Thursday, 1 June 2017

Nothing to see here: they are black holes

The latest news from LIGO: another observation of two black holes colliding. This one dates from January 4th.

The black holes were approximately 20 and 31 times the mass of our sun. For the record, this is similar to the first binary we found back in 2015. The main difference is that the new binary was almost twice as far away (or less favourably inclined to us), so the signal was about half as strong, making our measurements about half as accurate.

That doesn't sound very exciting, does it? The same thing again, but half as informative. Did we learn anything interesting?

I'm sorry, but "discovery of the century" is a hard act to follow. You will have to live with "science as usual": another data point, a small addition to our overall understanding, the tentative conclusions from previous observations sharpened. And that is good. If our picture of the universe was shattered every six months, that would not say much for our ability to understand it. Most of the time our new measurements reinforce the old ones, and that is a sign that we are doing a good job.

The first three observations in 2015 allowed us to make a rough estimate of how often black holes collide in the universe. If that estimate is correct, we would expect to make regular detections -- just like this one. (We found nothing in 2016 because the detectors were switched off for most of the time; it was that kind of year.)

If black-hole binaries are uniformly distributed out in space, then the further out we look, the more we will find. This means that we are most likely to observe them far away. The further away they are, the weaker the signal. That's why the first breakthrough detection was such a surprise -- it was more than twice as strong as the weakest signal we could measure. Most of the time we expect to see binaries at the edge of our range, with much weaker signals -- again, like the one we just announced.

So: these weak signals are exactly what we expect. That means that we should not be disappointed if we find ten or twenty or even thirty more just like it, before we find another one as strong as the first one.

If you have been following the LIGO story, you might say, “Hey! You said that in five years you were going to find hundreds of black holes. If you found only three binaries over 18 months, I find that hard to believe.” How that prediction plays out will depend on the detector sensitivity. The goal is for Advanced LIGO to be roughly three times more sensitive by around 2020. If it is three times more sensitive, it will be able to detect sources three times as far away, and that means it will be sensitive to 27 times as much of the universe. (Here is the relevant technical reference.) That means that a current detection rate of one per year would change to 27 per year, and with each binary we have three black holes (two in, one out), giving us 81 black holes. We have already found nine (or twelve, if you count that marginal detection), and that gets us pretty close to 100. That is just for one year, and that is for a pessimistic estimate of the current rate. So observing hundreds of black holes by 2020 is easy — if the detector sensitivity improves as we hope, and if there are no delays. (You know, like some looney in the White House cutting science funding.)

Of course, we could also have found a signal from a different source: neutron stars instead of black holes, or a supernova going off. If you were hoping for a change from boring old black holes, you might find the latest detection disappointing.

That’s your problem. I am not disappointed. I like black holes. Colliding black holes was what I always wanted to find with LIGO. Two years ago, black holes were the exciting source that we hardly dared to hope for. It just seemed too good to be possible. Hearing the sound of two of the most extreme objects in the universe blurring into each other? Making the most direct observation ever of a black hole? It seemed like a dream.

Two years later, and the murmuring at LIGO conferences is, "Of all the things we could have found next -- this is the most boring!" How times have changed.

What a strange feeling! Imagine you are trying to find aliens. Everyone thinks you're crazy. You're wasting your time. You'll never find aliens! Then you find one. Kaboom! Everyone goes bananas. This is the biggest discovery ever! Then you find another one. Oh my God -- there are more of them! The alien has a sister! Wow! Eighteen months later, you find a third. What is it? It's the first alien's little brother.

Really? We just keep finding members of the same dull family? Boring!

Let that be a lesson to you, in case you are out searching for alien life. Take your glory while you can.

Don’t get me wrong. I don’t need more glory. Sure, I am a little miffed that I am not cheered when I arrive for work every morning, but I am told that is merely a personality defect, and I have no legitimate cause for complaint. After all, I get to spend my days measuring black holes. That is no longer a surprise to anyone, but it is still wonderful.

More Gravitational-Wave Stories

February, 2016:
The Discovery
How it Felt
How We Squeezed Out the Juicy Science

March, 2016:
Trying to Explain Gravitational Waves (Part I) (Part II)

June, 2016:
Book Review: Black Hole Blues
Detection Number 2 -- Black Holes Rule
Rumours, Secrets and Other Sounds of Gravitational Waves

February, 2017:
One Year Anniversary (of being world famous)

June, 2017:
Detection Number 3 -- Nothing to see here: they are black holes
A hint of controversy

September 2017:
Detection Number 4 -- Virgo nails it

October 2017:
Did I just win the Nobel prize?


  1. We see a pattern emerging in which all black holes are colliding at roughly half the speed of light! Before aLIGO almost everyone working on black holes assumed that the mergers would occur at very close to the speed of light

    1. You're talking about the black-hole speeds just before merger? Modulo quibbles about what speed means in such a distorted spacetime, it's the relative speed of the black holes that is about half the speed of light; each black hole is going about quarter of the speed of light. This is typical for binaries where the black holes are of similar mass, and with low spins. (The speed has nothing to do with the total mass.) If the black holes were highly spinning, then this speed could be higher. This has been known for as long as we've been able to do computer simulations (i.e., since 2005), and could be fairly reliably inferred before that. Any assumption that the black holes merged at close to the speed of light was just loose talk; this was never a theoretical prediction.

  2. Human nature is interesting isn't it?
    You got ever increasing, irrefutable evidence of huge black holes, I mean, *f... black holes!* merging and giving out solar masses worth of energy and a couple of years later people go "Boooring...".

    The LHC found the Higgs boson and five year later "Particle Physics is in a crises".

    And, why stop there? Vaccines? The needle sting! It took me ten hours to go from Paris to New York, damn airlines. Netflix was off line last night and I could not choose among a few zillions movies coming through a tiny optical fiber.

    Let's face it, humans suck. Or... this nagging unhappy feeling is what makes us discover gravitational waves, the Higgs boson, vaccines. I honestly don't know, but I lean towards "we suck".
    Welcome back.

    1. Life is so thrilling that our tolerance for excitement is high. What's the problem?

  3. Mark
    The effective relative velocity of merging BHs is given by the post-Newtonian parameter v/c=(GMπf/c^3)^(1/3), where f
    is the gravitational-wave frequency calculated with numerical relativity and M is the total mass of the Binary system
    Here is the data :
    GW150914 M=70M* f=150Hz
    GW151225 M=22M* f=450 Hz
    GW170104 M=50.7M* f=200Hz
    All give v/c ~ 0.54

    1. Yes, although this brings up those quibbles about speed. This is a crude estimate, and requires that post-Newtonian estimates are still valid up to merger (not true, of course, since they are based on a point-particle approximation). The "frequency calculated with numerical relativity" also hides a trick: we have to estimate the GW frequency that corresponds to merger, which is also ambiguous. (The detection papers identify the frequency at the peak of the GW signal, which is as good a choice as any, but I don't know of any strong argument that this is the right point to choose, and since the frequency changes rapidly at merger, there there is a huge error bar.) If I look at the BH speeds in an NR simulation just before the horizon forms, I get a relative speed not much higher than 0.4c, but that also depends on coordinate choices. The easiest thing to do is a simple Newtonian calculation of the relative speed of two objects when they are 4M apart. That gives 0.5c, which is about as good as anything else.

      Plots illustrating the calculation above were shown in the first two detection papers. I'm glad to see that such a plot is absent from GW170104. I'm curious where you (Anonymous No. 1) saw it?

    2. Your reply highlights the nebulous nature of BH merger dynamics in which PPN and NR are pushed beyond their limits and guesswork is invoked. Also the Newtonian calculation has a severe contradiction. It assumes two point like particles falling from infinity to the edge of a virtual BH of diameter 4M, -conditions in which GR predicts a speed of c.
      I have applied Eqn. (54) from this paper to picture the dynamics near the event horizon.

    3. I cannot access the paper, but the statements in your reply are all wrong. NR is not pushed "beyond its limits", and no guesswork is involved. There is some ambiguity associated with assigning a speed to the black holes close to merger, but we know where that ambiguity comes from. We know what it means to calculate invariant quantities, and the BH velocity is not one of them. Fine. We can, however, put well-defined bounds on the speed close to merger. A rough estimate from a crude Newtonian model of the closest possible circular orbits of two masses of radius 2M happens to fall within those bounds. That is all I meant.

  4. Okay Mark

    My point exactly is that statements such as
    "The "frequency calculated with numerical relativity" also hides a trick: we have to estimate the GW frequency that corresponds to merger, which is also ambiguous." coming from a specialist do not convey a sense of confidence to non specialists on the methods used in the analysis as well as the resulting knowledge. However your second reply has clarified some issues. Thank you for your professional point of view.

    1. Fair point. I should not have said "trick". I meant that there is an approximation that's not explicitly mentioned, and the calculation portrays a false sense of high precision. We know that the relative speed of the black holes close to merger is roughly half the speed of light; greater precision is difficult to justify.

  5. I'm going to ask something stupid here. We are told (in introductory GR texts) that an outside observer will see that an in-falling object will take infinite time to cross the event horizon. We then learn that the proper time of the in-falling object is finite, so the object does cross, at least in the frame of a comoving observer. So what does that mean from earth? Are the astrophysical black holes that we are observing have their mass-energy in a shell just above the event horizon? And if so, does it matter? And are there any consequences for black hole mergers? (Or black hole neutron star mergers.)

    1. We are not observing the black holes, we are observing the gravitational waves, which are produced by spacetime being whipped up in the vicinity of the black holes. On the picture of particles in-falling into a black hole, the GR solution for a point particle is not the same as that for two comparable-mass black holes -- when we solve Einstein's equations for two black holes, a common horizon does form, and we could (in principle) do experiments to demonstrate that we are not seeing, for example, two black holes frozen very close to each other. Observing the gravitational-wave ringdown of the final black hole is an indirect way of doing that.

    2. Thanks for the reply. I'm still kinda confused though, so I'll ask a couple more questions, if you don't mind.
      As a black hole forms though gravitational collapse, the picture of the outer shell of the former star "frozen" at the horizon from earth perspective is accurate, right? If that is so, then as the black hole absorbs mass-energy (from the CMB, for example) and grows, the particles at the earlier horizon should be unaffected by this via Birkhoff's theorem (assuming symmetric for simplicity). Then in principle we can calculate a density as a function of radius of the black hole (as a external observer) if we know what it has been eating. Is this view even accurate?

      So when we have two black holes merging, and a common horizon forming, does this mean that the mass then redistributes itself to the new horizon? Is there any observable difference (via gravitational waves) between such astrophysical black holes with mass at the horizon and mathematical black holes with a singularity (and presumably all the mass) in the centre?

      If we have a neutron star merge with a black hole, is the right mental picture to have is the neutron star being smeared out around the (now larger) event horizon?

      TL;DR Is particles frozen at horizon picture accurate, and if so, is there any implications of this or we can just treat them as the mathematical solutions to the GR equations?

    3. I always work with vacuum spacetimes, so at some point I become the wrong person to ask. But I there is a problem with the view of a "frozen shell". The matter is not frozen outside the black hole. It falls in. It's just that we can never see it fall in -- any signal from it takes longer and longer to reach us, the closer the matter gets to the black hole. The signal is also redshifted, so it gets weaker. A view from outside would be that the matter appears to fade away. The outside geometry is indistinguishable from a lonely black hole. In the end the point is: there is no consequence for the gravitational wave signal of, say, a neutron star spiralling into a black hole.

    4. Thanks again for the reply. I mean, sure, optically it becomes indistinguishable via the dimming. However, I have always viewed the time dilation as a statement of when a event occurs in a reference frame (in this case from earth), regardless if it can be seen or not. Thus the matter doesn't fall in, not from the earth frame. However, the end result is indistinguishable (both optically and gravitationally) from a standard mathematical black hole. Is this view incorrect?

    5. There's a temptation to think that what we can (in principle) see from Earth is what is "really happening". That's not quite right. Imagine a computer solution of Einstein's equations for a stream of extremely bright matter swirling into a black hole. You could make a movie of the dynamics of the particles: they would all swirl into the black hole. In the end there is no matter left anywhere. If a neutron star comes along later, it meets a pure black hole, with no matter around. You could now get your computer calculation to work out what you would see of all of this from Earth. From Earth you would not see the particles "entering" the black hole. They would appear to slow down and fade away. You later see that a neutron star is approaching and think, "It's approaching a black hole with a collection of particles around it, because I never saw those particles actually go in," but of course that is not what the neutron star actually encounters.

  6. Isn't one of the core tenets about relativity being that what is "really happening" can differ between observers, but all are correct (in their own frame)?

    Thus what the neutron star encounters can be different from a co-moving observer and from earth frame, but can't both be correct? (I'm not trying to be contrarian, just confused. Thanks yet again for replying.)

    1. Yes, that's true, but focussing only on what an observer sees can be misleading.

      Here is another example. (These example are also helping me to get a clear picture of what happens... hopefully.) Imagine the same computer solution as above, but now so many particles fall into the black hole that its mass grows appreciably. Let's say that over time its mass has doubled. In the computer data, the particles all go into the black hole, and its mass grows, but a calculation of light rays shows that a distant observer would only see the particles slow down and fade away. You now ask how the distant observer's view can be reconciled with the time coordinates used in the computer code, which show the particles just falling in. Well, when each particle falls in it will slightly perturb the black hole, and as the black hole settles down it will give off some gravitational radiation. The radiation travels at the speed of light, and can be measured by the distant observer. The properties of this “ringdown” signal depend on the mass of the black hole. So, as the mass increases, the ringdown signal from each successive particle will change. The distant observer can measure that. So, they can determine that although they cannot see the particles fall into the black hole, they must have fallen in, because the ringdown radiation tells them that the black hole is growing in mass. If they measure the radiation accurately enough, they can determine that it is radiation from a pure black hole perturbed by just one particle — not a black hole with a big collection of particles all piled up next to the horizon. We know that this is what kind of black hole it must be, because we can set up our simulation so that each new particle is dropped in after the ringdown radiation from the last particle has passed the distant observer. In our computer calculation we see the particles all fall into the black hole, and our distant observer can also determine that that is what has happened, even though they never see the particles cross the horizon.

    2. From this example, it does seem that, yes, the particles do fall in both frames. Which suggests that the frozen star picture is wrong in someway, and must be adjusted, but in a way that makes what the observer see is not wrong. It seems to me that the simplest way to reconcile this would be that what happens in the distant observer frame is that the first particle + black hole forms a bigger black hole with a larger event horizon in a decent amount of finite time, which kinda resolves the problem of it not falling though the original event horizon, as it is now in the bigger black hole. This bigger black hole then ringdowns, which is what we observe via gravitational waves. Then the second particles comes into play. Of cause, this is just my imagination without any calculations, and (probably) requires numerical relativity to prove, which I know nothing about. (Obviously to disprove it, just pointing out a problem with it is enough.) Thanks for this enlightening example!


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