APOD: Simulation: Two Black Holes Merge (2024 May 10)

[APOD Robot]

Simulation: Two Black Holes Merge

Explanation: Relax and watch two black holes merge. Inspired by the first direct detection of gravitational waves in 2015, this simulation plays in slow motion but would take about one third of a second if run in real time. Set on a cosmic stage, the black holes are posed in front of stars, gas, and dust. Their extreme gravity lenses the light from behind them into Einstein rings as they spiral closer and finally merge into one. The otherwise invisible gravitational waves generated as the massive objects rapidly coalesce cause the visible image to ripple and slosh both inside and outside the Einstein rings even after the black holes have merged. Dubbed GW150914, the gravitational waves detected by LIGO are consistent with the merger of 36 and 31 solar mass black holes at a distance of 1.3 billion light-years. The final, single black hole has 63 times the mass of the Sun, with the remaining 3 solar masses converted into energy radiated in gravitational waves.

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[Ann]

Cool video.

What about the final parsec problem, though? In other words, how was this merger even possible?

BBC Sky at Night wrote:

In order to spiral towards one another, the two black holes must first shed energy.

To start with, that energy is transferred to surrounding material, including gas and dust.

Except when the galactic black holes get within a parsec of each other – just over three lightyears – it seems there’s no longer enough ‘stuff’ to shed energy to.

This has become known as the Final Parsec Problem.

Ann

[j green]

Isn't this a repeat of APOD on 2019 April 14th ? Or has the simulation been updated ?

[Guest]

According to the mathematics that I learned, 36 + 31 = 67, which is 4 (four) more than 63, not 3 more.
Of course, this could easily be a matter of rounding issues. But then, if the actual figures were known with greater precision, it would have been quite possible to supply those numbers instead of the ones that were given.
For instance: 35.7 + 30.7 = 66.4, and if the final mass would be 63.4, then the difference would indeed be precisely 3 solar masses while all the other "named " masses would round to the values that were actually given.

The way it is formulated in the APOD, there's an entire solar mass missing, presumably "gone fishing" or some such. Sloppy housekeeping, that.

[agardini]

Hello everybody,

I have a question about the BHs' masses.
I imagined that nothing could escape from a BH (except perhaps by Hawking radiation) but it seems that part of the mass of a couple of merging BHs is radiated as GW.
I suspect that the energy emitted as GW comes from the kinetic/gravitational/rotational energy of the BHs rather than from their "rest mass" but I am not fully sure.
Can anyone elaborate on point?
Thanks

[Rauf]

According to the mathematics that I learned, 36 + 31 = 67, which is 4 (four) more than 63, not 3 more.
Of course, this could easily be a matter of rounding issues. But then, if the actual figures were known with greater precision, it would have been quite possible to supply those numbers instead of the ones that were given.
For instance: 35.7 + 30.7 = 66.4, and if the final mass would be 63.4, then the difference would indeed be precisely 3 solar masses while all the other "named " masses would round to the values that were actually given.

The way it is formulated in the APOD, there's an entire solar mass missing, presumably "gone fishing" or some such. Sloppy housekeeping, that.

https://www.ligo.caltech.edu/news/ligo20160211

And here it says:
"Based on the observed signals, LIGO scientists estimate that the black holes for this event were about 29 and 36 times the mass of the sun, and the event took place 1.3 billion years ago. About 3 times the mass of the sun was converted into gravitational waves in a fraction of a second—with a peak power output about 50 times that of the whole visible universe. By looking at the time of arrival of the signals—the detector in Livingston recorded the event 7 milliseconds before the detector in Hanford—scientists can say that the source was located in the Southern Hemisphere."

29 and 36? Is this an old estimation and the APOD's text has been updated with newer ones?

[JohnD]

While the bare physics have to be right, and the simulation flawless, I was underwhelmed by the video - surely such an event will be accompanied by more fireworks, with accretion disks and jets exploding?

And thank you to Ann for telling me of the "Final Parsec Problem". I found this:
"When two galaxies merge, they often produce a supermassive black hole binary (SMBHB) at their center. Numerical simulations with cold dark matter show that SMBHBs typically stall out at a distance of a few parsecs apart, and take billions of years to coalesce. This is known as the final parsec problem. We suggest that ultralight dark matter (ULDM) halos around SMBHBs can generate dark matter waves due to gravitational cooling. These waves can effectively carry away orbital energy from the black holes, rapidly driving them together. To test this hypothesis, we performed numerical simulations of black hole binaries inside ULDM halos. Our results imply that ULDM waves can lead to the rapid orbital decay of black hole binaries."

Koo, Bak, Park et al, Final parsec problem of black hole mergers and ultralight dark matter, Astrophysics, https://doi.org/10.48550/arXiv.2311.03412

[Chris Peterson]

Hello everybody,

I have a question about the BHs' masses.
I imagined that nothing could escape from a BH (except perhaps by Hawking radiation) but it seems that part of the mass of a couple of merging BHs is radiated as GW.
I suspect that the energy emitted as GW comes from the kinetic/gravitational/rotational energy of the BHs rather than from their "rest mass" but I am not fully sure.
Can anyone elaborate on point?
Thanks

Neither black hole lost mass. The individual precursor black holes merged to form a new black hole, and it has a higher mass than either of the precursors. The total mass difference reflects the conversion of gravitational potential energy (as the two precursors got closer) into kinetic energy, and that into gravitational waves.

[agardini]

Hello everybody,

I have a question about the BHs' masses.
I imagined that nothing could escape from a BH (except perhaps by Hawking radiation) but it seems that part of the mass of a couple of merging BHs is radiated as GW.
I suspect that the energy emitted as GW comes from the kinetic/gravitational/rotational energy of the BHs rather than from their "rest mass" but I am not fully sure.
Can anyone elaborate on point?
Thanks

Neither black hole lost mass. The individual precursor black holes merged to form a new black hole, and it has a higher mass than either of the precursors. The total mass difference reflects the conversion of gravitational potential energy (as the two precursors got closer) into kinetic energy, and that into gravitational waves.

Thanks!

[johnnydeep]

Hello everybody,

I have a question about the BHs' masses.
I imagined that nothing could escape from a BH (except perhaps by Hawking radiation) but it seems that part of the mass of a couple of merging BHs is radiated as GW.
I suspect that the energy emitted as GW comes from the kinetic/gravitational/rotational energy of the BHs rather than from their "rest mass" but I am not fully sure.
Can anyone elaborate on point?
Thanks

Neither black hole lost mass. The individual precursor black holes merged to form a new black hole, and it has a higher mass than either of the precursors. The total mass difference reflects the conversion of gravitational potential energy (as the two precursors got closer) into kinetic energy, and that into gravitational waves.

Kinetic energy can get converted into gravitational energy? In the mundane world, kinetic energy clearly can get converted into heat (a bullet hitting
a steel plate for example), but does it also get converted to GWs (however miniscule an amount that might result in)?

[Chris Peterson]

Hello everybody,

I have a question about the BHs' masses.
I imagined that nothing could escape from a BH (except perhaps by Hawking radiation) but it seems that part of the mass of a couple of merging BHs is radiated as GW.
I suspect that the energy emitted as GW comes from the kinetic/gravitational/rotational energy of the BHs rather than from their "rest mass" but I am not fully sure.
Can anyone elaborate on point?
Thanks

Neither black hole lost mass. The individual precursor black holes merged to form a new black hole, and it has a higher mass than either of the precursors. The total mass difference reflects the conversion of gravitational potential energy (as the two precursors got closer) into kinetic energy, and that into gravitational waves.

Kinetic energy can get converted into gravitational energy? In the mundane world, kinetic energy clearly can get converted into heat (a bullet hitting
a steel plate for example), but does it also get converted to GWs (however miniscule an amount that might result in)?

In the mundane world, gravitational potential energy gets converted to kinetic energy, gets converted to gravitational waves all the time. Like when you drop a rock. But it takes something as massive as merging black holes or neutron stars to produce strong enough gravitational waves for our existing technology to detect them.

(Perhaps we should read this as an indicator that the "mundane world" is much less mundane than it superficially appears!)

[johnnydeep]

Neither black hole lost mass. The individual precursor black holes merged to form a new black hole, and it has a higher mass than either of the precursors. The total mass difference reflects the conversion of gravitational potential energy (as the two precursors got closer) into kinetic energy, and that into gravitational waves.

Kinetic energy can get converted into gravitational energy? In the mundane world, kinetic energy clearly can get converted into heat (a bullet hitting
a steel plate for example), but does it also get converted to GWs (however miniscule an amount that might result in)?

In the mundane world, gravitational potential energy gets converted to kinetic energy, gets converted to gravitational waves all the time. Like when you drop a rock. But it takes something as massive as merging black holes or neutron stars to produce strong enough gravitational waves for our existing technology to detect them.

Can you clear up that statement for me? Any missing words for example?

(Perhaps we should read this as an indicator that the "mundane world" is much less mundane than it superficially appears!)

Thanks. And indeed!

[Chris Peterson]

Kinetic energy can get converted into gravitational energy? In the mundane world, kinetic energy clearly can get converted into heat (a bullet hitting
a steel plate for example), but does it also get converted to GWs (however miniscule an amount that might result in)?

In the mundane world, gravitational potential energy gets converted to kinetic energy, gets converted to gravitational waves all the time. Like when you drop a rock. But it takes something as massive as merging black holes or neutron stars to produce strong enough gravitational waves for our existing technology to detect them.

Can you clear up that statement for me? Any missing words for example?

I don't think there are any missing words. When a mass is allowed to move in a gravitational field, its velocity increases, which represents a conversion of gravitational potential energy to kinetic energy. Right? And any accelerating mass generates gravitational waves ("acceleration" can be tricky here, involving reference frames, but the basic concept should be pretty clear). So a tiny bit of energy is actually taken out of the moving mass, slowing it down. That's why black holes spiral into each other. But the amount is far below what we have the technology to measure, except for these special cases of massive bodies merging.

[johnnydeep]

In the mundane world, gravitational potential energy gets converted to kinetic energy, gets converted to gravitational waves all the time. Like when you drop a rock. But it takes something as massive as merging black holes or neutron stars to produce strong enough gravitational waves for our existing technology to detect them.

Can you clear up that statement for me? Any missing words for example?

I don't think there are any missing words. When a mass is allowed to move in a gravitational field, its velocity increases, which represents a conversion of gravitational potential energy to kinetic energy. Right? And any accelerating mass generates gravitational waves ("acceleration" can be tricky here, involving reference frames, but the basic concept should be pretty clear). So a tiny bit of energy is actually taken out of the moving mass, slowing it down. That's why black holes spiral into each other. But the amount is far below what we have the technology to measure, except for these special cases of massive bodies merging.

That sentence still isn't parsing for me: Is it "gravitational potential energy gets converted to kinetic energy, [which can also?, which always? and?] gets converted to gravitational waves all the time"?

[Chris Peterson]

Can you clear up that statement for me? Any missing words for example?

I don't think there are any missing words. When a mass is allowed to move in a gravitational field, its velocity increases, which represents a conversion of gravitational potential energy to kinetic energy. Right? And any accelerating mass generates gravitational waves ("acceleration" can be tricky here, involving reference frames, but the basic concept should be pretty clear). So a tiny bit of energy is actually taken out of the moving mass, slowing it down. That's why black holes spiral into each other. But the amount is far below what we have the technology to measure, except for these special cases of massive bodies merging.

That sentence still isn't parsing for me: Is it "gravitational potential energy gets converted to kinetic energy, [which can also?, which always? and?] gets converted to gravitational waves all the time"?

Gravitational waves are a form of energy that is radiated from an accelerating mass. That energy is being "stolen" from the kinetic energy of that moving mass. If you wave your hand around you are radiating gravitational waves from it.

[johnnydeep]

I don't think there are any missing words. When a mass is allowed to move in a gravitational field, its velocity increases, which represents a conversion of gravitational potential energy to kinetic energy. Right? And any accelerating mass generates gravitational waves ("acceleration" can be tricky here, involving reference frames, but the basic concept should be pretty clear). So a tiny bit of energy is actually taken out of the moving mass, slowing it down. That's why black holes spiral into each other. But the amount is far below what we have the technology to measure, except for these special cases of massive bodies merging.

That sentence still isn't parsing for me: Is it "gravitational potential energy gets converted to kinetic energy, [which can also?, which always? and?] gets converted to gravitational waves all the time"?

Gravitational waves are a form of energy that is radiated from an accelerating mass. That energy is being "stolen" from the kinetic energy of that moving mass. If you wave your hand around you are radiating gravitational waves from it.

I still think there needs to be something between "energy" and "gets". Maybe "gravitational potential energy gets converted to kinetic energy, and that then gets converted to gravitational waves all the time"

EDIT: ok, I believe you're simply using the shorthand locution in the style of "a gets converted to B gets converted to C gets converted to D" to indicate a series of successive conversions in a chain. On to the next APOD!

[VictorBorun]

While the bare physics have to be right, and the simulation flawless, I was underwhelmed by the video - surely such an event will be accompanied by more fireworks, with accretion disks and jets exploding?

And thank you to Ann for telling me of the "Final Parsec Problem". I found this:
"When two galaxies merge, they often produce a supermassive black hole binary (SMBHB) at their center. Numerical simulations with cold dark matter show that SMBHBs typically stall out at a distance of a few parsecs apart, and take billions of years to coalesce. This is known as the final parsec problem. We suggest that ultralight dark matter (ULDM) halos around SMBHBs can generate dark matter waves due to gravitational cooling. These waves can effectively carry away orbital energy from the black holes, rapidly driving them together. To test this hypothesis, we performed numerical simulations of black hole binaries inside ULDM halos. Our results imply that ULDM waves can lead to the rapid orbital decay of black hole binaries."

Koo, Bak, Park et al, Final parsec problem of black hole mergers and ultralight dark matter, Astrophysics, https://doi.org/10.48550/arXiv.2311.03412

I think some confusion happens here.
Whether super massive BHs in galactic centres do merge as often as once a thousand years within 40 Gly from us is a question outside the LIGO detectors' net.
There is another branch of astronomy, namely correlating the irregularities in the observed ticking of millisecond pulsars (corrected to Solar system's barycenter) with angular distance between pulsars in the sky. Some longwave gravitational hum does exist:
In June 2023, NANOGrav published further evidence for a stochastic gravitational wave background using the 15-year data release. In particular, it provides a measurement of the Hellings–Downs curve,[12] the unique sign of the gravitational wave origin of the observations.

[VictorBorun]

Hello everybody,

I have a question about the BHs' masses.
I imagined that nothing could escape from a BH (except perhaps by Hawking radiation) but it seems that part of the mass of a couple of merging BHs is radiated as GW.
I suspect that the energy emitted as GW comes from the kinetic/gravitational/rotational energy of the BHs rather than from their "rest mass" but I am not fully sure.
Can anyone elaborate on point?
Thanks

Neither black hole lost mass. The individual precursor black holes merged to form a new black hole, and it has a higher mass than either of the precursors. The total mass difference reflects the conversion of gravitational potential energy (as the two precursors got closer) into kinetic energy, and that into gravitational waves.

Does a pair of BHs have to lose any of its total mass-energy to merge?
Can the two BHs just get closer (losing potenial energy and gaining kinetic energy) and then merge in a central collision?
It seems to me that a straight line collision would involve minimum of going around and radiating away one gravity wave after another…

[Chris Peterson]

Hello everybody,

I have a question about the BHs' masses.
I imagined that nothing could escape from a BH (except perhaps by Hawking radiation) but it seems that part of the mass of a couple of merging BHs is radiated as GW.
I suspect that the energy emitted as GW comes from the kinetic/gravitational/rotational energy of the BHs rather than from their "rest mass" but I am not fully sure.
Can anyone elaborate on point?
Thanks

Neither black hole lost mass. The individual precursor black holes merged to form a new black hole, and it has a higher mass than either of the precursors. The total mass difference reflects the conversion of gravitational potential energy (as the two precursors got closer) into kinetic energy, and that into gravitational waves.

Does a pair of BHs have to lose any of its total mass-energy to merge?
Can the two BHs just get closer (losing potenial energy and gaining kinetic energy) and then merge in a central collision?
It seems to me that a straight line collision would involve minimum of going around and radiating away one gravity wave after another…

Well, statistically I think a perfect straight line collision is effectively impossible. So it's just a theoretical construct. Still, you have accelerating masses, so they are radiating gravitational waves. But maybe not of a frequency or polarization that our detectors can deal with.

[VictorBorun]

Neither black hole lost mass. The individual precursor black holes merged to form a new black hole, and it has a higher mass than either of the precursors. The total mass difference reflects the conversion of gravitational potential energy (as the two precursors got closer) into kinetic energy, and that into gravitational waves.

Does a pair of BHs have to lose any of its total mass-energy to merge?
Can the two BHs just get closer (losing potenial energy and gaining kinetic energy) and then merge in a central collision?
It seems to me that a straight line collision would involve minimum of going around and radiating away one gravity wave after another…

Well, statistically I think a perfect straight line collision is effectively impossible. So it's just a theoretical construct. Still, you have accelerating masses, so they are radiating gravitational waves. But maybe not of a frequency or polarization that our detectors can deal with.

offtopic
Can a microscopic BH moving with a relativistically great velocity escape Hawking's evaporation and endure say from Bing Bang to nowadays?
In the cosmology reference system, a relativistic BH's mass-energy would be mostly kinetic energy.
Would such a BH radiate much energy in gravity waves?
Would it get slowed down by absorbing relic photons, intergalactic hydrogen and dark matter particles?

[Fred the Cat]

Simulating a camera’s eye view seems the best we can do.
But imagine what would happen to the camera.

Disorientating to both.

[johnnydeep]

Does a pair of BHs have to lose any of its total mass-energy to merge?
Can the two BHs just get closer (losing potenial energy and gaining kinetic energy) and then merge in a central collision?
It seems to me that a straight line collision would involve minimum of going around and radiating away one gravity wave after another…

Well, statistically I think a perfect straight line collision is effectively impossible. So it's just a theoretical construct. Still, you have accelerating masses, so they are radiating gravitational waves. But maybe not of a frequency or polarization that our detectors can deal with.

offtopic
Can a microscopic BH moving with a relativistically great velocity escape Hawking's evaporation and endure say from Bing Bang to nowadays?
In the cosmology reference system, a relativistic BH's mass-energy would be mostly kinetic energy.
Would such a BH radiate much energy in gravity waves?
Would it get slowed down by absorbing relic photons, intergalactic hydrogen and dark matter particles?

Very interesting ideas!