Thank you to Brilliant.org
for supporting PBS Digital Studios. Black holes are crazy enough on their own – but crash two together
and you end up with this roiling blob of inescapable space
that vibrates like a beaten drum. And the rich harmonics of those vibrations,
seen through gravitational waves, could hold the secrets to the nature
of the fabric of spacetime itself. Today on space time journal club
we’ll explore two papers that claim to have detected
black hole harmonics. We’ll also give you the latest updates
on the most recent – and in some cases quite bizarre -
LIGO detections. When physicists talk about black holes
they’re usually referring to highly theoretical objects –
static, unchanging black holes viewed from “infinitely” far away. This makes everything clean and simple
enough to attempt the already notoriously complex calculations of black hole physics. But real black holes are created
in the violent deaths of massive stars, and there’s
nothing clean about that. We now know
that black holes also merge – and in the process produce
gravitational radiation that we’ve only just managed
to detect with the miraculous work of the LIGO and VIRGO gravitational
wave observatories. In the instant after its merger, the new, joined black hole looks nothing
like the idealized theoretical black hole. Imagine it: two event horizons – two roughly spherical black surfaces
that are literal boundaries to our universe. They spiral together and touch
– instantly becoming a single surface. Technically, in that instant
we go from two black holes to one. But in the beginning this new black
hole looks nothing like its progenitors. It’s not even close to spherical
– it’s dumbbell-shaped, and then it’s an elongated blob,
and then it’s an oscillating spheroid – like a ball of water wriggling in space. But what exactly is oscillating here? The event horizon seems to define
the surface of the black hole, but really it’s the fabric of spacetime
itself that’s vibrating. The two inspiralling black holes
make powerful spacetime ripples – gravitational waves – which intensify as the black holes approach merger, only becoming observable
in the last fraction of a second. And then the merged black hole continues
to radiate these spacetime ripples as it oscillates, but these quickly die away as the black
hole settles into its final static form. This final phase is called the ring-down – an expression comes
from the analogy with a bell. When struck, a bell vibrates
with many different frequencies – many overlapping harmonics. As those vibrations give up their energy – in this case to sound waves – the vibrations fade.
The bell rings down. A “struck” black hole also vibrates
with many different harmonic frequencies. The harmonics of a vibrating sphere – be it a blob of water
in zero-g or a black hole – are analogous to the harmonics
of a vibrating guitar string or piano wire. In the latter cases
we can describe a vibrating string as a series of standing
sine waves of different frequencies, all happening at the same time. The lowest frequency the string
can support is called the fundamental mode – it’s usually the strongest or loudest,
and defines the note – middle-c, f-sharp, whatever -
played by that string. Higher frequency modes are called overtones,
and they provide richness and texture to the sound. The full set of possible frequencies
a string can support are called its harmonics. The harmonic oscillations of 2-D surfaces – like drum skins, bells,
or the event horizons of black holes – are a good bit more complex than in 1-D. In the case of the event horizon,
or any spherical-ish surface, we break down the oscillations not into
sine waves but into spherical harmonics. These are a set of functions pretty
analogous to 2-D sine wave on the surface of a sphere, and each spherical
harmonic can represent a single, pure oscillation on that
spherical surface with a set frequency. A harmonic oscillation that decays
over time is called a quasinormal mode. For a black hole, another way
to think of its quasinormal modes is as a set of gravitational waves
trapped in orbit around the black hole. They leak away over time, but while present
they warp the shape of the event horizon. OK, so a black hole can ring like a bell
when struck – in that case a black hole merger
is the biggest hammer strike of all. But what does the ring-down
of a black hole really look like? Well, we can answer that be asking what
harmonics are present in that oscillation, and how quickly do each
of those harmonics fade away. Many scientists had assumed
that in order to see the overtones you’d need to look at the tail
end of the ring-down, when the black hole was approaching
a more spherical shape. They thought that right after merger
the black hole would be too chaotic – the oscillations should be “non-linear” or in other words not well represented by
adding together a simple set of spherical harmonics. The problem is, at the tail-end
of the ring-down the LIGO signals are probably too weak to detect the overtones. Matthew Giesler, Max Isi, Mark Scheel
and Saul Teukolsky of CalTech and MIT went against this these prior
assumptions in their recent paper. They looked for overtones in the ring-down
from right at the point of black hole merger. Now this wasn’t a real black hole merger
– we’ll get to that shortly. Giesler and team first they found
the harmonics in a fake black hole merger. Specifically, a simulated merger by the SXS
– Simulating Extreme Spacetimes - project basically the result of teaching
a supercomputer general relativity and, among other things, telling it
to collide thousands of black holes. The advantage of first trying this
with a simulation is 1) you don’t have to use a signal
degraded by a billion years of travel, and 2) you know exactly
what parameters went into the signal – in particular black hole mass and spin, so you know if you got the right answer
when you try to predict these values. The researchers found
a few very surprising things. First, the waveform was nicely simulated
by spherical harmonic oscillations right from the point of merger, so it was
not the chaotic mess previously assumed. Second, when the ringdown begins some
of the overtones are actually stronger than the fundamental mode,
even though they do tend to die out more quickly. This means that these overtones
are potentially detectable in the real merger signals
from LIGO and VIRGO. And THAT has some
very exciting implications. The rich structure of overtones
in a musical instrument can tell you what instrument
you’re listening to. Similarly, the overtone structure
of a black hole ringdown can identify the fundamental properties
of that black hole – namely its mass and spin. The researchers found that
they could pinpoint the mass and spin of the simulated black holes with much
greater precision than if they’d just used the gravitational wave signal
from the lead-up to the merger. In astronomy, the analysis of the different
frequencies of light is called spectroscopy. So this sort of frequency
analysis of gravitational waves is being called gravitational wave spectroscopy. Now for this to be useful probably we’d want
to look at some real black hole mergers. And yes - The team totally did this – and reported the results in a follow-up paper, adding Will Farr to the team
for this one. Isi et al. looked at the merger and ring-down signal
from the largest black hole merger we’ve seen. Which, in fact, was also the first
one LIGO reported: GW150914 – a pair of black holes, each 30
or so times the mass of the sun, spiraling into each other
one and a half billion light years away. The team analyzed the harmonics
in the gravitational wave ring-down from this event and claim a likely
detection of at least one overtone – detected with a confidence of 3.6 sigma. That means it seems very likely
they really detected the overtone, but to effectively eliminate
doubt we’d want more observations. By analyzing the harmonics,
the team calculates the mass of the final black hole as 68.5 solar masses. They also get a spin for the final black hole – a so-called dimensionless
spin magnitude of .69 – where the spin magnitude
can vary between 0– not spinning at all or 1
– spinning as fast as possible. .69 means this is a rapidly
rotating black hole, which is unsurprising seeing as it just absorbed
the orbital angular momentum of two black holes. Both the mass and spin derived
from the ringdown are consistent with the estimate that
was previously obtained by analyzing the entire waveform but ignoring the
overtones. This is important, because the overtone
analysis ONLY looked at the ringdown, so this tells us that all information
on the nature of the final black hole properties is embedded
in those final oscillations. And that brings us to the last,
and perhaps coolest application of this technique – testing Einstein. General relativity predicts that black
holes should be completely defined by three properties –
their mass, spin, and electric charge. It doesn’t matter what fell in
to make the black hole – atoms, photons, dark matter, monkeys – all that information should be lost,
leaving only 3 properties. And this is the no-hair theorem
– black holes have no hair. Well, at most 3 hairs. And astrophysical black holes
are also expected to have no electric charge, so mass and spin should define everything – including the nature of the
oscillations during ring-down. The researchers test the no-hair theorem
by checking whether the frequency of oscillations and the time
for the decay of those oscillations agrees perfectly with Einstein’s predictions. They do – at least within
the uncertainties of the experiment. The oscillations are consistent with a
black hole purely defined by its mass and spin. The authors claim this as tentative
support for the no-hair theorem. It’s a long way from
the confirmation of the theorem – but with the analysis of more black hole mergers, any deviations from the pure-general
relativity, hairless black hole will either become apparent or become
less and less likely to exist. But for now, Einstein reigns supreme. And what about those new mergers? It’s been
a while since we saw a big press release from LIGO. The last was the incredible binary
neutron star merger that was also detected across the electromagnetic
spectrum as a giant explosion. Well, rest assured that detections have continued. LIGO and VIRGO have been in their
3rd observing run since April 1st after massive upgrades to sensitivity,
and this run will last for one year. The LIGO team typically waits until the run
is complete to announce findings because it takes a while
to fully confirm each signal. But the team isn’t nearly
as secretive as they once were. LIGO has a publicly available
alert system so that astronomers can follow up gravitational
wave detections with other telescopes. LIGO’s gravitational-wave candidate event
database reveals many, many candidate detections – many of which will prove to be real. So far the list of high-confidence events includes
around 20 new black hole-black hole mergers, a few black hole-neutron star,
and neutron star-neutron star mergers. The observatories are seeing a new
event roughly every 5 days on average, but sometimes on multiple days in a row. And on August 28th, two black hole
mergers were seen separated by only 20 minutes, and potentially
in the same part of the sky. This is currently looking
like just a coincidence, but if not it’ll be hard to come up
with a plausible explanation for why two pairs of binary black holes
should merge near each other at the same time. So, long story short –
the initial promise of LIGO and the first detection of gravitational waves
really seems to be panning out. Gravitational wave astronomy
is now really a thing. We’re seeing many, many mergers
of black holes and neutron stars, and we’re learning an awful lot
about these objects. And with the new subfield
of gravitational wave spectroscopy, we can now listen to the harmonics
of ringing black holes, and through them better understand the
fundamental nature of extreme spacetime. Whether you want to know the number of
possible multiverses or the likelihood of aliens, to challenge yourself
in the advanced levels of science you’re going to need to have a solid
understanding of probability. Brillaint.org has a new course
on probability fundamentals that include interactive challenges
and problems to solve. Honestly, that's the only way
to get math - to do it. You can Learn probabilistic basics,
such as fairness, expected value, and symmetry,
in their course Probability Fundamentals. Effective learning is about problem solving. To learn more about Brilliant,
go to brilliant.org/Spacetime.
