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Lecture 17 A105 Spin-Flip Radiation

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This content transitions from discussing stellar end-states to exploring galaxies, specifically focusing on our Milky Way. It delves into the historical discovery of other galaxies, the structure and scale of the Milky Way, and methods used to determine its central mass.

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All

right, guys. Let's go ahead and get

started. So, we've been talking about

stars, of course, the end states of the

stars, the white dwarf, neutron star,

black hole. But we also remember this

course is stars and galaxies. So, it's

now time to start talking about galaxies.

system is

galaxy. And if you go out in a rural

setting away from city lights and at

night, uh, low humidity, if you look up

basically overhead, you know, say

midnight, 1:00 a.m., you'll see a filmy

band of light, very faint, filmy band of

light overhead, and that's the Milky

Way. So,

rural

area. Let's do away from city

lights. You have to be away from city

lights. You won't see

it. It's so

sky. So, our solar system is in the the

Milky Way galaxy. And

then you could ask, well, how many

galaxies are there? And so there are

approximately 100 billion that's 10

Now, I want to kind of put this in

perspective. You know, that's today. We

know that today, but long ago, we

didn't we didn't even understand that

there was these things, galaxies and

that. And so we want to kind of revisit

the history of how it came to be that we

uncovered what galaxies

galaxies

are. And so we'll do a new bullet here.

Hubble.

Way. Okay. And then

so then Hubble did some amazing work and

photographs

of what we call

And he noticed in those photographs

M31. And we remember the seafoods are

those variable stars that have a

luminosity pulsation period relation.

And if we time out the pulsation period,

we can get a very accurate uh number on

the absolute magnitude of the

luminosity. And then by measuring the

amount of light we get here, we can then

very accurately determine how far away

that seafood is. That was the important

thing of the seafoods. So I notice sephids

sephids um

um in

inside of

M31. And I'll just say here

here

seafoods

have a

period pulsation period luminosity relation.

And because of

that, we can very accurately

accurately

Oh gosh. To the

uh see if it and if the see if it's

embedded in the object M31 then we know

uh how far away M31 is. Fate. So just to

remind you

uh out of the uh period luminosity

relation we're going to get our absolute

magnitude that's our big m and then

we're going to measure the amount of

light that we get from that seit. So we

can also so comma we

also know the light that reaches earth

m you know the apparent magnitude

apparent brightness and then if you know

those two you can get the distance

because we have our our distance

Put the big M in there. Put the little M

in there. And then I'll know the

distance to the seafood and then by

therefore know the distance to the

object known as

M31. And so what Hubble found out was

M31 was

was

Thus,

M31 was another galaxy. So, we have the

Milky Way galaxy, our own galaxy, and

then this object known as M31. Well,

it's a galaxy, too. So, thus M31 was

So we now recognize then that the

visible universe is much larger than we

thought because we just thought

everything was inside the Milky Way. And

I'm going to give you the data on the

Milky Way this size. But roughly from

one edge of the Milky Way to the other

edge is about a 100,000 light years. And

and that's large, but now we're talking

an order of 2 million light years.

So huge increase in the size of the universe.

universe.

So by the end of

Um, by the way, this

though. And you're going to find out

later on that there's some interaction

happening between our galaxy, the Milky

Way, and Andromeda that gives us some

additional information about what's

happening in the universe. We'll we'll

save that for later. So M31 is also

known as Andromeda. Okay. So this is the

great work done by Hubble and we're

going to visit revisit this in later on

a bit here. But now let's step back and

then start to talk about the Milky Way

galaxy, our galaxy. So let's do a Milky

um the Milky Way

galaxy and

uh is

a rotating there's a lot of stuff here. disc

shape and of course I'm being very

general here. We'll get to the details

later on. Rotating disc shape

collection of

matter, stars and

planets, other things you know

interstellar medium and and so forth.

uh this say collection of matter uh with

a spiral structure but again I'm kind

of we'll get into these details here shortly

um and from one edge so it's disc shape

so you know mostly two dimensional

object you know circular spiral

structure from if you look from overhead

but I'm unloading all these details, but

from one edge to the other, it's about

across, you know, to put that in

perspective, you have a flashlight at

one edge of the Milky Way and you turn

it on and shine it towards the other

side, that light beam is going to take a

100,000 years to traverse, you know, the

diameter basically, if you will, of the

of the Milky Way. So, it gives you a

center

is darn it is

nucleus, galactic bulge, nuclear bulge. This

This

same. They're interchangeable depending

on what

textbook you're looking at or

reading. And then our solar system is about

about

uh 27 and a

half. I don't know. Let's see. page this

is was page

page

three and this will be page

four. So our solar system let

me let me draw a picture here.

uh 275

275

about from

me on edge. If we look at it again, you

do. Okay. So from here to here is

years and then there's the center and

then our solar system. So there's 50. So

a little beyond that. So there there's

our sun and the our planets in orbit

around this our solar system. So from

here to here is about 275 27,500

lis and then depending on how you

measure this the

thickness is on the order of uh 2,000 light

years. Okay. And then so this this part

here is the galactic nucleus, the

nuclear bulge,

it. Just going back to these three terms

we had here. Galactic nucleus, nuclear

bulge, galactic bulge.

Okay. So if we're there and then we

recognize that the Milky Way is filled

with uh interstellar gas, interstellar

dust, then it obscures our view. And so

then how are we able to determine, you

know, how far away we are from the center?

center?

So let's talk about that.

dust. fly

clusters and the the globular

clusters orbit well above the

plane of the Milky Way. And then we're

we're able So, let's draw a

picture just so you can see. Oh, wait.

Let me let me say this.

this.

these and then we'll draw I'll draw you

this sentence and then we'll draw the

orbit above the

Galaxy. Yes. Yes. Yes. So, if I go back

and kind of draw a picture again, the on edge

picture.

Okay. Why are we having trouble? Okay.

So, there's the center. There's us.

Okay. But then there's these globular

clusters that are well out

out above

above

the plane and see. So we're able to

pinpoint. We have a very narrow band of

of interstellar medium that are we have

to pass through to see these. And then

we just need to get a few data points as

they move. And then from just those few

data points up here, we can predict the

entire orbital path. And we'll do that

for multiple globular clusters. And then

we'll average out the centers of all

those uh or uh orbits. And then that

pins down the center of the of the Milky

Way. Okay. So these are the globular

clusters. And I've kind

of mucked up this drawing. We have a

nice picture on the web page.

my my hand drawing here. Okay. And so

those motions, those orbital

motions of these globular clusters,

maybe I should here, maybe I should draw

one just

this chicken scratch. Okay. So I'm going

one.

Okay. And there it is. And there we are.

Okay. So line of

sight. And what we

do is we'll do look this, you know, for

six, seven, eight months. And what we

see is we we get all these data points

here and we can map out. And then you

don't need to follow it the entire path.

If you just because of the laws of grav

gravity Newton either Newton's laws or

Einstein with just a few data points you

can then predict the entire orbital path

of that globular cluster. So we'll do it

for that one then there'll be another

one and we'll do it for that and another

one and then the centers of all those

will pinpoint the center of the Milky

Way galaxy and that's how we're able

then to know how far away we are from

the from the galactic center. Okay. So

that gives us one piece of information.

Then the other thing if you go back and

look I said in back on my page three

look see spiral structure. So let's talk

about how we know that because you know

if you think about that that's weird

because we're embedded in the Milky Way

and yet if we stand if we imagine we get

in a spaceship and hover above the Milky

Way and look down we'd see a spiral

structure. And you're thinking, well,

how how can you know that when when we

ourselves are embedded in the in the

plane of the Milky Way and it's full of

the interstellar particles, dust, what

have you. How how does that work? And so

some interesting physics that helps us

there. And again, it's always the

quantum physics that that gives us the

answer or the little trick that we can

use. So let's do a new bullet here. We

want to discuss the spiral structure of

So we recognize that the universe is

full of hydrogen. Hydrogen is the

simplest of the atoms. A single proton

in the nucleus then orbited by a single

electron. Now both the proton electron

have what's called spin. Uh you can

think of it as like if you have a top

and you wrap a string around the top and

pull the string the top spins. Okay. So

our subatomic particles have this same

uh uh physical

attribute spin. Uh the technical word is

angular momentum but we call it spin.

And it turns out now in an

atom the spins are aligned either two

ways. So you have a spin axis for the

proton, you have a spin axis for the

electron. And in the atom, in the

hydrogen atom, they can line up two

ways. They can line up where both those

spin axises are parallel

or if we flip the electron the other way,

way,

antiparallel. So it's that's all that's

the only way it comes. Either the spin

axis will be

parallel or they'll be antiparallel.

Okay, parallel or antiparallel. Now,

there's an energy difference between the

two arrangements. The parallel structure

has slightly more energy when the spins

are aligned than the antiparallel. So if

you're in if the hydrogen atom is in the

parallel spin state and the electron

flips over to the antiparallel state,

it'll kick out a photon and the energy

of that photon is exactly the energy

difference between the parallel state

and the antiparallel state by so that we

satisfy conservation of energy and okay

so I'm going to write down what I said

just so you have it in your notes. So

tells

the

state for

for

state. Antip parallel

parallel spin

state. So the parallel has higher energy

than the antip parallel. So the

the reaction picture looks like this. So

we'll have I'll So we'll do here's the

proton and here's the electron. We're

going to put them in the parallel spin

state. So both the spin vectors are

pointing up and this I made this one

bigger. It's the

proton. It doesn't really matter. Technically

Technically

that's technically the electron is

bigger but oh I don't even want to go there

there

yet. From a mass standpoint no there's a

thousand factor a thousand between these

but from a size

perspective the electron is larger than

the proton guys that's a whole another

lecture. So okay so this is the parallel

spin state because both the spin

vectors are pointing up. So right here right

right

parallel and then what'll happen is on

occasion what'll happen that electron spin

spin

vector will flip.

So, and by virtue of conservation of

energy because this is a

electron and this is the antiparallel.

it's lower energy and so it a photon is kicked

out particle of

light and the energy of that photon

added to the energy of the antiparallel

state is exactly equal to the energy of

the parallel so right here below this

antiparallel guys remember this is

hydrogen the electron and so write

hydrogen up

hydrogen atom. This is a hydrogen atom.

Okay? And then that's a photon. Now,

because we know the energy of that

photon, we automatically know its

wavelength. So,

wavelength all this to just get to this

one important point. The wavelength of

is okay for our letters Greek letter

lambda 21 cm. So from one crest to the

frequency. It's not one you can see.

It's not infrared. It's in the radio

frequency. So we use radio telescopes

and with the radio

telescopes because there'll be some

motion involved then there'll be a

Doppler shift on that that

uh spin flip radiation. Okay. Yeah. So

this is called this this is called

and it's in the radio band. So, we use radio

telescopes. Those can detect radio

signals. And then what we'll see is

because of the spiral structure, we're

going to be able to we'll see Doppler

shifts at various locations. As we scan through

through

the plane of the um Milky Way, we'll see

Doppler shifts. And then we take all

that data, load it into computer, and

then it'll project the profile, the mass

distribution of the matter in the Milky

Way, and then we we see that spiral

structure. So we use radio telescopes And

the Doppler

shift of

We can

determine these are drifting off on me.

determine

the Milky Way.

So generically what if I take that data

and produce kind of a handdrawing an overhead

overhead

image basically we have the

uh galactic

nucleus nuclear bulge and then we have

these spiral like structures that come

off and

wrap and so from overhead this is the

sort of structure that we're talking

now I want to talk about so this is the

nuclear the

galactic nucleus nuclear bulge whatever

so let's I just want to say something

galactic nucleus. So, on

average, we can make a fairly accurate

statement on the number of stars that

are in the Milky Way. And that number is

also 10 the 11th. Now, 10 the 9th is a

billion. You get another factor too

that's 100. So, 100 billion. So there are

nucleus. Now remember, on average, if

you have a star, there'll be some

planets in orbit around that. That's

what a solar system is. So you're going

to have bunch of the stars here, planets

in orbit around them, bunch of solar

systems. So then if we kind of think

about if we if we're on a planet that's

in the galactic nucleus, what's the

situation? And it turns out that it's

kind of it's very different than what we

experience here. There's not a lot of

starlight in our nighttime sky. Uh but

that's not that would not be the case in

night. And the reason is is because you

have such a concentration of stars

there. You have so much starlight. Now

remember, night

is if you have a planet, it's an orbit

around a star. the planet itself

rotates. So when part of the planet is

on the back side away from the sun, then

the that surface of that planet that's

on the dark side, that's the nighttime.

That's what night is. Of course, then

the planet rotates and then oh, it's in

the morning and then noon and then

evening. Okay. But on the dark side of a

planet that's in the galactic um

nucleus, because there's so many stars

in the nighttime sky and they give off

so much light, you don't get that

experience of a dark night. And I can

just give you the numbers. Uh planet in

the galactic nucleus would never

experience a dark night. During

night,

about 200 full

So, you know, on a night you go out on a

full moon and a full moon kind of it

lights up the nighttime sky. Take that

number, multiply by 200, and that's the

darkest it's ever going to be for a

planet that's embedded in the in the uh

galactic nucleus. So, 200 full moons

worth of light.

Now, uh, now we want to, uh, kind of

we're still focusing on

the the galactic

nucleus, but we now want to kind of zero

in. There's a there's an issue. We'll

start that today and then the next

lecture we'll pick up and get into the

real details. So, we'll do a bullet

here that uh, we will call the

the [Applause]

[Applause] mass

mass in

the galactic

nucleus. So what we notice is there's a

very large concentration of matter i.e.

mass in the center, the exact center of

the Milky Way galaxy. And the way that

we do it is the following. Uh if we look

at the hydrogen gas

velocities that are in orbit around the

galactic center and using Kepler's third

law, we can fairly accurately make a

prediction on the amount of mass that's

in the center. So, we're going

the hydrogen

gas velocities. Remember, gravity pulls

things in. Any object that has some

tangential motion generates a

centrifugal force that repulses gravity

and that's what sets up a stable orbit.

Um, and if that object is not traveling

fast enough, then it'll get in closer.

If the object has no tangential

velocity, going to fall right into the

center. I mean, the moon, you think of

the Earth and the Moon system. The moon

is in circular orbit around the Earth.

If the moon's tangential velocity were

to go to zero, moon would come right in

and crash into the earth due to the

earth's gravity pulls on the moon. Okay.

near the

center using

using

K3L. You're gone. What's K3L? Kepler law.

We'll write it down. I'll explain

law.

We can um

estimate the amount of matter and that

you know the measuring of that is the

mass you know in kilograms the amount of

matter. So, I'll just put in here in parentheses

parentheses

center. Okay? And we're going to get to

that number. And then we get that

number, we'll end this. And then next

time we'll pick it up. There's another

important thing that comes out of that.

So, let me draw a picture

here to help you kind of we have uh two

bodies that are gravitationally bound

and one has more mass than the other.

So, it's mo that one that has more more

mass is basically located at the center

of mass point and then the other one

that doesn't have much mass basically is

in an orbit around the center. So, an

example would be and it's you know

applies to any two bodies that are

gravitational. Let's just look at the

moon. So here's the

earth and then here's the moon. Now

earth exerts a gravitational force on

that moon and it would pull the moon

into the earth but the moon also has a tangential

tangential

velocity and so by the uh laws of uh

Newton or the laws of Kepler or even

Einstein we can there's a relation here.

So the amount of gravity that earth

exerts on the moon is given well if I go

to Newton it's a very simple law. So the

gravitational pole that the earth exerts

on the moon looks like this. Let the

mass of the earth be big m. Let the mass

of the moon be little m. Okay. So it's

this the gravitational force that the

earth exerts on the moon. Big

g mass of the

earth mass of the

moon divided by the distance between

their center squared. So r squared. So r

That's Newton's law of gravity.

Gravitational constant. Mass of the

Earth, mass of the moon divided by the

distance between their two centers

squared. That's okay. So that's the

force of gravity. And that's the only

force that's acting on the

moon. So by the Newton's second law of

motion, some of the forces must equal

the mass times acceleration. We'll write

that one down.

So m * a. Now the m of course is the

thing that's the moving that's the moon.

So that's why I use little m and the a

then is the the acceleration. Now it

travels in a circular path. So the

acceleration is what we call the

centrial acceleration which is the velocity

squared divided by

the orbit radius.

So we can write this as m

v^2 over

r. Okay. So I'm going to relate the far

left to the far

right. Actually let's put some so this is

gravity and this is is equal to ma.

That's Newton's second law. So these two

are both Newton's second law. Sum of the

All right. Now, you see right away I

Okay, so next line. I don't want

to do all these cancellations in my

head. Then you'll say, "What's going on?

You're confusing us." All right, let's

write it down here. What we got? There's

what we

got. Okay. So, all right. So, that's the

mass of the moon. Mass the moon. So,

that goes away. And then I got an R

squared there and an R there. So we're

going to kill a power of that. Now what

I want is the mass of the Earth. We

already know the mass, but you'll see

where I'm going with

this. You we're going to generate the

formula and so that we can show what's

happening. All right. So I move this R

up there and then the big G I'll move

down. And so the mass of the

Earth is given by the following. So, r

v^2 / the gravitational constant.

constant.

Okay, so that's one

form of Kepler's third law, Newton's

laws of motion,

motion,

Einstein's general relativity,

Einstein's gravity. So m gives us the

earth. G is the gravitational

constant. I'll just say gravity

constant. You've had it before. 6.67 *

11. And r is the distance from the earth

to the moon. But it's measured not from

their surfaces but from their centers.

uh to the center of the [Music]

[Music]

moon. And then v is then the speed with

the moon. the orbital velocity of the

moon. So, I'll just say speed of the

moving? Now, here's the here's the

point. If you can look at a structure

and you notice that there's something

that's in circular orbit around the

center of the you know the structure

you're looking at, if you can measure

how far away that object is from the

center, that's the radius, the orbit

radius. distance from the center there

is the center mean also known as the orbit

orbit

radius but I wanted to spell it out so

confusion there it is r remember this

thing is in a circular

orbit around the earth the moon r is

orbit radius so if you can measure that

and then if you can also measure how

fast the moon is traveling with those

two pieces of information then you can

determine the mass of the earth. That's

how we weigh the earth. This is how we

weigh the earth. This is how we know the

mass of the earth. We examine the motion

of the moon or any for that matter any

satellite. All you need to know is how

far away is the satellite, the moon,

whatever that object is from the center

of the earth and then what's the

velocity of that object and put these

numbers in and then gives you the mass

of the earth. But this this formula has

universality in that it can be applied

to any system where you have a central

gravitating body and you have something

in orbit around that body. Using this

you can always get the mass of that

central gravitating

body. And see what we started out on

this was we wanted to find the amount of

matter the mass in the galactic nucleus.

So what we do is we

analyze the hydrogen gas velocities and

we know how far away they are from the

center and we can put those two numbers

in there. And

so using just about done here using m is

equal to r v^2 over g

both

the orbit [Music]

[Music] radius

radius

and speed technical word, you know, velocity

velocity for

the hydrogen

hydrogen

We can [Music]

galaxy. And here's the number. And I'm

going to quote it this way. So the M at the

center is or I'm going to write it this way

way

2.5* 10 6 multiplied by the mass of our

sun. So two and a half million times the

mass of our sun is

the mass at the exact center of the

Milky Way

galaxy. 2 and a half

million times the mass of our sun in the

center of the Milky Way galaxy. All

right. So folks, we'll end there and

then we'll next time we'll pick this up

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