How do we know the mass of stars?

Daniel talks about how astronomers can measure or deduce the mass of a star, and why it controls its fate.

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Episode Transcript

Speaker 1 (00:08):
Did you ever eat astronauts ice cream? As a kid,
that stuff seemed so exciting, but when you put it
in your mouth, it was always kind of gross and disappointing.
I remember my brothers and I wondering if it was
made four astronauts or maybe like made out of astronauts either.
For hey, it makes me wonder about something. You know,
how if you're on Earth and you eat too much

(00:30):
ice cream, you gain weight? Right, Well, if you're in space,
can you eat all the ice cream you want without
gaining weight? I think I just invented the world's most
expensive diet. For a hundred million dollars, or the price
of a ticket to the space station, you can eat
all the ice cream you want and still lose weight.

(01:06):
I'm Daniel, I'm a particle physicist, and I'm not here
to sell you some crazy weight lost scheme. No. Instead,
Welcome to the podcast Daniel and Jorge Explain the Universe,
a production of I Heart Radio. In our podcast, we
try to explain to you everything we do know about
the universe and everything we don't know about the universe.

(01:28):
We bring you to the forefront of science and introduce
you to the questions that scientists are asking today the
things that are puzzling physicists that are making them go,
what how does that work? Because we think that everybody
deserves to be out there on the forefront of knowledge,
wondering what the rest of humanity how there's amazing and
crazy and bonkers universe is put together. Unraveling that mystery.

(01:52):
Revealing the secrets of the universe, to me, seems like
the grandest journey of humanity. And it's amazing that it
even works, that we can by our minds and figure
out the way the universe works. And as we look
out into the cosmos, we see incredible stuff out there.
And so our podcast tries to explain to you what's
going on out there in the center of stars, around

(02:15):
the edges of black holes, in all the tiny little particles,
And we try to teach you also not just what
science does know, but how it knows it, because you know,
there is a pattern in the history of science where
we think we know something, it's sort of established wisdom
for a while, and then it gets overturned and we discover, oh,

(02:35):
the universe is actually something different, It works differently from
the way that we thought it did. Those are the
best moments, if you ask me, in the history of science,
when we're peeling back a layer of reality and discovering
that the universe is pretty different from the way our
intuitive experience led us to believe. And so when that happens,
you have to wonder, why do we think the old thing?

(02:57):
Why did we get it wrong? So it's important sometimes
them to dig into how do we know what we know?
And that's what we want to talk about on the
podcast today. When we look out at the stars in
the sky, we see some of them are bright and
some of them are dim. But when scientists talk about stars,
they're often not just talking about how bright they are.
They're talking about how big they are, how massive they are.

(03:21):
Stars with a lot of mass, stars with not so
much mass, black holes with a huge amount of mass.
But how is it possible to know that? So on
today's program, we'll be asking the question, how do you
measure the mass of a star? And it's not just me,

(03:41):
and it's not just you who's wondering about this question.
We actually got this question from a listener. Here's Dustin Hi,
Daniel and Horror Hey, I wonder how physicists come up
with the weight of planets and stars. Thank you things
doesn't very much for sending in your question. And this
is a really interesting and the important question. It's not

(04:01):
just an academic one, because the mass of a star
is really important. How much stuff you gather together to
form that burning plasma in the sky determines its fate.
Is it going to end up as a white dwarf,
is it going to turn into a neutron star? Is
it going to collapse into a black hole? All of
those outcomes are determined by how much mass it has,

(04:24):
and so understanding how much mass there is in stars
is really important and turns out not that easy. But
before we dig into how scientists actually do it, what
they do know, and what they don't know about the
mass of stars, I went out there into the wilds
of the internet to ask people how they thought scientists
did it or how they would do it themselves. So

(04:46):
thank you very much to everybody who volunteered their brain
to speculate how to measure the mass of something super
duper far away that you could never hope to touch.
And if you would like to participate in future baseless
speculations for our podcast, please don't hesitate right into us
two questions at Daniel and Jorge dot com. Here's what

(05:06):
people had to say, my guts, and it would be
to say that we know by how bright it is.
Perhaps it's done by measuring the gravitational lensing effect on
light passing around the stars, well, possibly with the help
of mass spect traumata readings. So you know what elements

(05:28):
you have in the star, and then you try to
figure out how much of them you have. I could
guess that poluminosity plays a part in it, and probably
the orbit, but but I'm not sure, so I would
say I don't know. I imagine that if we can
tell the distance to a star, we can probably figure
out its diameter, and from its light signature we can

(05:54):
tell its chemical composition, and from the brightness of the
star itself, I would imagine we could tell from the
combination of those three things what the mass is somehow
backing out from that information. All right. I love hearing
people think on their feet, trying to solve this really

(06:16):
hard problem from nothing, figuring it out from scratch, and
there's a lot of good ideas in there. You hear
people talking about how you need to know the mass
of other stars nearby or maybe you can connect it
to the brightness and hey, hey are on the right track.
So let's talk about how scientists can measure the mass
of stars. Well, in general, if you're looking at an

(06:37):
object in space, right, all you're getting is the light
from that object. It's basically impossible to know how big
or how massive that object is. Remember what mass is.
Mass is like how much stuff there is in a star.
It affects the stars inertia, like how it responds to forces,

(06:58):
and it also affects the stars gravity. You know how
hard it pulls on stuff. But none of that can
be directly observed from the star itself very easily. Mostly
that's the effect of other stuff on the star, right,
the inertia or the effect of the star on others stuff.
And so the short answer is is that in general,

(07:20):
it's impossible to directly measure the mass of an isolated star.
We had the same problem when we were measuring the
age of isolated stars for example. Right, we talked about
how to measure the age of stars, and it turns
out that you need to do it in big groups
because you're seeing how the stars, which are probably formed
together are probably dying together and you can use that

(07:40):
as a sort of clock for the population of stars,
but individual isolated stars, it's very hard to tell how
old they are. It's a similar problem for measuring their mass.
If the stars out there and there's nothing near by it,
nothing that can probe its gravity or be influenced by
its gravity, or give it a push or a pull,
it's all most impossible to measure its mass. But that

(08:03):
doesn't mean the problem is impossible. What we do in
this case is that we find a special category of
stars where we can figure out how to measure their
mass because they're near something, there's something nearby that's tugging
on them or that they are tugging on. We can
measure the mass for that sort of special category of stars,
and then we can try to fill in the gap

(08:24):
and figure out a way to extrapolate to all the
other stars. All right, so first let's talk about how
to measure it for a special category of stars where
you actually can see them doing some tugging or some pulling,
where their mass really is important for what we observe.
And the most powerful way to do this is to
see binary star systems. These are systems where you have

(08:48):
two stars nearby, and it seems sort of exotic, like
the kind of thing you might see in Star Wars
with multiple suns rising over the horizon. And you know,
I love that they do that because it's sort of
gives you a sense that an alien world. And so
we have the idea I think that binary star systems
are unusual, that they are weird, and that's just because

(09:08):
we're used to looking at one son. It turns out
binary star systems are not that rare. A lot of
stars are born in pairs, and if you think about it,
it makes a lot of sense actually, because how is
the star form? Do you have a big collection of
gas and dust and stuff that's swirling all around and
something happens to trigger its collapse and it rushes down

(09:28):
and collapses. But stars are not formed by themselves. You
have a huge cloud which usually forms many stars at
roughly the same time, and so it makes some sense
for those stars to be tugging on each other and
even for those stars to end up in orbit around
each other. So lucky for us, binary star systems are
not that rare. So what you can do is look

(09:50):
at the pair of stars, because if they are close
to each other, even if they are really really far
from us. Then we can see the effect of their
gravity on each other, which gives us a clue as
to what their mass is. Alright, so let's dig into
it and figure out how that actually works. If you're
looking at a binary star system, how do you use

(10:12):
what you're looking at what you see to actually figure
out what the mass of those stars is. Well. The
thing to remember about a binary star system, first of all,
is that it's not one star orbiting the other. The
two are orbiting each other, right, So there's some like
point in between them that the two of them are
both moving around. That's the center of mass. So both

(10:33):
stars are in motion. Right from the point of view
one star, the other ones moving, and from the point
of view of the second star, the first one is moving.
And what that means is that we can measure their
relative motion. As the star moves further away from us,
it's light gets stretched out, the wavelengths get a little
bit longer, and when it star is moving towards us,

(10:54):
it's light gets compressed a little bit. The wavelengths get
a little bit shifted. This is called red shift. When
it gets longer wavelengths as it moves away from us
and blue shift as it gets shorter wavelengths when it's
moving towards us. This is very similar to how you
discover a planet is orbiting around a star, because you
see the gravitational effect of the planet makes a star

(11:15):
wiggle a little bit and that changes the light that
we see. Now, in that case, you only have a
single star, and you're deducing the presence of the otherwise
invisible planet by looking at these Doppler shifts in the
light from the star. In this case, we have both stars.
So what you can do is look at the Doppler
shift from both stars independently, so you get both of

(11:38):
these curves right, and you can see how these curves change.
You can see, for example, oh, the star is moving
away from us. Oh, now it's moving towards us. So
it's moving away from us, and now it's moving towards us.
And so from those curves you can get some really
interesting information. First of all, you can figure out the
period of each star. How long does it take to

(11:58):
move around the other one. This is because you can
see when the velocity turns around right, it gets red shifted,
then it gets blue shifted. What it flips over is
that point when it's turning around, and so from those
flipover points you can figure out what is the period
of this star moving around the other one, And you
can also actually measure the velocity of each star around

(12:20):
the other one. This is determined by the amount of
red shift and blue shift, or at the larger the velocity,
the more red shift and blue shift you get as
it swings around the other star. So we can just
by watching the color of the light from these two
stars change figure out what the period is, how long
it takes for them to orbit each other, and their velocities.

(12:42):
And that's really awesome because then we could just plug
it into an ancient equation. Kepler's third law tells you
exactly what the combined mass of the system is if
you know the period and you know these velocities. So
that's pretty cool. Now we know just from the period
and those velocities, we know the total mass of this

(13:03):
binary star system, but we also know their relative velocities.
We know which one is moving faster than the other one. Say,
for example, they don't have an equal amount of mass.
It's not like two equal binary stars, but instead maybe
one of them is much bigger than the other one,
the bigger one is going to be moving slower and
the smaller one is going to be doing more of

(13:24):
the moving around the bigger one. So in the case
when the two stars have the same mass, will have
the same relative velocity. In the case when the two
stars have very unequal masses, when it's very asymmetric, then
one of them will be moving faster than the other one.
And so from this relative velocity, which again we know,
we can figure out how to split up the total

(13:45):
mass of the systems into the two masses, and so
boom that means from a binary star system, just from
watching their light wiggle, we can figure out what is
the mass of each star in the system. And one
of my favorite things about this is that it doesn't
just work for stars that are close by. It also
works for stars that are super duper far away, because

(14:06):
you just have to look at the light that's coming
from the star. It's not like you need to see
the gap between the stars or anything. You just need
to look at the light pattern. And the cool thing
about the Doppler shift is that it doesn't like disappear.
If there's a Doppler shift pattern in light that comes
to us from something really really far away, there's still
that same shift when it gets here. It will persist

(14:29):
over billions and billions of light years of space. And
so this is powerful because it lets us look at
even further away stars. So we get like a larger sample,
so we can learn like a more general trend rather
than just understanding something that's happening in our neighborhood. And
also we can tell whether it's something that's true here
and something that's true far away. We always want to

(14:51):
be open to surprises when we look out into the universe.
We don't want to draw too many conclusions just by
looking at our cosmic neighborhood. So it's important a technique
that works for nearby and also works for really far
away stuff, all right. So that's how we measure the
mass of binary stars of special star systems where we

(15:11):
have two stars that we can see and we can
measure their velocities from the wiggles in their light. But
we're interested in all the stars. We want to know
what is the mass of any given star we see
out there in the universe, even the ones that are
not in binary star systems. So how do we do that.
We'll talk about that in a moment, but first I
want to take a quick break. All right, we are back,

(15:47):
and we are blowing your mind by thinking about incredible
huge pockets of gas out there that are fusing themselves
and radiating photons which zoom across billions of light years
of the universe before they it to our eyes and
our telescopes and carry with them incredible nuggets of knowledge
about what's happening in far away corners of the universe.

(16:09):
And we're gonna use that light to figure out the
answer to a really interesting question, which is how big
is that star? How massive is it? What is its future?
Is it a huge blob of hydrogen which will eventually
collapse into a black hole or is it going to
end up a glowing white dwarf for trillions of years?
And that is entirely determined by how much mass it has.

(16:32):
So we talked about how to measure the mass of
a special category of star stars. Will we identify two
of them near each other that are orbiting each other,
so we can use their gravitational effect on each other,
which determines their relative periods and velocities of their orbits
to figure out how much mass there is exactly, But
now we want to move beyond that. We want to

(16:53):
understand can we talk about any arbitrary star. We see
a star in the sky, and we want to know
how much mass does it have? How can we figure
that out if it doesn't happen to have a big
massive object near it that lets us directly measure its mass,
And so here we have to be very careful. We
have no direct way to measure the mass of those stars.

(17:15):
But what we do is we look for a connection
between what we can measure, like the brightness of a star,
and what we want to know, like the mass of
the star. And we look for that connection not in
the actual stars out there in the universe, but in
the stars here in our computers at home. Because we
have an idea for how stars work, We have some

(17:37):
theory about it. We know the nuclear fusion that happens
inside stars. We think we understand something of the gravitational
pressure that's pulling these things down and making these things happen.
We compare a lot of these models to what we
observe about nearby stars. So we've been spending decades developing
these sort of like theory of how stars work, and

(17:58):
in that theory, at least in our computational models of stars,
we do see a relationship. We see a connection between
the mass of the star, which is the thing we
want to know but can't directly observe, and the luminosity
of the star, the brightness of the star. In fact,
we see a pretty direct relationship. While talking a minute

(18:19):
about what that relationship is and why we think it
makes sense the sort of physics that underlies the connection
between the mass of a star and its brightness, but
first let's make sure we're understanding the larger strategy. What
we're gonna do here is get a connection sort of
in our theory or in our simulations, between the mass
and the luminosity, and then we're going to calibrate that.

(18:40):
We're gonna make sure it's right by looking at binary
star systems. So binary star systems give us a way
to actually measure both the mass and the luminosity. And
then we have these calculations we can do that can
connect mass to luminosity, and we'll use the actual measurements
to make sure that calculation is correct and various points.

(19:01):
So we have like sort of a string that connects
mass and luminosity, and then we have various pushpins we're
gonna put into it to make sure that it's sort
of nailed down by actual measurements in reality, and between
those pushpins, between the actual measurements we make for the
binary stars were basically extrapolating the little bit of guesswork
and a lot of complicated nuclear theory, but it's not

(19:24):
something we actually know, and so there's, for example, a
gap where somebody could come in later and decide, oh,
it turns out our model for stars was actually wrong
and these extrapolations didn't quite work. So it's important for
you guys to understand while we actually know what we
actually can measure, which is the mass of a few
binary star systems, and where we get the rest of
the information which comes from this nuclear theory, which helps

(19:46):
us sort of interpolate between the examples that we can't
measure directly. Alright, So we have a connection in our
models between the mass and the luminosity, and it's really
kind of fascinating. It tells us that the larger the mass,
the brighter the star. Right, the bigger your original scoop

(20:06):
size of hydrogen, the brighter the star is the faster
it's gonna burn, And that means something else really cool,
which means that big stars burn bright, they burn hot,
but they don't burn for very long. So the big
ones are like flashy and exciting and very very bright
and shine their love into the universe, but not for
that long, whereas the little star that could it's sort

(20:28):
of out there pumping not nearly as much light, but
he can do it for a much much longer time.
These little stars can last for billions or maybe even
trillions of years, whereas the really really big stars only
last for like a few hundred million years before the
party is over. So what does that actually mean? Well,

(20:49):
the relationship for stars, like around the mass of our sun,
are a little bit less and then up to about
fifty times the mass of our sun, the luminosity of
a star goes like the mass to the fourth power.
That means that a star twice as massive as our
sun will be like almost sixteen times as bright as

(21:09):
our sun. A star twenty times the mass of our
sun will be a hundred and twenty thousand times as bright.
That's right, you double the mass of the star, you
don't just double the brightness, right, it goes up by
the power of four, and so it increases very very quickly.
And that gives you a sense for why these really

(21:31):
big stars burned out so quickly, because they were incredibly bright.
The bigger the star, the brighter the star, and the
faster it dies. It also means if you turn your
attention the other direction, that stars that are less bright
than the Sun are much much dimmer and burn much
much longer. For example, there are stars out there that

(21:53):
have a fraction of the mass of our sun and
they burn like one ten thousands as brightly as our sun.
Imagine living on a planet around the star that was
one ten thousands the brightness of our star. Right, you
could be much much closer to the star without it
being brighter than the Sun, which means it would fill

(22:14):
up a much bigger area in your sky. Right, so
you could have, for example, a nice, warm, toasty day
in front of a huge sun in your sky without
actually getting burned. So the opportunity is there for like
crazy science fiction ideas for what it would be like
to have a huge star in your sky seemed pretty

(22:34):
wide open to me. And so this relationship, this fourth
power relationship, is true for stars that are like half
the mass of the Sun up to about fifty times
the mass of the Sun, and then there's some kinks
in it. Like above fifty times the mass of the Sun,
there's a different relationship. It actually becomes linear, doesn't grow
as quickly, and below half the mass of the Sun,

(22:56):
the relationship changes again. It goes more like mass squared.
And so there's some details there, but let's understand sort
of the general idea. Why is it that a more
massive star would burn brightly and so much more brightly.
Why isn't the relationship just linear. Why isn't it that
if you have twice as much mass in the star,

(23:16):
it burns twice as bright and twice as hot. Well,
the answer comes from the details of the nuclear theory.
So let's dig into what's going on on the inside
of this star, right, Why is the star made at all? Right,
a star comes from the gravitational pressure. You have a
big collection of gas out there in space, and it's

(23:36):
gravity that's tugging it together. But gravity is not the
only thing active in a star, right. If it were,
then every star and every object would just collapse into
a black hole. Now, a star is a pretty steady
state object. It can last for millions or billions or
maybe trillions of years because there are two forces at play.

(23:57):
There are two things they're pushing against each other, which
is what keeps the star stable. So there has to
be some sort of outward pressure to keep a star
from collapsing. In the case of the most stars, that
pressure comes from the fusion, from the nuclear reaction that's
powering the star itself. And it's fascinating to me because
it's such a give and take, like gravity pushes on

(24:18):
the star, squeezes on the star. That's what actually causes fusion,
and that fusion releases a lot of radiation. That radiation,
that brightness, that energy pushes the star back out right.
So gravity causes fusion, which creates this sort of like
back reaction which pushes out on the star to keep
it from collapsing. And there's a whole fascinating rabbit hole

(24:41):
you could go down there, right because then that fusion
creates heavier elements, which increases the gravity dot dot dot.
But there's a whole other podcast episode about the life
cycle of stars. Let's focus right now and just what's
happening inside a star and why if a star gets
more massive, it also gets brighter. So the reason simply
is that a more massive star has more gravity. Right,

(25:03):
there's a bigger helping of mass, and each of those
little particles has a little gravitational force on it. Each
of them is then squeezing the center of the star.
So if you take a star the mass of our
sun and you wrap it in another helping of hydrogen,
another solar mass of hydrogen, there's gonna be additional gravitational forces. Right,

(25:24):
It's going to increase the pressure on the center of
the star. And so in order for the star to
be stable, for it to avoid collapsing into a black hole,
it needs more pressure outwards. Right. It needs to be
sending out more radiation. It needs to be brighter. And
you might think, well, just because it needs to be
brighter doesn't mean that it does. Right. Well, stars that

(25:46):
don't get brighter, that don't provide those pressures, they do
collapse into black holes. Right, So if there's a mechanism
to provide that pressure, that's what keeps the star is stable,
and in fact there is because increasing the pressure on
the core of the star increases the temperature. And when
you increase the temperature at the core. The nuclear theory

(26:06):
tells us something happens the fusion that's happening at the
core of the star, the merging of hydrogen into helium
and then helium into heavier elements to release more energy.
The rate of that fusion depends very sensitively on the temperature,
and so here's where that nonlinearity effect comes in. Here's
why doubling the mass of a star doesn't just make

(26:29):
it twice as bright, because the nuclear fusion at its
core is very very sensitive to the temperatures. That's the
nonlinear response. If you crank up the temperature of the
core of the star by just a little bit, you
can lead to a very large increase in the reaction rate.
And this is something that's very complicated and difficult to
wrap your mind around. But just because there's so many

(26:49):
particles involved, I mean, you have to sort of like
take your mind and go deep into the center of
the star and imagine all of those hygrogen atoms pushing
against each other. Because remember, hydrogen doesn't like to fuse.
It's nuclei are positively charged. You've got a bunch of
protons in there, and protons push away from each other.
In order to get the hydrogen to fuse and helium,

(27:11):
you've got to really squeeze it down. You have to
have a lot of pressure at the same time, you
have to have a lot of energy. You need a
high temperature because you need those hygen atoms to be
banging into each other, and so you can have conditions
at a very high pressure and temperature but without fusion,
and then all of a sudden fusion happens. You've sort
of overcome a threshold. And then once that threshold happens,

(27:34):
more fusion leads to more fusion because more of it
gets to that high pressure and temperature that you need.
So there's a very nonlinear effect there, because hydrogen doesn't
want to fuse at all, and once you've created the
conditions for fusion, it can lead to sort of a
runaway process. So that's the basic idea. The reason that
brighter stars are more massive is because there's a higher

(27:57):
temperature at their core created by this incredible gravitational pressure
from the additional mass, and that higher temperature leads to
a faster nuclear reaction. And of course that faster nuclear
reaction is not just gonna make the star brighter which
provides the pressure you need to keep the star alive.
It's also going to eventually kill the star because that

(28:18):
faster nuclear reaction uses up the fuel. These stars are
made out of a lot of hydrogen, but there's not
an infinite supply of it, right, Eventually the star is
gonna fuse so much hydrogen into helium that's gonna get
a helium core, and that helium is gonna fuse and
you're gonna get something denser and denser and denser, And
so that's just a ticking clock. Right. You have a

(28:40):
fixed amount of fuel. Once you've formed a star, it's
difficult for it to like create more matter unless it
has some like very close binary you can steal matter from.
So then it's just a question of like how many
fusion cycles can it have. If it's a really big star,
it will burn through those really really quickly and eventually
get to the stage where collapses. Or if it's a

(29:01):
little star and it's burning in a much lower temperature
and brightness, then it's sort of like biding its time
and it can last a lot lot longer. You might
expect it to be the opposite, right, You might expect
that big stars have more fuel and so they can
last longer into the deep future of the universe. But
it's sort of surprisingly the opposite. Those big stars do

(29:21):
have more fuel, but they also burn more fuel, and
they burn more fuel per second because they're burning hotter.
So that's an idea for why there's this connection between
the mass of the star and the brightness of the star,
and that helps us sort of connect the dots between
the things that we actually can observe. Those binary star systems,
the ones where we see the masses have an effect

(29:42):
on each other, and that tells us whether we get
in these calculations correct and it gives us confidence that
we can interpolate between the things that we can see.
But people are always working to improve these measurements. People
are always looking for other ways to double check it,
to figure out if this is wrong, to find another
way to measure these things. The best thing you can
do in sciences have two totally independent measurements, ones that

(30:05):
make maybe different mistakes or different assumptions that cross check
each other. And so there are a couple of other
ways we can get a handle on the mass of stars,
but they're even more specialized than the binary star system. Method.
One of them is called gravitational micro lensing. This is
a super fun one. It's when a star acts like
a lens. Because remember that the gravity of a star

(30:29):
isn't just a force pulling on things. It actually is
bending the shape of the space around the star. This
is Einstein's idea of how gravity works. Rather than being
a force, it's a change in the way space is curved.
In Einstein's idea of gravity, space is not just like
a backdrop. It's a thing that bends as mass gets

(30:50):
around it. And there's a complicated dance there, right, because
mass tells space how to bend, and then the bending
of space tells mass and other things how to move
in hooting light. And so a star out there in
the universe bends the space around it, and so a
photon coming to us from for example, a background galaxy
might get bent as it passes around that star, causing

(31:13):
a distortion. So if you're looking at a galaxy really
really far away, for example, and a star passes right
in front of that galaxy, it will distort that galaxy
in a very particular way, and in a particular way
that depends on its mass. So this is one way
we can measure the mass of an object without anything
else necessarily being near it by seeing how it distorts

(31:37):
light from background galaxies, because the distortion of that light
depends on the mass. The higher the mass of the star,
the more it will distort that light. And then of
course we can look at the brightness of that star
and we can look it up on our chart and
we can say, oh, does this follow the pattern that
we expect. Does this help us understand that the connections
between the luminosity and the mass of the star. And

(31:58):
so this is more difficult to do because it's not
something that happens very often. It's not something you can
necessarily predict. Is a sort of a chance encounter a
star wandering in front of another system that we were
already looking at. But when it does happen, it's a
very nice calibration and lets us look at a different
population of stars and get a direct measurement of their

(32:19):
mass as well. And then there's one extra cool, sort
of crazy idea for how to measure the massive stars,
and that's using astro seismology. These days, we can study
in real detail the light coming from stars, and some
astronomers think that variations in the light that comes from
a star might be due to seismic activity on the

(32:43):
surface of the star. That's right. These stars have sort
of like crusts, and you know how our son, for example,
sometimes blows out big coronal ejections or flares up and
flares down. If you're studying the light from that star
from really far away, you can tell when one of
these events happens because it affects the light that you see.
Because the star is spinning, there's a variable effect on

(33:06):
the light. So there's like a hot spot on one
side of a star. You'll see it as the star spins,
and then you won't see it as it spins away
from you. So you can see this sort of pattern
in the light from the star because of crazy effects
on the surface of the star. And there's some models
that tell us that there's a connection between the sort
of rate of these effects, how often this happens seismic

(33:29):
events in the crusts of stars, and the mass of
those stars. And so this astro seismology looking at the
pulsation on the surface of stars might also be able
to give us clues as to the mass of those stars.
All right, So we've been talking about how we measured
the mass of stars. I want to dig into what

(33:50):
we've learned, what is the range of mass of stars
and why that's important and what it tells us about
the history and the future of our universe. But first,
let's take another quick break. Okay, we're back, and we're

(34:15):
talking about how we know what we do know about
the universe and how well we know it, And specifically
today we're digging into the question of how do we
know the mass of a star, how do we measure that,
how do we figure it out when we can't measure it,
and how well do we actually know that? And so
we've been talking about how we measure it using binary
star systems and gravitational micro lensing, and how we interpolate

(34:38):
between those measurements using nuclear theory models about how a
star works, and now let's talk about what that means.
It turns out that the mass of a star is
basically the most important thing about it. The whole future
of the star, what's going to happen to it, its
whole life cycle, it's life span in fact, and then
the future of any civilized Asian living around that star

(35:01):
depends entirely on how much stuff went into the star,
what the mass serving was for the material that ended
up in that star. And there's a few outcomes that
are possible for a star. But this is awesome stellar
life cycle chart, which you encourage everybody to google and
take a look at. But the end points of this
are super fascinating. Basically, once you become a star, you

(35:25):
have a few possible outcomes. You can either become a
brown dwarf, which is like a failed star that never
really takes off and has the same kind of bright
fusion that's for very low mass stuff. Or you can
become like a normal star, which ends up as a
white dwarf actor blows out its outer layers and then eventually,
after trillions of years, cools to a black dwarf, so

(35:48):
you've got brown dwarves, white dwarves, black dwarves. Or if
you're even bigger, you can end up as a neutron star,
which might eventually turn into a pulsar. Or you can
end up a lack hole, and in some scenarios you
end up is just like this big super and over remnant.
The whole thing just sort of blows up and spreads
out into the universe. But the one that you end up.

(36:09):
Your eventual faith if you're a star, depends just on
how much stuff you have, because it's the amount of
stuff that drives the whole process, right, that makes you
burn hot and fast, or makes you burn slow and cool.
So the mass of the star is actually really, really important,
and it's not just important for understanding the fate of

(36:30):
an individual star. It's also really important for understanding the
whole collection of stars. Right. We want to know the
mass of stars because we want to understand, for example,
how the galaxy is rotating. Think about one of the
deepest and most amazing discoveries in astronomy in the last
hundred years, which was that galaxies are mostly not made
out of stars and gas and dust, that they're made

(36:52):
out of something else. This is an observation that came
out of just looking at the rotations of those galaxies
and asking how fast are those galaxies rotating? And is
there enough mass in the galaxy to explain how fast
it's rotating? Right? If you, for example, put a bunch
of ping pong balls on a Merry Go round and

(37:13):
spun it, they would fly off into space. The reason
that doesn't happen for stars in the galaxy, which is
basically a huge cosmic merry go round, is because there's
something holding them in. But you can measure the speed
of our galactic merry go round and ask is there
enough mass in the galaxy to provide the gravity you
need to hold the stars in place? Well, how do

(37:35):
you do that calculation? All you can do is look
at the stuff. You see. You look at all those
bright points of light in the sky, and you add
up their individual masses, And that's exactly the point. You
need to know the mass of all those stars in
order to do that calculation. If we had no idea
what the masses of stars were, we never would have

(37:57):
discovered dark matter because we would have looked at all
the stars in the sky and said, well, we have
no idea how much mass there is, so maybe there's
enough to provide the gravity we need to hold the
galaxy together despite how fast it's spinning. But no, we
do know the mass of those stars, and so we
were able to calculate how much mass there is in stars.

(38:19):
And we looked at that and we said, well, is
there enough mass to provide the gravity needs to hold
the galaxy together? And of course you probably know by
now the answer is not even close. The galaxy is
spinning at a crazy fast rate, and the mass of
the stars we can see does not provide enough gravity
to hold it together. That was the essential clue, the

(38:40):
first crack that told us that there was something else
out there in the universe. So doing these kinds of
studies things that might seem a little boring, like our
stars as bright as we expect them to be, how
much mass do they have? Can we explain it doesn't
make sense, seems sometimes like sort of scientific busy world,
But sometimes the answers don't add up, and they reveal

(39:03):
a huge cosmic mystery. So that's why it's important to
know the massive stars. That's why the mass of the
stars determined not just the fate of the individual objects,
but potentially how everything works. And now we know that
it's not actually the mass of stars that's determining like
the whole shape and future of our universe. It's actually

(39:24):
all of that dark matter, because there is five times
as much dark matter in the universe as there is
hydrogen and helium and the kind of stuff that makes stars,
and it's that dark matter that controls like why there's
a galaxy here and not over there. The reason is
that there was a big blob of dark matter and
it attracted all the hydrogen and helium, and it helped

(39:45):
compress all of that stuff, and it started the fire
in those stars. So we wouldn't even have stars and
galaxies the way we do today if it weren't for
that dark matter. And we wouldn't know about the dark
matter if we didn't have a careful measurement a way
to figure out the mass of individual stars. Alright, so
then let's talk about what the mass of the stars

(40:06):
actually are. Right, we look at our Sun. That's a
pretty standard candle. We think, let's use the Sun as
an example star and measure everything in terms of like
one solar mass. Well, right off the bat, we discover
the Sun is kind of unusual, is sort of a
large star. The most common star out there in our
galaxy is one called a red dwarf. Is significantly smaller

(40:30):
and colder than the Sun, and it's hard to see them, right.
These stars are much much dimmer than the Sun. Something
that's half as bright as the Sun is going to
be one six as dim. And there are a lot
of stars out there that are smaller than half the
mass of the Sun, and so they're much much dimmer,
which makes them hard to see. So we don't even

(40:51):
really have a complete catalog of all of those stars,
but none of the stars that are very nearby are
much larger. In fact, none of the stars that are
within thirty light years of the Sun is very much bigger,
Like the biggest star in our neighborhood is about four
times the mass of the Sun. And as you explore
out there into the universe, you discover something really interesting,

(41:13):
which is that there seems to be sort of a
limit to how big stars can be. And we discover
this just because there aren't stars that are much much bigger.
The limit seems to be somewhere around a hundred two hundred,
maybe up to two hundred and fifty times the mass
of the Sun. The biggest stars out there are just
about that big. And the reason is that stars that

(41:35):
have huge amounts of mass burn really really hot and bright,
and they push so hard from the inside that they're
basically unstable and blow themselves apart. Anything above that it
basically blows the excess off, So you just can't have
a stable blob of matter that's more than like two
hundred times the mass of the Sun. But we're gonna

(41:56):
dig into that in a whole other podcast episode about
the biggest stars in the universe. It's also actually fun
to think about the history of the universe. It turns
out that the massive stars changes as the universe gets older,
and the very very early universe. We think that the
stars that were first born, the first population of stars
that came together out of that hydrogen, were actually typically

(42:19):
much much bigger than the stars we see today. Those
are these so called population three stars. They're called population
three stars because our stars today are called population one,
and then the stars that they came from are called
population to sort of sort of counting back to the
beginning of the universe, it might make more sense to

(42:40):
you to think the first generation of stars are population one,
and we should be population three, But for whatever reason,
astronomers are counting backwards. So population three stars are the
first ones to form in the universe, and those were
much much bigger because there wasn't very much metal around
in the universe right after the Big Bang. The universe

(43:01):
was mostly hydrogen, with a little bit of helium and
a tiny bit of lithium. But overwhelmingly hydrogen, and hydrogen
doesn't clump as well as heavier metals, right, it makes
it harder to collapse into a small sample because molecular
hydrogen doesn't collapse as well. It's harder for it to
cool Or you get this big blob of gas in

(43:22):
which you need to form a star, is for it
to collapse gravitationally, And it turns out that that's easier
to do in smaller clumps when you have little blobs
of metal. That's sort of like seeds, smaller pieces. If
you just have a huge mass of hydrogen, then it's
harder for it to collapse into smaller clumps. It tends
to collapse into these much bigger objects because it's harder

(43:43):
for it to cool off. And so in the very
early universe we had really really huge stars, much more
massive stars than we typically see today. And then the
second generation of stars had more metal in them. Right,
because the first generation of stars burned and fueled helium
production of heavier stuff, and then that sea did the

(44:03):
next generation of stars. And because there was more helium
and heavier metals around when the second generation formed, you
tended to get smaller clumps. So that second generation of stars.
Some of them are still around, They are still burning
in the universe. We can see them. Check out our
podcast episode about the oldest stars in the Universe, and
you'll see that we've found something that we think our

(44:25):
second generation stars that are burning for billions and billions
of years. Those first generation, we think only lasted a
few hundred million years, if at all. And the crazy
thing is that we've never even really seen one of them.
Nobody's ever seen a population three star, and that's, of
course because they're all burned out, so there are none
of them in our neighborhood. In order to see when

(44:46):
you need to look really really far away, so that
light from that population three star would just be arriving
to our eyeballs and now, billions of years after it
already died out. The problem, of course, is that those
galaxies are super duper far away. We're talking about things
that are thirteen billion years ago, so they're basically at
the edge of the observable universe, and those galaxies are

(45:08):
hard to spot. We can see the galaxy, we know
it's there. We're getting light from that galaxy. We suspect
it's filled with population three stars. But we haven't ever
identified an individual population three star from the early universe,
and it would be super fascinating if we could. We
had an understanding of like how big were these things?
How much mass did they have? All Right, so today

(45:30):
we've dug into the details of how scientists know the
mass of these stars. It turns out to be really
important to the life of a star. Completely controls what's
going to happen to it, whether it's going to be
a black hole or end up as a white dwarf.
And eventually a black dwarf is just turned by the
original helping of hydrogen and other stuff that it got
when it was formed. And we can figure that out

(45:52):
by looking at binary star systems, by looking at gravitational
micro lensing, and then sort of extrapolating in between what
we do know to guess about what we don't quite know.
But there's still a lot of uncertainty because these calculations
we do they're hard, there's a lot of approximations we
have to make. We think they're probably not completely accurate.
We have some confidence that they're not way off because

(46:14):
we can calibrate them using the stars that we do see,
where we can measure their mass, but there's always room
for improvements, and so it's important to think about the
knowledge and also the uncertainty, because hey, most of the
universe is uncertain. Most of what we will learn about
nature and stars and the universe is ahead of us.
So thanks for coming on this ride to explore what

(46:36):
we do know and what we don't know, and our
speculation about what we will eventually know. Thanks everyone, tune
in next time. Thanks for listening, and remember that Daniel
and Jorge Explain the Universe is a production of My
heart Radio. Or more podcast from my heart Radio visit

(46:59):
the heart Radio app, Apple Podcasts, or wherever you listen
to your favorite shows.