How do merging supermassive black holes pass the final parsec?
quantamagazine.org
quantamagazine.org
My perception of the field (which is now about a decade out of date, so take it with a grain of salt), is that there is quite a bit of skepticism about invoking exotic physics to solve the last parsec problem. Galaxies are generally pretty messy places, and the centers of galaxies are especially messy, so it's hard to know if you've correctly modeled all the relevant physics. A lot of astronomers aren't convinced that there really is a last parsec problem.
The main "standard" approach to solve the last parsec problem is from scattering stars (which the article mentions). Basically, every now and then stars from the galaxy wander close to the orbit of the black hole binary and then get slingshotted out of the system. This removes energy from the orbit, and causes the black hole binary to shrink. The problem with this approach if you do a naive calculation is that the stars have to come from a particular set of directions, called the "loss cone" in the jargon. And since the orbits of stars in galaxies are probably fairly static, once a star gets kicked out of the loss cone, it doesn't come back. So over time the loss cone empties and the black hole orbit stops shrinking. The question is, does the orbit shrink far enough before the loss cone empties, and the answer to this question has generally been "no."
The way around this is to question how static the orbits of stars in galaxies really are. One of the more important papers on the topic found that if an elliptical galaxy is sufficiently triaxial (that is, sufficiently non-spherical), then interactions between stars in the galaxy can repopulate the loss cone and cause the orbit to keep shrinking. But as I vaguely recall, not everyone was convinced by that result.
I personally have had some ideas that galactic tides might contribute, especially right after the merger before all the orbits have had time to thermally relax. But I'm not in the field anymore and haven't really had time to really model this idea and see if it would work.
A system of one or two giant bodies orbited by a collection of tiny ones. Each tiny one spends most of its time in a very weakly-perturbed two-body problem, quasi-stably orbiting the giant one(s) with tiny deviations caused by all the other ones. So you have to do some statistics to see how often an assumed distribution of quasi-stable orbits results in the tiny bodies approaching each other closely enough to kick one another into meaningfully different orbits of the giant ones.
This gives you a better idea of how long is "long" and how it compares to the age of the universe
That's more or less captured by the loss cone calculation. On a very "long time scale" the loss cone will probably be occasionally replenished by stars coming in from scattering on larger scales, but the timescale for this to become significant for galaxies is substantially longer than the age of galaxies (and also longer than the Hubble time, which is the ~age of the Universe). So, at least from this back of the envelope calculation, that doesn't solve the final parsec problem.
See, e.g., https://www.astro.umd.edu/~richard/ASTRO620/Dynamics_Lec3.pd...
We can and we are already searching for dark matter directly [1] and indirectly [2]. The phase space is being closed every now and then and this is progress. This gives us information about where to look next.
[1] https://en.wikipedia.org/wiki/Direct_detection_of_dark_matte...
[2] https://en.wikipedia.org/wiki/Indirect_detection_of_dark_mat...
We aren't looking in only one place
> Another way to think of non-detection is as evidence that it doesn't exist.
Absence of evidence is not evidence of absence. Exhausting the parameter space until evidence is found is simply the normal scientific progress.
If P[X|Y] > P[X] and P[Y] is strictly between 0 and 1, then P[X|!Y] < P[X] .
So, if X is “dark matter is some kind of matter that can be detected directly” and Y is “Dark matter is/would-be detected directly by this experiment (when/if the experiment is/would-be done)” then, if we do the experiment and it does not directly detect dark matter, then, if we previously assigned some positive probability that it would, our probability that we can detect it in some way, should go down (though not necessarily by a non-negligible amount).
The normal spot on the shelf? …checking my pockets? …searching the bags I used to go shopping?
At each step, another of my theories about where my wallet is gets disproven — but none are direct evidence it’s not in my house.
We are playing the same game with dark matter: they keep checking spots and it keeps not being there. At what point does checking wrong theories start to suggest that the entire idea is flawed?
I’d argue that each failure in a strictly statistical sense makes it more likely the whole conception is flawed — if only a little. So every failure is statistical evidence that dark matter theories are wrong.
Just like each place I look for my wallet and don’t find it makes it slightly more likely that it’s not in my house.
The analogy with your wallet is misleading because we know your habits, we don't know about nature habits.
As I explained, when we exhaust the parameter space regions and can't find anything then this would tell us to give a shot to something else. Not that people are not doing this now already anyways.
William Wright [1]
This is unnecessarily negative. Physics progresses in fits and starts, with plenty of blind alleys and red herrings. Maybe we're in a phase akin to the aftermath of the Michelson–Morley experiment. Or maybe it really is that complicated out there.
I find dark matter seems to fit into the same pattern as epicycles. We can add additional complexity to the theory to make our models better match observational data, and that's useful but also strongly hints that something more basic about the model is fundamentally incorrect. That's depressing.
Just today I heard a talk about people looking at stellar motions in ultra faint dwarf galaxies, because standard dark-model theories predict they should have centrally cusped dark-matter density profiles -- and fuzzy dark-matter models predict different profiles, which they could potentially discriminate between.
However, it is very much true that different galaxies have different amounts and distributions of dark matter. There are many broad categories, and certain models about galaxy formation try to predict these, but not all galaxies fit these models. This has two effects: for one, for any galaxy with unexpected dynamics, you can fit a dark matter distribution to explain the dynamics (but! This is not unbounded, it still has to match certain other observations). The other effect is actually in favor of a dark matter approach: it means modifying parameters of our theories in a general way has little chance to reproduce the same properties, as each different galaxy is different.
> Then again, almost no one with a formal education in cosmology or partical physics at the PhD level does.
This is also just wrong. I think we're seeing a number of established voices starting to question the underpinnings of dark matter as a theory.
As for
>Which additional complexity has been added to dark matter?
Let's start with the fucking article we're discussing, where we now need to have "self-interacting" dark matter, as a new spin on the theory to account for the forces needed to explain what we're observing...
The article is also not adding complexity. We didn't get new evidence that required modification of DM. We got a phenomenon which has many potential explanations as the "fucking" article points out, one of which could be a subset of all DM theories. The final parsec problem isn't challenging DM at all, instead one particular flavor of DM could help explain the observation. If anything, it could constrain DM. Why wouldn't you explore this possibility?
We didn't get any new evidence that required modification of epicycles! We got a phenomenon which constrains the epicycle theory by adding more circles! <-- you.
> If anything, it could constrain DM. Why wouldn't you explore this possibility?
You're the only one suggesting that we throw out DM as a model right now... at no point have I even hinted at not exploring it. You are bashing someone who is simply suggesting that this model might not be correct (how fucking dare I...).
But the thing about models... no model is correct, but some models are useful.
Again - I'm not contesting that DM is currently a useful model for explaining some of things we're seeing. I'm suggesting that it might also be worth considering alternatives (how fucking dare I...).
Go back to trying to burn Galileo alive. It's the same energy.
Loving this comparison, and I hope this is the case.
The problem with cosmology is that it's based almost purely on theory and not data, to the point of speculation.
The period after the apparent failure to the present success has been incredibly fruitful.
When the original aether theory failed, they pointed out that you squish when moving in the aether, and so they detected aether waves rather than aether motion.
With an upgraded version of the same device.
The solution for both was posited to be a physical medium permeating space that had certain special properties, including very low interactions with other matter (explaining why we didn't directly detect it). Light would only propagate in this medium, and since this medium interacted very little with other matter, it explained why it wouldn't be dragged along by, say, a moving train. The speed of light would be mostly determined by the speed of this universal medium, explaining the constancy of the speed of light.
Current physics has nothing to do with these theories. The medium for light's propagation is the electric field, which is not a material medium at all. And Galilean relativity doesn't agree with Maxwell's equation because it is wrong - we have Einstein's special relativity as the successor explanation, and this doesn't require any kind of medium, and doesn't say anything about space-time waves.
General relativity does see space-time as something that looks more like a medium, except that, like the electric field and unlike aether, it is still not a material medium. And gravity waves have absolutely nothing to do with the aether wind. Gravity waves are specific phenomena triggered by specific events. They have a source and a direction of propagation like any other wave, and differenet gravity waves move in different directions. The aether wind was a fixed universal thing: all of the aether in the entire universe moved in a single direction, and had no source.
If you want to look at something that's actually closer to a modern aether, the quantum models of the void are actually much closer. Per quantum mechanics, all of space-time is permeated by fields and random fluctuations in those fields ensure that there exist virtual particles getting created and destroyed at every point in spacetime. So, in QM, there actually exists a physical medium that does permeate all of spacetime (but it doesn't have any of the other properties of the aether).
Light is an excitation of the EM aether — or if you prefer, “field”. (Which you then explain later, yourself.)
We failed to detect the aether with MM because we’re made of aether-stuff and so we squish in a way that cancels out what they were trying to detect with the original experiment.
> Current physics has nothing to do with these theories.
> [explanation of how fields are aethers]
Wilczek also points out modern theories are aether theories.
LIGO works because it detects waves in the aether — which do not suffer from the same squishing problem as in the original experiment. But that’s why a scaled up version of the original experiment worked: we’re fundamentally detecting the same thing.
Aether theories are more legitimate than dark matter theories: the MM test for the aether failed, but then they reformulated the theory and successfully observed an effect; dark matter has yet to find a working reformulation that is observable.
Also, LIGO is detecting something fundamentally different from what MM was looking for.
MM was trying to prove that light speed measured from the frame of reference of the Earth varies between times when the Earth is moving in the same direction as the Aether vs times the Earth is moving perpendicular to the Aether (since the Earth is orbiting the sun, and the Aether moves in a single direction, at some point in the year a beam of light sent in the same direction must pass between moving along a 0° angle and a 90° angle versus the Aether's direction).
This really has nothing to do with what LIGO observed. LIGO observed waves in space-time. The equivalent waves in the EM field/luminiferous aether are called "light" and we didn't need the MM experiment to discover that they exist.
So again, I agree that we can call fields "aethers", and that the EM field is in some ways similar specifically to the luminiferous aether. But it still doesn't have the property that MM were looking for: the EM field doesn't move globally, even if it fluctuates locally.
Both MM and LIGO were looking for evidence of “the stuff waves move through” — and LIGO found it by changing the experiment, because you can’t measure our own motion because we squish, as we’re also made of aether stuff.
Per wiki:
> The experiment compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter, including their laboratory, through the luminiferous aether, or "aether wind" as it was sometimes called. The result was negative, in that Michelson and Morley found no significant difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles.
You also have the MM experiment wrong — they weren’t looking for a pervasive wind, but for signal from our motion through a static aether, by looking for a difference in speed of light aligned with that motion versus perpendicular.
Which is why it’s cancelled by relativity.
The mistake of MM was thinking that the aether only pertained to light and matter was something else that could move through it — but it turns out everything is aether, including us.
Wilczek for instance points out that modern theories are aether theories.
That sounds like “stuff” is there.
> Stuff/substances is where you can talk about a chunk of it, and say where it is at some later time.
In what sense can you do this with a liquid but not spacetime?
Things that are Lorentz invariant are unlike fluids.
So you’ve failed to show a difference between spacetime and a fluid.
And to address your point directly:
Gravitational waves leave a wake that perturbs the medium.
https://www.sciencealert.com/gravitational-waves-could-be-le...
We can also coherently talk about a chunk moving, eg subluminal warp drives.
https://phys.org/news/2024-05-subluminal-warp.html
So we have two ways “where you can talk about a chunk of it, and say where it is at some later time”.
Fluids aren’t Lorentz invariant.
So I’m not following.
Perhaps you could explain how either of those operates without being able to identify chunks of spacetime as moving.
Then, in flat spacetime, as there is no curvature, then (by the contrapositive) there is no “movement of spacetime”?
But if some stuff is not moving in one inertial frame, then in another inertial frame it is moving.
But that implies that, if spacetime is stuff and such that, if it is moving then there is local curvature, it follows that in a different inertial frame, the spacetime is not flat.
But, whether spacetime is flat doesn’t depend on the choice of an inertial reference frame.
As for how to describe those things without talking about spacetime moving,
How spacetime works has the general coordinate invariance or covariance or whatever.
You have a manifold with a pseudo-Riemannian metric tensor. You can talk about like, geodesics and such.
For a warp bubble (suppose a sub-luminal one) you could talk about a non-accelerating time-like path that remains within the bubble, and talk about how the spacetime interval along it relates to the spacetime interval of some time-like path that starts in the bubble, leaves it, “travels besides it”, and finally re-joins the original path.
(Of course, in some reference frame, the bubble would not move.)
I don’t think it really makes sense to talk about spacetime moving, even in the case of a warp bubble. A position doesn’t have a position, or a time a time, but rather a position is a position, and a time is a time.
You can talk about how, in some particular coordinate system, with some particular foliation into space-like slices, some aspects/pattern of the metric tensor at some position and time coordinate values, correspond to those at a later time coordinate at a different position coordinate value, but this is relative to a choice of coordinate system.
I’m still not following your objection based on relativity:
We have one frame where I’m on Earth; we have another where I’m in a rocket traveling away at a fixed velocity. In one case we see the rocket traveling away; in the other, we see Earth traveling away. But neither one tells us that the spacetime itself is moving — they’re both just local coordinates.
In the case we see the spacetime itself move, eg with a gravitational wave, both the frame from the rocket and the earth agree that the manifold has been changed in a way that left a wake — moving relative to its local, original shape.
As a side note, “inertial reference frames” are a useful fiction: we’re always being accelerated, eg, by the galactic center, fellow galaxies, dark matter filaments, etc. Conclusions based on such a fiction may be practical, but cannot be used to derive conclusions about physical reality — as they don’t exist.
2) Why would something have to be in an inertial reference frame in order for inertial reference frames to “exist”? Doesn’t make sense to me.
In any case, that seems like just an excuse to ignore Lorentz boosts. One should address SR before addressing GR.
3) If spacetime were stuff, then it would be stuff always, not just when there are ripples or whatnot. But, in flat spacetime, you cannot describe it as a stuff in a way that is compatible with Lorentz symmetry, because the velocity of stuff changes under boosts, and so stuff can’t be stationary both when one doesn’t and when one does apply a boost. Therefore, it isn’t stuff.
But who knows, when one day someone will come up with a better model that does away with the "dark matter kludge", it will turn out that these phenomena actually have a common root cause?
Besides, epistemologically it is very good to suspect and investigate the effects of DM on all kinds of phenomena. Then, if it does not exist, we will have many more points of reference from which to derive experimental or theoretical contradictions.
It does not really matter if those exist or are an artifact of current theories, replacing relativity is not that easy and there are already a ton of physicists working on that anyway.
In the meanwhile of either having instruments capable of detecting these or a new theory that demostrates that those are artifact emerge... they have to exist. That's the point of them.
It's astronomy. It means "anything that is not shining like a star but we can detect it via inference." Light matter is stars. Dark matter can include MACHOS: neutron stars, black holes, brown dwarfs, rogue planets. No new physics required for MACHOs, as opposed to WIMPs.
There's nothing wrong with that part.
I do have a problem with the single-minded insistence on disqualifying any exploratory study on alternatives to a model that gets more and more partially falsified all the time¹. To the point that only iffy personalities that don't care for their careers decide to work on them. But on a situation like this, those other models would probably be tweaked too.
1 - I've never noticed it before, but that phrase gives me great "Superstring Theory" vibes.
[1] https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Ant...
That's terrifying. Imagine a rogue supermassive black hole floating in intergalactic space.
But I mostly want to know how badly self-interacting dark matter messes up the existing LCDM simulations that most astrophysicists sort of rely on?
Why terrifying? It's literally doing nothing, far away from anything. Seems like the safest place for it to be.
Damn straight! I dare to assume you ignorant jackasses know that space is empty. Once you fire this hunk of metal, it keeps going till it hits something. That can be a ship, or the planet behind that ship. It might go off into deep space and hit somebody else in ten thousand years. If you pull the trigger on this, you are ruining someone's day, somewhere and sometime. That is why you check your damn targets! That is why you wait for the computer to give you a damn firing solution! That is why, Serviceman Chung, we do not "eyeball it!" This is a weapon of mass destruction. You are not a cowboy shooting from the hip!A supermassive blackhole floating towards you would have very visible effects, it would be impossible to miss for millenias before it gets to you.
It's the micro black holes which can hit you without a warning.
Micro black holes are only hypothesized so far, but they could get very small - e.g. a black hole with Earth mass would have less than 1 centimeter in diameter.
The size itself is not that important for spotting black holes, though. Even if it's as large as a star, all you see staring at the black hole "object" is nothing. What's important are the gravitational effects on the environment, and there the differences are stark. At a distance of 1000 light years, it will be difficult to spot a stellar-mass black hole floating through empty space, because its pull is strong enough only at stellar distances and won't produce enough disturbance in interstellar space for us to notice. OTOH supermassive blackholes will deform whole surrounding star systems because of its immense mass and gravitational pull. A micro black hole (e.g. Earth mass) passing through the solar systems would likely go undetected unless it collides with something (which is improbable). There could be a measurable disturbance, but it would be one-off and difficult to attribute to a black hole.
Solar wind? Would it generate some interesting effects when coming too close to a black hole? All these protons accelerated to a near light speed, probably hitting each other and running away into a black hole.
I always imagined it as being caused by a rogue mini black hole zipping through.
It’s just that for black holes this effect is insignificant (a merger would take much longer than the age of the Universe) until they get close to each other, much closer than 1 parsec.
Here's a simple thought experiment disproving your claim. A person hovers just above the origin of a supermassive black hole. They chuck a massively charged object into the black hole. If what you said is true they should observe the charge instantly being transported to the singularity, since a black hole can't have any attributes such as where charge is distributed within the horizon.
Where it gets impossible is that someone very far away around the same supermassive black hole could observe a small charge increment. They in turn could chuck charged stuff into the black hole and now you've got faster than lightspeed communication.
I spent couple of minutes trying to understand your thought experiment and was puzzled why can't I understand it. It seems that it is probably because I don't understand what you mean by "just above the origin of supermassive black hole"?
I feel that you have something interesting to say but not clear.
The charge of an object thrown into a black hole doesn't need to "instantaneously" reach the singularity. In fact, it doesn't even "travel" in the sense that the observer would see a time delay based on where the charge is inside the horizon. The EM field generated by this charged object can still be observed outside the horizon before the object crosses the horizon. In classical GR, the exterior of a charged black hole is governed by the Reissner-Nordström metric [1], and it already includes the influence of charge. Once the object enters the horizon, the outside observer will perceive the black hole's external field to have changed. The field adjustment is instant for the outside observer because, from their point of view, the object never actually crosses the event horizon (due to infinite time dilation at the horizon from their perspective). The charge appears to have been "absorbed" by the black hole when the object is still outside the horizon.
So no-hair theorem doesn't imply that properties such as charge or angular momentum must be "smeared" instantaneously to the singularity inside the black hole. The theorem only describes how these properties manifest externally, not their behavior inside the horizon. Once a charge object passes the event horizon, the information about its charge is not causally connected to any observer inside the black hole (except in QM contexts, where the information paradox becomes relevant). However, the charges affects the external metric of the black hole immediately and completely as seen by external observers. Also it doesn't say that the charge or mass needs to be uniformly distributed or behave in any specific way inside the event horizon. It only states that from the outside, black holes look like point-like objects characterized by mass, charge, and angular momentum. The specifics of how charge is distributed inside the black hole’s event horizon aren't visible to outside observers and therefore don't affect the validity of the theorem.
[1] https://en.wikipedia.org/wiki/Reissner%E2%80%93Nordstr%C3%B6...
> The no-hair theorem (which is a hypothesis) states that all *stationary* black hole solutions of...
https://en.m.wikipedia.org/wiki/No-hair_theorem
> The field adjustment is instant for the outside observer
And as my above thought experiment shows, any instant changes like such could be used for FTL communication.
I doubt you could usefully exploit this behavior, because any charges would still need to travel to and away from the black hole at no more than light speed, and because time slows down the further you get to the event horizon the shortest path "around" a black hole would probably not go through it.
I am really not getting what you are trying to say?
For supermassive black holes, this process might seem slow due to the massive scale of spacetime curvature near the event horizon, but there is no requirement for instantaneous changes. In fact, relativistic causality ensures that no information can propagate faster than light, so updates to the black hole’s charge, mass, or angular momentum are constrained by the speed at which signals (gravitational or electromagnetic) can travel.
IIRC the event horizon expands to encompass the object just before it gets to the original horizon, due to the Schwarzschild formula.
Also IIRC, the electric field is blurred out by the geodesics by this point, as if it were from the interior. But that's based on what I've heard, I have yet to derive useful results from the Einstein field equations, even though I think I should give it a go and I can follow them well enough to code a simple simulation…
That said, it's the no hair theorem. It could of course still be wrong...
Saved you a click.