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Lecture 11 A105 Main Sequence Birth

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This content explains the process of star formation, focusing on how stars reach the main sequence on the Hertzsprung-Russell (HR) diagram and the factors influencing their evolution and lifespan.

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Guys, let's go ahead and get started.

Um, so we want to discuss how the stars

form and how they appear on the main

sequence line. Um, so we're going to be

talking about the birth of stars.

So, got a bullet up here. Let's do main sequence

stars. Not going to see it today,

but we will in the upcoming lectures. is

that once we explain how the star

appears on the main sequence

line, the formation of those other

types, the giants, the super giants, the

white dwarfs. So those are just end

states of main sequence stars. So the HR

diagram in itself is a snapshot of in

you know the entire process of stellar

evolution. So the first point the first

uh thing that we want to focus in on is

that you start with uh you know the

basic ingredients of stars and then

what's the process of how they appear on

the main sequence line. In other words,

born in a nutshell? Basically it's

gravity. Gravity is an attractive force

that clumps together matter. And if you

have enough matter and if it's dense and

cold, gravitational forces can clump it

together. And that's the basis of the

there. My

gosh, underline that word. So, what is

the interstellar

up. Just small particles that account

for about 10% of a galaxy's mass. Of

course, they're mostly hydrogen and helium.

You may think 10% that's a small

fraction and you would be correct and

you would say well where's the other

90%. Oh my gosh that's another lecture

off in the future is very important.

Actually it's not one lecture it's

probably two or three. Where is that

other 90%? But we're not there yet.

That's that's a ways away. So, okay,

hydrogen. That's the simplest atom.

proton in the nucleus and a a single

electron. And then 25% of the

interstellar medium is helium. That's

the second most simple atom. Um two

protons, two neutrons in the nucleus and

then surrounded by two

electrons. The production in the

hydrogen and the helium, they're not by

chance. They're at the end state of what

we'll get to later on. Big bang theory.

So when the universe is born various

processes we'll talk about that the

production of the hydrogen and the

helium and then we're short on 1%. So 1% others.

Now of course the others will include you

you

know carbon and uh lithium uh oxygen

uh some

others fundamental uh atoms. So if we

molecules. In fact, the hydrogen will

often form what's called molecular

I'll just put here H2. So you got a

hydrogen bond between another hydrogen

monoxide. That's

CO carbon and oxygen. And so that that's

in the others. So you get the carbon,

oxygen. Um now if you got oxygen, you

got molecular hydrogen, then it's

H2CO that basically the molecular

hydrogen and the carbon monoxide will

bind up to form the formaldahhide. Um,

this an L. Um,

cold. And because it's very cold,

uh, it'll emit very little

electromagnetic radiation. In fact, it

emits almost no radiation in the visible

range. So interstellar medium is very

emits most

most no

visible

But we have some

tricks to help locate interstellar

medium. And the goal is once you locate

interstellar medium, that's the point

where a star can be born.

So one of the things

that interstellar

medium will do is this effect we call u

starlight passes

It is

explain. It's somewhat technical, but

I'm going to use pink void. So take Pink

Floyd, Dark Side of the Moon album

cover, the glass prism, and come in here

light. And the glass prism is going to

bend the light. And the one that gets

bent the most is the blues and the

purples. And the one that gets bent the

least is the

reds. So here you have the rainbow, the

purples and the blues.

And then the one that gets bent the

least is the reds. So red, orange,

just

blue or

purple light. is

most easily

easily

bent. Kind of the technical word.

scattered. Okay. So then if

we think about let's go to the picture to

help you show. So imagine we have a distant

star. I'm going to try to fit this in

here so I don't have to start another

page. And the distant star will produce

black body radiation in the visible

range. That means basically all the

colors of the rainbow.

i.e. white light just like just like right

there. Uh and then we have an

interstellar medium. So just think of

medium. Now, in the white light, the

colors that the two colors we want to

focus on is the blue and the

red. And what happens is the red's going

to come through. It's not going to get

bent at all or scattered at all. It's

the one that gets bent the least. And

then the one that gets most scattered is

So because they get

scattered, they scatter out of that beam

of light that comes from the distant

star. And then so here we are on Earth.

And so that light that comes from that

distant star when it passes

passes

between, you know, us and the

interstellar medium, the the hue of that

starlight will shift to the reds because

it's going to scatter out the purples

and the

blues. And that's what we call interstellar

interstellar

reening. Okay. So now I'm just going to

go to the next page and then just kind

So thus

Hence it takes

hue. So an interstellar medium will do

that and that tells us if we watch a

star then all of a sudden we see a shift

in the spectrum of the light and we see

a shift to the reds. it takes on a much

more reddish color. Then we know that an

interstellar gas cloud has passed

between us and that distant star. So

that we know okay somewhere between us

and that star is a is a interstellar

medium gas

cloud. Now you say well is that similar

to what happens on earth? Absolutely. So [Music]

um I don't

earth. All right. So, if you look up,

you go out on the middle of the day, say

it's lunchtime, and there's no clouds,

and you look up into the sky. Don't look

at the sun, but look up into the sky,

away from the sun. What do you see? You

see blue

light. And then people want to know

where the blue light come from. So,

we're going to I'm going to tell you

where it comes from. You already know.

And then, let's say it's evening, early

in the morning, and you look back on

along the horizon towards the sun. The

sun is either setting if it's in the

evening or rising if it's in the

morning. When you look back along the

sun, what you see is those reddish

colors. Same thing. Okay. So, yeah, I

wrote a daytime sky on Earth,

but would explain what happens in the

morning and the night. All right. So,

So, same

same [Music]

[Music] thing

thing

happens on

Earth. And what we mean by that is that

blue. Daytime

sky is [Music]

[Music]

blue. And then either the morning or

Okay. So, let's let's go through and

draw the

picture. And the picture looks like

this. So, give yourself a little space

here. And do that. That's the Earth.

Now, I'm going to put a person

here. And I want to put another person

here. And again, I'm always going to put

my favorite phrase, not to

scale. Not to

scale. Oh my gosh.

gosh.

Actually that causes a lot of you know

problems you when you teach

physics astronomy astrophysics it's not the

the

scale the sun is huge earth is small but

in this

picture you don't see it all right sun is

above this person so this person it's

noon the sun's directly overhead so this is

noon and and this

Depending on where we are on Earth, this

is either dusk or dawn because the sun

is low in the horizon. So we could say dawn

and earth is spinning this way. So

eventually, you know, this will get

later in the day and then this person

will be over here being lunchtime for

them. All right. And so we have an

atmosphere and there's particles in our

atmosphere and those particles scatter

the sunlight just like the particles in

the interstellar

medium scatter the sunlight. So we're

going to focus on one of the particles.

Let's say we got a particle right

here. So I just drew a little blob.

atmosphere. All right. So the sun is a

black body radiator.

range. So, we're going to draw that

light. Again, we're going to focus on

along blue and red.

before, red just going to pass through

hardly not get scattered at all. And the

blue's going to get scattered the

most. So, the blue gets scattered. So,

ping was

blue and the red doesn't get scattered

at all. Ping. Where's the red light?

So that explains you see this person no

matter where they look up in the

sky the predominantly the light that's

going to come in their eye is the blue

light that's been scattered off the

particles in the atmosphere and that's

what paints the daytime sky blue. Now,

contrast that to a person that's either,

you know, in the morning or the evening.

Oh, we could have done in the evening

and then in honor of Led Zeppelin, we'd

evening. If you go on my web page, I've

got the uh song in the evening. It's one

of my favorite songs by Led Zeppelin. In

the evening, In through the Outdoor, the

album cover in Through the Outdoor is

amazing. if you bought. So, back in the

day, we didn't have CDs, you know, there

was no MP3. My my daughters would call

them giant CDs. They're LP LPS

records. They call them giant

CDs. The uh

original album cover for In Through the

Outdoor by Led

Zeppelin was a magical album cover. When

you bought it, it was black and white

the cover. But if you took a sponge with

water and sloshed it over the cover of

the album, then all the colors would

come up

through. So that was now most people

didn't know that. Of course that they'd

have be at a party and drinking beer and

beer would slosh on there and then boom,

they go, "Oh, isn't that awesome?"

So back to the picture then the person

in the morning and the evening as they

look back along the horizon towards the

sun then the blue light has been

scattered out so it takes on a reddish

hue and so that's why when the sun rises

or either sets right above the horizon

you see the light will be red along that

region when you look back towards the

sun. Same sort of deal.

Now, you're probably saying if you go

back to the Pink Floyd, dark side of the

moon picture and you think about the

rainbow, you know,

um the color that gets scattered the

most actually is purple. It's not blue,

it's purple because it's red, orange, yellow,

yellow,

green, blue, and purple.

And you're thinking, "Wait a minute. Why

is the sky blue? Why is it not

purple? It's a logical question. I mean,

I just gave you some physics, and then

somehow I've twisted the physics."

physics."

Well, there's another little issue you

got to keep in mind. We've already

talked about it, but it probably slipped out.

out.

If we look at the the profile of the

sunlight that our sun produces, we go

back to the black body profile.

wavelength. Our sun has a surface

temperature of 5,800 Kelvin, close to

this. The peak is green. Then down

here's the blues. So, if I kind of just

in, down here is the

purple. Then this region is the

blue and then this region is the green.

So, because our sun is roughly

6,000 Kelvin, the black body profile

tells us it produces a lot

more blue

light than it does purple or violet

light. Okay? And so that's why it's just

that the sun doesn't produce much of

this light. Okay? So, it produces a lot

more blue light and that's why this the

skies are are blue.

Now, what we'll see later on, and I'm

getting really off on a tangent here,

but I don't

care. We saw the mass luminosity

relation, and the greater the mass, that

also increases the surface temperature,

which shifts the black body profile. So

if our sun was more massive, then the

profile would shift up over

here, say if it was on the order of, I

don't know,

12,000, 15,000, whatever Kelvin, then

there would be a lot more purple light.

There'd still be that blue light. And

then our sun would this would due to the

fact that it's larger and it would

producing more blue or purple light we

would start to see the skies take on a

purple hue. So if

massive sky

sky would

would

It's imagine that's the case. Our sun's

large. Then imagine we have a rainstorm

and it's raining and then the clouds

break. You know what we would

have? Deaf purple

print. Okay. So just a little bit bigger

on the

sun. So there's more purple. And then

imagine it's a rainy day and you're

going to have purple rain. So, you

didn't think purple ring existed? Well,

there it

exists. All right. Now, I'm getting off

on this tangent.

Uh, next topic.

monoxide. So, that's CO.

So remember with the discussion was on

the interstellar medium um which was

um would scatter starlight and you it

take on a reddish shoe and that was one

way that you would could say well

between us and that distant star there's

a giant cloud of interstellar medium.

Here's the other way that we can locate

a vast cloud of of interstellar medium

and that's through this one of the

effects of carbon monoxide. So, um, so another

locate interstellar medium. It's a lot of

writing. Gas

cloud is to Look

monoxide and here's the reason

why. So carbon monoxide is CO. So CO

emits a electromagnetic signal. So I

better do your n EM it's a electromagnetic

electromagnetic

wavelength I remember this sometimes ask

this so the wavelength for carbon

monoxide is

2.6 millm 2.6 six millimeters and that's radio

radio

frequency. So what we do is we use a uh

radio telescope. Those are giant dish

telescopes. And then if we find a region

in the sky where we have a strong

signal, this is supposed to be

strong strong uh signal at a wavelength

of 2.6 millimeters. That means we've

located carbon monoxide. Now, if you

locate carbon monoxide, then in that

same vicinity, you have a heck of a lot

of hydrogen. And the reason is as

follows. Um, for every So, let's see,

what am I at? Page five. for

for

every one carbon monoxide molecule. So CO

molecule

there are about

about

10,000 H2 molecules.

So anytime we look up into the nighttime

sky and we see a signal that has a you

know a strong a region of space that has

a very strong emitter of a very strong

radio signal at 2.6 millimeters we know

we've located large amount of hydrogen

gas H2 molecular hydrogen and that's

where a star can be born. So then we get

to the next topic which is called genes instability.

And it is

sufficiently one

one cold,

cold,

two dense has to be both those has to be

gravity will

cause it to

collapse. Gravitational forces will

start clumping together and it starts

from the center. Collapse starts in the

center and then works its way out. So,

gravity will cause it to collapse um

region. You have to have both these

cases. It has to be cold and it has to

be dense. If it's not cold, then the uh

kinetic motion of the particles are it

that produces kinetic pressure and that

repulses the effects of gravity warming

to clump it together. And the dense

gives you this. The more matter you have

in a region, the stronger the forces of

gravity. Okay? So you have to have

strong enough gravity. You get gota have

a lot of matter in a small volume of

space so that the gravity can cause it

to collapse. And then once that happens,

that's what we call genans instability.

instability.

Okay? So gravity will cause it to

collapse from the inside to the outer

in the

Period. Next topic. But it it it folds

in here right to what the next sentence.

But I got to put the bullet here so you

can later on going through your notes

protoar. So the mass in the center will increase.

increase. Thus

Thus a

protoar has

formed. Okay.

Now, so you have a gas cloud and in the

center the mass has really started to

build up and because of the nature of

the gravity force it acts along a line

between two particles it will pull all

the matter together to form roughly a

sphere. There'll be some asymmetry from

the sphere due to the angular momentum

but to first order it's a sphere. So

protoar

does not

fusion. It's not hot enough yet. So,

birth of a main sequence start goes

through these three steps. First step is

the protostar forms. The second step is

the pre- main sequence star forms. And

then the third step is

the birth or the formation of the main

sequence. Okay. Um now that's a protoar

form. Note the protoar does not have any

due to

increase in its temperature. Now when I

say glow, that's going to be in

infrared. So glow implies gives off infrared

infrared

radiation. So

Now you've got surrounding the the proto

stars the interstellar medium gravity is

matter is

is pulled

pulled

inward and

mass of the

All right, next

topic. The PMS

star that the PMS star is pre

sequence PMS

star.

Now as the mass builds up. So go back to

the pro store. the mass is building up

and what happens is now the temperature

is is increasing due to the increased

mass. Okay? So the temperature increases

because the gravity is squeezing. You

take any material and squeeze it. It

heats up. I mean that's how your car

works. It takes the atmospheric gas and

it compresses it and that heats it up.

It ignites it. But it is the heat

contained in the compression of that gas

that gives the energy. Okay. Now the

same thing is happening. Gravity is

doing that in the in the prostar. It's

acquiring mass, but it's getting hotter.

Now, eventually, as it gets hotter, what

happens is the electromagnetic

radiation, that's an outward flow of

photons, starts to push back and you get

to a point where it's no longer accreing

any mass. The mass accretion stops and

that's when the pre-main sequence star

flow

forms. Okay. So now you don't have any

more mass buildup. You've now got the

PMS star. And what happens is this

outflow of photon pressure is countering

any effects of gravity wanting to clump

any more mass. And so then the mass is

set in the star when it's at the PMS

stage. But the next thing that starts to

happen is now that it's a PMS star,

gravity takes the mass that is there and

begins to contract it.

So onto my page seven. We're still in

the PMS star, the pre-made sequence. So

seven. So but

gravity now

now begins

begins to

This can

take up

to and it's quite a range between a

million to 10 million to 100 million but

we just say 10 million up to 10 million

years. So we'll write down 10 million

years. Now, as you continue, as gravity

continues to contract, the mass that is

there deep in the core in the center,

the temperature is going to elevate,

going to get hotter and hotter.

Eventually, it's going to get to that

threshold of about 10 million Kelvin.

Boom. That's hot enough for hydrogen to

fuse via the proton proton chain to then

produce the helium and the sunlight. So

uh this can take up to 10 million years but

Kelvin. Okay. And then then you have the main

sequence. So when

when core

reaches a tilda so that means about 10 million

And that means then you go from a PMS to

a main sequence. So PMS then becomes main

sequence. Now when it's main

sequence contraction stops because now

you have a perfect balance. You're in

that state of hydrostatic equilibrium.

You have a perfect balance between

gravity which wants to compress it and

then the kinetic pressure which is due

to electromagnetic radiation the photon

pressure flowing out balances that and

it it sets and stabilizes the size.

forces. Photon pressure which flows

outward is

halts the gravity forces which wants to

cause compression. So I'll just say photon

pressure is exactly equal to gravity.

They work in opposite directions. Of

course photon pressure is an

outward force and gravity is an inward

force but they're in balance.

Hydrostatic equilibrium they're in

balance and then so the size is stable

when it's in sequence.

it's in the when it's protoar the mass

is building up. So in the protostar

stage the mass is building up and as the

mass builds up the temperature increases

and then the electromagnetic radiation

the photon pressure increases.

Eventually it no longer accretes mass

and then at that point you transition

from the prostar into the pre-main

sequence PMS star the in the PMS star

you have

contraction so the size is now getting

smaller and smaller we're not adding

mass but what's happening is the size is

getting smaller that's

contraction and then that happens

eventually the the core temperature gets

to 10 million Kelvin nuclear fusion begins

And then you have a tremendous release

of photons because you have that you

know you go back to the proton proton

chain you have all those gammaray

photons that are flying out of there and

those gammaray photons then generate the

photon pressure which halts any further

contraction. That's the main that's when

your main

sequence. Okay. So I want to draw some

pictures just to tie together these three

three

stages. So I'm going to go to page

eight. The picture for the protoar looks like

this. So you draw interstellar medium

and then in the center here draw a

circle and then label that circle protoar.

Now what's happening on the protostar is the

mass from the interstellar medium is

being pulled onto the

protostar. So we have mass accretion

which means the mass of the protostar is increasing.

increasing.

So right here these arrows. So this is

am and these arrows here represent the

matter flowing in. So mass

mass

Now, it does

glow and give off, you know, weak infrared

infrared

radiation gives off. Geez. Gives off.

Folks, go back to page six. Gives off. I

mean, I know I've got not a million, but

let's say thousands of spelling errors

because I don't look at my notes. I just

write. I should look at them. even in my

not so there's there's words that are

misspelled. All right. Gives off

infrared light. All right. Here we

go. So that's the protoar. Now we're

going to do PMS star. So in the PMS

circle. But now these rays coming off

here are really

strong. That's the electromagnetic

radiation. And now there's no matter flowing

flowing

inward. So there's no

no mass

on to the PMS. Oh yeah, label this

PMS. Okay. But what's the PMS doing?

It's contracting.

So draw little arrows like this. And

that's the force of gravity is causing

the PMS star to

contract. And actually as this radiation

gets stronger and stronger, it starts to

blast away. The interstellar medium

actually gets blasted away. So it

actually goes in the opposite direction

now because the photon pressure is just

so great. It's so what we do. So these

contraction. So the PMS star is getting smaller.

Okay. So protostar

protostar mass

increases. Okay. Then in the PMS the

mass is set but the size

set but size

decreases. And then we're at the main

sequence. So main sequence page nine draw

So this is MS mean sequence and then you

have the forces of gravity but the it's

now stable. Okay. So you have the of

course the mass is already stable. It's

stable when it's PMS but now the size is

stable. So in the MS star

size is now

now

set or another word or

stable. And we go back to that we're in

hydrostatic equilibrium. have a balance.

You took it didn't focus on any

mass region in the main sequence star

and there's gravity wants to pull it in

but the gammaray photons want to push it

out and so the forces are in balance. So

size is now set or stable and of course

we have sunlight we have nuclear fusion

core. So you have the conversion of the

hydrogen into the helium and the

byproduct is the gamma rays and the

gammaray photons is the sunlight. These

rays are sunlight and you get the entire

spectrum. You get x-rays, you get

ultraviolet, visible infrared, you get

them all. And then we're on Earth and we

go, "Wait a minute. Are we getting

beamed by X-rays and ultraviolet?" No.

Thankfully, our atmosphere saves our our

our bacon on that. Okay. All right. Um,

so couple of things that just want to

highlight here. Getting down to the end

massive a PMS

is star because it's pre-main sequence

star. So the more massive a PMS star

is, the more quickly it becomes main

sequence. And that's just because all

those processes are sped up due to the

mass. The forces of gravity that go

ahead and increase the core temperature

more quickly. So the more massive a PMS

quickly the more

becomes main

sequence. MS is main sequence.

sequence.

Now, now there's this other thing that

can that can happen and it's happened in

our own solar system. So, we should

probably talk about that. So, let's do

bullet here.

dwarfs. Brown

dwarfs. So, you there is a situation where

where

um you can get to, you know, the PMS

stage and there's just never enough mass

to get the core temperature to reach

that 10 million Kelvin. And so that it

just stays in that PMS stage. And

another word for a PMS star, a long-term

PMS star is a brown dwarf. So basically

if the PMS

temperature never gets

clo never gets

Kelvin really and it just sits in that

age. So you basically have a gas giant

hydrogen and helium spherical globe that

just doesn't have enough mass so that

you get a core temperature to 10 million

Kelvin. That's a brown dwarf. That's

dwarfs. And in our own solar system, the

classic example is

Jupiter. So that you can call Jupiter a

planet or you can call it a PMS star,

you can call it a brown

it. All right. Then if we go the other

way, if you go back to the HR diagram

and you think and you we look at our we got

got

our data on all the stars and what and

we you know we look at the mass and we

get the mass through the through the

binaries um we actually see an upper

limit on main sequence masses and that

upper limit is about 100 times the mass

of the sun. So let me go to the next

We do not

not often

often

see main sequence

above 100

times the mass of our sun.

And the reason is is what happens is

with those high masses if they you know

they start out high mass and then be

when the nuclear fusion kicks in when

the proton proton chain kicks in you

have a tremendous release of those

gammaray photons and they actually blast

away the outer region of the star and

that represents mass loss and so it the

mass drops down into that somewhere

under the hund.

So I don't know you would have

so so 100 times so um you would have a

that the mass

below the

sun. Okay, next topic. We have two more

and we're done. So next

topic. So now the star once it's main

sequence boom it shows up on the main

sequence line on our HR

diagram. And then the question is so

when it's on main sequence the line

there all it's doing all it's doing

what's doing is pretty amazing. I

shouldn't say the only thing that is all

it's doing it's converting the hydrogen

into the helium. And the question is how

long does that last? Well, it's mass

dependent. So, bullet is um main

So and and it and just if you think

about the more massive the star is the

more quickly it's going going to convert

the hydrogen into the helium because

temperature is going to be greater which

is going to increase the the rate of the

proton proton chain which increases the

conversion rate. So eventually it's

going to consume all the hydrogen. It'll

all be converted into helium and then it

leaves the main sequence line. Okay,

that's then we start the death process

of the star. So main sequence uh

uh uh

time on

line is

The more

massive, let's put it in quotation. The more

life. So just put together a little

table here guys and we'll get this one

more thing and we'll be done. All right.

So the table is is the following. So

mass of this star. So we're talking

about stars on main sequence and these

will be in units of the mass of the

lifetime. So this is how long it spins

And this will be in

years. Oh gosh. All right. There we

go. So, I want to start at kind of the upper

upper

uh edge, upper limit, and then work

down. So, let's look at a star that's 25

times more massive than our sun.

It spends its life on main sequence only

8 million

years. Now I know I said only 8 million

and you guys are oh 8 million is a long

it is. It is 8 million is a long time

relative to humans

but cosmically speaking or galactically

speaking 8 million is like a

blink. Okay let's do 15. So now we're

talking about stars that are 15 larger

than our sun. So they will about double.

So it's 15

million. Now you really start to see it

jump up. So one and that's our

sun. Total lifetime total time to

convert the hydrogen into helium 10

billion. And then something that's half

the size of our sun, say

0.5, 200

billion. And that gets us to our final

topic of the day.

bullet,

red dwarf. Okay, now we had brown dwarf.

We talked about white

dwarfs. Oh my gosh. Oh, they're all

different. A white dwarf. Talked about

those. We didn't go in the details, but

you know where they are on the HR

diagram. Then I just we just did the brown

brown

dwarfs. Page

nine. Now we're doing red

dwarf. These are low mass main sequence

stars. Low

mass main sequence

stars. And the reason is is they're

small and they have a low surface

temperature. So the dominant color they

give us is red. And that's where that

word comes from. Red dwarf. Low mass

main sequence

Okay. And usually we say if it's on the

order of a tenth of the mass of the sun.

So usually so just around

around

say 10% mass of the sun. That and lower.

That's a red dwarf. Um they'll have a

very low surface temperature. you know,

somewhere 3,000 or under, you know, under

3,000 Kelvin on the surface

surface

and very extreme on their lifetime. In

fact, you'll see that on the order of

live for around

500 billion years. Now, just to put the

billion years. Now, just to put the universe is only 14 billion years. You

universe is only 14 billion years. You I'm I'm giving you a piece of

I'm I'm giving you a piece of information that we're going to learn

information that we're going to learn later on. So, just universe itself is

later on. So, just universe itself is only

14 14. So, these red dwarfs

Nobody's seen them die yet. I mean, that's that's they're going to live a

that's that's they're going to live a long time. Oh my gosh. All right,

long time. Oh my gosh. All right, guys. We are done for today and pick it

guys. We are done for today and pick it up next time.

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YouTube Transcript:Lecture 11 A105 Main Sequence Birth