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."
[THEME MUSIC]
