WEBVTT

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Prof: Okay,
we're talking about the origin

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and fate of the Universe.

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And let me remind you of the
story so far.

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There are basically two sets of
observations that are important

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here.

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One is the existence of the
Hubble Diagram and Hubble's Law,

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which is the observational
relationship between distance

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and velocity for galaxies.

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And this leads you to the idea
of a universal expansion.

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And the other is what we
discussed last time:

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that if you look back into the
past,

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if you observe at a large
distance--that is to say,

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a large lookback time--what you
discover is that things were

01:19.110 --> 01:22.500
different in the past.

01:22.500 --> 01:27.900


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That the Universe,
as a whole, looked somewhat

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different and,
in particular,

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was significantly denser,
which is exactly what you would

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predict if the Universe was
expanding.

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And these two things--these two
observational facts put together

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are really what lead to the idea
of a Universe with a Big Bang

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cosmology.

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And this is great because you
can then use this assumption

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that everything is governed by
the scale factor of the

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Universe.

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And the scale factor starts
either at zero,

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or very close to zero,
and gets bigger with time.

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And you can use that concept to
do all sorts of wonderful

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things.

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You can describe the past.

02:26.460 --> 02:30.960


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And in particular,
one of the things we did last

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time was to calculate the age of
the Universe from the

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observations of the Hubble
Constant.

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And you can predict the future.

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And the future depends on how
the expansion of the scale

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factor changes.

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If the scale factor just
continues to expand at its

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current rate,
the Universe will continue to

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expand and gradually get sparser
and sparser,

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and colder and colder,
and more and more boring.

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But it's not expected that the
expansion rate stays the same.

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It's expected that the
expansion rate will change.

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And, in particular,
it's expected that the

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expansion rate will slow down.

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Why?

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Because there's matter in the
Universe, and matter exerts

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gravity, and gravity tends to
pull things back together again.

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And so, this is where we ended
up last time.

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If you assume that gravity is
the dominant force--that is to

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say that any changes in the
expansion rate of the Universe

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will be due to gravity,
then, you can derive this

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critical density,
which we did last time,

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which is a quantity equal to
3H^(2) / 8 π G.

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H, you measure.

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The other things are just
constants, and you can calculate

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what this quantity is.

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Now, at this point,
let me write down a piece of

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astronomical jargon,
which I didn't do last time.

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The actual density of the
Universe, divided by this

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critical density,
is given a letter of its own.

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This is written down as a
capital Omega.

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So Ω is the true--the actual
density of the Universe,

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whatever that turns out to be,
divided by the critical

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density.

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And then, you can describe the
future of the Universe,

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depending on what Ω is.

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If Ω is greater than 1,
that means that the density's

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greater than the critical
density.

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And this leads to re-collapse
and the "Big Crunch"--whereas,

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if Ω is less than 1,
the Universe expands forever.

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Somebody asked,
what happens if Ω is exactly

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equal to 1?

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In that case,
there is no Big Crunch.

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The Universe expands forever,
but the expansion rate

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asymptotically approaches zero.

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But, of course,
in real life,

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it's very hard to get something
that's exactly some--any

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physical quantity to be
precisely equal to any

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theoretical value.

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And so, with this in mind,
it then becomes very important

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to actually go out and measure
the average density of the

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Universe because,
then, you could divide it by

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this critical density.

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We've already measured
H, so we know what this

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quantity is.

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And then, you could figure out
what's going to happen.

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So, the goal here is to
determine the density of the

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Universe.

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And conceptually,
this isn't such a hard thing to

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do.

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You go out and measure the mass
of everything you can see.

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You try and do it over a large
volume, because what you want to

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avoid--the mistake you want to
avoid is to measure the density

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of a piece of the Universe that
doesn't represent the overall

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average.

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If we measured the density of
material in this room,

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it would be something like 27
orders of magnitude bigger than

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the critical density.

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And if we assume that the
Universe were just like this

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room, obviously,
it would re-collapse.

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In fact, it would have
re-collapsed long ago.

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But, we don't do that because,
of course, most of the Universe

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is not like this room.

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Most of the Universe is empty.

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So, you say,
well, we better include a lot

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of stars and the empty spaces
between them.

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But even that's a mistake,
because you're measuring stars

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in our galaxy.

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So, you say,
well, we better include lots of

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galaxies and the empty spaces
between them.

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That still doesn't work for a
while, because there are

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clusters of galaxies.

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There are clusters of clusters
of galaxies.

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And so, you have to go really,
quite far out,

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before you have a fair sample
of what the average conditions

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in the Universe are like.

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But, in principle,
that's certainly possible to

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do.

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You just keep measuring things
further and further and further

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away, until you get to a point
where,

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if you increase the
distance--where,

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as you increase the distance,
that density doesn't change

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anymore.

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So, you're out to the part
where you've really achieved the

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average.

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How do you know you've achieved
the average?

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Well, you look out twice as far
and you get the same answer.

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And so, in principle,
the way you do this is,

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you add up all the mass in some
sizeable chunk of the

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Universe--in a sufficiently
large chunk of the Universe,

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where sufficiently large is
sufficiently large to average

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over any local perturbations.

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So, you add up all the mass and
you divide by the volume.

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You divide by the volume that
that mass occupies.

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And so, obviously,
you have to identify all the

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different kinds of mass.

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And you have to make sure that
whatever volume you've taken,

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you've found all the mass in
it.

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You add it all up.

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You divide by volume.

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You determine--that gives you a
value for density.

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You divide by the critical
density and you know what's

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going to happen to the Universe.

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Okay.

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Now, how do you find the mass
of things?

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Determining mass.

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Well, one way you can do it is
you can just go out and measure

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how bright – yes,
go ahead.

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Student: Can you put the
other slide up?

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Prof: Oh,
put this back for a second.

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Top part?

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Bottom part?

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What do you-.

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Student: [Inaudible]
if you don't mind putting it

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on.

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Prof: Yeah, yeah.

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So, you've determined the
density of the Universe by

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adding up the mass.

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Divide it by volume.

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And then, the question becomes,
"How do you determine the

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mass?"

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And one way you can do it is,
you look at how bright things

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are.

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Add up the light you see.

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And then, you assume some value
for the amount of mass it takes

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to create a certain amount of
light.

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So, that's assuming what's
called a mass-to-light ratio.

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And so, you can do that,
you know.

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If it's the Sun,
then one solar mass produces

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one solar luminosity.

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If all stars--if all objects
are exactly like the Sun,

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then everything would be like
that.

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It turns out that isn't the
case, but you can take local

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samples of stars and figure out
what the average mass-to-light

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ratio is.

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And if you have some value that
you're happy with,

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of mass-to-light ratio,
then you multiply the amount of

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light by the mass-to-light
ratio,

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and this gives you a mass.

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Student: Do you need to
adjust for distance?

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Prof: Sorry.

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Student: Do you need to
adjust for distance?

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Prof: Well,
what you mean by light is

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the--do you need to adjust for
distance?

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What you mean by light is the
intrinsic light.

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You mean the equivalent of the
absolute magnitude,

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which takes the distance into
account.

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So, what you need to ask is not
how bright it looks,

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but its intrinsic brightness in
this particular case.

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Yes.

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So, you do need to account for
the distance,

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and so, you need to be thinking
about absolute magnitude rather

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than apparent magnitude,
yes.

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And that's one of the problems.

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That's hard to do.

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The other problem,
of course, is this awkward

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word, here ["assume"],
which is the kind of thing that

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makes people nervous,
because you could get that

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wrong.

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If you're looking at one kind
of star and it's actually some

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other kind of star,
which happens to be much more

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massive but dimmer,
like white dwarfs or something

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like that,
then you're going to make a

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mess of this.

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So, there's an alternative
method, which you may already

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have considered,
because we've done it in both

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of the previous parts of this
class,

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which is, you measure orbits.

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And you do the same thing we
did with--in part one and part

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two of the class.

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You find some star in the
distant portion of the galaxy,

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orbiting around the galaxy.

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You figure out how fast the
thing is going.

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You figure out how far the
thing is going.

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You use Kepler's Laws.

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And you determine the mass from
orbital theory,

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from Kepler's Laws,
basically.

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And, in particular,
you know, V^(2) =

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GM/a. And so,
you can measure this from the

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Doppler shift.

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You can determine this;
basically, in the case of

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galaxies, galaxies are big
objects.

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You can physically measure the
angular separation on the sky.

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Use the small angle formula,
if you know the distance,

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to determine this.

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So, this can also be measured,
and therefore,

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this can be calculated.

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And so, you go and do that for
a whole bunch of galaxies.

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And this has been done.

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And let me give you some
examples, here.

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Let me actually write down some
numbers and do some

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calculations.

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Supposing you have a galaxy at
a distance of 20 megaparsecs

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[Mpc].

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And supposing it has an
apparent magnitude of,

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something like,
14.

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These are kind of typical
numbers for nearby galaxy

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clusters.

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There's a particular--the
nearest big galaxy cluster to us

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is a cluster in the
constellation of Virgo,

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known as the Virgo cluster.

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If you want to know about the
Virgo cluster,

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ask Hugh Crowll [
a graduate teaching assistant

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for the course]
who is devoting his life to the

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study of this object and the
galaxies within it.

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But these are sort of
quasi-typical numbers,

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adjusted slightly because it's
actually 17 Mpc,

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which is kind of a pain.

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All right.

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So, what do you know about the
mass?

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What can you determine about
the mass of such a galaxy?

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Well--oh, and let me warn you
before we even begin that,

13:56.558 --> 13:59.048
of course, astronomers have
played you a dirty

13:59.045 --> 14:02.475
trick--namely,
that the symbol we use for

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magnitude is M.

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The symbol we use for mass is
also M.

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So, you've got to keep those
clear in your mind.

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All right.

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So, what do we know about this?

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We know the relationship
between apparent and absolute

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magnitude.

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And, as I said just a minute
ago, it's the absolute magnitude

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that we need to know in order to
actually determine anything.

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m - M = 5 log
(D / 10 parsecs).

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So, let's figure out the
right-hand side first.

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That's 5 log (2 x 10^(7)).

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That's 20 Mpc.

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1 Mpc is 10^(6).

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Over 10.

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That's 5 log (2 x 10^(6)).

14:51.760 --> 14:53.100
Now, what do I do about that?

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Let's see.

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That's 5 times log of 10^(6),
that's pretty straightforward,

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plus the log of 2.

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Because, if you add logs,
then you multiply the thing

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inside the parentheses.

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So, log (2) + log (10^(6)) =
log (2 x 10^(6)).

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log (10^(6)) = 6.

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log (2) = .3.

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It's just a useful number to
know.

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The log of 2 is around .3.

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The log of 3 is around .5.

15:29.920 --> 15:32.050
The log of 5 is around .7.

15:32.050 --> 15:34.680
You could look it up.

15:34.679 --> 15:39.919
And so, this is equal to 5 x
6.3.

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5 x 6 = 30.

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5 x .3 = 1.5.

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So, this is 31.5.

15:46.320 --> 15:51.450
Let me caution you at this
point.

15:51.450 --> 15:55.560
So, let me give you a little
side note, here.

15:55.560 --> 16:01.530
Do not approximate magnitudes.

16:01.530 --> 16:05.050


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Why not?

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I mean, we approximate
everything else in this course.

16:10.840 --> 16:14.340
Magnitudes are a logarithmic
quantity, right?

16:14.340 --> 16:20.180
And so, you don't approximate
magnitudes for the same reason

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that you don't approximate the
exponents.

16:24.429 --> 16:28.229
You can't say,
10^(7) is equal to 10^(6).

16:28.230 --> 16:32.520
You can say 7 equals 6,
but you can't say 10^(7) is

16:32.524 --> 16:35.884
equal to 10^(6),
because that's a factor of 10

16:35.877 --> 16:39.117
difference, whereas the
difference between 7 and 6 is

16:39.118 --> 16:41.048
just a little more than 10%.

16:41.050 --> 16:43.100
Similarly, this .3.

16:43.100 --> 16:46.250
You would have been tempted to
get rid of it,

16:46.247 --> 16:46.817
right?

16:46.820 --> 16:50.950
Because who cares about the
difference between 6 and 6.3?

16:50.950 --> 16:54.440
But, in fact,
it comes out of this log of 2.

16:54.440 --> 16:59.260
And so, .3 in the log is
actually a factor of 2.

16:59.259 --> 17:02.959
And so, you got to not
approximate the exponents.

17:02.960 --> 17:03.970
This is important.

17:03.970 --> 17:04.700
Yes?

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Student: Does this mean
we should also try to be more

17:06.452 --> 17:07.792
precise when we're dealing with
magnitudes?

17:07.790 --> 17:09.280
Prof: Well, yes.

17:09.279 --> 17:11.759
That's saying--I guess that's
saying the same thing.

17:11.760 --> 17:12.720
You should be more precise.

17:12.720 --> 17:14.130
That means you shouldn't
approximate.

17:14.130 --> 17:15.930
Yeah, so, I guess.

17:15.930 --> 17:22.910
But, it's for the same reason
that you don't approximate the

17:22.910 --> 17:24.330
exponents.

17:24.329 --> 17:27.689
And it's also true that the
numbers are easier to work with,

17:27.690 --> 17:31.160
because it turns out that you
add them rather than multiplying

17:31.163 --> 17:34.413
them most of the time,
so, it's not such a bad thing.

17:34.410 --> 17:38.930
Anyway, here we are at 31.5,
so what have we got?

17:38.930 --> 17:45.660
We've m - M =
31.5.

17:45.660 --> 17:50.440
This M was stated in the
problem to be 14.

17:50.440 --> 17:56.000
So, 14 - 31.5 = M.

17:56.000 --> 18:00.300
So, M = -17.5.

18:00.300 --> 18:05.670


18:05.670 --> 18:07.840
Okay.

18:07.840 --> 18:09.350
That's not such a bad number.

18:09.350 --> 18:10.800
We can work with that.

18:10.799 --> 18:13.509
So, now we know the absolute
magnitude.

18:13.510 --> 18:14.960
We know how bright the thing is.

18:14.960 --> 18:18.730
So, now we can figure out how
many times brighter than the Sun

18:18.734 --> 18:19.234
it is.

18:19.230 --> 18:20.780
Why is that a useful thing?

18:20.779 --> 18:22.969
Because if you then make the
assumption that the

18:22.971 --> 18:25.071
mass-to-light ratio is the same
as the Sun,

18:25.069 --> 18:27.919
that this galaxy consists
entirely of Sun-like stars,

18:27.916 --> 18:30.266
then you can determine how
massive it is.

18:30.270 --> 18:31.970
So, let's do that.

18:31.970 --> 18:39.900
How many Suns--and this is the
other magnitude equation.

18:39.900 --> 18:42.670
This is, you know,
M_1 –

18:42.670 --> 18:46.760
M_2 is equal
to--for two different objects,

18:46.759 --> 18:52.509
is equal to -5/2 log of the
brightness of 1 over the

18:52.509 --> 18:55.439
brightness of the other.

18:55.440 --> 18:58.610
But I think I want it in the
other form.

18:58.609 --> 19:03.819
I think I want it in the form
of 10^(-0.4),

19:03.824 --> 19:09.294
or 10^(-2/5 (M1-M2)) =
b_1 /

19:09.286 --> 19:12.386
b_2.

19:12.390 --> 19:16.160
This is the exact same
equation, as you'll recall,

19:16.160 --> 19:19.470
just having been--getting rid
of the log,

19:19.470 --> 19:22.950
taking everything,
putting it into 10 to the

19:22.952 --> 19:24.412
something power.

19:24.410 --> 19:27.690
The reason I want it in this
form is that this is the answer

19:27.689 --> 19:28.189
I want.

19:28.190 --> 19:29.640
I want b_1 /
b_2.

19:29.640 --> 19:33.210
I want one to be the galaxy.

19:33.210 --> 19:36.060
I want two to be the Sun.

19:36.059 --> 19:41.359
So, then, I've got 10^(-2/5),
and then, the galaxy is -17.5,

19:41.363 --> 19:44.243
that's the absolute magnitude.

19:44.240 --> 19:50.890
The Sun is 5,
has an absolute magnitude of 5.

19:50.890 --> 19:54.520
And that's going to give me the
brightness of the galaxy over

19:54.524 --> 19:56.224
the brightness of the Sun.

19:56.220 --> 20:03.660
That's 10^(-2/5 (22.5)) .

20:03.660 --> 20:03.880
Let's see.

20:03.880 --> 20:06.300
The minuses cancel out,
so that's a plus,

20:06.295 --> 20:06.955
actually.

20:06.960 --> 20:09.550
2/5 x 22.5 – well, let's see.

20:09.550 --> 20:12.100
2 x 22.5 = 45.

20:12.100 --> 20:14.680
A fifth of 45 is 9.

20:14.680 --> 20:18.520
So, this is equal to 10^(9).

20:18.519 --> 20:22.239
So, this galaxy is a billion
times brighter than the Sun,

20:22.235 --> 20:24.685
10^(9) times brighter than the
Sun.

20:24.690 --> 20:27.300
So, if it were made out of
Sun-like stars,

20:27.295 --> 20:30.405
it would have a mass of a
billion solar masses.

20:30.410 --> 20:40.770
So, mass would equal 10^(9)
times the mass of the Sun,

20:40.769 --> 20:45.459
if all Sun-like stars.

20:45.460 --> 20:48.450
But, it turns out that galaxies
tend to be somewhat dimmer than

20:48.445 --> 20:49.645
the Sun, per unit mass.

20:49.650 --> 20:53.790
Most stars are a little bit
less massive than the Sun,

20:53.793 --> 20:55.673
but a lot less bright.

20:55.670 --> 20:58.300
This is just the way stars turn
out to be.

20:58.299 --> 21:02.579
And so, typical mass-to-light
ratios of populations of stars

21:02.575 --> 21:06.415
tend to be on the order of 10,
or something like that,

21:06.415 --> 21:07.715
times the Sun.

21:07.720 --> 21:12.550
So, probably it needs to be
more massive,

21:12.551 --> 21:18.471
because typical stars are
fainter than the Sun.

21:18.470 --> 21:23.380
Typically, stars are fainter.

21:23.380 --> 21:27.290
So, you could guess and say,
mass, maybe,

21:27.290 --> 21:32.280
should be, I don't know,
10 times greater than that,

21:32.276 --> 21:34.716
10^(10) solar masses.

21:34.720 --> 21:38.470
And you can see why this
particular line of reasoning

21:38.472 --> 21:42.592
starts to get pretty dubious,
because I picked this number

21:42.585 --> 21:44.745
completely out of the air.

21:44.750 --> 21:46.950
There's actually some modest
basis for it,

21:46.951 --> 21:48.831
but you could pick other
numbers.

21:48.829 --> 21:52.319
You could argue about this
endlessly and you wouldn't get

21:52.315 --> 21:52.995
very far.

21:53.000 --> 21:54.520
Why should it be 10 times the
Sun?

21:54.520 --> 21:55.290
Maybe it's 100.

21:55.290 --> 21:56.290
Maybe it's 1,000.

21:56.290 --> 21:57.690
Maybe it's less than the Sun.

21:57.690 --> 21:59.210
How would you really know?

21:59.210 --> 22:04.640
And so, let's go back and do
the other approach--namely,

22:04.644 --> 22:09.984
figure out its mass from orbits
of things around it.

22:09.980 --> 22:13.280
So, let's look at--supposing
it's an edge-on galaxy.

22:13.279 --> 22:16.569
Here's the center of the
galaxy, or--and,

22:16.572 --> 22:20.032
actually, let's look at it from
the top.

22:20.029 --> 22:22.929
So, here's a nice spiral galaxy
of some kind.

22:22.930 --> 22:24.430
Here's the center of the spiral
galaxy.

22:24.430 --> 22:27.360
Here's some star way out on the
edge.

22:27.359 --> 22:31.029
That star is moving around the
center of the galaxy.

22:31.029 --> 22:32.829
It has to be,
or it's going to fall in.

22:32.829 --> 22:35.019
So, it's orbiting around the
center of the galaxy,

22:35.020 --> 22:36.630
presumably in some circular
orbit.

22:36.630 --> 22:40.190
You're down here,
looking at this thing.

22:40.190 --> 22:42.250
And, of course,
you can measure the velocity of

22:42.247 --> 22:44.927
that star by the Doppler shift,
because it's moving away from

22:44.932 --> 22:45.292
you.

22:45.289 --> 22:48.619
And so, one can measure this
velocity.

22:48.620 --> 22:52.270
You can measure this distance.

22:52.269 --> 22:55.659
That would be the equivalent of
a in our formulas,

22:55.660 --> 22:59.050
because it's the distance
between the orbiting object and

22:59.051 --> 22:59.961
the center.

22:59.960 --> 23:03.300
Stars are much less massive
than galaxies so we don't have

23:03.299 --> 23:05.759
to worry about the motion of the
galaxy.

23:05.759 --> 23:09.559
And you can use a familiar
equation--namely,

23:09.560 --> 23:12.920
V^(2) = GM /
a.

23:12.920 --> 23:15.900
So, now, let's give this some
numbers.

23:15.900 --> 23:19.790
Typical velocities of things
orbiting around the galaxy turn

23:19.788 --> 23:23.148
out to be something like 200
kilometers a second,

23:23.150 --> 23:27.570
or 2 x 10^(5) meters per second.

23:27.569 --> 23:30.419
And the size of a typical
galaxy, you know,

23:30.416 --> 23:33.666
out to where it stops being
easy to see stars is,

23:33.670 --> 23:37.060
oh, I don't know,
what number did I take here?

23:37.060 --> 23:42.080


23:42.080 --> 23:43.330
Yeah.

23:43.329 --> 23:52.709
Let's call it 20 kiloparsecs,
which is 2 x 10^(4) parsecs.

23:52.710 --> 23:56.180
And a parsec is 3 x 10^(16)
meters.

23:56.180 --> 24:00.330
So, this is 6 x 10^(20) meters.

24:00.329 --> 24:03.659
So, now, let's calculate
M.

24:03.660 --> 24:14.550
M = V^(2) a /
G. [(2 x 10^(5))^(2)(6 x

24:14.546 --> 24:19.986
10^(20))]
/ (7 x 10^(-11)).

24:19.990 --> 24:30.690
Get rid of those--let's see,
that's (4 x 10^(30)) /

24:30.694 --> 24:33.054
10^(-11).

24:33.049 --> 24:36.869
4 x 10^(41),
this is in kilograms.

24:36.869 --> 24:43.879
One solar mass,
you recall, is 2 x 10^(30).

24:43.880 --> 24:48.160
So, this mass,
in units of the Sun,

24:48.159 --> 24:55.329
(4 x 10^(41)) / (2 x 10^(30)),
which is something like 2 x

24:55.333 --> 24:58.483
10^(11) solar masses.

24:58.480 --> 25:03.110


25:03.109 --> 25:06.269
And now, we have a problem,
right?

25:06.269 --> 25:09.779
You probably don't remember
what the answer to the previous

25:09.779 --> 25:13.289
version of this problem was,
where we did it with light.

25:13.289 --> 25:19.569
That came out to a magnitude
of--the brightness was about

25:19.570 --> 25:22.150
10^(9) times the Sun.

25:22.150 --> 25:24.680
Maybe the mass is 10^(10) times
the Sun.

25:24.680 --> 25:27.250
But now we've just calculated
it in this other,

25:27.246 --> 25:29.586
more reliable way,
and it's 2 x 10^(11).

25:29.589 --> 25:34.389
It's 20 times more massive than
you thought it was going to be,

25:34.388 --> 25:38.178
given how bright the light from
this thing was.

25:38.180 --> 25:39.150
Yes, question?

25:39.150 --> 25:39.970
Student: [Inaudible]
mass of the galaxy?

25:39.970 --> 25:42.480
Prof: This is the mass
of the galaxy,

25:42.479 --> 25:42.829
yes.

25:42.829 --> 25:46.429
Now, before I go on let me just
point out--those of you who have

25:46.430 --> 25:49.860
taken a look at the problem
set--what I've just done here,

25:49.859 --> 25:52.589
this calculation I've just
done, is problem one of the

25:52.592 --> 25:54.502
problem set, except done
backwards.

25:54.500 --> 25:57.090
On the problem set,
what I did is,

25:57.092 --> 26:01.572
I told you what the density
was, what the critical density

26:01.571 --> 26:04.531
was,
and then, you had to derive

26:04.529 --> 26:08.239
characteristics of the galaxies
from that.

26:08.240 --> 26:10.490
Here I've told you what the
galaxies are like.

26:10.490 --> 26:15.020
We figured out how big--how
massive they are.

26:15.019 --> 26:19.409
If we divide by the volume,
we'll get a density.

26:19.410 --> 26:21.120
So, we're doing the same
problem backwards.

26:21.119 --> 26:23.489
I should say,
the numbers I've chosen here

26:23.493 --> 26:25.983
are different,
so, you can't know the answer

26:25.982 --> 26:29.692
to the problem set by looking at
the premises of these particular

26:29.687 --> 26:30.437
things.

26:30.440 --> 26:34.480
But, what I'm doing is the
exact same set of calculations,

26:34.480 --> 26:36.040
only done backwards.

26:36.039 --> 26:39.259
So, that may or may not be
helpful.

26:39.259 --> 26:44.339
But let's pause here for a
moment, because this is

26:44.340 --> 26:49.110
now--we're now up to--we're
making progress.

26:49.109 --> 26:53.969
We're now up to Frontiers and
Controversies circa 1985.

26:53.970 --> 27:01.830


27:01.829 --> 27:03.579
You'll remember,
in 1920, they were worried

27:03.581 --> 27:06.001
about whether the spiral nebulae
were actually galaxies.

27:06.000 --> 27:09.240
In 1950 they were worried
about, maybe the "steady state"

27:09.238 --> 27:10.798
was the correct response.

27:10.799 --> 27:18.299
And by the time 1985 rolls
around, the big issue is mass is

27:18.301 --> 27:22.571
determined by orbital rotation.

27:22.569 --> 27:30.789
So, what you might call
dynamical masses--that is to

27:30.793 --> 27:39.503
say, determined by orbits of
things around galaxies.

27:39.500 --> 27:42.740
Orbits around galaxies.

27:42.740 --> 27:46.020
And also, I should say,
galaxy clusters.

27:46.019 --> 27:49.969
You can have galaxies orbiting
around each other and galaxies

27:49.971 --> 27:53.991
orbiting around whole clusters
of galaxies, and the same thing

27:53.989 --> 27:54.779
is true.

27:54.779 --> 28:05.859
And so, around galaxies and
galaxy clusters--are much bigger

28:05.861 --> 28:14.691
than you expect from the light
they give off.

28:14.690 --> 28:20.220
And therefore--by about a
factor of 10.

28:20.220 --> 28:22.450
By approximately a factor of 10.

28:22.450 --> 28:25.700
So, there's 10 times more mass
than you can account for by

28:25.698 --> 28:27.178
adding up all the stars.

28:27.180 --> 28:30.090
Now, there's mass in other
forms than stars.

28:30.090 --> 28:33.500
There's also dust.

28:33.500 --> 28:34.370
There's also gas.

28:34.369 --> 28:36.739
These are things you can detect
in other ways.

28:36.740 --> 28:41.680
You add them all up and you're
still off by about a factor of

28:41.678 --> 28:42.088
10.

28:42.089 --> 28:45.659
So, there's 10 times more mass
than you have any way of

28:45.657 --> 28:46.777
accounting for.

28:46.779 --> 28:52.479
This is the so-called dark
matter problem.

28:52.480 --> 28:56.730
So, this is Frontiers and
Controversies in 1985.

28:56.730 --> 28:59.160
There's all this dark matter.

28:59.160 --> 29:02.710
Most of the matter in galaxies
is in some form that we can't

29:02.708 --> 29:03.248
detect.

29:03.250 --> 29:05.560
It's dark matter,
and what is it?

29:05.560 --> 29:09.280


29:09.279 --> 29:12.759
Now, unlike Frontiers and
Controversies in 1920 and 1950,

29:12.760 --> 29:16.370
this is one that we haven't
solved yet, so I don't know the

29:16.366 --> 29:17.046
answer.

29:17.049 --> 29:20.499
For a quarter of a century,
people have been busy trying to

29:20.499 --> 29:21.569
figure this out.

29:21.570 --> 29:23.990
There's still no good answer.

29:23.990 --> 29:26.760
And ten years ago,
when I taught this course,

29:26.758 --> 29:30.408
this question of what is the
dark matter was a big focus of

29:30.408 --> 29:32.168
this part of the course.

29:32.170 --> 29:36.360
Now, I'm going to talk about it
only in this class,

29:36.362 --> 29:40.132
only in one lecture,
because we got way bigger

29:40.134 --> 29:42.654
problems, even,
than this.

29:42.650 --> 29:44.360
That's saying a lot.

29:44.359 --> 29:47.879
I've just told you that we
don't know what 90% of the mass

29:47.884 --> 29:50.674
in the Universe is,
and then, we've got bigger

29:50.667 --> 29:52.087
problems than that.

29:52.089 --> 29:56.209
So, things are getting a little
murky, here, and not just

29:56.207 --> 29:58.337
because the matter is dark.

29:58.340 --> 30:01.480
Okay.

30:01.480 --> 30:03.970
But, let me pause a little bit
on dark matter,

30:03.968 --> 30:06.068
because it's an interesting
problem.

30:06.069 --> 30:09.469
And, as I say,
we have no idea what this stuff

30:09.471 --> 30:09.851
is.

30:09.850 --> 30:11.700
What are the possibilities?

30:11.700 --> 30:16.070
So, here's a hypothesis.

30:16.069 --> 30:24.749
Hypothesis #1 is that what this
stuff is, is some kind of

30:24.750 --> 30:29.400
unknown sub-atomic particle.

30:29.400 --> 30:34.860


30:34.859 --> 30:37.149
And it has to have two
characteristics,

30:37.148 --> 30:39.978
this sub-atomic particle,
for it to work out.

30:39.980 --> 30:41.690
It has to have mass.

30:41.690 --> 30:43.240
That's pretty basic.

30:43.240 --> 30:45.780
If you're using it to explain
mass, you can't have photons,

30:45.779 --> 30:46.129
right?

30:46.130 --> 30:48.180
Photons don't carry any mass.

30:48.180 --> 30:53.570
It has to have mass,
but it has to not interact with

30:53.565 --> 30:54.405
light.

30:54.410 --> 31:01.740
No interaction with light.

31:01.740 --> 31:03.820
If it absorbs light,
it would be opaque,

31:03.823 --> 31:06.973
and we would know it was there,
because galaxies behind this

31:06.974 --> 31:08.314
stuff would look dim.

31:08.309 --> 31:11.999
Alternatively,
if it gives off light,

31:11.995 --> 31:13.935
then we'd see it.

31:13.940 --> 31:17.960
And so, it has to not interact
with light, or interact with

31:17.958 --> 31:19.688
light only very weakly.

31:19.690 --> 31:27.190
And so, these are given the
name, generically,

31:27.191 --> 31:35.361
Weakly Interactive Massive
Particles, or WIMPs.

31:35.359 --> 31:39.179
So, here's the hypothesis:
the Universe is 90% WIMPs.

31:39.180 --> 31:43.150
This is not such a crazy idea
as it might, at first,

31:43.154 --> 31:43.704
seem.

31:43.700 --> 31:47.440
There are known sub-atomic
particles that have these

31:47.437 --> 31:48.387
properties.

31:48.390 --> 31:50.250
There's something called the
neutrino.

31:50.250 --> 31:52.870
There are trillions of them
going through this room every

31:52.869 --> 31:53.289
second.

31:53.289 --> 31:57.709
They have mass and they don't
interact very much with

31:57.705 --> 31:58.635
anything.

31:58.640 --> 32:01.650
They're known to exist from
particle accelerator

32:01.647 --> 32:05.867
experiments, and they have been
detected from celestial sources.

32:05.869 --> 32:08.829
Now, we know that--for various
reasons, that the dark matter

32:08.826 --> 32:10.376
doesn't consist of neutrinos.

32:10.380 --> 32:14.200
But, there could be many other
kinds of particles with these

32:14.200 --> 32:17.760
kinds of characteristics,
and indeed, some are predicted

32:17.762 --> 32:19.902
by current particle theories.

32:19.900 --> 32:22.740
As I say, WIMPs have been
detected--I'm sorry,

32:22.743 --> 32:26.033
WIMPs have not been detected,
but neutrinos have been

32:26.028 --> 32:26.848
detected.

32:26.850 --> 32:27.960
Here's how they do it.

32:27.960 --> 32:29.180
It's kind of an amazing
experiment.

32:29.180 --> 32:34.060
They took a mineshaft in South
Dakota and filled it with

32:34.061 --> 32:35.571
cleaning fluid.

32:35.569 --> 32:38.869
And the reason they did that
was that every so

32:38.866 --> 32:42.816
often--neutrinos don't interact
with light, but they do

32:42.823 --> 32:46.343
interact, occasionally,
with chlorine atoms.

32:46.339 --> 32:50.189
And the effect of a neutrino
banging into a chlorine atom is

32:50.192 --> 32:51.762
to turn it into argon.

32:51.759 --> 32:54.619
And so, this happens--there
are--as I say,

32:54.621 --> 32:58.321
trillions of neutrinos flow
this mine every second.

32:58.319 --> 33:01.369
Once a day or so,
one of them will hit a chlorine

33:01.369 --> 33:03.909
atom just right,
create an argon atom.

33:03.910 --> 33:05.050
So, here's what you do.

33:05.049 --> 33:07.179
You fill your mineshaft with
cleaning fluid,

33:07.184 --> 33:09.914
a large fraction of which is
chlorine, and you count the

33:09.914 --> 33:11.904
argon atoms that bubble off the
top.

33:11.900 --> 33:14.150
And this has been successful.

33:14.150 --> 33:17.860
They detected neutrinos emitted
from the Sun.

33:17.859 --> 33:21.919
The Sun is--all stars that have
nuclear reactions going on in

33:21.923 --> 33:25.853
them, emit neutrinos as part of
the output of these nuclear

33:25.851 --> 33:26.801
reactions.

33:26.799 --> 33:30.359
And then, they had a problem,
because they had predicted how

33:30.357 --> 33:34.157
many neutrinos you ought to see
from the Sun in an experiment of

33:34.155 --> 33:36.455
this kind,
and they didn't see enough of

33:36.458 --> 33:36.758
them.

33:36.760 --> 33:38.740
They only saw a third of them.

33:38.740 --> 33:41.510
And it turns out--and then,
there was a big debate for a

33:41.514 --> 33:42.124
long time.

33:42.119 --> 33:45.949
This is Frontiers and
Controversies circa about 1975.

33:45.950 --> 33:47.960
There was a big debate for a
while.

33:47.960 --> 33:49.770
Where are all the solar
neutrinos?

33:49.769 --> 33:53.169
Is it possible that we don't
understand nuclear reactions in

33:53.173 --> 33:53.753
the Sun?

33:53.750 --> 33:57.970
Is it possible that we don't
understand the chemistry of

33:57.966 --> 33:59.496
chlorine or argon?

33:59.500 --> 34:01.940
After all, you're counting
individual argon atoms,

34:01.938 --> 34:03.778
so that's kind of a difficult
task.

34:03.779 --> 34:06.419
No, it turned out that what was
going on was,

34:06.420 --> 34:08.400
we didn't understand neutrinos.

34:08.400 --> 34:10.760
And it turns out there are
three kinds of neutrinos.

34:10.760 --> 34:14.010
And neutrinos switch back and
forth between these different

34:14.013 --> 34:17.383
kinds, and you could only detect
one kind by the chlorine.

34:17.380 --> 34:21.980
And so, they were all emitted
from the Sun as if they were in

34:21.983 --> 34:26.283
the form that you would have
been able to detect them.

34:26.280 --> 34:29.530
But as they traveled from the
Sun to us, some fraction of them

34:29.529 --> 34:32.459
flipped back and forth between
all these other kinds,

34:32.460 --> 34:35.310
and you ended up only with
about a third of them.

34:35.309 --> 34:37.769
So, it was a big piece of
particle physics that was

34:37.770 --> 34:38.410
discovered.

34:38.409 --> 34:42.699
We have also detected,
by now, neutrinos coming from

34:42.696 --> 34:44.626
supernova explosions.

34:44.630 --> 34:48.080
So, there are--11 of them,
I think, were detected,

34:48.083 --> 34:49.073
all at once.

34:49.070 --> 34:52.120
And if you're detecting things,
sort of, once per day,

34:52.121 --> 34:55.751
and then you suddenly detect 11
of them over the course of a few

34:55.749 --> 34:58.649
minutes,
you've seen something exciting

34:58.653 --> 34:59.173
occur.

34:59.170 --> 35:03.590
And that is now known to be
this supernova explosion that

35:03.588 --> 35:06.348
occurred in a neighboring
galaxy.

35:06.349 --> 35:09.479
And so, there are a bunch
of--so, by analogy with that,

35:09.484 --> 35:12.564
people are looking for the
WIMPs that make up the dark

35:12.561 --> 35:13.201
matter.

35:13.199 --> 35:15.489
If all this dark matter is in
WIMPs, there are lots,

35:15.489 --> 35:17.819
and lots, and lots of these
things, and they're going

35:17.823 --> 35:19.083
through us every second.

35:19.079 --> 35:23.129
So, there are a whole bunch of
experiments with the same basic

35:23.133 --> 35:24.333
characteristics.

35:24.329 --> 35:27.539
You have a huge vat of
something, and something is

35:27.543 --> 35:29.643
supposed to happen,
occasionally,

35:29.642 --> 35:33.252
when one of these WIMPs hits
whatever's in the vat.

35:33.250 --> 35:36.280
So, the Japanese have,
sort of, a cubic mile of

35:36.279 --> 35:39.309
distilled water,
and they're looking for little

35:39.309 --> 35:43.589
light flashes when the neutrino
runs into the water molecule.

35:43.590 --> 35:46.390
They busted all their detectors
recently, and they had a sort of

35:46.391 --> 35:48.311
earthquake,
and it was bad for the little

35:48.312 --> 35:51.092
light detectors they had put on
the inside of these things.

35:51.090 --> 35:53.800
But there are a lot of such
experiments.

35:53.800 --> 35:56.230
Dan McKinsey,
here in the Physics Department,

35:56.228 --> 35:58.048
is a big player in one of them.

35:58.050 --> 36:02.400
And the hope is that you will
see the interaction between one

36:02.404 --> 36:05.314
of these WIMPs,
of which there must be an

36:05.306 --> 36:08.496
incredibly large number,
with something.

36:08.500 --> 36:10.990
This has, so far, failed.

36:10.989 --> 36:13.809
So, there is no direct evidence
from WIMPs.

36:13.809 --> 36:14.959
The other hope,
I should say,

36:14.962 --> 36:16.982
is that every time you build a
bigger collider,

36:16.980 --> 36:19.060
you make new kinds of
sub-atomic particles,

36:19.062 --> 36:21.892
and that they'll eventually
make something that looks like

36:21.889 --> 36:23.029
it could be a WIMP.

36:23.030 --> 36:25.420
And that hasn't been--happened
either.

36:25.420 --> 36:28.870
So, no detections yet.

36:28.870 --> 36:35.990
No direct detections.

36:35.989 --> 36:38.979
With considerable effort,
you know, this is going to turn

36:38.980 --> 36:41.330
out to be 90% of the mass in the
Universe.

36:41.329 --> 36:44.009
So, you would like to detect it
because if you do,

36:44.013 --> 36:45.823
they'll give you a Nobel Prize.

36:45.820 --> 36:48.520
All right, that's one
hypothesis.

36:48.520 --> 36:51.190
There's another hypothesis.

36:51.190 --> 36:54.230
So, here's Hypothesis #2.

36:54.230 --> 36:58.560


36:58.559 --> 37:01.409
It's just, you know,
dark chunks of something that

37:01.408 --> 37:02.278
doesn't glow.

37:02.280 --> 37:05.600
Ordinary matter--chunks.

37:05.599 --> 37:07.799
Student: Do these
hypotheses exist today or

37:07.804 --> 37:08.344
[inaudible].

37:08.344 --> 37:10.464
Prof: Yes,
yes, yes, all of the--we don't

37:10.460 --> 37:12.440
know what it is,
and so, nothing has yet been

37:12.440 --> 37:13.250
ruled out.

37:13.250 --> 37:16.220
What happens is that they--you
know, they continue to conduct

37:16.219 --> 37:18.549
these experiments,
so, you can rule out WIMPs with

37:18.546 --> 37:19.926
certain kinds of
characteristics,

37:19.925 --> 37:21.645
because you would have detected
them.

37:21.650 --> 37:23.730
Similarly, you can rule out
some of these other things with

37:23.732 --> 37:25.672
certain characteristics,
because you would have noticed

37:25.671 --> 37:26.391
they were there.

37:26.389 --> 37:29.819
But both of these hypotheses
are still more or less viable.

37:29.820 --> 37:35.510
Chunks of ordinary matter that
just don't glow,

37:35.510 --> 37:38.480
that don't emit light.

37:38.480 --> 37:40.690
Now, there's some limitations.

37:40.690 --> 37:46.170
These chunks can't be too
small, because if what you've

37:46.174 --> 37:49.734
got are tiny,
you know, micron-sized

37:49.728 --> 37:53.078
particles, we call that dust.

37:53.079 --> 37:54.879
And, basically,
that's what it is.

37:54.880 --> 37:56.120
It would just be dust.

37:56.119 --> 37:59.409
The problem with dust is,
dust in large quantities is

37:59.411 --> 38:01.881
opaque, and you can't see
through it.

38:01.880 --> 38:04.740
And therefore,
you would know it was there,

38:04.735 --> 38:08.265
because it obscures the light
of things behind it.

38:08.269 --> 38:10.559
And, indeed,
we see cosmic dust this way all

38:10.563 --> 38:11.153
the time.

38:11.150 --> 38:14.130
It's just, there isn't nearly
enough of it to account for any

38:14.126 --> 38:16.206
substantial fraction of the dark
matter.

38:16.210 --> 38:28.460
So, dust would be observed
because it--by obscuring light.

38:28.460 --> 38:36.580
And it also tends to glow in
the infrared.

38:36.579 --> 38:39.999
And so, we know that dusts
exists but we can count how much

38:39.997 --> 38:42.587
of it there is,
because it obscures light and

38:42.589 --> 38:45.299
it makes its presence known in
other ways.

38:45.300 --> 38:49.500
It's also true that these
chunks of ordinary matter can't

38:49.495 --> 38:50.465
be too big.

38:50.469 --> 38:54.629
They can't be the size of whole
galaxies, or even a substantial

38:54.627 --> 38:56.167
fraction of a galaxy.

38:56.170 --> 39:01.210
You can't take all your dark
matter and put it into one lump

39:01.208 --> 39:06.328
per galaxy, or even 100 lumps
per galaxy because if they were

39:06.331 --> 39:10.331
very large masses,
you'd see it,

39:10.328 --> 39:19.128
because it would disrupt the
orbits of stars around the

39:19.130 --> 39:20.760
galaxy.

39:20.760 --> 39:23.700
So, if there was some huge
unknown mass,

39:23.702 --> 39:26.572
you'd see things orbiting
around it.

39:26.570 --> 39:27.990
And, in fact, we do.

39:27.989 --> 39:30.939
We see these supermassive black
holes in the centers of galaxies

39:30.939 --> 39:34.199
and we know they're there,
because we see stars orbiting

39:34.201 --> 39:37.971
around them, just like the
problem on the last Midterm.

39:37.970 --> 39:40.550
And so, it can't be too small.

39:40.550 --> 39:41.500
It can't be too big.

39:41.500 --> 39:44.970
But, you could,
perhaps, have,

39:44.970 --> 39:49.040
sort of, a bunch of star
massed;

39:49.039 --> 39:54.499
so, you could have sort of a
bunch of star massed,

39:54.500 --> 40:00.630
or planet massed dark things
in--it would have to be,

40:00.630 --> 40:02.810
for various technical reasons
that I won't go into,

40:02.812 --> 40:04.822
it has to be in the outer parts
of galaxies,

40:04.820 --> 40:09.450
in the halos of galaxies.

40:09.449 --> 40:11.089
So, that, in principle is
possible.

40:11.090 --> 40:13.190
We wouldn't have any direct way
of detecting them.

40:13.190 --> 40:24.180
These things are called Massive
Astrophysical Compact Halo

40:24.181 --> 40:26.111
Objects.

40:26.110 --> 40:28.950
[Laughter] Some people get it.

40:28.949 --> 40:31.199
Massive, because they have to
carry mass.

40:31.199 --> 40:33.219
Astrophysical,
because they're not particles.

40:33.219 --> 40:35.539
Compact, because if they were
big you'd--you know,

40:35.543 --> 40:37.443
they'd block light and you'd
see them.

40:37.440 --> 40:40.280
Halo, because that's the part
of the galaxy they're in.

40:40.280 --> 40:43.290
These are MACHOs, right?

40:43.289 --> 40:45.779
And so, the alternative to
WIMPs is MACHOs.

40:45.780 --> 40:49.550
And so, the alternative
explanation is that 90% of the

40:49.547 --> 40:51.037
Universe is MACHOs.

40:51.039 --> 40:54.939
There's been a very clever
experiment carried out to try

40:54.938 --> 40:56.638
and find these things.

40:56.640 --> 40:58.700
Here's how you do it.

40:58.699 --> 41:00.659
You do it with gravitational
lensing.

41:00.660 --> 41:09.300


41:09.300 --> 41:16.010
Lensing MACHO searches;
remember gravitational lensing?

41:16.010 --> 41:19.190
This is this business that mass
bends light.

41:19.190 --> 41:21.280
So, here you are.

41:21.280 --> 41:23.720
You're looking at some star.

41:23.719 --> 41:28.739
And, in between you and the
star is a MACHO of some kind.

41:28.740 --> 41:30.100
So, here's the MACHO.

41:30.099 --> 41:34.949
You can't see the MACHO,
but the presence of the MACHO

41:34.946 --> 41:38.326
changes the direction of the
light.

41:38.329 --> 41:44.309
So, it comes into you like
this, and it basically acts like

41:44.311 --> 41:45.241
a lens.

41:45.239 --> 41:50.629
And, in particular,
the way it acts like a lens,

41:50.625 --> 41:56.355
in the case of MACHOs lensing
stars, is it makes it

41:56.355 --> 42:00.705
brighter--makes the star
brighter.

42:00.710 --> 42:03.890
Now, in order for this to work,
the alignment has to be

42:03.886 --> 42:05.176
essentially perfect.

42:05.179 --> 42:07.539
All of these objects are moving
around.

42:07.539 --> 42:09.859
They're orbiting the galaxy and
stuff.

42:09.860 --> 42:20.660
So, the alignment holds for a
few weeks, typically.

42:20.659 --> 42:23.549
So, what you'll see is,
you'll see this star become

42:23.546 --> 42:24.466
much brighter.

42:24.469 --> 42:26.999
And it can really become much
brighter--we're talking tens to

42:26.998 --> 42:29.188
hundreds of times brighter than
it ordinarily was.

42:29.190 --> 42:32.710
This lasts for a few weeks,
and then, it goes away.

42:32.710 --> 42:34.440
These have been observed.

42:34.440 --> 42:36.740
These lensing events have been
observed.

42:36.740 --> 42:44.320
Lensing events observed.

42:44.320 --> 42:54.210
But there are too few of them
to explain the dark matter.

42:54.210 --> 42:55.360
Now, there are still ways out.

42:55.360 --> 42:56.190
Let's see.

42:56.190 --> 42:59.970
If you have particularly low
mass MACHOs, so--supposing the

42:59.967 --> 43:04.067
whole Universe is filled with
things about the mass of Earth,

43:04.070 --> 43:11.210
those cause lensing events that
might be too small to see.

43:11.210 --> 43:13.600
Alternatively,
supposing you have things that

43:13.603 --> 43:16.273
are many thousands of times the
mass of a star,

43:16.269 --> 43:20.019
but not big enough to totally
disrupt galactic orbits,

43:20.020 --> 43:24.550
then, there are many fewer of
them for a given amount of mass,

43:24.550 --> 43:27.490
and there aren't enough MACHO
events that you would have

43:27.490 --> 43:30.110
expected to see any substantial
number of them.

43:30.110 --> 43:33.820
So, there's still a way around
the result of these experiments,

43:33.817 --> 43:35.907
if you want to believe in
MACHOs.

43:35.910 --> 43:37.610
But it's getting very tough.

43:37.610 --> 43:45.260
So, no WIMPs detected so far.

43:45.260 --> 43:46.460
No MACHOs.

43:46.460 --> 43:49.850


43:49.849 --> 43:53.689
You could still postulate kinds
of WIMPs and kinds of MACHOs

43:53.689 --> 43:57.529
that might explain the dark
matter, but it's getting kind of

43:57.529 --> 43:58.179
tough.

43:58.179 --> 44:01.759
Most people,
I think, believe in WIMPs.

44:01.760 --> 44:05.690
Most people tend to believe in
this.

44:05.690 --> 44:09.860
But, and as far as I can tell,
that's because the particle

44:09.855 --> 44:14.235
physicists keep coming up with
new candidate WIMPs that might

44:14.239 --> 44:16.699
exist,
but that we haven't quite been

44:16.699 --> 44:17.909
able to see, so far.

44:17.909 --> 44:22.729
And so, there's a theoretical
basis for the existence of these

44:22.725 --> 44:25.405
things, whereas,
with these MACHOs,

44:25.408 --> 44:29.038
if you ask the astronomers –
well, fine.

44:29.039 --> 44:33.049
So, you want to have 90% of the
Universe be in little Earth-like

44:33.052 --> 44:37.002
things just floating around with
no star, how did they--how did

44:37.000 --> 44:38.020
that happen?

44:38.020 --> 44:39.370
How did these come into being?

44:39.369 --> 44:41.789
We really have no answer at all
for that.

44:41.789 --> 44:45.329
So, there's no theoretical
basis for any of the

44:45.325 --> 44:48.165
still-allowed categories of
MACHOs.

44:48.170 --> 44:51.190
And so, at the moment,
people tend to believe WIMPs

44:51.192 --> 44:54.942
over MACHOs, although there's no
direct evidence for either.

44:54.940 --> 44:55.700
Yes?

44:55.699 --> 44:58.989
Student: If 90% of the
matter of the Universe is made

44:58.988 --> 45:02.168
of little Earth-like objects,
then wouldn't that be 90% of

45:02.165 --> 45:04.055
the Universe is made of metal?

45:04.060 --> 45:06.010
Prof: Oh, Earth.

45:06.010 --> 45:08.930
Earth-mass objects is what I
meant.

45:08.929 --> 45:10.309
I don't care what it's made out
of.

45:10.309 --> 45:14.549
Yeah, maybe there are little
Earth-sized balls of hydrogen.

45:14.550 --> 45:16.080
That would be fine too.

45:16.080 --> 45:18.060
Except how do you get them?

45:18.059 --> 45:22.579
We know something about how
balls of hydrogen form and what

45:22.579 --> 45:23.669
they become.

45:23.670 --> 45:25.250
They turn into stars.

45:25.250 --> 45:26.740
This is well known.

45:26.739 --> 45:30.759
And one of the popular kinds of
MACHOs was just very,

45:30.756 --> 45:32.066
very dim stars.

45:32.070 --> 45:35.040
And this is one of the things
that the space telescope helped

45:35.035 --> 45:37.605
to rule out, because it can see
really faint objects,

45:37.605 --> 45:38.935
and they weren't there.

45:38.940 --> 45:41.330
And so, no WIMPs.

45:41.330 --> 45:43.230
No MACHOs.

45:43.230 --> 45:48.710
And so, we don't know what's
going on.

45:48.710 --> 45:51.720
That was a digression.

45:51.719 --> 45:59.019
And what I digressed from was
the fact that this galaxy that

45:59.020 --> 46:05.830
we had measured the mass of
turned out to be 2 x 10^(11)

46:05.826 --> 46:12.426
solar masses,
or around 4 x 10^(41) kilograms.

46:12.429 --> 46:21.319
If you have these things,
one such galaxy every--I don't

46:21.323 --> 46:28.443
know, 2 Mpc, or so,
what's the density of the

46:28.437 --> 46:30.537
Universe?

46:30.539 --> 46:34.089
Remember, that's where we
started--of the Universe.

46:34.090 --> 46:36.720
So, now, let's finish this
calculation.

46:36.719 --> 46:41.749
Let's see the density is equal
to M/V.

46:41.750 --> 46:47.020
4 x 10^(41),
from observing these orbits.

46:47.019 --> 46:51.269
And the volume,
down here, is going to 2 Mpc

46:51.269 --> 46:52.059
cubed.

46:52.059 --> 46:57.449
That's 2 x 10^(6),
times 2--sorry,

46:57.445 --> 47:00.705
times 3 x 10^(16).

47:00.710 --> 47:02.610
That's 1 parsec.

47:02.610 --> 47:06.680
So, this is 6 x 10^(22).

47:06.680 --> 47:08.210
I want to cube it.

47:08.210 --> 47:09.670
6^(3).

47:09.670 --> 47:14.780
6 x 6 = 36, times another 6,
is 200.

47:14.780 --> 47:23.210
So, that's 200 x 10^(66),
or 2 x 10^(68).

47:23.210 --> 47:25.600
So, then, the density of the
Universe.

47:25.599 --> 47:35.449
(4 x 10^(41)) / (2 x 10^(68)),
that's equal to 2 x 10^(-27)

47:35.446 --> 47:40.196
kilograms per meter cubed.

47:40.199 --> 47:46.479
And real critical can be
calculated--turns out to be,

47:46.478 --> 47:52.878
as you'll discover on the
problem set, 6 x 10^(-27) in

47:52.878 --> 47:54.808
these units.

47:54.809 --> 48:00.109
ρ over ρ_critical
is equal to about 1/3.

48:00.110 --> 48:04.480
So, if you buy that,
the Universe is going to keep

48:04.478 --> 48:09.198
expanding, because Ω,
the ratio of the density to the

48:09.203 --> 48:12.683
critical density is only about
1/3.

48:12.679 --> 48:15.369
But the problem is,
we've got all this dark matter

48:15.370 --> 48:18.610
around and what we're doing is,
we're adding up galaxies.

48:18.610 --> 48:21.500
How do you know that there
isn't a whole bunch of dark

48:21.501 --> 48:23.521
matter where there aren't
galaxies?

48:23.519 --> 48:25.999
And where there's nothing to
see orbiting around,

48:26.003 --> 48:27.973
you have no idea what this
stuff is.

48:27.969 --> 48:30.209
And, indeed,
most of the WIMP kinds of

48:30.213 --> 48:32.763
ideas, sort of,
postulate some kind of dark

48:32.759 --> 48:35.669
matter that, kind of,
pervades the Universe.

48:35.670 --> 48:38.780
And so, you'd expect there to
be somewhat more of it than you

48:38.783 --> 48:40.343
can see in any given galaxy.

48:40.340 --> 48:44.330
Well, somewhat more than 1/3
gets you into dangerous

48:44.330 --> 48:46.210
territory;
namely near one,

48:46.213 --> 48:49.703
which is the thing we're trying
to distinguish--whether this

48:49.695 --> 48:51.755
number is greater than 1 or not.

48:51.760 --> 48:53.930
And so, you need a new approach.

48:53.929 --> 48:56.069
This isn't going to get you the
answer.

48:56.070 --> 48:58.680
And so, there is a different
approach.

48:58.679 --> 49:02.849
And that's what we'll talk
about next time.

49:02.849 --> 49:06.619
And that will finally bring us
up to Frontiers and

49:06.617 --> 49:09.997
Controversies in the
twenty-first century.