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Lecture 18 A105 Dark Matter | Brian Woodahl | YouTubeToText
YouTube Transcript: Lecture 18 A105 Dark Matter
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Summary
Core Theme
The Milky Way galaxy's center hosts a supermassive black hole, and its rotational velocity profile deviates significantly from predictions based on visible matter, strongly suggesting the presence of a dominant, unseen component known as dark matter.
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All right, guys. Let's go ahead and
begin. Uh, so we'll pick up where we
left off last time. We were
analyzing the matter at the center of
the Milky Way uh, galaxy. So, I'm just
bullet here analyzing matter at center
Milky Way continued and we left off.
we're able to determine using Newton's
laws or if you could call Kepler's third
law if you want to the mass at the
center of the galaxy is 2.5 * 10 6* the
mass of our sun. So that's 2 and a half
million times the mass of our sun at the
center of the
uh Milky Way.
Now continuing on
uh the so to get that number remember we
had you know the formula that we used
just to rewrite that but we had it
yesterday. So it's r
v^2 over g. And we're again we're you
know you're analyzing the hydrogen
uh particles that are in a tight orbit
around that central mass and and so the
particles that's r is the distance out
and then the v is the uh the
velocity. And um if you then try to pin
down a size on the on the mass that's at
um 10 raised to the 10 m which is close
to 1 AU 1 AU being the distance from the
sun to the earth. Um, so just to put
this in perspective, this is we're able
to kind of, you know, pin down the size
of what that that mass that's at the
center of the uh, galaxy. And of course,
there's the actual value. So now we have
these two
numbers, the size and we have the
mass. And and after we got those then it
became apparent well we should check
something and so what we want to check
is we want to do the calculation on the
Schwarz child radius of of this uh mass
this. And so we'll go ahead and write that
down. We had that earlier.
So any black hole uh will satisfy this
equation. Uh that's the mass of the
black hole and then that's the
shortchild radius which is the basically
the size of it. You know the radius out
to the event horizon. So you know
because we have these two data points
here about the size of this object and
the mass of this object we could put
those in the Schwarz child radius and
and see what we get. If we get uh an
agreement there, then we can make a
statement about that object that's at
the center of the Milky Way galaxy. So,
let's just go ahead and put these
numbers in and see what we get. So based
upon that mass, let's see what the
Schwarz sheld radius is and then we'll
compare it to this number we got here 10
the 10th and just see what what we Okay,
so we've
got two the gravitate ah come on two the
gravitational constant the mass of the
object and then we divide by the speed
of light squared. So go ahead and put
those numbers in. So two is two
gravitational constant 6.67
67 10 - 11. Now I got to do the
mass. So
that's 2.5 * 10 6 * the mass of the sun.
The mass of the sun is 2 * 10 30. So
I've got 2.5
* 10 6 and then I multiply that by the
mass of the sun which is 2 * 10 30 and
we divide that by uh the speed of the
light squared. So 3 * 10 8 and we square
that. Okay. So when you do the
calculation what you see
is you get a Schwarz child radius that's
10 the 10 m and that's what we see when
we measure the size of that. So we can
make this statement now this is a very
big black hole okay and it's you know
two and a half billion times the mass of
our sun and because it's so large we
call this a super massive black hole. So there
Okay. And that just comes out of the the
two data points, you know, that we've
calculated. What's the mass there? Uh,
using Newton's laws. And then based upon
the visual evidence, what constraining
that that mass, what size do we get? And
And that tells us it's a black hole. So
super massive because very large mass.
Now there's additional evidence that
supports the existence of a very large black
hole. So let's do a new bullet here. Other
evidence. So if we look at uh the center
of the Milky Way galaxy, what we see is
we see three pieces of uh basically
radiation that uh would be produced as
production
Uh let me tell you about synretron
radiation. Of course X-rays are high
energy photons. Posetrons are like
electrons are the the antiparticle of
electron. Anytime matters violently
smashed together you can get posetrons.
Okay. Now this but let's talk about the
synretron I got too many
here. Spell this.
radiation. Anytime you have uh charged
particles in particular, they're usually
electrons and they're trapped due to a a
field either gravitational or magnetic
some sort of field where they travel in
a tight orbit. They give off what's
called synretron
radiation. So synretron radiation so
uh high-speed electrons trapped by fields
A field could be magnetic. It could be
gravitational. Whatever. High-speed
electrons trapped by a
um electromagnetic
radiation and this radiation is because
it's traveling in a circle. It's
accelerating due to its acceleration due
to its uh
uh well centrial acceleration but that's
due to the fact that the velocity vector
is changing direction. Let me let me
just say due to its acceleration. We'll
just leave it at
that. That's synretron radiation. high-speed
high-speed
electrons which are charged particles
and because they're traveling in a
circle by virtue of Maxwell's equations
anytime you have a charged particle
that's undergoing acceleration it'll
give off electromagnetic radiation the
EM stands for electromagnetic radiation
and that's that's synretron radiation
okay uh and the X-ray production is
anytime you take matter and smash it
together high speeds you can produce X-rays
X-rays
X-rays again are high energy
electromagnetic radiation. So what's
happening you see as matter falls into
the black hole the tidal forces slam it
together. You just think of a black hole
is kind of a funnel and matter gets
slammed together as it falls in and then
that v that violent collision is then
producing these three pieces of
uh radiation that we see. Okay. So we
see that coming from the center of the
Milky Way and that's what's giving us
additional evidence that we have a very
large black hole there that we call a
Um, okay. So, now I want to talk
about we get away from the galactic
nucleus and start talking about
the outer structure of the the Milky Way
get into kind of a problem. Okay. So
tangential
velocity of the Milky Way. And I know this
sounds
technical, but it's a very important
important
study. All right. So, just
picture, the Milky Way galaxy is the
following. This is the model you should
think about. There's a very large very
massive black hole at the center and of
course that exerts a tremendous
gravitational pole on all the stars and
the solar systems in the Milky Way. Now
just like if we think about our own
solar uh system, we have the sun in the
center and then orbiting the sun are the
planets and the sun exerts a
gravitational pull on those planets. But
the planets do not fall into the sun
because each planet has a tangential
velocity that gives rise to a
centrifugal force that counters the
gravitational pull of the sun. And so
that's why you know it same applies to
the moon in orbit around the earth. The
earth exerts gravitational pull on the
moon but the moon has a tangential
velocity that gives rise to a
centrifugal force that counterbalances
that gravitational pull that the earth
exerts on the moon. And the same with
the planets in orbit around the sun in
our solar system. Each planet has a
tangential velocity and that counters
the gravitational pole of the sun. And
in the same model, we we envision that
the the Milky Way galaxy is the same
way. I mean, you've got a a very large
black hole at the center and then you've
got all the stars and everything that
make up the the Milky Way and they're
that that black hole is exerting a
tremendous gravitational pull on all the
stars, all the solar systems. But
because that they're moving with a
tangential velocity, they're able to
counter that immense gravitational pull
uh that the black hole exerts on the
matter. So what we were wanting to do is
to make sure we completely
understood the tangential velocities,
these orbital speeds of the stars that
are in the Milky Way and measure those
speeds and then hopefully you know they
would agree with you know basic uh
Newton laws of
motion and uh that everything would be
would be fine And of course the story
ends in a different manner and that's
what we want to investigate. So what we
actually looked at is we would wanted
wanted to measure the the Doppler shift
on that uh
uh
the spin flip radiation the 21 cm spin
flip radiation of hydrogen because the
the galaxy's full of hydrogen. So
hole. Okay.
And so we wanted to very accurately
measure all the velocities as if you
know for each star each location.
Actually we looked at each location
because we actually looked at the hydrogen
hydrogen gas.
observations of the
hydrogen. Uh
reveal the
of
these rotation velocities or the
tangential. I'll say
rotation, but then I'll put in here
tangential. Those two words are
interchangeable. I use tangential here
in the title of the bullet, but it's
they're both the
And of course what they do is they you
measure the Doppler shift on that spin
flip radiation and then get the velocity
and you do it for certain distances out
you know map out the entire Milky Way
galaxy. So you're going to be able to
then have a velocity profile versus
distance. Okay? And so that was the
goal. Now before I get you to the answer
of what we found, I I kind of got to
talk about uh velocity
profiles for objects that move that have
rotation. Okay, so we want to look at
uh velocity profiles for
for you know different situations,
different objects. So, the first one
we're going to look at is what's called
rotation. All
right. So, this is the situation where
imagine you have a platform
uh like a merrygoround with no no none
of the horses just just flat platform,
no horses, no nothing. And
uh I put you on the platform. I turn it
off and then I allow you to walk up,
step on the platform, and then I'm going
to turn on the platform.
Now, I'm going to first tell you, go to
the center of the platform. And so,
you're standing at the center. Now, I'm
going to turn it on. And now what you'll
notice is if if you stand there kind of
in the center, you you know
your your little circular speed isn't
very fast. But then if you start to walk
out towards the
edge, your tangential speed, your
rotational speed will be much quicker.
And that's what we mean by solid body rotation.
rotation.
There's a linear relationship between
the distance out from the center and the
the rotational speed or the tangential
speed and any body any object that
exhibits that then we say well that has
solid body rotation. Okay. So solid body
this. Okay. So the horizontal axis is
the distance out from the center.
Another word for that is
radius. But I just want you to think if
we go back to the merry-go round, this
is the center of the merrygoround. And
then out here's the edge of the
merrygoround. Okay? I allow you to step
on it. Then I turn the power on so it
starts rotating. Okay? And then the
vertical axis is your tangential speed,
your rotational speed. Okay, so I'm
gonna put that in
here. I know the word tangential, you
know, it just means tangent to the edge
of the circle. That's what tangential
And when you have solid body rotation,
any object that's undergoing solid body
rotation like that
merrygoround, then the plot looks like
this. It's just a straight
line. And so as you're if you're in
close to the center, you're down here
this distance, you go up to the line and
you have a very small tangential
speed. But then as you walk out to the
edge, you're way out here near the edge.
go up here and go over, you have a very
large tangential speed. So there's a a
linear relationship with the distance or
the radius out from the center and
versus the tangential speed. That's
solid body rotation. Any object that's a
solid that is
rotating, the farther out you are from
the axis of rotation, the center point,
the greater the tangential speed. Okay,
that's what we mean by solid body
rotation. Okay, that's one type of
rotation. Now, we're going to talk about
another that's based upon gravity and
that's called capillarian rotation. So,
we're going to do a new bullet here. So,
velocity is
proportional to the radius for solid
body. V, this is V and the radius is R.
Okay. And so as you increase r the
tangential speed the velocity increases.
So there that means proportional to the
velocity is proportional to the radius.
Okay. It's nice linear line there. The
slope is actually the angular rotational
speed of the merrygoround of the solid
body. But I don't want to get into all
the little
uh kinematics there. just velocities
proportional to R. Now we're going to
look at is we're talking about another
type of rotation. This is the rotation
that exists actually in our own solar
system or for that matter any uh bodies
that are orbiting around a central mass,
you know, like a plan a planet if it's
got moons or a sun if it's got planets
around it and so forth. And this is
called Keplerian rotation in honor of Kepler.
Now to explain Keplerian rotation, I'm
going to just kind of walk us through
just the data in our own solar system.
So, this is what I want to say. Let's
plot the orbital speed of each planet in
our solar system and we'll see what we
get. So, we're going to move this up.
We're going to do
again a two-dimensional
two-dimensional
plot. All right.
So this is the excuse me the distance
out from the sun. So you know the orbit
radius of the planet. So I'll just put
radius here. So orbit
radius how far away is that planet from
the sun. So right there's the sun and
then you know there's Mercury and you know
know
not the scale but just Mercury, Venus,
Earth, Mars, asteroid belt, Jupiter,
Saturn, Uranus and Neptune. Okay. So we
go out and then this will be the or orbital
orbital
orbital. All right. So if we do that
plot, the first one of course is we got
Mercury and it's up. So this is the sun
and then this is out at the edge here
out here where Neptune is. Okay? Because
you're far away. This is right up close.
So the closest planet is Mercury. So
Mercury has a very high orbital speed.
So here's
Mercury and then
Venus and
Earth and
Saturn, Uranus, and
Neptune. So if we go ahead
those. So let's just it this is
Mercury. Don't
um Venus, Earth. I mean, I'm not going
to label them all. These are just all the
the
planets, you know, Mars, Jupiter,
Saturn, Uranus. Here, let's put Neptune
down here just so you understand. Here's
system. Now, this is this line that fits through
through
there just comes from Kepler's
laws. Okay? So and if
so this is what we call capillarian
rotation where the plot looks like this.
rotation and the scaling of the velocity
the velocity is proportional to one over
the square root of the radius. And that
just comes out of Kepler's laws or
So
any system of where you have objects
that are gravitationally bound to a
central host object. Now those objects
are in in orbit around that host
object because of the laws of gravity
they should obey capillarian rotation.
rotation.
Okay. Now so we have the solid body
rotation. the velocity is proportional to
to
r and then we have kept rotation where
the velocity is proportional to one over
the square root of r. So what we see is
the velocity is very large and then it
rapidly drops off. So you get farther
and farther away.
Now, prior to looking at the data in the
Milky Way, we thought it had to look
like this because the Milky Way, you
have a central gravitating mass, i.e.
the super massive black hole, and then
you've got a bunch of matter, star in
solar systems, and they're
gravitationally bound. And so, it should
model exactly our own solar system. So
when we looked at the data from the Milky
Milky
Way, what we
got was not Kepler but goes by the name
of differential rotation. And
um I want
to draw
But before I do that, I'm also going to
just say we have the profile for the
Milky Way, but we've also done the same
thing for other
um galaxies. And then if you kind of all
average them out, they kind of always
look like this. So differential
So again this is radius distance out
from the center and then this is the
object. And so all the profiles if you
kind of average them out they kind of
look like this. They start here at the
center and they have a steep climb and
then they kind of flatten out and then
that looks nothing like Keplerian
rotation. Actually, if you look at it in
closer, it's solid body. So, in near the
super massive black hole, there's so
much matter that the way the force of
gravity is, it kind of holds that matter
together and it all rotates like a solid
body. But then out here, you don't
really see anything like
that. Okay? You don't see this Keplerian
drop off that we would expect. And so
this is the differential rotation of the
galaxies. Now I'm going
to draw more
accurately the one for the Milky Way and
then then let's see I'm on page five. So
the Milky Way actually looks like this.
of this is a big problem because you go
wait a minute why isn't it'll have that
Keplerian drop
off that we see now this decay here is
goes by the name Keplerian decay because
it drops
off. Go back to this other drawing. just
decay. So, Milky Way differential
rotation and so drawing the Milky Way
one and again this is kind
of excuse me you've smooth we've
smoothed it out but I just want
to again
speed. So there's a little kind of
undulation here. So you come
up and then there's a little curly cue
like that. Then it comes down and then a
slight rise and then this and then
there's a last kind of kick up like
that. And believe it or not, our our
solar system is right there. So our sun
is right
there. you know about 27,500
27,500
lys. Okay. And of course out here's 40
somewhere and then here's the center.
Okay. So this is a Milky Way again. It's
it's this differential where you have no
concrete capillarian drop off. So we
don't know
there's see if it was Kepler and we'd
expect this thing to start to really
drop off here and we don't see that.
This is the Keplerian drop off. We don't see
that. So we're
baffled what's going
on. Okay. Now in close we see
hints right here of solid body effects.
here.
Okay. But when you don't have solid body
and things are gravitationally bound by
the laws of Kepler and Newton you expect
the Keplerian drop off just like we see
in our
own solar system. We don't have that.
Now I want to give you some just some
important data related to the Milky Way
and related to our sun. Actually let
here. So you know this number. So this
about 2.3 * 10 5 m/ second and that's
about about 500 miles hour. So our solar
system is in orbit
around you know traveling in a giant circular
circular
orbit about
27,500 lys
um at a velocity of 2.3 times 10. That's
space now because you know how you know
you know let me go to another picture.
overhead.
Okay, there's our sun and the planet.
system 2.3
* 10 5 m/s. That's the speed. And
then there's the RRS, the
27,500 lys.
So because you know the speed and you
know the circumference of a circle, it's
2 pi r. You know the total distance
around here. So if you take the total
distance around here and you divide by the
the
speed 2.3 * 10
5 m/s, you could compute the time that
And we can we can find we can find the
orbit. All right. And that time is about
years. So that's how long it takes our
solar system to complete one orbit as it
orbits around that super massive black
hole that's, you know, right there,
right there in the center. 230 million
years. So the last time you're at this
location, the dinosaurs though, the
ancient dinosaurs, not the more modern
that really ancient
dinosaurs, you're talking 230 million,
you know, not 80 million, 230 million.
The ancient dinosaurs were ruling the
So
that's little bit of data we get just
because we know our
distance and we know our speed we're
able to determine our orbit time. So
this is called the orbit time tech
orbital period. I should write it orbital
period orbital time timing period mean
the same thing.
Okay, now I want to go
back because we need we really want got
to talk about something that's really
important. So, we want to go back. So,
I'm on to page
seven and we're going to do a bullet
here. And I let the cat out of the bag
by writing the the name of this bullet,
but I don't care. Here we go. Dark
matter. Okay, so now you've heard about
dark matter. Here's where dark matter
comes from. So, we're going to look at
again. Okay. For the Milky Way. So, here we
we
right. Big steep climb here. Little lat
uprise. Little kick and a kick up.
I'm just redrawing what we did right there.
there.
Okay. And here we are. Here's our sun
system. Okay. And as we said, we don't
non-existent. No Kepler decay. Oh, I
should say
This is the radius distance out from the
center. And then this is the orbital
speed. So here's
the here's what we think. There
There
is some mysterious matter in the
galaxy that is effectively gluing
together all the matter in the galaxy.
All the stars, the solar systems, gluing it
it
together so that it has this sort of
profile where it kind of it basically
flattens out. I mean if you go from here
to here this is basically yeah there's
these little undulations but basically
we get this flattening out. So I used to
call it flattening
out after you get beyond the the steep
climb. Then if you just if you go back
to this one where we you know the
average of all the the
galaxies and trauma and all the other
ones that we can get the data on you
average them all this what they look
like. You basically get yeah a little
kick here and there but basically
flat and that's the sometimes they say
the flat rotation curve. So instead of
rotation the technical is differential
differential
but the flat differential whatever.
So the idea is that on this dark matter
is that there must be a bunch of
matter in the Milky Way that acts
through gravity and gravity alone. So it
doesn't and doesn't give off any other
signature. No electromagnetic so we
can't see it. That's where the word dark
comes from. And there's got to be a lot
of it because it's got to basically act
like a gravitational kind of glue and
just glue everything together such that
all the matter as you get out away, you
know, not in close, but it
all just has this flat rotation curve.
So it acts like kind of a glue.
expected capillarian drop off or capillary
because we really thought we'd see, you
know, we should see a drop off just like
we see in our own solar
system. We don't see that. You get out
far away from the center of the Milky
Way and it just flattens out
basically. So, the idea is that okay,
there has to be some matter that we
can't see that's acting kind of like a
glue. It's gluing together together all the
the objects
objects
that make up the Milky Way
galaxy. So thus and I say we think
because you know we we are looking for
the dark matter and we
haven't we have no candidates and we say
oh we found dark
matter that
acts like a glue. [Music]
gravity. Now, because it's hidden, what
that means is we can't see it. Doesn't
give off any signature, any
electromagnetic radiation. So, if you
can't see it, it's like dark. So, that's
where we get the word
dark. And then because it's matter, it's
where we get the word dark [Music]
[Music]
matter. Okay, so we envision that the
the Milky Way galaxy is just full of
this stuff. This dark
matter gives off no electromagnetic
radiation, no signal that we can
pinpoint and but yet we believe it's
there because it's acting like kind of a
gravitational glue and gluing the stuff
that we can see the luminous stuff such
that we're getting this sort of profile.
Okay? And that's the basis of dark matter.
Now, even, you know, if you kind of
think about it, swallowing mad, I've
just thrown up this thing, dark matter.
I mean, just like
crazy. You can't we can't see it. We
don't know what it is. We don't have
any. We have some candidates, particle
candidates, but we'll get into those
later. But none of them are all really
that that good. They just would count
for a trivial amount. We need quite a
bit. I want to talk about quite a bit
here shortly. Um, but it's matter. So,
it's acting through the force of
gravity. That's it. It's kind of gluing
together everything in the in the galaxy
and but we can't see it. So, dark
matter. Now, we get to the
question swallowing this is hard enough,
but it even it gets a little more challenging.
challenging. is
um okay.
sure. You see that's kind of a problem
when you don't really now I can tell I
can tell you this you're not sure a
fraction very small fraction and the
reason it's fractional is based
upon big bang
uh nucleioynthesis and the amount of
matter that's produced at the big bang
we kind of know what the distribution of
these other things I'm going to talk
about are but they would not account
enough for what we need to glue together
the Milky Way such that we get that
profile that flattening out. So a
matter could
could
And we know nutrinos do not give off.
They they do not interact. They do have
a little mass. So they could they would
be a candidate for dark matter. Okay?
Because they have mass. And so there's a
small fraction of dark matter could be nutrinos.
nutrinos.
holes and we would think of like
primordial black holes. These very small
black holes that would have been
produced very early stages of the big
bang. those because they have matter,
they would act.
Okay. And you know, then you get in
possibly cold gases and some other
things, but
but that's really all that we have right
now. Okay. So, of of particles that we
know and uh it'd only be a fraction of
those because we know the amount of
these on average in the universe. And
you expect kind of the distribution in a
galaxy to be roughly the average what
you'd see in the universe. There's just
not enough. So let me get to the point
then is is you would ask to me, well,
how much dark matter do we need? So we
can run the computer models. If we start
out with the computer models and we put
in just the stars, the solar systems in
the Milky Way, then you see the
Keplerian drop off because the only you
have the central gravitating body, the
the super massive black hole and then
you've got stars in orbit around that.
So those are going to obey Kepler's law.
So you can do that Kepler and drop off.
So then if you start putting in your
computer simulation, just putting in
little particles, little they're
actually little strands of of of dark of
dark matter, and you start to put it in,
then you you see how much you need to
get that that profile.
So how much
much dark
dark
All right. Now, here's the this is this
will blow your mind. So, if we look in
the in the in our galaxy, so in the Milky
Way, all the normal matter, all the
stuff that we can
see is this. So
all the I don't even like to use the
word normal, ordinary, whatever. All the normal
matter would be
10%. Dark matter is
90%. That's
insane. That's insane. We have a galaxy
and we only know 10% of it. the ordinary
stuff, the stars, the planets,
everything that we can see, it's
luminous, you know, luminous matter,
they'll say use that instead of normal
or ordinary. And then all this the other
stuff that we need, the dark matter
stuff is 90%. That's like crazy. It's
like you don't really know what the
thing because 90% of it you don't know
yet. The 10 only 10% of it you don't know.
know.
So that's the one that's really hard to
glue together the Milky Way such that we
have the flattening out of the rotation
curve means
that 90% of the
galaxy has to be comprised of dark
matter. And so we're searching for dark
matter. And and that's that's the big
one of the big pushes that we're wanting
to uncover. What is the dark matter? All
right, guys. We'll end there and
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