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5. Frontiers/Controversies in Astrophysics: Planetary Transits
Poziom:
Temat: Edukacja
Professor Charles
Bailyn: I have spent a very
enjoyable weekend reading your
Pluto comments.
No, that was fun.
It is a surprisingly--it's a
surprisingly deep topic.
There are technical issues
about how orbits of planets
work.
There are these interesting
cultural and political currents
that underlie the whole thing.
And also some sort of deep
philosophy, or what the literary
professors like to call
"theory,"
about what it means--what it
means to name something,
and what the consequences of
particular names are.
And so I thought I would make a
couple comments on the Pluto
thing first, before we get back
to the Hot Jupiters.
Let's see.
The first thing I would
say--let me encourage you all,
when you get this kind of a
question--answer the question
that's asked.
The biggest problem in the
answers that I saw was that
sometimes you just didn't
address the specific question
that was asked.
What I asked was,
"To what extent is the Pluto
controversy a scientific
controversy?"
You don't answer that by a
narrative describing what
happens.
If you say, "Well,
they discovered Eris,
and then that threw the
scientific world into confusion,
and then they had this big
meeting and there was all this
fuss, and then people started to
get involved who weren't
scientists,"
and so forth--that doesn't
answer the question.
Because the question was,
"To what extent is this a
scientific controversy?"
There are two possible
categories of answer to that
question.
One is, "Yes,
it is primarily a scientific
controversy."
And the other category is, "No.
It was primarily not a
scientific controversy."
And if you didn't say one of
those things,
or something somewhere in
between, then that's not kind of
responsive to the question.
I would say that you could
answer that particular question
in this case,
in both directions,
perfectly well.
If you want to make a case that
it's a scientific issue,
you say, "Look,
classification is very
important to science."
I made that point in class
on--a week ago,
and that, you know--you've got
to have your classifications
right in order to understand
what's going on.
And what has happened?
Here is--new data has come in,
which has thrown the old
classifications into question.
Although, it should be noted
that there wasn't officially a
definition of "planet" that goes
back to antiquity.
And one of the things they were
trying to do was to create one.
But that--as new data came in
from the outer parts of the
Solar System,
we had to revise our
classifications.
And this is a key point of
science, and therefore the whole
thing is, at root,
a scientific issue.
But you could also argue the
opposite, in that,
you know, the scientific issue
was not really in doubt.
Nobody was questioning whether
Pluto and Eris and all those
things ought to be in the same
category as Jupiter.
Clearly they're not.
That wasn't the issue.
The reason this became so
controversial is because there
were a lot of people who
--scientists and non-scientists
– who thought that it would be
nice if Pluto could remain a
planet.
And therefore,
they came up with these rather
convoluted definitions,
in order to maintain the idea
that Pluto should remain a
planet.
And then, they got into
trouble, because fifty other
things would,
therefore, also have to be
planets.
But it's rooted in a
non-scientific desire for Pluto
to remain a planet,
and for very few other things
to be admitted to this pantheon.
And that is fundamentally not a
scientific thing,
and you could argue that that's
the whole root of the entire
issue.
Now, one of the interesting
things is that these
non-scientific things affect the
scientists too.
A lot of you quoted this guy,
Alan Stern, who's a
planetary--a famous planetary
scientist,
who objected to the way it all
ended up by saying,
look, one of the definitions
that they've put down is that
you have to clear out your
orbit.
And Pluto doesn't make it in
that--in that context,
because it crosses the orbit of
Neptune, which is a much bigger
thing.
But, Stern goes on to say,
Neptune also crosses the orbit
of Pluto.
And so, obviously,
there's some hidden assumption
here about, you know,
the thing that's much more
massive counts,
and the thing that's less
massive doesn't count.
But that hasn't actually been
stated, and so this is a lousy
definition.
And so he objected on
scientific grounds to this
definition.
And some of you noted that
Stern is the principal
investigator of the New Horizons
Mission, but I don't think you
noted the implications of that.
The New Horizons Mission is a
planetary probe that is on its
way now to Pluto.
And the reason that it was
launched--Al Gore was actually
very enthusiastic about this
when he was Vice President.
The reason that this was
launched was because Pluto was
the only one of the planets that
Voyager didn't go to.
And so, we have these fabulous
pictures of, you know,
Saturn and Uranus and Neptune.
We have no fabulous pictures of
Pluto because nothing had gone
there.
And in the late 1990s people
thought, well,
this is dumb.
There is a planet out there
that hasn't been explored.
We've got to have a mission to
go to this planet.
So now, it's seven years
later--the mission just went
past Jupiter actually.
So it's on its way out,
and all of a sudden,
the thing that it's going to
has been demoted.
This is awkward.
[Laughter.]
You know, we're spending 100
million dollars of your money to
go see the last of the planets,
and now it's not a planet
anymore.
And here's the guy who's in
charge of that mission.
And so, of course,
he objects to the change in
definition that demotes his
object--which he's spending
fifteen years of his life and
100 million dollars of your
money to study--has now been
kicked out of the realm of the
planets.
So, not surprising that he
would take that particular point
of view.
Mike Brown's another example.
That's the guy who discovered
Eris.
And he has a lovely thing on
his web site about how "planet"
ought to be a cultural
definition.
And he kind of advocates for a
thing where, because it's
cultural, you've got to keep
Pluto in.
And because you've got to keep
Pluto in, you've got to allow
anything bigger than Pluto.
So you just have an arbitrary,
culturally enforced cutoff at
the mass of Pluto.
And then--and things that are
more massive get to count also,
because otherwise it would be
unfair.
Look what this does though.
It means Eris is a planet and
none of these other things are,
which means Mike Brown is one
of the four people in the
history of humanity who has
discovered a planet.
[Laughter.]
And so that's a very convenient
definition.
And so, you know--and then he
actually very graciously goes on
to say, well,
I'll settle for being the
discoverer of the largest dwarf
planet until a bigger one gets
discovered.
But you can see,
he's not really happy about it.
He'd much rather the thing be
decreed the tenth planet,
and perhaps reasonably so.
So, the scientists are also
affected by these kinds of
things in ways that you have to
think a little bit about
before--as you interpret what
their take on the scientific
parts of the controversy really
are.
So let me summarize all of
this--this is going to be--I
mentioned in the first class
that I was going to tell fables
about science with morals
attached to them,
and that you could then explore
these further in your optional
paper, if you choose to write
one.
So here's a fable,
which is "The Demotion of
Pluto."
And one could ascribe a variety
of morals to this,
but let me write down one
version that happens to appeal
to me,
which is just the fact that I
think science can be affected by
culture.
And you need to keep your eye
on that kind of thing when you
interpret things that scientists
say;
particularly if they're saying
it to journalists.
They're often much more
circumspect in the things that
actually get published in the
journals.
Okay.
There was one kind of argument
that rubbed me the wrong way a
little bit when some of you said
it,
which was--people had a little
bit of a tendency to say,
you know, all this definition
and classification stuff,
that's--the word ‘trivial' or
‘silly' is sometimes used.
That's kind of unimportant,
and it detracts from the
science.
And, I have to say,
I don't agree with that.
I think it's important for the
science to get these
classifications right,
because otherwise you don't
know how to describe what you're
looking at.
You don't know how to interpret
it.
Oh--I should mention something
about grading,
I guess.
It was six points on that
problem.
The way I did it was,
I started out--everybody sort
of started out with five of
those six points,
and if you said things that
were incomplete or incoherent or
dumb in some way,
you got points taken off.
But there was also an extra
point you could get for being
especially coherent or
especially original or
interesting,
or just generally waking me up
after I'd read forty others of
them.
I bring this up just to point
out that if you get five out of
six on that particular problem,
that doesn't mean you've done
anything wrong.
It wasn't that we started with
a perfect score of six and
started subtracting things off.
It just meant that I felt that
there were others in the pile
who were somehow more coherent.
We'll hand these things back at
the end of the class,
by the way.
And I'll make some remarks
about grading of the overall
problem set at the end.
Okay.
Another general point that
showed up in other parts of the
problem set was a kind of issue
about velocities and the center
of mass.
Let me--here's the center of
mass of some orbit,
and, of course,
that's not a physical object.
That's just a point in space.
And the key thing to understand
about the center of mass is,
the center of mass doesn't
move.
It doesn't move in space.
That's a fixed point in space.
So, this doesn't move--actually
I should be more precise.
Its motion doesn't change.
So, if it's stationary in some
coordinate system,
it sits there.
If it's moving at some
velocity, it continues to move
at precisely that velocity.
So the--it's--and then,
you can redefine the coordinate
system so it doesn't move in
some other coordinate system.
But it doesn't go around in
circles or ellipses or anything.
What does go around are the
things going around it,
one of which is the planet,
which is over here--the other
of which is the star,
which is over here.
And the way these two things
move, they have to stay one on
each side in a straight line
that--woops,
I'm going to miss--in a
straight line that goes through
the center of mass.
I drew that wrong,
so let me redraw it here.
There we go.
Yeah.
And so it balances, right?
That's what the center of mass
is.
It's the balance point.
And so the star has to stay
exactly opposite to the planet.
How big are each of these
things?
Well, that depends on the ratio
of the masses in an equation we
wrote down before.
The consequence is that as
these things go around they stay
on opposite sides of the center
of mass.
So the amount of time it takes
the planet to go around the
center of mass--that's the
orbital period--has to be the
same as the amount of time it
takes the star to go around the
center of mass,
also the orbital period.
So the orbital periods,
P, are required to be
the same because it has to take
them the same amount of time to
go around this center of mass.
Because they have to stay on
opposite sides of it the whole
time.
The P is--So the orbital
period, P,
is the same for the planet and
for the star,
whereas the velocity and the
semi-major axis are different.
Because, while it takes the
same amount of time to go
around, the star is going for
much less distance.
So the distance is shorter,
and therefore the velocity has
to be less for the star.
So we can talk about the
V_star versus
V_planet and
a _star versus
a _planet.
And we can add these things up
to make V
_total and a
_total.
But you don't do that with the
period.
The period is the same.
Okay.
So that's an important concept.
Questions?
Let me point out that this
concept of the center of mass
gets more complicated when
there's more than one planet.
Because again,
the center of mass is still a
fixed point, even when you've
got two planets – and so one
of the things--so the star is
going around the center of mass
because of this planet,
but it's taking other extra
little wiggles as a result--if
there's a second planet,
as a result of that planet.
The center of mass has to stay
exactly in the same place.
And the consequence of this is
that the motion of one planet is
actually a little bit affected
by the gravity of the other
planet.
So it, too, is executing extra
little wiggles due to the
presence of the second planet.
Those wiggles are very small
compared to the motion that's
induced by the Sun,
because the other planet's much
less massive.
But they really are there,
and, in fact,
the planet Neptune was
discovered because the orbit of
Uranus had extra wiggles in it
that couldn't be accounted for
by the known planets.
And so, in the nineteenth
century, a couple of clever
mathematicians figured out from
the motion of Uranus where
Neptune had to turn out to be,
in order to explain these
extra, unexplained motions.
And then some astronomers
looked, and there it was.
It was a huge triumph for
Newtonian physics and a damned
hard math problem,
too.
And so, this concept becomes a
little more complicated in the
case where there are more than
one planet.
But in fact,
the way we're going to deal
with that is just to separate it
into one planet at a time.
Let me give you an example of
that.
Let's see, I don't think we
need to change the lighting.
Woops!
Backwards.
Here we go.
All right.
So, this is a radial velocity
curve of some star,
and it--you can see these
points.
Here are the observed radial
velocities at a variety of times
over a course of three or four
years.
And then they've drawn in a
sine curve--or it's actually not
quite a sine curve.
It's close to a sine curve.
And you can see that the sine
curve more or less goes through
these points,
which is nice because that
indicates the presence of a
planet.
And you have velocity over
here, but I should mention
something about velocity.
What they mean is not actually
velocity.
What they mean here is radial
velocity.
And this is an important point.
It's not that the speed changes.
What changes is--between here
and here on this plot – is not
the speed of the thing,
but its direction.
Because at plus 200,
that means it's going away from
you at 200 meters per second.
At minus 200,
it means it's coming toward you
at 200 meters per second.
That's why you can have a minus
velocity.
At zero, it does not mean that
the thing has stopped.
It's going at the same speed as
it was up here and the same
speed as it goes down here,
but in a different direction.
So, it's going still at
200-plus meters per second,
only it's going sideways.
And so it's neither coming
toward you nor going away from
you.
Therefore, its radial velocity
is zero, and you measure no
Doppler shift.
Remember these plots are
created by measuring the Doppler
shift, and the Doppler shift
tells you how fast something is
either coming toward you or
going away from you.
So, that's an important point.
You can have dramatic changes
from positive to negative in the
radial velocity without changing
the speed of the object at all.
All you have to do is change
its direction.
So first, it comes toward you,
then it goes sideways,
then it goes away from you,
then it comes sideways again.
So that's what this plot
represents.
And you can see that these
points go up and down,
as they should if something is
in orbit around the center of
mass.
And these little points down at
the bottom are--represent the
difference;
actually, they've put it down
here, this should be zero on the
scale.
This is the difference between
the observed points and this
sinusoidal model that they've
put up there.
So, they've just calculated the
differences, and there's some
scatter.
But it basically follows pretty
well, the scatter is a whole lot
less than the changes in the
velocity.
But it turns out,
you can do better than this.
And here is an example.
Now, what the line is now is
not one, but two sine curves
added together,
one of which was the one we saw
before.
So they fit for two planets now.
And the other is another sine
curve with a different
amplitude, because that planet
induces a smaller motion in the
star and also a different
period.
And so, at certain points,
the periods line up and you get
big deviations.
Then at other points,
you get wiggles on top of
wiggles, and these things kind
of beat against each other.
So this complicated pattern of
this line here is just two sine
waves added together.
And now, the points line up
much better.
If you recall,
these deviations between the
points in the lines before were,
you know, of up to,
say 50 meters a second.
And now they're much smaller.
The things fit much better.
I'll show you a blowup now of
this region of the plot where a
lot of these points are,
and you'll see what I mean.
Here are the points.
Here is the line,
and you can see that this
complicated line really fits
these points quite well.
That's evidence that there are
two planets in this system.
But, in fact,
it gets even better than that
because what they then did was
they said, all right.
Here's what we're going to do.
We're going to take these
so-called residuals.
We're going to subtract off our
two-planet model.
And we're going to see whether
we can see anything interesting
going on in what's left over
after those two planets have
been taken away.
And when they did that,
they saw this.
This is--they sort of grouped
them all together,
and they found something with a
period of 1.9 days that now has
what looks like a sinusoidal
wiggle of about a few meters per
second.
Remember, where we started,
the deviations were 200 meters
a second, but you now subtract
off this--these two planets –
and you're left with a third.
And so this system is now
known--this particular star that
they were observing is now known
to have three different planets
around it,
of which this one is the one
that has the shortest orbit,
1.9 days.
So there are now several
examples of things in which we
know that there's actually more
than one planet in one of these
systems.
And this is how we find that
out that the motion of the star
is not just one sine curve,
but the superposition of two
– or, in this case,
even three of these things.
Now, one of the interesting
things about this is it's quite
a short orbit,
1.9 days.
That's one of the shortest
orbits known.
It also has a relatively low
amplitude.
The velocity--the radial
velocity changes are quite
small.
So, the induced speed in the
star is quite small.
Those two things put together
give you a relatively low mass
of the planet for reasons I'll
make specific in just a second.
This is one of the lowest mass
planets that's been discovered
in this way.
It's only about ten times the
Earth's mass.
That's kind of comparable to--a
little less than Neptune and
Uranus.
And so, in this case,
it isn't actually clear whether
you should think about this
thing as a kind of low-mass
outer planet or a big Earth-like
rock.
And so, that isn't clear in
this particular case.
Let me make this a little more
specific here.
What are the inputs that you
need to know to figure out how
big--what the amplitude of that
sine curve is--how big the
wiggles are?
You need to know a couple of
things.
You need to know the velocity
of the planet,
which isn't what you observe.
Remember, you're observing the
velocity of the star.
So, velocity of the planet,
which is approximately equal to
the total velocity.
As one of the exercises on your
problem set, you can demonstrate
that that is equal to GM
/ a,
the square root of
GM over a.
So that means--Yeah?
[Unintelligible student voice.]
Oh, yes.
Good.
Thank you.
[Adjusts overhead projector.]
How about that?
Yeah.
Okay.
So, this means short orbits
give you small a,
large velocities of the planet.
This makes sense.
If you're in close to the star,
you have to move faster to keep
yourself in orbit.
But, of course,
you don't observe the velocity
of the planet--you observe the
velocity of the star.
The velocity of the star is
equal to the velocity of the
planet, times the mass of the
planet over the mass of the
star.
And so, large planet masses
generate large star velocities.
So the two things you need to
know is: how short is the orbit
and how massive is the planet.
And so if you have a short
orbit, that'll give you high
V _planet.
And if you observe--so you
observe the short orbit.
And the other thing--if the
other thing you observe is a
low, relatively speaking,
V _star,
then it must be true that you
have a low planet mass.
Because if this is big and this
is small, you've got to
compensate for it by having a
small value out here.
And we'll come back to this
kind of reasoning in a minute.
Does that make sense?
So in fact, that particular
planet with its very short
orbital period but its low
induced velocity in the star--so
short period,
short semi-major axis,
but also small V
_star,
is the lowest mass planet,
I think, at this point,
that has been observed by this
particular method.
Okay.
But as it turns out,
most of the ones--the
short-period planets--that have
been observed are more massive
than that.
And we've got these Hot
Jupiters.
And so the argument here,
using the same kind of
reasoning, is that you have
short periods,
moderate values,
moderate to high values as
these things go for V
_star,
and that tells you it's a
massive planet.
And as I pointed out last time,
this is deeply disturbing in
terms of what we know or what we
think we know about planetary
formation.
So, short period plus massive
is, to put it mildly,
unexpected--so unexpected that
they almost weren't discovered
at all.
What happened,
this--the discovery of the
planet around 51 Pegasus
happened in 1995.
And the way this worked out
was, there was a team of
astronomers, Geoff Marcy and
Paul Butler,
chief among them,
in California,
who had the best equipment for
doing these kinds of very
high-precision radial velocity
measurements.
And they had embarked on a
campaign to find Jupiter-like
planets, which they thought they
could do.
And they were piling up data on
many stars.
They were looking at many
Sun-like stars.
And then one day in 1995,
they woke up and a bunch of
people in Switzerland announced
the discovery of the first
planet,
which disturbed them mightily,
because they had been scooped.
And, it disturbed them even
more when they discovered that
the particular star that this
planet was around--this 51
Pegasus thing that I was talking
about last time – was one of
the stars that they themselves
had been observing.
But the thing was,
the period, you remember,
was four days.
And Marcy and Butler and Co.
were expecting the periods to
turn out to be ten years.
So they hadn't checked to see
whether there were four-day
variations.
And as soon as this paper by
these other astronomers,
these Swiss astronomers who
discovered the thing,
was published,
they said, damn!
We've got a big pile of data on
this particular object in our
desk drawer.
We ought to take a look and see
whether these other guys are
right.
So they looked at it and within
a week of re-analyzing their
data, they were able to confirm
the fact that this really was a
planet in a four-day orbit.
And, annoyingly to them,
they already had the data that
they could've announced it
first,
if they'd looked at it and
asked the question,
"Does this thing actually have
a four-day orbit?"
But it didn't occur to them
because it's well known,
you can't have a Jupiter in a
four-day orbit.
So, they kind of didn't check.
So here's another fable for
you, "The Discovery of 51-Peg
b."
That's how you label these
planets.
A is the star,
B is the planet.
And the moral--I guess you
could say this in a couple of
ways.
One would be to say,
"Expect the unexpected."
And the other would just be to
say, "Look at your data."
But look at your data so that
you could see things that aren't
the thing that you expect to see
in your data.
And that's kind of an important
lesson, I think.
Anyway, it turned out,
it was relatively easy to find
these Hot Jupiters,
and within a few years
they--Marcy,
and Butler, and the Swiss,
and some other teams as well
– had found literally dozens
of these things.
So within a few years,
there was dozens of Hot
Jupiters known around many
stars.
And so they hadn't yet,
of course, found anything like
our own Solar System.
Because they hadn't been
looking for ten years yet.
The orbit of Jupiter,
you will remember,
is ten years long.
So, they found all these Hot
Jupiters, and this might have
suggested that ordinary Solar
Systems are rare--Solar Systems
like our own.
Planetary systems are rare.
But I'll put a question mark
after that, because it isn't
really at all clear that that's
true.
And the reason is that Hot
Jupiters are easier to find than
ordinary Solar Systems,
for exactly the reasons that I
wrote down just a minute ago.
The fact that they have short
periods and massive planets
generates larger values of
V_star.
Both of those factors make for
large values of the thing that
you're actually trying to
observe, which is the velocity
of the star.
So, of course,
if you go out and you have some
new technology and you're trying
to observe something,
the first ones you'll observe
are the ones that have the
largest signal of the kind
you're trying to observe.
So if you're observing radial
velocities, you're trying to
measure V
_star,
the first ones that are going
to pop out at you are the ones
with large values of that.
It's also true that it's easier
to observe these shorter
periods.
If you've got a four-day period
and you observe the thing for a
month, you've watched it go back
and forth, you know,
eight times or something.
If you want to wait for eight
orbital periods of Jupiter,
that's 80 years--and it's just
going to take you longer.
There's a general rule in
science that no project can take
longer than it takes one
graduate student to get a Ph.D.
Because, of course,
it's the graduate students who
do all the work,
and it's just hard to recruit a
graduate student to work on a
project that won't be completed
until they're 70.
And so these shorter periods
are easier to observe,
just because they're short,
in addition to the fact that
the thing you're observing is
much easier to see.
This is called a "selection
effect."
So you're just more likely to
see certain kinds of objects
than others for the
straight-forward reason that
they're easier to see.
And those will be the ones you
find first.
And if you don't take this into
account in thinking about the
statistics of these things,
you're going to screw up
because, of course,
you see the easy ones first.
Of course, you see lots of them
before you see the others.
Nevertheless,
the existence of even one Hot
Jupiter was a crisis for
planetary formation theories.
Because there's no way any such
thing ought to exist.
But even one Hot Jupiter messes
up our theory;
so, I'll just write that down,
"messes up theory."
And so, as soon as even the
first of these was discovered,
people started to think about
what the alternatives might be.
And there are two kinds of
alternatives,
ways to explain the data
without having a Hot Jupiter.
So, alternative number one was
that a so-called "low
inclination double star" – so,
I'll explain that in a second.
The second object in this is
supposed to be a star,
not a planet,
and there are known double
stars with short periods.
They're formed in a very
different way.
Double stars don't form--the
second star doesn't necessarily
form out of a disk around the
first star.
It's formed--I don't know –
by splitting the star in half at
some early part of its
evolution.
And so you get a very different
expectation for what kinds of
periods you have,
and there are many double stars
known with short periods of this
kind.
But so, then,
how do you explain--if it was a
double star, you would expect
that the induced velocity would
be much,
much bigger because the star is
much more massive.
And so, what you do is,
you explain it by saying,
well, here is your--here is you
observing it and the orbit,
the orbital plane is like this.
It goes up and down.
So the stars are orbiting each
other this way.
So they neither come toward you
very much, nor go away from you.
And therefore,
the velocity is high,
but the radial velocity,
which is the thing you observe,
is low.
So, high velocity,
but low radial velocity because
the system is going
sideways--orbits are,
the technical term here is
"face-on," not "edge-on."
Okay.
So, that was one hypothesis.
This didn't work out for two
reasons.
Problem number one,
no evidence for light from more
than one star.
Stars are much brighter than
planets, right?
So, if you're looking at a
star-planet system,
all you expect to see is the
light from one star.
And that's what is observed.
If you've got a second star in
that system, the second star
shines like a star.
And so, you would expect to see
some evidence of light from a
second star in that system,
and none of those was observed.
The other problem is a kind of
statistical one.
There are many Hot Jupiters.
Now, if you're going to explain
all these things by having
face-on orbits with respect to
us,
imagine what some observer
somewhere else in the
galaxy--with all these
things--here's us in the middle
of our galaxy,
or somewhere in our galaxy.
And all these objects happen to
be lined up exactly face-on
toward us.
Some other astronomers would
have to see them edge-on and so
forth.
So why is it--what cosmic
conspiracy has caused all these
things to be lined up face-on
toward us?
It's as if someone had
carefully set up all these
double star systems to fool us
into thinking that Hot Jupiters
existed.
This is the kind of argument
that people tend to reject
because it requires that we are
in a very special place,
or that some very special
coincidence has taken place.
And that isn't--and as you keep
finding more and more of these
things, you wonder,
well, how come--aren't some of
them lined up edge-on?
And in fact,
it has to be very close to
face-on, and so the odds that
all of these things are face-on
to within plus or minus one
degree starts to become really
small as you pile up more and
more of these objects.
Many Hot Jupiters--they can't
all be face-on.
And so, as more and more of
these things were discovered you
could explain any one or perhaps
two of them as being face-on
star systems.
But it starts to get more and
more difficult to believe that
all of them are in that
category.
Okay.
Let me see--what do I want to
do here?
Okay.
Alternative number two is
pulsating stars.
Now, this is interesting.
Stars do pulsate.
The Sun pulsates just a little
bit, not enough so that you
could see it in this way,
but there are other stars known
that pulsate by large amounts.
They go out, they go in.
Think about what happens if you
observe a pulsating star.
Here it is when it's small but
getting bigger.
So, all of the star is
expanding.
But if you look at that star,
you only see the half of the
star that's on your side of the
star.
So you only see this part over
here.
And all of the surface of that
star is coming toward you.
Right?
Because this part--it's
expanding--so this part's coming
toward you;
this part's going
half-sideways,
half-toward you.
This part's going
half-sideways,
half-toward you.
So if you add up the light from
all this, it has a net bulk
motion coming toward you.
Now, supposing you look at it
when it's at a different part of
its pulsation cycle.
So now it's big,
but going--but falling in.
Now, you'll see the opposite.
All of the parts of this star
are moving away from you.
Some are moving sort of
sideways, but others are moving
away from you.
And so you expect that if you
observe a pulsating star you'll
see first positive radial
velocity,
then negative radial velocity,
then--as it pulses back out
again--positive radial velocity.
And that starts to sound very
familiar.
Right?
That's pretty much what we
observe.
It goes up, it goes down.
And so the suggestion was that
these things might actually be
some kind of pulsating star.
Okay.
So, problems with the pulsating
star explanation.
Basically, solar-type stars,
which these were--stars aren't
supposed to pulsate like
this--aren't supposed to have
large pulsations.
And it's also true that
pulsations, in general,
don't lead to sinusoidal
variations in radial velocity.
An orbit naturally gives rise
to a sine wave if the orbit's
close to circular.
Pulsations--there's no
particular reason to have that
pattern.
You could have sudden rises and
then gradual decays and then
things of that nature.
You don't expect it to be
sinusoidal.
But both of these things--you
know, what's weirder?
That there a lot of Hot
Jupiters in the world,
or that you have some kind of
pulsation mechanism that you
haven't experienced before.
Both of them are sort of
equally in violation of current
theory, and so you might as well
assume that you have weird
pulsations as well as having
weird planets.
However, it turns out that the
pulsation theory makes a
testable prediction.
And to explain this prediction
I have to take a little
digression and talk a little bit
about how Doppler shifts are
actually measured.
So, measuring Doppler shifts.
What you do is you look at
what's called a spectrum.
Those of you who--no,
gosh, I've spelled that wrong.
"Spectrum."
Spectrum is just a plot of
intensity, how much light there
is, against wavelength.
And if you work out--if you
measure the spectrum of any
particular astronomical object,
you'll see that at certain
wavelengths there is much less
intensity or much more intensity
than at many other wavelengths.
So, you'll get a plot that
looks kind of like this.
There'll be certain specific
wavelengths that have abnormally
large or abnormally small
amounts of light coming from
them.
These are referred to as
spectral features,
or sometimes,
lines.
And when you have too little,
these are called absorption
lines.
These are called emission lines
because you have extra emission
or absorption of radiation at
those particular wavelengths.
There's a good explanation of
why this happens from atomic
physics.
I won't go into it in detail,
but let me just say that there
are specific wavelengths with
much less or much more
emission--or more emission--and
each one of those wavelengths is
caused by atomic transitions,
which emit more or absorb
particular wavelengths of light.
So, it's caused by atomic
transitions.
I won't explain what those are
in detail, but each comes from a
specific chemical element.
So, hydrogen has particular
wavelengths associated with it.
Helium has particular
wavelengths associated with it,
and so on and so forth.
And this, by the way,
is how you can determine what
stars are made out of--determine
composition of stars.
But for the present purpose,
the point is that you can go in
with a bunch of hydrogen in the
laboratory,
and measure what the
wavelengths of these spectral
features are if nothing is
moving.
So--can measure these
wavelengths at rest in a lab.
And so you know in advance what
the rest wavelengths of these
things are.
You go out and measure them in
stars, and it turns out they're
not quite where they're supposed
to be.
And that's how you determine
what the Doppler shift of any
particular object is,
by comparing these spectral
features to where they are in
the lab.
Now, here's--so if we go back
to talking about pulsations,
so here is--this is kind of a
blow-up of an absorption line
this case.
So here's intensity,
and here's wavelength,
and it looks something like
this.
And so there's a particular set
of wavelengths that are
absorbed.
Now, if the whole star moves,
if the star is moving because
there's a planet around it--what
happens when it gets redshifted?
Well, this whole thing moves to
the right to longer wavelengths,
and you get something that
looks, you know,
sort of like this.
So this is--whole star moves
away from you.
And so, the whole thing shifts
back and forth.
But pulsations are a little bit
different.
When you get a redshift due to
pulsation, it's because,
you know, you're looking at
something that does this.
Part of the star moves away
from you, but part of the star
moves sideways.
And so, only part of the
emission is redshifted,
but other parts of the emission
are not.
And so what you do is,
you sort of--it's not like the
whole thing moves sideways.
It's that it sort of gets
smushed out.
Because part of the star moves
sideways, but--part of the
absorption line moves sideways,
but part of the absorption line
doesn't move because it's
coming;
you know, it's,
like, coming from this part of
the star, which is going
sideways to you.
And so what you do is you get
something that looks more like
this.
So this is--part of the star
moves away.
So the center of this line has
moved.
Here's the center here.
It's gotten even more
redshifted than in the case I
drew there.
But part of it has been left
behind.
And so the prediction is that
for pulsations the shape of
these spectral features
changes--shape of "lines"
change--whereas for orbital
motion,
only the position of the lines
change.
So this can be observed.
You can go out and observe,
and you can see whether the
shape of the lines change or
not.
And they did that,
and it's not pulsation,
but is consistent with orbits.
I think this is kind of a cool
experiment.
Because, you know,
this looks a lot like science.
Right?
There's two hypotheses,
each of which makes a different
prediction.
Prediction one--hypothesis one,
it's got to change its shape.
Hypothesis two,
it does not change its shape.
You go out, you measure the
thing, and you find out which
hypothesis is right.
This is just what they told you
in eighth grade and,
therefore, just what I told you
a couple of days ago never
happens in astronomy.
But sometimes it does.
And so this is yet another
fable, "The Disproof of
Pulsation as Explanation for the
Velocity Curves."
And the moral here is,
"sometimes science works like
science."
So there were,
for several years,
all of these attempts to try
and explain the Hot Jupiter,
the radial velocity curves,
without actually having to bite
the bullet and believe that Hot
Jupiters exist.
None of them were very
convincing.
This double star hypothesis
didn't seem to work out.
The pulsation hypothesis didn't
seem to work out.
But nevertheless,
people kept trying to come up
with alternative explanations,
until something happened that
pretty much nailed down the idea
that these things really,
honest-to-goodness, are planets.
But I don't have time to tell
you about that now,
so we'll talk about it on
Thursday.
Okay.
