Gravitational waves from a binary black hole merger observed by LIGO and Virgo
ligo.caltech.edu
ligo.caltech.edu
Many observatories like the VLA, Chandra, Fermi, Gemini, have a rapid response trigger for the detection events, where within minutes they will stop their current operations. Observations in the EM spectrum are crucial for learning about a huge number of questions in astrophysics, like what kinds of galaxies do the merger events originate from, where are they located in those galaxies, how does the luminosity decay at different wavelengths, etc. It will be seriously exciting when the first counterpart is discovered!
We're currently only active and collecting clean data ~50% of the time for each detector. We need at least two detectors active for a detection, and need three detectors for this kind of beautiful directional isolation. So having extra detectors decreases our skymap areas significantly, which helps in EM followup, but it also significantly reduces GW detector network downtime. And it allows for graceful degradation; with 5 detectors, you can afford to have a couple detectors down and still detect an event with good direction reconstruction.
We also have tons of downtime for upgrades. Now that our second observing run is over, we have a ~1.5yr upgrade cycle. There's no point in running VIRGO without LIGO (except for engineering reasons); having more detectors will increase flexibility in this regard, too.
When KAGRA and LIGO India come online, we should see much better skymaps, but we will also see much higher uptimes (and hence higher detection rates).
It's especially exciting to see improved direction reconstruction given that VIRGO has faced setbacks this year with their mirrors. I wasn't expecting to see such beautiful skymaps until our third observing run! Needless to say it was an exciting summer :)
- grad student working on LIGO
Can you expand on why it takes so much time to do an upgrade?
I'm guessing it's due to the complexity of the system, kinda like with the LHC? or is it something different?
I mean, having equipment that expensive on downtime for more than a year seems like a lot!
In the downtime until O3, new optics are to be installed. As these are 40kg each and suspended from monolithic fused silica fibres (each a couple hundred microns thick), this process is complicated and requires great care to avoid damaging either the fibres or the optics during installation. In addition, both LIGO and Virgo are going to get squeezed light sources installed, which allow for reduction of limiting quantum noise at high frequencies. These are immensely sensitive to light loss in the optical path, so commissioners need to be very careful to minimised scattered light and ensure good alignment.
After making all of the planned upgrades, the interferometers then need to be recommissioned: all of the control loops (of which there are thousands) need to be re-tuned from their settings as of now, given the changes in the behaviour of the interferometer due to the upgrades. This takes a lot of person power and a lot of time to get right - for the first observing run this process was basically also 1.5 years.
Great explanation. Thanks!
I just can't start to fathom the complexity of these instruments.
Also... how cool that you get to work on such interesting field and with such cool "lab" devices!
Since our search volume is naturally the cube of our max search distance, a twofold increase in range yields and eightfold yield in search volume, and hence event rate.
Put another way, if you can get better than a 30% increase in search distance by upgrading half of the time and running the other half, you're doing better than breaking even (1.3^3 > 2) because your increase in event rate more than makes up for the downtime.
This is why it actually makes more sense for us to do these thorough, ambitious upgrades than to just leave the detectors on all the time.
That said, I don't know if anyone has looked at our data in the vicinity of e.g. DPRK nuclear tests to see if any nuclear detonations are visible in the strain timeseries.
Is that a large enough margin? What would be typical delay between noticing gravitational wave event and seeing the related EM waves?
Yes, if you have a long event, that smears out the time during which EM radiation might have been emitted. But for just observing the event, you expect a long-lived afterglow. It starts out hot and radiates gamma and x-rays, then cools through UV, visible, IR, etc. all the way to radio waves for weeks after the event. You can learn a lot about the event and the material that was ejected from it from a detailed analysis of this cooldown.
Both kinds of waves are slowed when passing through media, but because EM is much stronger than gravity, the effect from interstellar dust should be much stronger on EM than on gravity.
Even a 1-in-a-million slowdown of the EM versus gravity would mean that everything outside of ~100ly would arrive at least an hour later. Every intergalactic bit of light is passing through at least a few thousand lightyears of galactic dust, and potentially much more.
Not that it would make much difference. The delay due to dispersion goes down quadratically with increasing frequency. At the lowest frequency that Google tells me is used in radio astronomy, 13 MHz, the delay would be (if I've understood the dispersion equations correctly and done the math correctly) about a minute compared to visible light or gravity waves, and so not very useful.
If you went down to 1 MHz, the delay would be a much more respectable 3 hours, but I'd expect that there would be way too much noise from terrestrial sources to do any useful radio astronomy anywhere down around there.
Even so, there's likely mass in accretion disks, and it will likely get very hot in the bh-BH merger process. That's what you referred to, I guess.
There are also probably pulsars and (maybe) other signals out there that are nearly periodic and that we are hearing all the time! But those would be much much quieter (think of a burning flame vs. an explosion; the faster you release your energy, the more noticeable it is).
Furthermore, those sources should be pretty close to a pure sine wave. That's hard to detect, because so much of our noise looks similar. We look at compact binary coalescences so closely in part because they are so distinct that we can be fully confident that our detector didn't produce them (we have a very talented and suitably paranoid approach to studying our background noise without prior assumptions of its form).
You can't be so sure with these faint, continuous sinusoidal signals UNLESS you do a fully coherent search over long periods of time. Our detectors are not equally sensitive in all directions, and they can pick up direction as a phase-delay between the detectors in our network. As the earth rotates, both detected direction and strain amplitude from a a continuous source should vary. You can imagine doing what is basically a very, very long timescale fourier transform of the signal; the longer you integrate over, the more you filter out sine waves with frequencies nearby your chosen frequency. But this is a computationally expensive approach because longer integration times mean you need to test more frequencies as well as doing the longer integration.
There are approaches to finding good compromises re: fully-coherent search windows, and I'm sure there's plenty of other clever voodoo that goes into the continuous waveform searches, but I don't know much more than that.
I wonder then if there's work to understand how much GW noise there is, and work on lowering the local non-GW noise floor further, etc. I guess that just means ever larger detectors - and of course correlating results from detectors around the world.
All very cool and interesting work anyways.
This is such a staggering amount of energy to be released in such a short time.
[1] https://en.wikipedia.org/wiki/Gamma-ray_burst#Energetics_and...
> No known process in the universe can produce this much energy [1 solar mass equivalent] in such a short time.
These scales are incomprehensible, at least to me.
> When this effect is taken into account, typical gamma-ray bursts are observed to have a true energy release of about 1044 J, or about 1/2000 of a Solar mass (M) energy equivalent
So more, by about 6000 times.
This is consistant with WolframAlpha's output for amount of energy: 5.361e47 J. I tried to convert this to "number of years we could power the Earth", but it just changed it from one mind boggling number into another.
Copy-paste error here from losing sup/sub formatting, that's 10^44 J, not 1044 J.
If I drop my bowling ball, it has lower potential energy, but can't some of that be compensated for by the Earth-ball system radiating a gravitational wave (rather than all being converted into kinetic energy)?
Similarly, don't orbiting bodies emit gravitational waves? I forget the exact dynamics, but the way that they drag just a little bit as they orbit creates waves that radiate power out of the system -- I think the Sun and Jupiter radiate something like 55 watts of gravitational waves.
If you take two things that are each tens of times larger than the Sun and set them spinning an appreciable amount of the speed of light very nearby -- to the point they eventually collide -- it's not surprising they emit quite a bit more than our solar system.
Think of it this way:
Two large objects start orbiting slowly far apart. But because they're large and the system is big, they have a lot of orbital momentum.
They pull each other close, but as they get closer, that orbital momentum has nowhere to dissipate, so they orbit faster and faster!...
...Except that because they're so massive, they slightly tug space around with them as they orbit. And because they're orbiting so fast, space doesn't have a good way to smooth itself out. So some of the momentum from the heavy things spinning far apart gets stored in wrinkles in space as they come together.
Which then radiates away from there to us, ...and slightly stretches one direction of reality as it passes by. Which we detect by measuring how long two perpendicular lines are very accurately a few different places on a nearly spherical object.
...So you can model it as just the way that mass interacts with spacetime if you remember to include things like the distribution of your mass as a source of potential energy that can itself be used to generate gravitational waves. However, this does not make the whole situation any less weird to explain.
Reports just tend to convert the amount of energy released through mechanisms like that in terms of mass, because it's the only thing vaguely comprehensible. (eg, 3 suns)
Nothing wrong with your comment, but I just want to emphasize that for objects smaller than stars, the amount of energy carried by gravitational waves ranges from tiny to unimaginably tiny. The Earth-Moon system emits about 7 microwatts of gravitational waves. A bowling ball in low earth orbit would radiate about 5*10^-41 W, which is roughly equivalent to one photon of visible light every quadrillion years.
(Not sure where I first heard this explanation, but I can definitely say that I didn't originate it!)
[1] I mean, we usually imagine we can retrieve things when they drop into a hole, but that's not really a thing in this case. (Excepting Hawking radiation and the absurd amount of computation/time you would need to reconstruct the original state information from that. If you thought the time-of-evaporation for a Black Hole was long, you've got another thing coming when it comes to reconstructing the state from that evaporated radiation! Not that this has has any practical bearing, but it's fun to think about, right?)
Barbell-like configurations of matter emit gravitational radiation when they spin about an axis perpendicular to a line through both bodies' centres of mass. A binary star system is barbell-like, with two heavy masses at opposite ends of an so-infinitesimally-thin-it's-not-really-there bar. This "barbell" rotates around the barycentre, which for all practical purposes lies along a line through the two stars' centres-of-mass. Even more massive binary objects can have a rotating-barbell type of arrangement.
More detail here if you want it: https://www.wikiwand.com/en/Gravitational_wave#/Sources
Rotation of each black hole is relevant in black hole mergers in the late stages of the inspiral, and there have been several numerical relativity studies of BHs with extreme rotation rates (each BH rotating around its own axis, and possessing only axisymmetry rather than approximately spherical symmetry). The results are interesting, but don't really have an impact on the shedding of gravitational radiation; that comes down to the barbell-like configuration.
In order for there to be frame-dragging one must first fix a frame of reference. If you fix Cartesian coordinates with the origin at the middle of a bucket of water, and then you spin that bucket around on a rope, you're dragging those coordinates around with the rope. If the coordinates serve as the basis of a frame of reference then presto, you have frame-dragging. But if you have a suitably heavy bucket of water and spin it hard enough, you'll notice the barycentre shifts outside of your body along the rope towards the bucket. Congratulations, you're now shedding gravitational radiation!
That gravitational radiation is there even if you only ever calculate in coordinates where the origin is on the floor of the corner of the room in which you and the bucket are spinning; that ("laboratory") frame of reference is not being dragged by you.[1] In the lab frame and in the bucket frame, your precession as you struggle with your footing are pretty different: the rope remains the same length so you are at a constant position in bucket-basis coordinates, but you are moving around relative to the lab coordinates.
You can even fix (0,0,0,t) on some part of your own body; you are dragging those coordinates around as you spin the bucket, and the bucket eventually settles at some fixed point in your coordinates. The walls of the lab move around in those coordinates though, and might move inwards and outwards from you as you spin around.
The Lense-Thirring effect is similar to how the walls move around in your coordinate basis as you spin around. It arises when one uses an exact solution of the Einstein Field Equations (typically the Kerr metric) and a set of coordinates suitable for a static observer. A static observer is one who sees [a] no change to the gravitational or matter fields over time and [b] can slice spacetime into space+time in a particular way. Static observers are not realistic observers in a universe full of moving matter. The Kerr metric is unsuitable for the real Earth, since it's lumpy inside. These approximation choices are mathematically convenient, but come with the side effect of needing to import fictitious forces to explain orbital precessions.
The extra mathematics of Lense-Thirring precession however are much much more convenient than dealing with a more realistic metric and set of coordinates for Earth. Moreover, it is perfectly reasonable to do physics in preferred frames of reference (Kerr + Boyer-Lindquist, in this case) as long as you admit to yourself that that is what you are doing. There exists a Bogoliubov transformation from this preferred frame of reference to any other reasonable frame of reference, so you're not "stuck" with Lense-Thirring.
You are however stuck with the physical result that something orbiting such that 24.something orbits "should" give it the same view below (and above!) but doesn't. We've shown this around various artificial satellites put into polar orbits around various bodies in the solar system.
The underlying source of this precession is a combination of gravitational and special-relativistic time dilation. These are not "forces", though.
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[1] It is being dragged around by the Earth's movements though; if you treat it as an exact inertial frame and do extremely sensitive experiments you'll see deviations in motions of things that you may be tempted to describe using e.g. coriolis forces. If you use exquisitely precise atomic clocks and insist on Cartesian coordinates, you will eventually discover that you are not in an inertial frame after all, and will have to take the local curvature of spacetime into account in the basis of your frame of reference, or shrug and use fictitious forces as corrections to Newtonian or special relativistic geometry. The magnitudes of the fictitious forces will be small.
Is there a rule of thumb one can give to predict this, for 31 and 25 solar mass black holes? Is there a limit that we expect (e.g., 2 <= mass lost <= 5), or could it go up to 31+25-56=0?
P = -32/5 G^4/c^5 \frac{ (m1 m2)^2 (m1 + m2) }{r^5}.
The key adjustable here is the orbital distance r. As it goes down, power goes up, but it's still extremely even for large masses until the two masses are practically in contact. You can plug in kilograms for masses m1 and m2 and use metres for r5. We are already doing a linearized approximation here, so we can bite the bullet and circularize the orbit of Earth-Moon at the average orbital distance and find a value that's a few microwatts; doing the same for Earth-Sun gives us a couple of hectowatts. Putting a pair of tens-of-solar masses at r ~ 1000 km gives us a much much larger power.
We can take the integral of power P over time and arrive at the radiated energy. We can in turn consider an r that shrinks over time. We can also flip this on its head and consider that it is equally reasonable to say that r shrinks in response to energy loss or energy loss increases in response to r shrinking. More on that below.
The calculation grows much more complicated for realistic orbits especially when the orbital distance is small, but you only asked for a rule of thumb, not a detailed explanation of, say, the Bondi-Sachs mass loss equation. :-)
> Do you know why [large mass] were converted into gravitational energy?
Sure. Very roughly, angular momentum depends on frame of reference. If you choose to work in a frame of reference in which a black hole binary has significant angular momentum in the mutual orbit (e.g. in the cosmological frame), then you have to get rid of a chunk of that for two reasons.
Firstly, angular momentum needs to drop in order for bodies of constant mass to drop into a closer mutual orbit. Although there are other interactions at work when the distances are large for a binary BH in a galactic core, when the binary BHs are near the end of their inspiral, the orbital distance shrinks very quickly. The only reasonable mechanism to shed that angular momentum that quickly is gravitational radiation.
Secondly, the "no hair" theorem means that there is only a three-component angular momentum J an at any given time coordinate for a black hole once it has stabilized. But as each of the merging BHs has its own nonzero angular momentum there are excess multipole moments that count as hair on the asymmetric configuration at the end of the inspiral, and so balding has to happen. This causes excess momentum either to be swallowed into the merged black hole (which will have some final angular momentum) or radiated to infinity. Swallowing is limited by the final mass of the merged black hole. Superextremal black holes are forbidden, for example, and in practice merged BHs are unlikely to rotate near he maximum possible speed for their mass. Consequently the rest must disappear as gravitational radiation, since it can't escape in any other way.
> could [the whole configuration be radiated away]
A real answer would be quite deep since mass in General Relativity is not so straightforward. However, the individual black hole masses m1 and m2 will change very very little during the inspiral and merger; and the end black hole will be very close to m1+m2. What gets radiated away is maybe best understood as some of the quantity that works against the BHs simply falling straight down onto one another at the speed of light, which is something no observer sees. I discussed this a bit more at https://news.ycombinator.com/item?id=15353970
(In reality the mass contribution due to the gravitational potential energy is included in the "mass", this is just illustrative.)
Since the negative energy ultimately wins, there must be less and less positive energy holding the bodies apart. The positive energy has to go somewhere, and that somewhere is gravitational radiation.
One could equivalently be very Machian and rotate with the system and consider that the gravitational attraction of "the whirling distant stars" is working to keep the black holes from colliding. The distant matter loses because the binary black holes move positive energy (holding the BHs apart) out towards the distant stars (which also lets the BHs move a bit further away from the distant stars).
s ---+ B1 --++ B2 ---+ s -> s ---++ B1 -- B2 ++---s
Even if we consider inspiralling stars (no horizons to be found), we're lifting relatively little mass-energy out of them, rather than dealing with the energy that keeps them from colliding. The mass-energy of the system (which you measure in Joules or solar masses) when considered in the cosmological frame is what has the excess ~ 12% that gets radiated away.
Finally, in Special Relativity the angular momentum and energy-momentum of localized systems is frame-dependent; the addition of gravitational fields in a linear approximation of GR does not change that, and gravitational waves are a result in linearized gravity. It certainly is useful to discuss dimensionful quantities like the ones you listed, but it's important to remember that different observers are free to disagree violently about the numbers. Thinking about how and why they might do so is often enlightening.
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[1] Although the convention is mostly there because in Newtonian gravity, one takes T + U = const. for a body felling gravity, and since by virtue of having been described earlier T (kinetic energy) is positive so U (gravitational potential) must be negative, with the result that F = - \nabla U. We break the conservation of T + U in General Relativity quite happily, but retain the notion of the gravitational interaction as negative in many useful frames, so in the footnoted paragraph we have a generalized T and U available by a suitable choice of frame of reference in the weak limit.
I'll try an explanation, hopefully it's useful to you or another reader.
General Relativity gives us $\nabla_\mu T^{\mu\nu} = 0$, which reads that the covariant derivative of the contravariant stress-energy tensor (the matter tensor) generally vanishes. When remembering the heart of General Relativity: G_{\mu\nu} = T_{\mu nu}, that is, the gravitational interaction arises from moving matter, we observer that changes in the gravitational field match changes in the arrangements and/or motions of matter and vice-versa.
This is a fancy way of saying that there is a global conservation of stress-energy-momentum, even when you work in coordinates or gauges in which there is no global conservation of energy.
For simplicity, here and below I am setting some constants to 1, only considering classical behaviour, completely ignoring strain-squash modes, and otherwise being only very mildly post-Newtonian.
In a system like a rotating barbell with a very thin, almost massless stick, like in a Cavendish apparatus ( http://en.wikipedia.org/wiki/File:Cavendish_Torsion_Balance_... ) the masses on the end of each bar will influence the motions of masses near them, and vice-versa, because their masses attract one another. We are free to choose whatever coordinates we want to describe this sort of setup, including one in which the two grey M balls move in response to the proximity of the two red m balls, with the point where the bar is suspended taken as an origin of some useful coordinates (e.g. spherical polar ones). In particular, as the ms pass close to the Ms, the rotation of the bar is dragged on, and one is free to model that as angular momentum leaving the rotating barbell under a gravitational interaction.
We can treat two massive objects (stars, for example) in a binary orbit as a barbell-like system; the bar itself simply has no mass and is in free-fall rather than suspended on a wire. However, just like in the cavendish experiment, concentrations in the distant mass on either end of the bar will cause the bar to stretch and the system's rotation to slow, while sparsenesses in the distant mass on either end of the bar will cause the bar to contract (the "bar" itself is just the gravitational interaction between the binary masses).
With a clever change of point of view, we may ignore the influence of nonuniformities in the distant masses and just talk about the momentum leaving the rotating system in response to defined (or discovered) changes in the length of the "bar". That momentum is gravitational radiation, and its amplitude and frequency depend on the masses and orbital periods of the ends of the shrinking "invisible bar" of their mutual gravitational interaction. Near the very end of the inspiral, the bar shrinks rapidly, and the amount of angular momentum that is shed is consequently enormous.
Spacetime enters into the picture here via a linerization of the General Relativity picture of inspiralling massive objects: we start by picking out a flat spacetime (\eta [1]) and a field of perturbations on that spacetime (h) and then get the real metric tensor g via g = \eta + h (+ h^2 + h^3 ...). We drop the higher order perturbations on the spacetime (h^2 + h^3 + ...) and have a linear theory that is approximately General Relativity and is very very very close practically everywhere outside of event horizons and the extremely early universe. Gravitational waves are simply excitations in h that obey the massless wave equation.
Spacetime is pretty much meaningless without a measure of lengths and durations between bits of matter, or equivalently, spacetime is the measure (i.e., geometry) of distances in space and time between bits of matter.
Since gravitational waves are waves in an addend of the metric of spacetime, they are equally waves of spacetime.
We can consider a region of spacetime in which we find the "barbell" of merging compact massive objects (black holes, neutron stars) and discuss how, since the momentum of what's inside it decreases as the "bar" shortens, that momentum must flow outside the region to elsewhere. Matter elsewhere in turn picks up some of that momentum, just as the grey M balls pick up some momentum inwards as the red m balls pass near them.
Gravitational waves are seen when one makes some deliberate choices of coordinates and a linearizable approximation of the "real" metric. On that basis it is perfectly reasonable to treat them as physical, even though you could use a very different description the gravitational interactions between the inspiralling bodies and all the other masses in the universe, in a Machian sort of way. The descriptions are to all practical purposes equivalent, and this can be demonstrated mathematically.
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[1] g_\mu\nu, \eta_mu\nu, and h_\mu\nu all have covariant indices, but I'll just stop writing them now because they are distracting. g is a component of G in the G = T mentioned near the top of this comment, where G is the gravitational field and T is all the stress-energy (the non-gravitational fields, or just "matter").
Correct me if I'm wrong, but another way to explain this would be to say that the mass->energy conversion reduces the general amount of mass in an area, which would then reduce the pull of other objects towards it, which is the same as changing the shape of space nearby. Since this particular energy conversion was so large, and doesn't happen all at once or at a consistent rate, it's detectable like a ripple in a pond.
No, probably it isn't. However there are other readers. :-)
I'm sorry that my answer to the rest of your comment is going to seem very complicated and is certainly going to be very new to you. However, you did literally write "correct me if I'm wrong", and you are partly wrong. :-)
> mass->energy conversion
Special and General Relativity are very different when it comes to this sort of thinking, and unfortunately intuitions gained from experience with the former are usually counterproductive when actual gravitation is involved.
What we can do is draw a boundary around a region of spacetime and calculate the stress-energy within that region. That quantity will include contributions from matter, and from the matter's movement, and from quantities like pressure, stress and shear. The quantity is expressed in a sort of a 4x4 matrix called the Stress-Energy Tensor, and at every point in our region there will be a tensorial value.
In General Relativity, stress-energy is conserved; this is more general than the conservation of energy, and in many physically reasonable curved spacetimes the conservation is violated enormously on the largest scales, but stress-energy is conserved. In the case of our selected region of spacetime, it lets us say things like all the stress-energy that went into it in the past can exit it in the future.
That stress-energy includes the quantity that keeps the binary black holes from quickly falling onto each other. Typically you would want to work in a frame of reference in which that quantity is identified with angular momentum, but that's not obligatory in General Relativity.
We can instead do something like put ourselves above the barycentre of the binary black hole, rotating with the system, so that (wilfully blinding ourselves to distant stars and so forth) we do not see angular momentum, we only see something preventing the two masses from falling straight onto one another. This is making a choice of frame of reference in which we can work with fictitious forces to our advantage.
Einstein had an analogy here: consider two identical elastic spheroids alone in space, not too close to one another. One is exactly spherical, one is an oblate spheroid; they are arranged on a line that extends along the semimajor axis of the oblate spheroid through the centre of the exact sphere. An small observer at the midway point on this line between the objects can adjust its rotation so that either -- but not both -- objects appear to be rotating according to the observer. How does the observer decide if either object is the one the observer should be still with respect to?
Our observer can do perfectly reasonable physics if either or neither is rotating with respect to her. The choice often introduces fictitious (specifically, d'Alembert) forces into the picture; an example being centripetal or centrifugal forces.
The solution in modern physics is to be agnostic about whether either has "absolute rotation", and rely upon modern physics written in generally covariant form, and use tensors; or to bite the bullet and not be afraid of d'Alembert forces.
So we have just taken the latter path.
d'Alembert forces are encoded in the stress-energy tensor (an expert screaming "ARGH!" here should consider f^\lambda = -\Gamma^lambda_\mu\nu u^\mu P^\nu; whether you want to call them forces of affine connection, inertial forces, or whatever, they can be locally transformed away into a LFF frame).
So we have a fictitious-force quantity that's separating the binary black holes, and it's part of the local stress-energy, and we can export stress-energy from a region. We just need a mechanism.
Here we introduce another "ARGH!"-able thing: a stress-energy-momentum pseudotensor. We choose it carefully so that it can disappear in a local free falling frame, and we do so not so much for mathematical convenience but for conceptual utility.
For this comment, let's just call it a tool that lets us treat some of the left hand side of the Einstein Field Equations as the right hand side: we treat some of the "gravitational field" as if it were a component of the stress-energy tensor. Our goal is to transform our fictitious force separating the binary black holes into something that we can radiate out of the region of spacetime we've drawn around them. That something is identifiable with gravitational radiation.
So, the vanishing of the "force" separating the binary black holes as the black holes fall towards each other is tied to the emission of gravitational radiation. Moreover, as the binary black holes get ever closer, the amount of the force needed to keep them from just falling onto each other is ever higher, so the amount of gravitational radiation that is emitted at each tiny shortening of the distance between them goes up. When they are very very close together, the amount of gravitational radiation goes up to an extreme.
It is perfectly reasonable to say, "hang on, don't you have to keep adjusting the rotation rate of your frame of reference so that the black holes stay on, say, the X axis at all times?" Sure, but we're allowed to do that; in fact, it's almost encouraged in General Relativity.
> changing the shape of space
This you have right enough. Shifting contents of the stress-energy tensor outside our chosen region of spacetime must change the curvature of the spacetime in that region because in General Relativity spacetime curvature and matter must balance.
It's not quite that easy, though. Distances and lengths (which describe the geometry of spacetime) are encoded in the metric tensor. The arrangement of the stress-energy in our region determines the metric. Our region with the binary black hole sources some metric that we do not know exactly, but there are several approximate metrics that would describe the region reasonably well. Alternatively, we can take a well-known exact metric and perturb it based on the stress-energy in the region. We can use the post-Newtonian expansion in v/c. Or we can integrate the field equations numerically. Any of these approaches is reasonable, but one has to think about the two approaches a little differently, in order to avoid being misled about what is physical and what is not.
Wolfram Alpha gives a solar mass as 1.988435×10^30 kg. Multiply that by (299,292,458 m/s)^2, you get ~1.78×10^47 Joules.
The most powerful manmade explosion in history was Tsar Bomba, a Soviet hydrogen bomb with 210 Petajoule (210×10^15 J) yeild.
Amount of energy released by the black holes merging is 8.48×10^29 times greater, so you'd need to set off that many Tsar Bombas to get equal total yeild.
The universe is 4.3×10^17 seconds old, meaning if you set off a Tsar Bomba every second since the beginning of time, you'd still be off by a factor of 1.953×10^12.
You need about 2,000,000,000,000,000,000 Tsar Bombas every second since the big bang to match it.
The mind boggles.
So how big is the remaining 2x10^12 bombs per seconds?
Wikipedia has some other suggestions:
~10^12 stars in the Andromeda galaxy
1.98x10^12 links on Wikipedia
3.04×10^12 trees on Earth in 2015
3.5×10^12 estimated fish in the ocean
Thanks again to bonzini for spotting the rather large error!
That's what I get for trying to do math in a <textarea> instead of on paper.
So it's "only" a million billions (10^15) tsar bombas (10^15) every second (10^17, 15+15+17=47).
This may help[1]
I realize that I've never really considered what it would be like to be 'near' (say a few 10's of thousands of light years away) from an event like this. With all that energy, at what level would it pulverize a planetary body?
The main issue is that the gravitational waves only couple with you (or rather your microscopic bits) very slightly.
If you get close enough (~ 10^2-10^4 GW wavelengths depending on the system) then you have several sensory systems that in principle could -- with some awkward assumptions about signal transduction in the middle of some even more awkward changes of gauge -- produce something noticeable. The principal problem is that while a cell at one end of your body may move noticeably compared to a cell at the other end of your body from the perspective of someone watching a cell in the middle of your body, these three cells don't move around much with respect to their neighbouring cells, and the "guts" of each cell move around even less with respect to the cellular membranes. Some senses rely on groups of cells moving with respect to one another; some rely on intracellular activity alone.
There is the possibility of a small slosh in your inner ears, where there are some structures that are exquisitely responsive to small strains; that might make you nauseous, or it might trigger an episode of tinnitus. It might also go unnoticed.
That close to the merger you're likely to be vaporized by non-gravitational radiation, though. ( https://news.ycombinator.com/item?id=15352994 )
Finally I think intuitions break down before you get to the near field regime, and nobody can really tell you what to expect within a couple of wavelengths of the source of the gravitational radiation even some time before the merger. Certainly linearized gravity fails to produce gravitational waves thanks to an explosion of non-linearities. You can only really say that the dynamical spacetime is even more full of distortions in that regime. Unfortunately if we had a purely linear gravity in reality (i.e., if gravity wasn't itself a source of gravity), it is also the regime where one would expect several human senses would be obviously stimulated.
The fundamental nature of the force that rips you apart during spaghettification is exactly the same. And you would definitely feel that one.
It all boils down to how strong the distortion is at one extreme of your body, versus the opposite extreme. If it's about the same, you won't feel it. If the difference is sizable, you would feel it to some extent. If it's very large, it's a meat grinder.
I am not an astrophysicist, but was also wondering the same thing.
Gravitational waves move at the speed of light. Here is a graph showing the wavelength of gravitational waves from various sources
http://www.tapir.caltech.edu/~teviet/Waves/gwave_spectrum.ht...
The Ligo sensitivity range is about 10^6 meters. The speed of light is about 3*10^8 m/s. So peak to trough a few hundred per second. Much higher frequency than earthquake.
(Again, assuming an amplitude somewhere between perceptible and lethal, and assuming you're protected from other almost certainly lethal forms of radiation at that distance)
Edit: A sibling comment has a physics exchange link to a proper answer
https://www.youtube.com/watch?v=QyDcTbR-kEA
If you turn it up real loud and press your hand against your speaker maybe it would be some idea of what it would feel like.
To make things dangerous I reckon you'll need to have a strain on the order of 1, and since strain is inversely proportional to distance that would give a distance of 10^-11 ly, or around 100 km. Which is not a 'safe' distance to a black hole in any scenario.
You'll need to simulate the black hole merger to figure out where exactly it would be unsafe, but it looks like it would be distance that's pretty unsafe even without the merger.
In an otherwise expanding vacuum solution, the radiated momentum just propagates to future null infinity. Since we have other matter in our universe, the gravitational radiation can donate some of the original momentum to matter outside our chosen region, causing bits of matter along a lightlike path to move a small amount (or if you want to switch to an energy picture, ordinary matter outside our chosen region will become a tiny bit hotter upon feeling the gravitational radiation).
Although the amount of stress-energy-momentum radiated out of our region comprising the inspirallers is enormous (and at peak is so brief that the power is almost unimaginably enormous), the coupling of gravitational radiation to matter is extremely weak, so there will be very little scattering or absorption by matter outside the region. Consequently, most of the momentum crossing to the outside of our Schwarzschild-like boundary around the merger will still go to future null infinity.
It's this weak coupling that leads to your intuition about a human having to be very close to the merger itself in order to feel anything noticeable from the gravitational radiation.
By comparison one would expect balding to happen so that we recover a no-hair state from the merged BH, and there are decent reasons to expect more than gravitational radiation to be shed during balding. Additionally the individual BHs may have a lot of energetic particles entrained around them, and much of that will be moving on geodesics conducive to extremely high energy interactions (think of a pair of BHs whose rotational axes are parallel but with each BH dragging its accretion disc in the opposite CW/CCW direction, and we can add in extreme inverse Compton scattering just prior to contact as the photon rings around each BH interact relativistically with charged particles around the other). And of course this picture is likely to be much more dramatic in the case of an NS-BH merger.
Another way of thinking about this is that the build-up of momentum due to gravitational interactions is typically slow (and steady) but may have no upper limit, and that's the source of danger rather than a quick (and briefly high amplitude) gravitational interaction that doesn't take away more than a few percent of the built-up momentum of the matter at and near the source of the burst of gravitational radiation.
A human being close enough to the merger to feel the effects of gravitational radiation is thus likely to be feeling an awful lot more from excitations in the non-gravitational fields, or alternatively, the nearby human being is at risk of collision with ultrarelativistic (i.e., ultra-high-momentum) matter.
Unfortunately, for gravitational waves this is trivial, since they are vacuum--so T^{\mu\nu} itself is zero, and its covariant divergence is trivially zero.
There are ways to mathematically compute the "energy carried away by gravitational waves" from an isolated system like a black hole merger, but you have to use global methods to do it. For example, you can compare the ADM mass with the Bondi mass of the system; the latter decreases over time as GWs carry energy away, while the former stays the same.
On that last point, the latter (ADM) always stays the same, doesn't it? In early spacelike slices when the binary system is radiating basically nothing, the quantities you will find in the GWs in later slices are just clustered around the black holes.
Mass in General Relativity will give anyone a headache; I was trying to side-step that without being caught shuffling gravitational radiation off to the source side using pseudotensors. :-)
On spacetimes where it is defined, yes, I believe it does.
100km from the horizon.
"Distance" from the singularity does not actually make sense; the singularity is best thought of as a moment of time, not a place in space.
Sure, if you're a pansy. HOLD MY BEER!
Your buddy could be holding your beer for a very long time though, because gravitational time dilation at a given small distance outside the horizon increases with the mass of the black hole, and it will take you more of your own proper time to move through the region near a very large black hole than through the region near a small one.
http://www.businessinsider.com/what-gravitational-wave-feels...
http://www.scottaaronson.com/blog/?p=2651
The alternative take is that LIGO's detectors are unfathomably sensitive, detecting when its ~4km arms stretch by just 10^-19 meters. That's a 10,000th the width of a proton, where the proton is just a 100,000th the width of an atom, and the atom is about a 1,000,000th the width of a hair.
Wow. Hearing the sensitivity described in those terms is absolutely mind-blowing.
"To understand how sensitive the LIGO is, imagine each arm stretched out as far as the sun. Even if we had the resources to build an object this big, we still would not be able to get people to understand this intuitively at all."
So from the article:
> Black holes [merging] produce gravitational waves but not light.
So really, if you were orbiting such a pair of about-to-merge black holes, the gravitational waves produced by the merger would cause just nm-scale fluctuations?
Also, 1 AU seems awfully close to a pair of orbiting ~25 solar-mass black holes. I skimmed the paper, and didn't see anything about how the orbital distance evolved, leading up to the merger. One could probably calculate that from the mass and spin estimates, it's over my head. So maybe, at 1 AU, the about-to-merge black holes would look effectively like a point mass. Anyone want to venture a guess?
https://en.wikipedia.org/wiki/Accretion_disk
A 25 solar-mass BH is about 150km in diameter, and the gravitational waves emitted won't be appreciable until the two BHs had spiraled inward to a separation of a few hundred km. You would need to be roughly 1,000 km away to experience a 1% strain during the merger
https://physics.stackexchange.com/questions/235285/how-stron...
I don't think spin is important at the order-of-magnitude level (for naturally occuring BHs).
"we find that the data strongly favor pure tensor polarization of gravitational waves, over pure scalar or pure vector polarizations"
..taken from the paper. Thanks!
Any gravitational wave polarization can be considered as a tensor. There are several constraints that reduce the dimensional of that tensor though. For example, it must be symmetric and thus reducing its dimension from 16 to 10. Further constraints reduce it to 6. For physically meaningful waves (under the most accepted theory of gravitational waves), all but 2 of those are 0. This leaves us with 2 polarizations of waves. One of the polarization applies only on the diagonal (of the tensor) and the other on the anti diagonal.
From this background, I interpret "we find that the data strongly favor pure tensor polarization of gravitational waves, over pure scalar or pure vector polarizations" to mean that the polarization was not purely of the diagonal polarization and was instead a combination of the two. Alternatively, it could be a property that the tensor representation is more robust to noise or that a non-standard theory is correct and the polarization doesn't fit cleanly into the accepted theory.
[1]: http://eagle.phys.utk.edu/guidry/astro616/lectures/lecture_c...
Here scalar means that the field that describes the phenomenon can be described as a single scalar value at each point of space, like density, as is the case of sound waves.
Vector is more complex; although "charge" is a scalar, electromagnetic waves do not propagate by inducing charge in the surrounding space, but by propagating through the free-space Maxwell equation (that is, where the charge density is zero). So the polarization of an electromagnetic wave can be described by a single vector at a point, and the measurement of the magnitude of the wave will depend on how closely the measurement axis corresponds to the polarization axis for a polarized wave. For a general wave, it can be described as some linear combination of the orthogonal polarizations.
Although "tensor" is a general linear object of which vectors are a subset, in this case of gravitational waves, we require a 2-tensor to describe the polarization of the wave. Effectively that means the polarization (the strength of the signal with respect to a given detector) can only be described by two independent vector that describe the evolution of the wave. Since the three detectors (Ligo Hanford, Ligo Livingston, and Virgo) are not exactly aligned with one another, it should be possible to get good evidence that the polarization cannot be adequately described by the superposition of two orthogonal vectors, but instead two independent pairs of orthogonal vectors.
There's got to be some interesting implications here for cosmology.
If there's a whole class of objects (black holes around 20 to 50 solar masses) that were previously thought to be virtually non-existent, and now turn out to pretty common, does that mean we can explain away at least some of the proposed dark matter?
What if we keep finding more non-radiant objects that still (presumably) made of ordinary matter?
Can these classes of objects account for the "missing" matter in galaxy rotation curves? Or would their distribution be simply wrong?
Exciting times to live in, for sure!
https://en.wikipedia.org/wiki/Massive_compact_halo_object http://iopscience.iop.org/article/10.1086/319636
We've looked for signs of black holes in our galaxy's halo (they would gravitationally lense nearby background objects like the LMC and M31 such that we could already pick out the distortions. Our galaxy may be unusual (Sag A* is fairly low-mass, for instance) but the density requirement for MACHO to be a large component of the flat rotation curve of most galaxies (ours being special) would seriously violate the Copernican principle. Moreover, it's really really hard to get a stable galactic evolution when you make MACHOs the sole invisible contributor to rotation curves.
Worst of all, baryon acoustic oscillations appear in the cosmic microwave background more and more clearly as we study it more closely, which effectively rules out large Jupiters/brown dwarfs/neutron stars, and nobody knows how to get enough black holes that survive billions of years when you have to have them already exist between reionization and recombination. But who knows, maybe we'll see a lot of signs of primordial BHs evaporating in halos by (big) surprise.
Yeah, the rate of intermediate mass black hole mergers was totally unexpected and has caused a bunch of active discussion on formation mechanisms.
In short, intermediate mass black holes are too big to be generated from star collapses, which means they (likely) come from smaller BH mergers. But because these things take so long (GWs radiate energy very slowly until the bodies are very close and fast), we didn't previously expect there to be large populations of them. It has been surprising to see that there are enough of them to sustain a pretty decent IMBH merger rate.
BH/NS and NS/NS mergers are exciting because they involve conventional matter and are likely to give off neutrinos and light as well as GWs. This means that EM followup is more likely to be worthwhile.
The smaller mass of neutron stars means they are more common, and the NS event-rate is expected to be much higher than the BH event rate. But BH events are louder due to the extra mass, so we can search in a much much larger volume of space, which so far has been favorable for BBH (binary black hole) merger detections.
Another interesting thing about BNS mergers is that, because they get closer/faster before merging, their signal should climb to higher frequencies and spends much, much longer in our sensitive band than BBH mergers (this is also true for lighter BBH mergers vs. heavier ones). This is really cool because it means that BNS mergers can be fit much more tightly to model waveforms, allowing for more precise parameter estimation (among other things) given the same peak signal-to-noise ratio.
It would be cool if we could hear a NS-NS collision of sufficient masses such that we could hear a BH being born for the first time.
Will we reasonably ever hear a supermassive BH collision? I would assume their loudness to rarity ratio is just too low.
LIGO's sensitivity range is in about the same range of frequencies as the human ear. NSNS mergers reach our sensitivity sweet spot for a few seconds; intermediate mass BHBH mergers get into the low end of our sweet spot. Supermassive black holes merge at very low frequencies outside of our sensitive band.
LISA is a planned space-based observatory that would be sensitive in those bands: https://lisa.nasa.gov/
> Will we reasonably ever hear a supermassive BH collision?
Hopefully! They'll certianly be looked for. There are some extremely massive SMBHs out there (e.g. Blazar QSO B0218+357), and it's reasonable to think that at least some of them are the result of mergers of SMBHs rather than, say, a rain of smaller BHs (and dust, gas and stars) onto an already big BH (which may also happen).
https://www.youtube.com/watch?v=vw2sLcyV7Vc
https://www.youtube.com/watch?v=ow9JCXy1QdY
http://newscenter.lbl.gov/2017/08/02/new-space-simulations-n...
It's just like how we have optical telescopes for visible light and radio telescopes for light at different frequencies. Different interferometer designs will pick up different phenomena based on what their sensitive band is.
I guess the main problem is that you'd need friction to slow down matter that's attracted by the black hole, so it doesn't just orbit it...
For one thing, it's probably not ordinary matter falling into the black holes. When ordinary matter falls into a black hole, it usually forms a bright, glowing accretion disk. We would see that with an ordinary telescope, especially given just how much matter would need to be accreted. (We're talking about dozens of suns worth of mass for each of these intermediate mass black holes!)
You can also have three-body interactions. A pair of black holes in a circular orbit at a decent distance will merge on a timescale of billions of years. But if a third black hole comes in and disrupts the orbit, it can knock those two black holes closer together, at which point the GW power gets much higher and the merge can finish on a reasonable timescale.
For these reasons, some papers I've seen suggest that there might be large collections of black holes that are dense enough for three-body interactions to be relatively common.
(Probably a very silly question)
1. It's infinite and homogeneous 2. It's finite but periodic (like the Earth; go straight long enough and end up where you were) 3. It's slowly varying, so that within our Hubble volume (the volume within the horizon receding from us at the speed of light, beyond which we can't see) everything looks isotropic; in other words, it varies, but slowly
So what you're saying is true from our position in space, but it should also (if points 1 and 2 are true) be true everywhere in space, and the question of the large scale structure of the universe remains valid.
Is this correct? I thought that it would produce a lot of light, but the light is more easily absorbed by interstellar gas and dust, so it's more difficult to see it.
Perhaps not the black holes doesn't emit light directly, but the surrounding gas will be extremely hot.
And when the two event horizons collide, the virtual particles should be very confused and scape in huge numbers, in a process like the Hawking radiation, but much bigger.????? I'm far from being an expert in this, so this is only a conjecture and unsupported handwaving. But I would be very surprised to confirm that the event has no emission of light.
Yes, but not every black hole is surrounded by gas.
> the virtual particles should be very confused
In general, physics does not work like this.
However, massive bodies experiencing rapid acceleration emit gravitational waves. This is something that happens due to a black hole's mass and not it's event horizon properties (in principle you can also detect neutron star interactions). But this is emitted due to the motion of the objects themselves, not from accretion disks (which may not be present for some black holes). So the event itself does not produce light.
I find it interesting that much ado is made about "black holes" existing when by the theory by which they are proposed, they cannot exist in our finite universe. The time dilation effects, which is a part of the theory, will not allow any such theoretical entity to be formed in our finite time universe.
With that said, the observations of LIGO do not confirm the existence of such entities as "black holes". What these observation do do is indicate that there is something happening. We just don't know yet what this is. Going down the rabbit hole of sticking to the "black hole" model only engenders ignorance.
These are interesting experiments and results and it behooves an open mind to try to further our understanding of what is causing these observational event. Unfortunately, the "dogma" of worshipping Einstein and his "holy works" only locks us into a position of not furthering our understanding.
Note: I have used "worshipping" and "holy works" specifically because of the attitudes of those who will not countenance any different views from Generally Relativity et al. Whether or not, GR and SR have long term merit is still a question being pursued. Some variation of these may be more suitable. But that doesn't mean that GR and SR are correct (as is the usual defence given).
The last couple of decades have been an interesting case study in terms of an unwitting increase in dogmatic push for specific theories and models in quite a few areas. When it boils down to it, these theories and models are subject to change and even throwing them out for different and better models.
To get emotionally caught up in defending a specific theory and model as the "Truth" does not put science in a good light for the general populous. I have said it elsewhere, science is about the discovery of the universe around us and finding applicable theories and models that are useful for our understanding. If you want "Truth" then go and study philosophy and religion.
Every theory you want to follow needs to have a good defence, but not to the extent of getting so emotionally caught up in it that you ignore discrepancies and results that disagree with your preferred theory and model.
How often has the "Truth" that the general science community has promulgated been overturned? We need to be careful not to get so entrenched in a specific viewpoint that we cannot see the merit in other theories or models. It is history that tells us to be careful here.
Also, he Hawking radiation is an intrinsic property of the black holes, you can't disconnect it. I doubt that anyone has calculated if the Hawking radiation increase or decrease during a black hole - black hole collision. My guess is that it increase and if you are nearby you would see a flash of light. The technical detail that the light doesn't come from inside the black holes is not meaningful. The whole black hole - black hole collision also includes all the Hawking-like radiation emitted.
Mass of Universe is estimated to be of 6e51kg. Mass of Sun is 1e25kg. This event is about 50 Sun masses. So that one event is about morphing 1e-26 part of Universe. I suspect that matter collapsing into black holes happens significantly more frequently than that. Do we have enough non-black-hole matter available for our (humanity) life time?
Yet worth to mention that black holes "return" mass by not only Hawking–Zel'dovich radiation but also by such events - this particular merge emitted 3 solar masses as energy.
It's how we get the mass of many interstellar objects, and it's how we know that dark matter exists.
http://astro.physics.uiowa.edu/ITU/glossary/keplers-third-la...
https://www.wired.com/story/strange-noise-in-gravitational-w...
[1] http://www.preposterousuniverse.com/blog/2017/06/18/a-respon...
There is no practical way to harvest this energy. Gravitational waves interact very weakly with matter. This is part of why they are useful for observations: GWs can travel from the core of violent events unmodified, unlike light, which gets blocked by surrounding matter. You can't see the center of a core collapse supernova with light, but you can see it with GWs and neutrinos. They also won't get bent by EM or gravitational fields, meaning that the direction they come from in the sky points straight back to the source. And unlike very high energy gamma rays, they don't pair produce into electrons.
This all makes them great for astronomy and totally useless for extracting energy.
So, what happens to the energy - does some of it get converted into 'normal' potential energy by changing the (amount of gravity? gravitational fields?) of the stuff that it passes through - the weak interaction that you refer to?
And, if it interacts very weakly, does all of the energy eventually get used up this way - do GWs get 'used up' before they travel across the universe?
(Probably a meaningless question): can GWs hit the edge of the universe, and if so, what happens then?
Yup. It's like ocean waves carrying energy. The difference is that it's hard to interact with GWs, so instead of "riding" them and capturing their energy, you find them mostly passing through you. They have tons of energy, but very little of it is dissipated back into matter.
In a flat universe, they go out to lightlike infinity without redshifting, but with the amplitude falling off 1/r rather than the 1/r^2 of light. Eventually they become too weak to be detected unless we can detect a single graviton of a particular frequency (which is going to be unimaginably difficult technologically).
> can GWs hit the edge of the universe?
This is an excellent question! Neither of the above types of universe has an edge; there is a lightlike infinity that electromagnetic and gravitational waves head towards. What's there? Who knows! For all practical purposes, these waves just depart from us and everything we can see, never to return.
We can have an edge to a universe that is contracting rather than expanding, or one that eventually contracts.
This is really hard to think about and I had to look around, and found http://jetp.ac.ru/cgi-bin/dn/e_042_06_0943.pdf [I sadly have had almost no previous exposure to the authors, and somewhat regret it; this paper is from the "Third Soviet Gravitational Conference" in 1972. Wow!]
It will take more time to digest it than is reasonable for a real response, but section 3 is relevant for a universe that is like ours in most ways except that it won't expand forever but rather will eventually collapse. However, essentially (and this matches my intuition), for a typical source the gravitational waves will radiate outwards from the source, slow down, and come back. Depending some choices of Friedmann parameters, they could even return as convergent waves focusing on whatever moved purely timelike from the source (e.g. the remnant of the merger) during the GWs lightlike journey; more likely they'd smear out in a larger region; and possibly they might not actually converge (or smear into the same general region) until very near the future singularity having undergone gravitational blueshifting. After converging they'd depart, and rapidly get lost in nonlinearities. This is not super-different from ripples on a pool that spread out, bounce back and lose structure.
This also raises the question of what significantly blueshifted gravitational waves might do. Drag matter a bit faster towards the future singularity is my guess. It also raises questions about constructive interference, but in that direction lies strong gravity, and there's not going to be an answer to those questions in the linearized gravity that we use to model gravitational waves.
I answered some of your other questions in other comments on this thread, I think. If not, ask again!
There have been plenty of technologies pioneered by the collaboration in the development of the detectors - control of optical cavities via radio frequency signals being one big one, and low thermal noise monolithic silica fibre suspensions being another. The discovery of gravitational waves, however, simply improves our understanding of the universe and has no known practical applications.
It's great to live in a time when countries are willing to fund such bold leaps into the unknown, without obvious monetary pay-offs.