B Gravitational Waves: Comparing Effects on Earth

[Devin-M]

TL;DR Summary

What is the potential destructiveness of gravitational waves to a planetary sized object?

If we compare 2 scenarios... A) 2 solar mass black hole hyperbolic flyby of Earth at 5000km/s far enough not to cause a tidal disruption event vs B) an extremely close binary pair of 1 solar mass black holes whose barycenter hyperbolically travels past Earth at 5000km/s, also far enough not to cause a tidal disruption event

How much more additional heating on Earth will be caused if any by scenario B on account of gravitational waves?

I ask because I ran a simulation of scenario B in Universe Sandbox and it heated the Earth’s surface to 25000C in a few seconds without tidal disruption... is this accurate?

(I believe this simulation gif is slowed to around 1/300th normal speed so the black holes orbit each other many hundreds of times per second)

 

[Ibix]

I very much doubt that any commonly available software is accurately modelling gravitational wave emissions and their interaction with a solid body. It might be doing something like calculating the average power of emitted gravitational waves, but I don't know how you'd go about modelling the absorption of the Earth. I rather doubt it's very high for waves in the kHz range as you seem to be suggesting this system emits. That would suggest little heating.

The animation also looks odd to me. The camera appears to be following one black hole, but the background isn't circling as I would expect if the holes are mutually orbiting. It's also difficult to judge distance without knowing the "camera" settings, but the holes don't look very far from the Earth. How close are they supposed to be and what masses do they have?

 

[Devin-M]

This is a page on how the software calculates tidal heating:

https://universesandbox.fandom.com/wiki/Tidal_Heating

This page describes how it handles “roche fragmentation”

https://universesandbox.fandom.com/wiki/Roche_Fragmentation

 

[PeterDonis]

Moderator's note: Moved thread to the relativity forum since that seems like a better place to potentially get responses about a gravitational wave problem.

 

[PeterDonis]

A) 2 solar mass black hole hyperbolic flyby of Earth at 5000km/s far enough not to cause a tidal disruption event vs B) an extremely close binary pair of 1 solar mass black holes whose barycenter hyperbolically travels past Earth at 5000km/s, also far enough not to cause a tidal disruption event

This is not a well specified scenario; you can't just wave your hands and say "far enough not to cause a tidal disruption event". You need to give specific numbers. You did it for the speed, why not for the distance of closest approach?

This is a page on how the software calculates tidal heating

This page describes how it handles “roche fragmentation”

I'm confused; it seems like in your OP you are saying tidal effects should be negligible. But then why should tidal heating or roche fragmentation be present?

How much more additional heating on Earth will be caused if any by scenario B on account of gravitational waves?

Additional heating? Additional to what?

 

[PeterDonis]

I very much doubt that any commonly available software is accurately modelling gravitational wave emissions

I very much doubt that it's including gravitational waves in its model at all.

 

[Ibix]

I very much doubt that it's including gravitational waves in its model at all.

The wiki linked above does indeed have no page for "gravitational wave", nor even "gravity wave".

@Devin-M - the tidal heating page you linked links on to a Wikipedia page, which states a tidal heating formula without derivation. I don't think this is simulating gravitational waves. I presume the extreme heating is some effect of the model of tidal heating, probably because the orbiting holes are rapidly changing distance from the planet. I rather suspect, though, that the model isn't valid because the Earth can't deform much on a kiloHertz timescale, so can't absorb as much energy as it could with a slower change.

 

[pervect]

I concur that it's unlikely that the program includes gravitational waves, or any other GR effects. So I'd guess that it only includes Newtonian gravity. Which I would think would be sufficient, as long as the distance of the BH away from the Earth >> the Schwazschild radius of the black holes, which is about 3km for a solar mass.

Why you are seeing a difference in heating is unclear. What I'd expect is that the tidal force would vary as 1/r^3 in the far field, and I think the displacement and heating would scale the same way, though I could be wrong about the scaling of the heating / displacement. I could also be incorrect in assuming that the distance was large enough to be in the far field.

So if there was a large difference in r, that could explain the difference. But you haven't given us any information on the distance or the ratio of distances. It's also possible that it has something to do with a rapidly oscillating displacement (you mentioned that the BH's were rotating around each other several hundered times a second), as others have mentioned. If the displacement calculations that estimated the power flows assumed slow changing fields, they might be way off, giving a large rapidly oscillating displacement that would overestimate the heating power.

If you can reach the author for comment it might give you some insight. I would not believe the answer from a game without working through the math in detail. Which would be a fairly arduous task.

That said, I was reasonably impressed when I looked up the integration algorithm, http://universesandbox.com/forum/index.php?topic=13479.0, and found that the developer I said spent some time discussing the advantages of a symplectic integrator.

Possibly you could post to the same website above and a developer might have comments about how accurate their simulation was in the circumstances you describe.

One other point - if the simulation did include gravitational radiation, I'd expect the frequency of the BH's orbiting each other to vary with time, giving rise to a "chirp" signal as was seen for the inspiral LIGO detected. From your description, there was no such chirp signal, further suggesting that Gravitational waves were not modeled in the simulation.

I have not tried to estimate the details of the chirp - I believe there was some discussion of the "chip mass" in https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102, the first Ligo detection paper. With enough effort you could try and estimate the time-to-inspiral for your BH scenario, and then get an idea of the power emitted in GW. I'm not sure where you'd get a good estimate of the Earth's efficiency at receiving GW's of such frequency. There have been papers that have looked at using the Earth as a GW detector that I've glanced at, I don't recall any of the details though.

 

[snorkack]

The closest distance where Earth could be from a pair of 1 solar mass black holes with no tidal disruption and no tidal heating is about 4 million km.
Indeed, that is the distance where Earth would have a 24 hour orbit around a 2 solar mass central body. Tidally locked to the pair of holes, no disruption or heating.
How would the fluctuation of gravity due to mutual orbit of holes affect Earth under this circumstance?

 

[PeterDonis]

that is the distance where Earth would have a 24 hour orbit around a 2 solar mass central body. Tidally locked to the pair of holes, no disruption or heating.

The Earth could be tidally locked with a different orbital period; the fact that Earth's orbital period happens to be 24 hours now does not mean it must be 24 hours under any conceivable circumstance.

 

[Devin-M]

In the scenario, the binary’s barycenter moves 5000km/s so it crosses the inner solar system in less than a day and flies by the diameter of the Earth in about 2 seconds. I ran another simulation to see what effects a 2 solar mass black hole passing through the inner solar system perpendicularly to the ecliptic would have at this velocity, and subsequently the Earth's orbit and surface temperature was not drastically perturbed (in the simulation). Is the Roche limit different when the trajectories are hyperbolic?

 

[Ibix]

In the scenario, the binary’s barycenter moves 5000km/s so it crosses the inner solar system in less than a day and flies by the diameter of the Earth in about 2 seconds.

You still haven't told us how far from the Earth it is, nor how far apart the holes were.

I ran another simulation to see what effects a 2 solar mass black hole passing through the inner solar system perpendicularly to the ecliptic would have at this velocity, and subsequently the Earth's orbit and surface temperature was not drastically perturbed (in the simulation).

Again, you aren't describing what you did except in the vaguest terms. How close did it come? At what speed, relative to what?