Professor Charles
Bailyn: Okay,
we're talking about the origin
and fate of the Universe.
And let me remind you of the
story so far.
There are basically two sets of
observations that are important
here.
One is the existence of the
Hubble Diagram and Hubble's Law,
which is the observational
relationship between distance
and velocity for galaxies.
And this leads you to the idea
of a universal expansion.
And the other is what we
discussed last time:
that if you look back into the
past,
if you observe at a large
distance--that is to say,
a large lookback time--what you
discover is that things were
different in the past.
That the Universe,
as a whole, looked somewhat
different and,
in particular,
was significantly denser,
which is exactly what you would
predict if the Universe was
expanding.
And these two things--these two
observational facts put together
are really what lead to the idea
of a Universe with a Big Bang
cosmology.
And this is great because you
can then use this assumption
that everything is governed by
the scale factor of the
Universe.
And the scale factor starts
either at zero,
or very close to zero,
and gets bigger with time.
And you can use that concept to
do all sorts of wonderful
things.
You can describe the past.
And in particular,
one of the things we did last
time was to calculate the age of
the Universe from the
observations of the Hubble
Constant.
And you can predict the future.
And the future depends on how
the expansion of the scale
factor changes.
If the scale factor just
continues to expand at its
current rate,
the Universe will continue to
expand and gradually get sparser
and sparser,
and colder and colder,
and more and more boring.
But it's not expected that the
expansion rate stays the same.
It's expected that the
expansion rate will change.
And, in particular,
it's expected that the
expansion rate will slow down.
Why?
Because there's matter in the
Universe, and matter exerts
gravity, and gravity tends to
pull things back together again.
And so, this is where we ended
up last time.
If you assume that gravity is
the dominant force--that is to
say that any changes in the
expansion rate of the Universe
will be due to gravity,
then, you can derive this
critical density,
which we did last time,
which is a quantity equal to
3H^(2) / 8 π G.
H, you measure.
The other things are just
constants, and you can calculate
what this quantity is.
Now, at this point,
let me write down a piece of
astronomical jargon,
which I didn't do last time.
The actual density of the
Universe, divided by this
critical density,
is given a letter of its own.
This is written down as a
capital Omega.
So Ω is the true--the actual
density of the Universe,
whatever that turns out to be,
divided by the critical
density.
And then, you can describe the
future of the Universe,
depending on what Ω is.
If Ω is greater than 1,
that means that the density's
greater than the critical
density.
And this leads to re-collapse
and the "Big Crunch"--whereas,
if Ω is less than 1,
the Universe expands forever.
Somebody asked,
what happens if Ω is exactly
equal to 1?
In that case,
there is no Big Crunch.
The Universe expands forever,
but the expansion rate
asymptotically approaches zero.
But, of course,
in real life,
it's very hard to get something
that's exactly some--any
physical quantity to be
precisely equal to any
theoretical value.
And so, with this in mind,
it then becomes very important
to actually go out and measure
the average density of the
Universe because,
then, you could divide it by
this critical density.
We've already measured
H, so we know what this
quantity is.
And then, you could figure out
what's going to happen.
So, the goal here is to
determine the density of the
Universe.
And conceptually,
this isn't such a hard thing to
do.
You go out and measure the mass
of everything you can see.
You try and do it over a large
volume, because what you want to
avoid--the mistake you want to
avoid is to measure the density
of a piece of the Universe that
doesn't represent the overall
average.
If we measured the density of
material in this room,
it would be something like 27
orders of magnitude bigger than
the critical density.
And if we assume that the
Universe were just like this
room, obviously,
it would re-collapse.
In fact, it would have
re-collapsed long ago.
But, we don't do that because,
of course, most of the Universe
is not like this room.
Most of the Universe is empty.
So, you say,
well, we better include a lot
of stars and the empty spaces
between them.
But even that's a mistake,
because you're measuring stars
in our galaxy.
So, you say,
well, we better include lots of
galaxies and the empty spaces
between them.
That still doesn't work for a
while, because there are
clusters of galaxies.
There are clusters of clusters
of galaxies.
And so, you have to go really,
quite far out,
before you have a fair sample
of what the average conditions
in the Universe are like.
But, in principle,
that's certainly possible to
do.
You just keep measuring things
further and further and further
away, until you get to a point
where,
if you increase the
distance--where,
as you increase the distance,
that density doesn't change
anymore.
So, you're out to the part
where you've really achieved the
average.
How do you know you've achieved
the average?
Well, you look out twice as far
and you get the same answer.
And so, in principle,
the way you do this is,
you add up all the mass in some
sizeable chunk of the
Universe--in a sufficiently
large chunk of the Universe,
where sufficiently large is
sufficiently large to average
over any local perturbations.
So, you add up all the mass and
you divide by the volume.
You divide by the volume that
that mass occupies.
And so, obviously,
you have to identify all the
different kinds of mass.
And you have to make sure that
whatever volume you've taken,
you've found all the mass in
it.
You add it all up.
You divide by volume.
You determine--that gives you a
value for density.
You divide by the critical
density and you know what's
going to happen to the Universe.
Okay.
Now, how do you find the mass
of things?
Determining mass.
Well, one way you can do it is
you can just go out and measure
how bright – yes,
go ahead.
Student: Can you put the
other slide up?
Professor Charles
Bailyn: Oh,
put this back for a second.
Top part?
Bottom part?
What do you- Student:
[Inaudible]
if you don't mind putting it
on.
Professor Charles
Bailyn: Yeah,
yeah.
So, you've determined the
density of the Universe by
adding up the mass.
Divide it by volume.
And then, the question becomes,
"How do you determine the
mass?"
And one way you can do it is,
you look at how bright things
are.
Add up the light you see.
And then, you assume some value
for the amount of mass it takes
to create a certain amount of
light.
So, that's assuming what's
called a mass-to-light ratio.
And so, you can do that,
you know.
If it's the Sun,
then one solar mass produces
one solar luminosity.
If all stars--if all objects
are exactly like the Sun,
then everything would be like
that.
It turns out that isn't the
case, but you can take local
samples of stars and figure out
what the average mass-to-light
ratio is.
And if you have some value that
you're happy with,
of mass-to-light ratio,
then you multiply the amount of
light by the mass-to-light
ratio,
and this gives you a mass.
Student: Do you need to
adjust for distance?
Professor Charles
Bailyn: Sorry.
Student: Do you need to
adjust for distance?
Professor Charles
Bailyn: Well,
what you mean by light is
the--do you need to adjust for
distance?
What you mean by light is the
intrinsic light.
You mean the equivalent of the
absolute magnitude,
which takes the distance into
account.
So, what you need to ask is not
how bright it looks,
but its intrinsic brightness in
this particular case.
Yes.
So, you do need to account for
the distance,
and so, you need to be thinking
about absolute magnitude rather
than apparent magnitude,
yes.
And that's one of the problems.
That's hard to do.
The other problem,
of course, is this awkward
word, here ["assume"],
which is the kind of thing that
makes people nervous,
because you could get that
wrong.
If you're looking at one kind
of star and it's actually some
other kind of star,
which happens to be much more
massive but dimmer,
like white dwarfs or something
like that,
then you're going to make a
mess of this.
So, there's an alternative
method, which you may already
have considered,
because we've done it in both
of the previous parts of this
class,
which is, you measure orbits.
And you do the same thing we
did with--in part one and part
two of the class.
You find some star in the
distant portion of the galaxy,
orbiting around the galaxy.
You figure out how fast the
thing is going.
You figure out how far the
thing is going.
You use Kepler's Laws.
And you determine the mass from
orbital theory,
from Kepler's Laws,
basically.
And, in particular,
you know, V^(2) =
GM/a. And so,
you can measure this from the
Doppler shift.
You can determine this;
basically, in the case of
galaxies, galaxies are big
objects.
You can physically measure the
angular separation on the sky.
Use the small angle formula,
if you know the distance,
to determine this.
So, this can also be measured,
and therefore,
this can be calculated.
And so, you go and do that for
a whole bunch of galaxies.
And this has been done.
And let me give you some
examples, here.
Let me actually write down some
numbers and do some
calculations.
Supposing you have a galaxy at
a distance of 20 megaparsecs
[Mpc].
And supposing it has an
apparent magnitude of,
something like,
14.
These are kind of typical
numbers for nearby galaxy
clusters.
There's a particular--the
nearest big galaxy cluster to us
is a cluster in the
constellation of Virgo,
known as the Virgo cluster.
If you want to know about the
Virgo cluster,
ask Hugh Crowll [
a graduate teaching assistant
for the course]
who is devoting his life to the
study of this object and the
galaxies within it.
But these are sort of
quasi-typical numbers,
adjusted slightly because it's
actually 17 Mpc,
which is kind of a pain.
All right.
So, what do you know about the
mass?
What can you determine about
the mass of such a galaxy?
Well--oh, and let me warn you
before we even begin that,
of course, astronomers have
played you a dirty
trick--namely,
that the symbol we use for
magnitude is M.
The symbol we use for mass is
also M.
So, you've got to keep those
clear in your mind.
All right.
So, what do we know about this?
We know the relationship
between apparent and absolute
magnitude.
And, as I said just a minute
ago, it's the absolute magnitude
that we need to know in order to
actually determine anything.
m - M = 5 log
(D / 10 parsecs).
So, let's figure out the
right-hand side first.
That's 5 log (2 x 10^(7)).
That's 20 Mpc.
1 Mpc is 10^(6).
Over 10.
That's 5 log (2 x 10^(6)).
Now, what do I do about that?
Let's see.
That's 5 times log of 10^(6),
that's pretty straightforward,
plus the log of 2.
Because, if you add logs,
then you multiply the thing
inside the parentheses.
So, log (2) + log (10^(6)) =
log (2 x 10^(6)).
log (10^(6)) = 6.
log (2) = .3.
It's just a useful number to
know.
The log of 2 is around .3.
The log of 3 is around .5.
The log of 5 is around .7.
You could look it up.
And so, this is equal to 5 x
6.3.
5 x 6 = 30.
5 x .3 = 1.5.
So, this is 31.5.
Let me caution you at this
point.
So, let me give you a little
side note, here.
Do not approximate magnitudes.
Why not?
I mean, we approximate
everything else in this course.
Magnitudes are a logarithmic
quantity, right?
And so, you don't approximate
magnitudes for the same reason
that you don't approximate the
exponents.
You can't say,
10^(7) is equal to 10^(6).
You can say 7 equals 6,
but you can't say 10^(7) is
equal to 10^(6),
because that's a factor of 10
difference, whereas the
difference between 7 and 6 is
just a little more than 10%.
Similarly, this .3.
You would have been tempted to
get rid of it,
right?
Because who cares about the
difference between 6 and 6.3?
But, in fact,
it comes out of this log of 2.
And so, .3 in the log is
actually a factor of 2.
And so, you got to not
approximate the exponents.
This is important.
Yes?
Student: Does this mean
we should also try to be more
precise when we're dealing with
magnitudes?
Professor Charles
Bailyn: Well,
yes.
That's saying--I guess that's
saying the same thing.
You should be more precise.
That means you shouldn't
approximate.
Yeah, so, I guess.
But, it's for the same reason
that you don't approximate the
exponents.
And it's also true that the
numbers are easier to work with,
because it turns out that you
add them rather than multiplying
them most of the time,
so, it's not such a bad thing.
Anyway, here we are at 31.5,
so what have we got?
We've m - M =
31.5.
This M was stated in the
problem to be 14.
So, 14 - 31.5 = M.
So, M = -17.5.
Okay.
That's not such a bad number.
We can work with that.
So, now we know the absolute
magnitude.
We know how bright the thing is.
So, now we can figure out how
many times brighter than the Sun
it is.
Why is that a useful thing?
Because if you then make the
assumption that the
mass-to-light ratio is the same
as the Sun,
that this galaxy consists
entirely of Sun-like stars,
then you can determine how
massive it is.
So, let's do that.
How many Suns--and this is the
other magnitude equation.
This is, you know,
M_1 –
M_2 is equal
to--for two different objects,
is equal to -5/2 log of the
brightness of 1 over the
brightness of the other.
But I think I want it in the
other form.
I think I want it in the form
of 10^(-0.4),
or 10^(-2/5 (M1-M2)) =
b_1 /
b_2.
This is the exact same
equation, as you'll recall,
just having been--getting rid
of the log,
taking everything,
putting it into 10 to the
something power.
The reason I want it in this
form is that this is the answer
I want.
I want b_1 /
b_2.
I want one to be the galaxy.
I want two to be the Sun.
So, then, I've got 10^(-2/5),
and then, the galaxy is -17.5,
that's the absolute magnitude.
The Sun is 5,
has an absolute magnitude of 5.
And that's going to give me the
brightness of the galaxy over
the brightness of the Sun.
That's 10^(-2/5 (22.5)) .
Let's see.
The minuses cancel out,
so that's a plus,
actually.
2/5 x 22.5 – well, let's see.
2 x 22.5 = 45.
A fifth of 45 is 9.
So, this is equal to 10^(9).
So, this galaxy is a billion
times brighter than the Sun,
10^(9) times brighter than the
Sun.
So, if it were made out of
Sun-like stars,
it would have a mass of a
billion solar masses.
So, mass would equal 10^(9)
times the mass of the Sun,
if all Sun-like stars.
But, it turns out that galaxies
tend to be somewhat dimmer than
the Sun, per unit mass.
Most stars are a little bit
less massive than the Sun,
but a lot less bright.
This is just the way stars turn
out to be.
And so, typical mass-to-light
ratios of populations of stars
tend to be on the order of 10,
or something like that,
times the Sun.
So, probably it needs to be
more massive,
because typical stars are
fainter than the Sun.
Typically, stars are fainter.
So, you could guess and say,
mass, maybe,
should be, I don't know,
10 times greater than that,
10^(10) solar masses.
And you can see why this
particular line of reasoning
starts to get pretty dubious,
because I picked this number
completely out of the air.
There's actually some modest
basis for it,
but you could pick other
numbers.
You could argue about this
endlessly and you wouldn't get
very far.
Why should it be 10 times the
Sun?
Maybe it's 100.
Maybe it's 1,000.
Maybe it's less than the Sun.
How would you really know?
And so, let's go back and do
the other approach--namely,
figure out its mass from orbits
of things around it.
So, let's look at--supposing
it's an edge-on galaxy.
Here's the center of the
galaxy, or--and,
actually, let's look at it from
the top.
So, here's a nice spiral galaxy
of some kind.
Here's the center of the spiral
galaxy.
Here's some star way out on the
edge.
That star is moving around the
center of the galaxy.
It has to be,
or it's going to fall in.
So, it's orbiting around the
center of the galaxy,
presumably in some circular
orbit.
You're down here,
looking at this thing.
And, of course,
you can measure the velocity of
that star by the Doppler shift,
because it's moving away from
you.
And so, one can measure this
velocity.
You can measure this distance.
That would be the equivalent of
a in our formulas,
because it's the distance
between the orbiting object and
the center.
Stars are much less massive
than galaxies so we don't have
to worry about the motion of the
galaxy.
And you can use a familiar
equation--namely,
V^(2) = GM /
a.
So, now, let's give this some
numbers.
Typical velocities of things
orbiting around the galaxy turn
out to be something like 200
kilometers a second,
or 2 x 10^(5) meters per second.
And the size of a typical
galaxy, you know,
out to where it stops being
easy to see stars is,
oh, I don't know,
what number did I take here?
Yeah.
Let's call it 20 kiloparsecs,
which is 2 x 10^(4) parsecs.
And a parsec is 3 x 10^(16)
meters.
So, this is 6 x 10^(20) meters.
So, now, let's calculate
M.
M = V^(2) a /
G. [(2 x 10^(5))^(2)(6 x
10^(20))]
/ (7 x 10^(-11)).
Get rid of those--let's see,
that's (4 x 10^(30)) /
10^(-11).
4 x 10^(41),
this is in kilograms.
One solar mass,
you recall, is 2 x 10^(30).
So, this mass,
in units of the Sun,
(4 x 10^(41)) / (2 x 10^(30)),
which is something like 2 x
10^(11) solar masses.
And now, we have a problem,
right?
You probably don't remember
what the answer to the previous
version of this problem was,
where we did it with light.
That came out to a magnitude
of--the brightness was about
10^(9) times the Sun.
Maybe the mass is 10^(10) times
the Sun.
But now we've just calculated
it in this other,
more reliable way,
and it's 2 x 10^(11).
It's 20 times more massive than
you thought it was going to be,
given how bright the light from
this thing was.
Yes, question?
Student: [Inaudible]
mass of the galaxy?
Professor Charles
Bailyn: This is the mass of
the galaxy, yes.
Now, before I go on let me just
point out--those of you who have
taken a look at the problem
set--what I've just done here,
this calculation I've just
done, is problem one of the
problem set, except done
backwards.
On the problem set,
what I did is,
I told you what the density
was, what the critical density
was,
and then, you had to derive
characteristics of the galaxies
from that.
Here I've told you what the
galaxies are like.
We figured out how big--how
massive they are.
If we divide by the volume,
we'll get a density.
So, we're doing the same
problem backwards.
I should say,
the numbers I've chosen here
are different,
so, you can't know the answer
to the problem set by looking at
the premises of these particular
things.
But, what I'm doing is the
exact same set of calculations,
only done backwards.
So, that may or may not be
helpful.
But let's pause here for a
moment, because this is
now--we're now up to--we're
making progress.
We're now up to Frontiers and
Controversies circa 1985.
You'll remember,
in 1920, they were worried
about whether the spiral nebulae
were actually galaxies.
In 1950 they were worried
about, maybe the "steady state"
was the correct response.
And by the time 1985 rolls
around, the big issue is mass is
determined by orbital rotation.
So, what you might call
dynamical masses--that is to
say, determined by orbits of
things around galaxies.
Orbits around galaxies.
And also, I should say,
galaxy clusters.
You can have galaxies orbiting
around each other and galaxies
orbiting around whole clusters
of galaxies, and the same thing
is true.
And so, around galaxies and
galaxy clusters--are much bigger
than you expect from the light
they give off.
And therefore--by about a
factor of 10.
By approximately a factor of 10.
So, there's 10 times more mass
than you can account for by
adding up all the stars.
Now, there's mass in other
forms than stars.
There's also dust.
There's also gas.
These are things you can detect
in other ways.
You add them all up and you're
still off by about a factor of
10.
So, there's 10 times more mass
than you have any way of
accounting for.
This is the so-called dark
matter problem.
So, this is Frontiers and
Controversies in 1985.
There's all this dark matter.
Most of the matter in galaxies
is in some form that we can't
detect.
It's dark matter,
and what is it?
Now, unlike Frontiers and
Controversies in 1920 and 1950,
this is one that we haven't
solved yet, so I don't know the
answer.
For a quarter of a century,
people have been busy trying to
figure this out.
There's still no good answer.
And ten years ago,
when I taught this course,
this question of what is the
dark matter was a big focus of
this part of the course.
Now, I'm going to talk about it
only in this class,
only in one lecture,
because we got way bigger
problems, even,
than this.
That's saying a lot.
I've just told you that we
don't know what 90% of the mass
in the Universe is,
and then, we've got bigger
problems than that.
So, things are getting a little
murky, here, and not just
because the matter is dark.
Okay.
But, let me pause a little bit
on dark matter,
because it's an interesting
problem.
And, as I say,
we have no idea what this stuff
is.
What are the possibilities?
So, here's a hypothesis.
Hypothesis #1 is that what this
stuff is, is some kind of
unknown sub-atomic particle.
And it has to have two
characteristics,
this sub-atomic particle,
for it to work out.
It has to have mass.
That's pretty basic.
If you're using it to explain
mass, you can't have photons,
right?
Photons don't carry any mass.
It has to have mass,
but it has to not interact with
light.
No interaction with light.
If it absorbs light,
it would be opaque,
and we would know it was there,
because galaxies behind this
stuff would look dim.
Alternatively,
if it gives off light,
then we'd see it.
And so, it has to not interact
with light, or interact with
light only very weakly.
And so, these are given the
name, generically,
Weakly Interactive Massive
Particles, or WIMPs.
So, here's the hypothesis:
the Universe is 90% WIMPs.
This is not such a crazy idea
as it might, at first,
seem.
There are known sub-atomic
particles that have these
properties.
There's something called the
neutrino.
There are trillions of them
going through this room every
second.
They have mass and they don't
interact very much with
anything.
They're known to exist from
particle accelerator
experiments, and they have been
detected from celestial sources.
Now, we know that--for various
reasons, that the dark matter
doesn't consist of neutrinos.
But, there could be many other
kinds of particles with these
kinds of characteristics,
and indeed, some are predicted
by current particle theories.
As I say, WIMPs have been
detected--I'm sorry,
WIMPs have not been detected,
but neutrinos have been
detected.
Here's how they do it.
It's kind of an amazing
experiment.
They took a mineshaft in South
Dakota and filled it with
cleaning fluid.
And the reason they did that
was that every so
often--neutrinos don't interact
with light, but they do
interact, occasionally,
with chlorine atoms.
And the effect of a neutrino
banging into a chlorine atom is
to turn it into argon.
And so, this happens--there
are--as I say,
trillions of neutrinos flow
this mine every second.
Once a day or so,
one of them will hit a chlorine
atom just right,
create an argon atom.
So, here's what you do.
You fill your mineshaft with
cleaning fluid,
a large fraction of which is
chlorine, and you count the
argon atoms that bubble off the
top.
And this has been successful.
They detected neutrinos emitted
from the Sun.
The Sun is--all stars that have
nuclear reactions going on in
them, emit neutrinos as part of
the output of these nuclear
reactions.
And then, they had a problem,
because they had predicted how
many neutrinos you ought to see
from the Sun in an experiment of
this kind,
and they didn't see enough of
them.
They only saw a third of them.
And it turns out--and then,
there was a big debate for a
long time.
This is Frontiers and
Controversies circa about 1975.
There was a big debate for a
while.
Where are all the solar
neutrinos?
Is it possible that we don't
understand nuclear reactions in
the Sun?
Is it possible that we don't
understand the chemistry of
chlorine or argon?
After all, you're counting
individual argon atoms,
so that's kind of a difficult
task.
No, it turned out that what was
going on was,
we didn't understand neutrinos.
And it turns out there are
three kinds of neutrinos.
And neutrinos switch back and
forth between these different
kinds, and you could only detect
one kind by the chlorine.
And so, they were all emitted
from the Sun as if they were in
the form that you would have
been able to detect them.
But as they traveled from the
Sun to us, some fraction of them
flipped back and forth between
all these other kinds,
and you ended up only with
about a third of them.
So, it was a big piece of
particle physics that was
discovered.
We have also detected,
by now, neutrinos coming from
supernova explosions.
So, there are--11 of them,
I think, were detected,
all at once.
And if you're detecting things,
sort of, once per day,
and then you suddenly detect 11
of them over the course of a few
minutes,
you've seen something exciting
occur.
And that is now known to be
this supernova explosion that
occurred in a neighboring
galaxy.
And so, there are a bunch
of--so, by analogy with that,
people are looking for the
WIMPs that make up the dark
matter.
If all this dark matter is in
WIMPs, there are lots,
and lots, and lots of these
things, and they're going
through us every second.
So, there are a whole bunch of
experiments with the same basic
characteristics.
You have a huge vat of
something, and something is
supposed to happen,
occasionally,
when one of these WIMPs hits
whatever's in the vat.
So, the Japanese have,
sort of, a cubic mile of
distilled water,
and they're looking for little
light flashes when the neutrino
runs into the water molecule.
They busted all their detectors
recently, and they had a sort of
earthquake,
and it was bad for the little
light detectors they had put on
the inside of these things.
But there are a lot of such
experiments.
Dan McKinsey,
here in the Physics Department,
is a big player in one of them.
And the hope is that you will
see the interaction between one
of these WIMPs,
of which there must be an
incredibly large number,
with something.
This has, so far, failed.
So, there is no direct evidence
from WIMPs.
The other hope,
I should say,
is that every time you build a
bigger collider,
you make new kinds of
sub-atomic particles,
and that they'll eventually
make something that looks like
it could be a WIMP.
And that hasn't been--happened
either.
So, no detections yet.
No direct detections.
With considerable effort,
you know, this is going to turn
out to be 90% of the mass in the
Universe.
So, you would like to detect it
because if you do,
they'll give you a Nobel Prize.
All right, that's one
hypothesis.
There's another hypothesis.
So, here's Hypothesis #2.
It's just, you know,
dark chunks of something that
doesn't glow.
Ordinary matter--chunks.
Student: Do these
hypotheses exist today or
[inaudible]
Professor Charles
Bailyn: Yes,
yes, yes, all of the--we don't
know what it is,
and so, nothing has yet been
ruled out.
What happens is that they--you
know, they continue to conduct
these experiments,
so, you can rule out WIMPs with
certain kinds of
characteristics,
because you would have detected
them.
Similarly, you can rule out
some of these other things with
certain characteristics,
because you would have noticed
they were there.
But both of these hypotheses
are still more or less viable.
Chunks of ordinary matter that
just don't glow,
that don't emit light.
Now, there's some limitations.
These chunks can't be too
small, because if what you've
got are tiny,
you know, micron-sized
particles, we call that dust.
And, basically,
that's what it is.
It would just be dust.
The problem with dust is,
dust in large quantities is
opaque, and you can't see
through it.
And therefore,
you would know it was there,
because it obscures the light
of things behind it.
And, indeed,
we see cosmic dust this way all
the time.
It's just, there isn't nearly
enough of it to account for any
substantial fraction of the dark
matter.
So, dust would be observed
because it--by obscuring light.
And it also tends to glow in
the infrared.
And so, we know that dusts
exists but we can count how much
of it there is,
because it obscures light and
it makes its presence known in
other ways.
It's also true that these
chunks of ordinary matter can't
be too big.
They can't be the size of whole
galaxies, or even a substantial
fraction of a galaxy.
You can't take all your dark
matter and put it into one lump
per galaxy, or even 100 lumps
per galaxy because if they were
very large masses,
you'd see it,
because it would disrupt the
orbits of stars around the
galaxy.
So, if there was some huge
unknown mass,
you'd see things orbiting
around it.
And, in fact, we do.
We see these supermassive black
holes in the centers of galaxies
and we know they're there,
because we see stars orbiting
around them, just like the
problem on the last Midterm.
And so, it can't be too small.
It can't be too big.
But, you could,
perhaps, have,
sort of, a bunch of star
massed;
so, you could have sort of a
bunch of star massed,
or planet massed dark things
in--it would have to be,
for various technical reasons
that I won't go into,
it has to be in the outer parts
of galaxies,
in the halos of galaxies.
So, that, in principle is
possible.
We wouldn't have any direct way
of detecting them.
These things are called Massive
Astrophysical Compact Halo
Objects.
[Laughter] Some people get it.
Massive, because they have to
carry mass.
Astrophysical,
because they're not particles.
Compact, because if they were
big you'd--you know,
they'd block light and you'd
see them.
Halo, because that's the part
of the galaxy they're in.
These are MACHOs, right?
And so, the alternative to
WIMPs is MACHOs.
And so, the alternative
explanation is that 90% of the
Universe is MACHOs.
There's been a very clever
experiment carried out to try
and find these things.
Here's how you do it.
You do it with gravitational
lensing.
Lensing MACHO searches;
remember gravitational lensing?
This is this business that mass
bends light.
So, here you are.
You're looking at some star.
And, in between you and the
star is a MACHO of some kind.
So, here's the MACHO.
You can't see the MACHO,
but the presence of the MACHO
changes the direction of the
light.
So, it comes into you like
this, and it basically acts like
a lens.
And, in particular,
the way it acts like a lens,
in the case of MACHOs lensing
stars, is it makes it
brighter--makes the star
brighter.
Now, in order for this to work,
the alignment has to be
essentially perfect.
All of these objects are moving
around.
They're orbiting the galaxy and
stuff.
So, the alignment holds for a
few weeks, typically.
So, what you'll see is,
you'll see this star become
much brighter.
And it can really become much
brighter--we're talking tens to
hundreds of times brighter than
it ordinarily was.
This lasts for a few weeks,
and then, it goes away.
These have been observed.
These lensing events have been
observed.
Lensing events observed.
But there are too few of them
to explain the dark matter.
Now, there are still ways out.
Let's see.
If you have particularly low
mass MACHOs, so--supposing the
whole Universe is filled with
things about the mass of Earth,
those cause lensing events that
might be too small to see.
Alternatively,
supposing you have things that
are many thousands of times the
mass of a star,
but not big enough to totally
disrupt galactic orbits,
then, there are many fewer of
them for a given amount of mass,
and there aren't enough MACHO
events that you would have
expected to see any substantial
number of them.
So, there's still a way around
the result of these experiments,
if you want to believe in
MACHOs.
But it's getting very tough.
So, no WIMPs detected so far.
No MACHOs.
You could still postulate kinds
of WIMPs and kinds of MACHOs
that might explain the dark
matter, but it's getting kind of
tough.
Most people,
I think, believe in WIMPs.
Most people tend to believe in
this.
But, and as far as I can tell,
that's because the particle
physicists keep coming up with
new candidate WIMPs that might
exist,
but that we haven't quite been
able to see, so far.
And so, there's a theoretical
basis for the existence of these
things, whereas,
with these MACHOs,
if you ask the astronomers –
well, fine.
So, you want to have 90% of the
Universe be in little Earth-like
things just floating around with
no star, how did they--how did
that happen?
How did these come into being?
We really have no answer at all
for that.
So, there's no theoretical
basis for any of the
still-allowed categories of
MACHOs.
And so, at the moment,
people tend to believe WIMPs
over MACHOs, although there's no
direct evidence for either.
Yes?
Student: If 90% of the
matter of the Universe is made
of little Earth-like objects,
then wouldn't that be 90% of
the Universe is made of metal?
Professor Charles
Bailyn: Oh,
Earth.
Earth-mass objects is what I
meant.
I don't care what it's made out
of.
Yeah, maybe there are little
Earth-sized balls of hydrogen.
That would be fine too.
Except how do you get them?
We know something about how
balls of hydrogen form and what
they become.
They turn into stars.
This is well known.
And one of the popular kinds of
MACHOs was just very,
very dim stars.
And this is one of the things
that the space telescope helped
to rule out, because it can see
really faint objects,
and they weren't there.
And so, no WIMPs.
No MACHOs.
And so, we don't know what's
going on.
That was a digression.
And what I digressed from was
the fact that this galaxy that
we had measured the mass of
turned out to be 2 x 10^(11)
solar masses,
or around 4 x 10^(41) kilograms.
If you have these things,
one such galaxy every--I don't
know, 2 Mpc, or so,
what's the density of the
Universe?
Remember, that's where we
started--of the Universe.
So, now, let's finish this
calculation.
Let's see the density is equal
to M/V.
4 x 10^(41),
from observing these orbits.
And the volume,
down here, is going to 2 Mpc
cubed.
That's 2 x 10^(6),
times 2--sorry,
times 3 x 10^(16).
That's 1 parsec.
So, this is 6 x 10^(22).
I want to cube it.
6^(3).
6 x 6 = 36, times another 6,
is 200.
So, that's 200 x 10^(66),
or 2 x 10^(68).
So, then, the density of the
Universe.
(4 x 10^(41)) / (2 x 10^(68)),
that's equal to 2 x 10^(-27)
kilograms per meter cubed.
And real critical can be
calculated--turns out to be,
as you'll discover on the
problem set, 6 x 10^(-27) in
these units.
ρ over ρ_critical
is equal to about 1/3.
So, if you buy that,
the Universe is going to keep
expanding, because Ω,
the ratio of the density to the
critical density is only about
1/3.
But the problem is,
we've got all this dark matter
around and what we're doing is,
we're adding up galaxies.
How do you know that there
isn't a whole bunch of dark
matter where there aren't
galaxies?
And where there's nothing to
see orbiting around,
you have no idea what this
stuff is.
And, indeed,
most of the WIMP kinds of
ideas, sort of,
postulate some kind of dark
matter that, kind of,
pervades the Universe.
And so, you'd expect there to
be somewhat more of it than you
can see in any given galaxy.
Well, somewhat more than 1/3
gets you into dangerous
territory;
namely near one,
which is the thing we're trying
to distinguish--whether this
number is greater than 1 or not.
And so, you need a new approach.
This isn't going to get you the
answer.
And so, there is a different
approach.
And that's what we'll talk
about next time.
And that will finally bring us
up to Frontiers and
Controversies in the
twenty-first century.
 
