We have two open ends that I want to close.
One is I talked about mass transfer as a mechanism for generating blue stragglers.
And the other is that I sort of said that the end of our sun, after the beautiful
light show that is the planetary nebula is a slowly cooling solar mass earth size
chunk of carbon that will eventually when it cools crystalize, so that's a pretty
nice diamond in the sky, but, is a white dwarf really the end for
a star. It will be for our sun,
but it need not be. There's still life in them, there are
white dwarfs despite the fact that they're fusion-wise, completely inert.
And, the trick is the phenomenon of mass transfer, so we need to understand it and
the mathematics is due to our old friend Roche, who we all love and remember for
his work on tidal forces. And so,
thing to remember is that the real question we want to ask in a binary
system, of course, every object in a binary system, is in some sense rotating,
orbiting both stars each star is orbiting the common center of gravity.
And if you throw a rock in there, it'll also orbit in some complicated way, both
stars. But,
we want to describe this in a way that gives us a sense of what orbits which
star, which matter is bound to which star,
and the complication is that the two stars themselves are rotating.
So if you wanted something to be sitting next to a star, it has to not just orbit
that star, but also follow it on its orbit around the common center of mass
and this is the problem that Roche addressed.
And it turns out that if you ask the question, drop,
imagine the whol universe rotating with the system, imagine that the stars are in
circular orbits. And somewhere on this, in this rotating universe and drop a rock
and ask where it will fall, the combination of gravity and the rotational
motion is described by this Roche potential.
here is the Roche potential drawn for a combination of two stars relatively close
to each other one of whom has twice the mass of the other, and so, the surface
here is the potential. So that if you drop something here, it will slide that
way, if you drop something here, it'll slide
down into the star. there's a complication that the rotation
introduces just like the rotation of the earth.
something called the Coriolis Force, for the same reason that winds and artillery
shells in the northern hemisphere turn to the right.
If we imagine that this is the direction which the stars are orbiting, then
indeed, everything will turn to the right.
So that for example, a stone left here will not actually fall down the
potential, but will go into some kind of crazy orbit around this so called
Lagrange point, but that's not what interests us.
the point is that this allows us by join a particular level surface of this
potential, particular region where you can move from
one to the other without experiencing any gravitational force is this particular
surface that meets itself at a point. This top of this saddle right there or
the bottom, depending which way you count it in a saddle.
And this divides the region near the stars into two lobes, the larger of which
corresponds to the more massive star the point in in between where the two lobes
meet is not quite the center of mass. It's shifted closer to the notice, it's
closer to the lighter star than it is to the more massive star, whereas the center
of mass is closer to the massive star. But the idea is that this is the region
in which the gravity of this star dominates,
this is the region which the gravity of this star dominates.
If you drop something from here, it will go into orbit around this star.
Drop something here, it will go into orbit around this star.
Drop something here and it can move around in an orbit like this, which is
some complicated orbit around both stars. So,
typically for two stars in a binary system this is a very interesting thing
if you're going to add planets for example into the system, but why is this
interesting when you have two stars? Well, here's the picture and Algol, our
friend al Ghul, the ghoulish star in Perseus is the prototypical example and
Algol presents astronomers with a puzzle. We can appreciate the puzzle now.
This Algol has two members. 3.6 solar mass main sequence primary and
a 0.79 solar mass subgiant secondary. Huh?
That can't be right. The reason it can't be right is because
the two members of a binary would have formed from the collapse of the same
cloud absorbing the angular momentum. And if they form together, then the more
massive primary should have evolved earlier.
How is it that a 3.6 solar mass member is on the main sequence while the less
massive, secondary, is already done with its main sequence life and is already a
subgiant? that's a problem.
the hint to the answer is that Algol is a very close binary system.
The distance between the two stars is, 0.062 AU,
that's only twice the distance between the sun and Mercury and both this star,
because it's a massive main sequence star, and this star because it's a
subgiant, are much larger than the sun. And so, imagine sticking another sun
twice as far out as Mercury is then make them both big, these stars are almost
touching. The answer to the Algol puzzle is that,
just as we talked about for blue stragglers, B actually started out what
is now the secondary, started out as the more massive star.
So how come it's less massive now? Well as long as they were both main
sequence stars, they orbited each other and each lived within its Roche lobe and
so, the atmosphere of each was part of a well-defined object, the star.
But then, when B turned into a subgiant and started to puff up, it leaked its
outer atmosphere, leaked outsides its Roche lobe.
when it leaked outside, some of it was captured onto A, which is now gaining
mass while B loses mass, which means the Roche lobes move.
B's Roche lobe gets smaller because its less massive, A's Roche lobe gets larger
because it's more massive. And eventually, you get a run away
process of mass transfer from B to A to the point where now a large fraction,
remember, B was more massive then A initially, a large fraction of the mass
of star B has been transferred to star A, which is now more massive.
And this matter in the same way that we'll see later on, comes in with a lot
of angular momentum from the rotation. So it forms a excretion disk around star
A, and then, as material looses angular momentum and energy, it spirals in and
eventually falls onto star A and star A's atmosphere is increasing while star B is
losing mass. So this is a curiosity, it's a very
interesting phenomenon. It's fun that we can understand both the riddle and its
solution. What is this got to do with, and it's
clear how this might resolve the issue of blue stragglers.
If you start with a star that's not very massive, then it sucks a lot of mass from
binary partner, then you would find in your globular cluster a star that is more
massive but still on the main sequence, because it used to be a not so massive
star and evolved very slowly. So far, so good.
What has this got to do with white dwarfs?
Well, imagine, if in a close binary system, the more massive partner evolves,
finishes its main sequence life, ejects a planetary nebula and leaves us
with a white dwarf, while the less massive partner is still on the main
sequence. Eventually, the less massive partner also
will load up and become a giant and when it becomes a giant, the less massive
partner now might extend past its Roche lobe and this time its partner is a white
dwarf. So that means that matter can be
transferred, we can have mass transfer from the less massive partner to,
remember, now the white dwarf is probably the less massive object.
Because it, it lost all of its atmosphere,
but on to the white dwarf and model show us that in a close binary, that rate of
mass transfer can reach a 100 millionth of a solar mass per year that's a
substantial rate of mass flow. What happens to this gas?
Well, when it falls onto the, a white dwarf, this is the white dwarf acquiring
a little bit of a hydrogen atmosphere. Of course, this is nothing like earth's
atmosphere, because gravity is hundreds of thousands of times more intense at the
surface of a white dwarf. And so, remember this is a earth-sized
object with solar mass, and so, the hydrogen is immediately
compressed to degeneracy and heated by the immense surface gravity.
So you have this very tightly bounded degenerate atmosphere.
Moreover, it turns out that it's important that at its base there's
turbulent mixing because of the heating and that enriches the gas with carbon,
nitrogen, and oxygen, the materials out of which the white dwarf is made.
And then what happens is that when the white dwarf has accumulated about a
hundred, a 10,000th of a solar mass of this atmospheric hydrogen the bottom, the
base, the temperature at the base at the bottom of this atmosphere which is very,
very thin in metric terms, but contains a 10,000th of a solar mass the temperature
reaches the magic number 10 million Kelvin.
When the temperature reaches 10 million Kelvin, you can start efficient CNO
hydrogen fusion, the CNO process, and again, we have a degenerate atmosphere,
because it's degenerate, it does not expand when fusion starts, so the fusion
is explosive and essentially the entire atmosphere fuses to helium.
simultaneously, this, well, not the entire atmosphere, only about 10% gets to
fuse, because after 10%, the temperature rises to a 100 million K and the thermal
pressure overcomes degeneracy pressure. At this point, the luminosity of the
object can reach a 100,000 solar luminosities. This is a 100,000 times as
luminous as the sun. And it's not like the helium flash,
because it's not heated, it's exposed, we will see something with a 100,000 solar
luminousities. once you reach that temperature,
radiation pressure ejects the ramainder of the ecreted material. The total energy
released is on the order of 10^38 Jules over a few months that if you think about
it is comparable or slightly more by a factor of ten than the total energy the
sun will release over its entire history. and this can recur, you know, when mass
reaccumulates, so novas can recur every 10,000 or few tens of thousands of years.
And this ejected matter initially glows at about 9,000 Kelvin,
sort as a characteristic high frequency light signal.
And these novae are pretty common, we see a few per year in the Milky Way, but we
don't see far into the Milky Way, because of dust obstructions.
We see better into, say our neighboring Andromeda Galaxy M-31, and there about 30
novae per year detected in, in 31 and the citizen scientists are instrumental in
discovering these as well, the variable star observers.
Here is a visible light image of a nova that exploded in Cygnus in 2010.
And so, this is three days prior and this is three days
later you see why the name nova was given.
If the star was too dim to be visible before,
this presumably is not the white dwarf, but its partner.
But a star could be too dim to see, and then suddenly, it's 100,000 solar
luminosities. You certainly notice that object at great
distance, nova, for new star.
the nova, these novae, live, leave behind interesting remnants that are being
carefully studied. All these structure in the ejecta.
This is the ejecta still glowing many years after the supernova, after the nova
exploded, and in the center, the white dwarf is getting ready to do it again.
And so, white dwarf need not be the end of the
road if you have a partner to mooch off of.
Now, this brings up an even more interesting possibility. Nova is a very
cool object and very interesting and brilliant,
but there's something even more exciting which goes under the name supernova.
What is super about a supernova? Well, supernova is the answer to the
question, a type 1a supernova, is the answer to the question.
Well, wait a minute. So accretion is adding to the mass of a
white dwarf. What happens if you add so much mass that
it exceeds the trandosacar limit, remember, a white dwarf cannot have a
mass more than 1.44 solar masses, it would collapse.
as modeling and this is a difficult problem shows the mass of a white dwarf
never, doesn't exceed 1.44 solar masses. As the mass becomes close to the
Chandrasekhar limit, the white dwarf compresses, remember, at 1.44 solar
masses, it would have zero radius and zero volume.
The, so as the mass increases, pressure and temperature in this compressed
degenerate carbon-oxygen combination object are increasing.
And eventually, a turbulent convection phase starts out that leads to the
ignition of carbon fusion. And again, your indegenerate matter,
the heating from the fusion does not lead to expansion,
so we get a violent explosive process which fuses a substantial fraction of an
entire solar mass of carbon within a few seconds.
Oxygen fuses too, although less completely,
this heats the, the, the object to temperatures of a billion Kelvin.
it releases a total of 10^44 Joules, that's like a million novae,
this deserves the title supernova. It blows the star completely away by
releasing a shockwave that ejects material at very high speeds throughout
the neighborhood. the typically, the donating partner, if
there was a partner that was from which the white dwarf was accreting, that
partner would be blown away at high speed and become what's called a runaway star.
luminosity of the supernova can be a billion solar luminosities or more,
that's characteristic of the luminosity of a galaxy.
So you have a very small target, a point object glowing with the luminosity of a
galaxy. You can see these way far off in the
universe and they're characterized by a spectrum that has absorption lines of
silicon which is found inside the white dwarf and is formed by fusion, but very
few hydrogen and helium lines, because this was formed in an object which was
essentially carbon, nitrogen, and oxygen. And
the shock wave drives fusion to heavy elements from carbon to nickel to iron
and beyond uranium and, and other heavy elements are produced within the
shockwave driven by a supernova. This creates a lot of radioactive
nucleotides and their decay sort of contributes to the late time luminosity.
So the energy of the shockwave, some of it, goes into forming these radioactive
nuclei and they release their energy over years, over the next few months or a
year, and so, we can trace the half lives of
the isotopes that created it by tracking the light curve.
Very exciting objects, more exciting than you might think.
What do we know about them? Well, understanding this explosion is
difficult. Understanding how they happen is not
obvious. So, we know that a type 1A supernova
happens when a white dwarf approaches the Chandrasekhar limit.
Where did it gets get its mass? There are two possible suggestions this
might remind you of the blue straggler debate.
One is called the SD or the single degenerate
model, where the donor is a main sequence or giant star in a very close binary pair
with the white dwarf and the donor exceeds its Roche lobe and
that is how matter accretes under the white dwarf.
You have to be careful, you have to make sure matter accretes fast enough that the
white dwarf does not have time to nova it away and before it approaches the
Chandrasekhar limit. the competing proposal is what's called
the DD or double degenerate model where the donor is another white dwarf, and for
some reason imagine two white dwarves orbiting each other.
Well, they're going to orbit each other, nothing is going to happen.
they're not, white dwarves don't grow outside their Roche lobes, they're tiny,
but, if you manage to make them orbit so close that their distance was of the
order of their size, that's the earth's radius that's two
stars rotating within orbiting each other within an order of magnitude of the
earth's size. How do you do that?
Well, if you only had some friction that could slow them down,
but there's no atmosphere because it's a white dwarf.
We'll learn later that there is a kind of friction that could slow them down and
bring them into this very close orbit. When they get close enough, the
gravitational forces of the slightly more massive one will rip apart.
The less massive one, you get dramatic mass transfer through the Roche lobe,
and essentially, you have a merger of two white dwarfs.
And which of these is the correct scenario?
Recent observations suggest that both occur,
but the tide is turning, the single degenerate was the older model
and more and more people are convinced that this at least has to play a role.
We'll see some evidence for that in a minute.
the nature of the explosion itself is very hard to understand, it's very hard
to model such a nonequilibrium turbulant process.
For example, its not even clear whether fusion proceeds as burning defiligration
or an honest detonation where the speed with which the fusion reaction expands
faster than the sound speed, which is quite high inside this dense degenerate
object. is there an actual triggering of the
initial explosion by degenerate flash of degenerate helium in the atmosphere or
does it start, as I suggested, by internal carbon oxygen fusion?
But there's one important fact. And the fact is observational and very critical,
critically important, but we understand what's going on.
Essentially, no matter how you got there, a type 1a supernova is the ex, the
complete fusion of an object made out of carbon and oxygen whose mass is 1.44
solar masses or essentially, as close to the Chandrasekhar limit as this object
can get. So, type 1a supernovae are essentially
all the same. And indeed, when we, they occur in
clusters and galaxies, to which we know the distance, we can compute their
luminosity measuring their brightness and comparing the distance that we know,
and indeed, the luminosity is almost exactly the same.
Amazingly uniform objects compared, say to the differences in luminosity among
stars, and in fact, if you make some corrections based on the shape of the
light curve then you can actually use these things as standard candles.
Here's how you build a standard candle, here are the light curves of several
supernovae. You can see that this one was considerably more luminous than that one.
But, after making corrections for subtleties in the spectrum and the shape
of the light curve, put them all on this one exact curve,
this is brilliant, because this means, if you measure a type 1a supernova at its
peak, then you know the luminosity of the object you measured and this is an object
with a luminosity of a billion suns. So you can see these things way far off
in the universe, these are measuring sticks for large
distances and much of what we've learned about the structure of the universe at
large distances is due to this understanding of type 1a supernova being
the standard candle. We'll come back to that aspect. I was
talking about the double generate model, these are recent observations that lend
it some credence. the image on the left is a beautiful
image of the remnant of a supernova. And what is observed is that we can
pinpoint the direction in which we should have seen the white dwarf remnant the,
the, the partner remnant had there been a partner, the white dwarf blew itself
apart. The remnant should have been there.
The, the other star, had it not been completely ripped to smithereens and
sensitive searches have found nothing there.
And even more exciting version of this is these x-ray data from the Swift
satellite, where basically they took 53 type 1a supernovae and superposed them on
top of each other, so that, so that their centers completely coincide and look for
the x-ray signal. And what they find is nothing,
in other words, were there a surviving partner to these supernovae, then that
partner should have been heated to extremely high temperatures by the
explosion. You would have expected an x-ray signal,
there is none. What that means is that the partner was
completely destroyed. these are both evidence, but not
conclusive for the DD model. Computing the number of supernovae we see,
comparing it to the probability of binary binary white dwarf pairs still suggests
that the single degenerate model has to make a contribution to these amazing
objects.