waves during the merger of two supermassive black holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as 4000 km/s."

Meaning that a merged black hole may give itself enough of a kick to eject itself from most galaxies. I've found several other articles in arxiv, and I've found this presentation:

How black holes get their kick: Gravitational radiation recoil from - recoilPoster.pdf

It has a nice diagram in it showing how the less massive object has greater emission.
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Old 07 Oct 2017, 01:35 PM   #677773 / #8
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From that third link-
Quote:
The nature of our perturbation calculations restricts us to the small mass ratio limit. However, we expect that larger recoils will result from mergers of more comparable masses. So we would like to be able to extrapolate our results to large mass ratios.
Some guidance on this issue is provided by calculations of the energy flux from head-on collisions of two black holes using both numerical relativity and BH perturbation theory.
Detweiler and Smarr found that when the perturbation results were “scaled-up” to larger mass ratios, they agreed with the numerical relativity calculations. This scaling up was accomplished by replacing the small mass with the reduced mass, and the large mass with the total mass.
We can do something similar for the momentum flux. In the extreme mass ratio limit, the momentum flux is proportional to the mass ratio squared (m1/m2)2. In the comparable mass case, Fitchett’s quasi-Newtonian calculation shows that the momentum flux is proportional to a dimensionless function of the mass ratio f(m1/m2) that reduces to (m1/m2)2 in the small mass-ratio limit. Fitchett & Detweiler suggest that the correct way to scale-up perturbation theory results for the momentum flux is to simply replace the factor (m1/m2)2 with f(m1/m2) in the momentum flux formula. We believe that this scaling-up will be reasonably accurate (~20%), but only a full-blown numerical relativity calculation will be able to say for certain.
In Fig. C, we have scaled-up our value for the recoil at the ISCO of the 0.1 mass-ratio system in Fig. B (257 km/s). We also show what Fitchett’s calculation predicts for inspiral up to that radius (r = 1.46M). We can see that maximum recoil velocities of 820 km/s are possible (while Fitchett would have predicted over 3000 km/s). Note also that the recoil peaks for mass ratio around 0.38 and is zero for equal masses.
So part of my intuitive guess is right- equal-mass BHs merging will not experience any GW rocket effect. But I would have said that the rocket effect would have been greater for larger discrepancies in the masses of the two colliding holes- but according to that bolded part, I'm wrong there. I admit I don't understand why this is; I would think that a black hole of 1,000,000 suns colliding with another of mass 100,000 suns would result in a larger rocket effect. Instead, it appears that the effect is greatest if the relative masses are around 3 to 1. Why?

Last edited by Jobar; 07 Oct 2017 at 02:01 PM.
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Old 07 Oct 2017, 01:48 PM   #677774 / #9
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Quote:
Originally Posted by lpetrich View Post
Here's a scenario where a black hole might kick itself out of a galaxy. That galaxy was formed by the merger of two other galaxies, each one with a central black hole. When they merge, the BH's have plenty of inertia, and they go back and forth in the core of the combined galaxy. Passing near stars slows them down and makes them orbit closer to the combined-galaxy center, but they still have elongated orbits. Eventually, they pass close enough to emit a burst of gravitational radiation. This slows them down enough to make them go into orbit around each other.

But they are in a very eccentric orbit, and the BH's radiate a burst of GW's when they are closest to each other. That makes them spiral inward, and it also reduces their orbit's eccentricity and causes their orbit to precess. But when they are close enough to touch, they emit a big burst and they merge, making a single new BH. But this burst carries enough momentum to give the merging BH's a big kick, enough of a kick to eject it from the galaxy.


That scenario might be somewhere in the professional literature, but I'd have to search for it.
But...Does that leave a galaxy without a BH center?
So it would seem.

But any galaxy or pair of galaxies that goes through this process is going to be seriously perturbed. I have no idea how things would eventually settle down- or if, indeed, the merged galaxy could even survive. Imagine a supermassive black hole blasting through the Milky Way at 1000 km/sec...
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Old 08 Oct 2017, 01:23 PM   #677811 / #10
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Also, if GW are created in the process and those waves are sufficient to eject a BH from the center of a galaxy...why is it that those GW don't seem to be scattering stars along the directions of those GW?

So...To be ignorantly waggish, is the accumulation of DH ejected from multiple galaxies over time responsible for the mysterious 'dark matter' of the universe? Or, are all the BH in the universe delimited within the cores of the galaxies? This seems to indicate the former.

Do galaxies accrete around a black hole or incubate new black holes in their cores?

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Old 08 Oct 2017, 07:00 PM   #677828 / #11
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Quote:
Originally Posted by Jobar View Post
So part of my intuitive guess is right- equal-mass BHs merging will not experience any GW rocket effect. But I would have said that the rocket effect would have been greater for larger discrepancies in the masses of the two colliding holes- but according to that bolded part, I'm wrong there. I admit I don't understand why this is; I would think that a black hole of 1,000,000 suns colliding with another of mass 100,000 suns would result in a larger rocket effect. Instead, it appears that the effect is greatest if the relative masses are around 3 to 1. Why?
That's because
  • The smaller one does a greater fraction of the emitting, because it moves faster
  • The overall emission is less because the smaller one has less of the mass

I'll now do a handwaving estimate of how much energy, angular momentum, and linear momentum gets emitted. I'll do so in the long-distance, post-Newtonian limit, and I won't calculate any numerical coefficient values.

Energy: (3rd time derivative of mass quadrupole moment)2

Mass quadrupole moment = m1 * a12 + (1 <-> 2)
= m1 * m22 / M2 * a2 + (1 <-> 2)
= mr * a2

a = overall semimajor axis
M = total mass = m1 + m2
mr = reduced mass = m1*m2/M

Energy emission = mr2 * a4 * w6

where w = angular velocity = sqrt(M/a3) (ignoring the gravitational constant)

Thus, the energy emission rate is mr2 * M3 / a5

At merger, a is close to M, and the rate is (mr / M)2.

The angular-momentum energy rate is roughly the energy emission rate divided by w.

-

For the linear momentum, one replaces one of the mass quadrupoles with a mass sextupole and an angular-momentum quadrupole, both about the same size. This gets us

(m1 * a13 * w4) - (1 <-> 2)
= m1 * m23 / M3 * a3 * w4 - (1 <-> 2)
= md * mr / M * a3 * 24

where md = m2 - m1 is the mass difference.

This gives a momentum rate of
md * mr2 / M * a5 * w7
= md * mr2 / M5/2 * a-11/2

At merger, it is md * mr2 / M3

So the total momentum kick is about md * mr2 / M2
and its velocity about md * mr2 / M3
I find 0.018 for the velocity or 5400 km/s -- in rough agreement with estimates like 3000 km/s or 4000 km/s.

-

For constant total mass, this is at maximum if the ratio of masses is about 2.6. Though this is a post-Newtonian calculation, the number is nevertheless close to 3.

Last edited by lpetrich; 14 Oct 2017 at 07:14 AM. Reason: Fixed a typo
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Old 08 Oct 2017, 07:39 PM   #677831 / #12
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Also, if GW are created in the process and those waves are sufficient to eject a BH from the center of a galaxy...why is it that those GW don't seem to be scattering stars along the directions of those GW?
Because the GW intensity drops off a lot at their distance.

A billion-solar-mass black hole has a BH radius of about 3 billion km, while the closest stars are a few trillion km away, about 1000 times farther.

G-wave amplitude goes as 1 / (distance), so it would be 10-3 at most, or more like 10-4 at the nearest stars to the BH. This means that the distances between those stars would go up and down by that fraction.

More important, however, is the more familiar sort of gravitational interaction, the one that we are all familiar with in the Newtonian limit. The BH will scatter stars as it travels through the galaxy. At 3 trillion km from it, the escape velocity will be 10,000 km/s. So stars near it will get a big swerve.
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Old 13 Oct 2017, 05:10 PM   #678223 / #13
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Do galaxies accrete around a black hole or incubate new black holes in their cores?
I would have assumed the former much like in our solar system, wherein the planets are of significantly less mass than the sun at the center. Passing objects can become captured in the gravitational well and begin to orbit the central body. I've always heard the central BHs of (non-globular) galaxies are of the supermassive variety and thus this seemed plausible to me. I guess I'm not sure how a spiral galaxy would form without a super massive central BH.
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Old 13 Oct 2017, 08:38 PM   #678231 / #14
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So part of my intuitive guess is right- equal-mass BHs merging will not experience any GW rocket effect. But I would have said that the rocket effect would have been greater for larger discrepancies in the masses of the two colliding holes- but according to that bolded part, I'm wrong there. I admit I don't understand why this is; I would think that a black hole of 1,000,000 suns colliding with another of mass 100,000 suns would result in a larger rocket effect. Instead, it appears that the effect is greatest if the relative masses are around 3 to 1. Why?
That's because
  • The smaller one does a greater fraction of the emitting, because it moves faster
  • The overall emission is less because the smaller one has less of the mass
...
Ah! I see.

I once read that spiral galaxies are thought to result from merging globular clusters or more amorphous galaxies. Given how common spiral galaxies are, this implies that over the life of the universe there have been a LOT of galactic collisions- and so I wonder if ejected black holes may be more common than we realize. I don't know if Roo's speculation that ejected BHs might explain the missing mass is correct- but it does seem worth investigating.
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Old 13 Oct 2017, 08:49 PM   #678233 / #15
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I also wonder how we might detect ejected BHs which are unaccompanied by any attendant visible stars. What sort of effects would we see from such a BH intersecting a normal galaxy?
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