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On June 15, the LIGO team announced
their second detection of a gravitational wave.
It got some press but certain questions
were not well-covered.
That's what I'm going to do now and following
that, I'll get to the solution to the nuclear physics
challenge question.
On September 14, 2015, the Laser Interferometer Gravitational
Wave Observatory, LIGO, detected the gravitational waves
from the merger of two black holes.
We reported it here when the discovery was officially
announced in February.
The signal was in the form of oscillating changes in the path
lengths of the LIGO interferometer arms
as the gravitational wave stretched and compressed
the fabric of space as it passed by.
These oscillations echoed the final 1/10
of a second of the end spiral and merger
of a pair of black holes, each around 30 times
the mass of the Sun.
This incredibly important observation
was hailed at the time as representing
the dawn of gravitational wave astronomy.
However, that's only true if we ever detect
another gravitational wave.
Well, now we have.
On December 26, LIGO again observed the merger
of two different black holes.
This time, they're a bit smaller,
at 14 and eight solar masses.
OK.
So what are the burning questions
about this new announcement.
Question number one, are we sure?
Well, the first detection in September
was pretty unmistakable, even to the eye.
The waveform looked just like what the researchers were
expecting from theoretical calculations, a periodic change
in the interferometer arm lengths
that increased in both amplitude and frequency
as the black holes approached before dying
away again after the merger.
Also, the same signal was seen in the two LIGO
detectors located in Livingston, Louisiana
and Hanford, Washington.
It's calculated that LIGO would need
to observe for over 200,000 years
to see the same signal arise from random vibrations.
Or another way to put this is that there's
a one in 20 billion chance that this signal was
from random vibrations.
The weaker December signal doesn't look nearly as clear,
at least to the eye.
This new signal caused a change in LIGO's arm lengths
of about 1/1000, the diameter of a proton
and a few times smaller than the more powerful September signal.
But it's still a highly certain detection.
There's only a one in 10 billion chance of this one just
being due to random noise.
We're able to be this certain because the signal lasted much
longer, nearly a second compared to 1/10
of a second of the early detection.
That's due to the fact that the smaller black holes
took longer to coalesce as they became very close.
Two more factors help with the certainty.
One, extremely sophisticated signal processing technology
is used to "see" the signal.
It's the same very well-understood tech
that we use to process radar signals and at this point,
we have a lot of confidence in how this works.
Two, exhaustive computer simulations
test how often this signal processing
tech gets tricked into falsely reporting a detection.
The answer is almost never for signals of the sort that
were seen last year.
As a testament to LIGO's carefulness,
they already knew about the December signal
when they announced the first gravitational wave
detection back in February.
However, they hadn't had time to give due care to the newer
signal so they decided to keep quiet about it
until they were sure sure.
In actual fact, LIGO probably saw a third gravitational wave
back in October but it wasn't quite strong enough
to satisfy the team's strict standards
and so they're not calling it a detection.
If it were real, it would also be from merging black holes.
Question number two, did we learn anything?
It's kind of amazing that the signals observed look exactly
like what we expect them to from the predictions
of general relativity.
Beyond the detection of gravitational waves,
this is another awesome validation of the theory.
We now have more confidence in our understanding
of the space-time around black holes.
We also now know that our estimates
of the number of binary black holes
in the universe and their masses are at least
in the right ballpark.
This is good because it means we're
going to see a lot more black hole mergers.
As we do so, we'll start to nail down
the astrophysics of black hole formation and growth.
And question three, what will we see in the future?
So far, we've only seen black holes merging.
That's not surprising.
They were always expected to produce
the strongest signal, which means they'd be detectable
more often.
We should eventually see mergers between two neutron stars
or a neutron star and a black hole,
as well as supernova explosions.
But these events need to be a lot closer
to be detectable by LIGO so we have to wait longer for one
to happen because we're sensitive to a smaller
volume of the universe.
At the moment, LIGO isn't particularly
good at figuring out the direction
that the wave came from, which is determined
by the time difference in the signal between the two
detectors.
But that only limits us to a long streak across the sky.
When European Virgo comes online later this year,
we expect a massive improvement in our ability
to locate the source of the waves.
Then we can turn all of our telescopes to that spot
as soon as a wave is detected.
Who knows what we'll see?
OK.
For our last challenge question, we
asked you to calculate the probability
that an alpha particle-- so a package
of two protons and two neutrons--
would tunnel out of the nucleus of a polonium-212 atom,
causing the atom's radioactive decay.
You had the half-life-- so the average time
for the decay of a polonium-212 nucleus.
It's 0.3 microseconds.
You needed to figure out how many times the alpha particle
would encounter the walls of the nucleus in this time.
All those individual probabilities
combine to give you a 50% chance of decay
after 0.3 microseconds.
To do this, you needed to assume that the alpha particle bounces
back and forth between the walls of the nucleus
with a constant velocity.
That combined with the size of the nucleus
gives you the number of encounters with the wall
and so the number of tunneling chances in that 0.3
microseconds.
You get the alpha particle velocity
from its kinetic energy, which I gave you,
and you get the size of the polonium nucleus
from the nucleus size relationship of the Fermi
model.
You'll get that there's approximately a 10
to the power of minus 15 chance of the alpha particle tunneling
on each encounter.
And that's actually close to the number
you get from doing this with quantum mechanics
so that's cool.
The details of the calculation are linked in the description.
And the extra credit question asked,
what physical distance does the particle actually tunnel?
For this, you needed to calculate
how far from the center of the nucleus, the Coulomb
potential of the nuclear protons,
reaches the 8.78 mega electron volts of the alpha particle's
kinetic energy.
The answer is 27 femtometers.
So how far did the alpha particle tunnel?
Well, it started tunneling at the edge
of the nucleus, around seven femtometers,
and tunneled to 27.
So it's basically teleporting 20 femtometers, give or take.
The details of this calculation are also in the description.
OK, nice going if you got either part right.
We chose three random correct answers
from both the main and extra credit questions-- names
listed right here.
If your name appears, you're a winner.
No, you're all winners but if you see your name,
you're the most "winnery" of all.
You should email your name, address, US t-shirt size,
and let us know which of these awesome t-shirts you'd like
and we'll get them out to you.
And I'll see you next time for a brand new episode
of "Space Time."
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