PAUL: So we've seen that classical novae,
the explosion of a thin layer of hydrogen
around the surface of a white dwarf.
The mass slowly builds up as more stuff gets dumped onto the surface,
and eventually the pressure crosses that magic threshold,
and the whole thing goes kaboom and explodes.
BRIAN: And one of the interesting things about these objects
is they're not all the same.
Sometimes you get great big explosions that
happen very rarely, and other times it'll
be smaller explosions quite frequently.
And we think this has a lot to do with how big the white dwarf is because you
could imagine, if you've got a really heavy white dwarf,
it's going to have a lot of gravity, which
means that the hydrogen's going to want to blow up
when there's not very much there.
And so you'll get quite frequent, small explosions.
But imagine a bigger white dwarf, or a lighter white dwarf,
well that's one which has less gravity.
And so you can build up a lot more on the surface before it goes kaboom.
PAUL: And you might also have different sorts
of things being dumped on the surface.
For example, do you have more helium landing
on the surface that might fuse a different-- you'd
have to assume a higher pressure and temperature to actually fuse that?
It would still happen eventually.
BRIAN: Yeah, because there are these binaries.
It turns out when you make these binaries
with a white dwarf and other star, sometimes
they do a very intimate dance with each other, exchange bodily fluids,
and in the process end up converting a lot of it to helium.
And so you might dump helium onto the white dwarf instead of hydrogen.
And helium you have to get really hot and really dense
before it's going to ignite.
PAUL: And presumably it's not just going to be a single explosion.
But if there's an explosion, blows stuf, there
might be a thin layer left behind, because not to generate anymore.
In that case, it could just burn for awhile like a normal star.
BRIAN: Yes, and we also have the possibility
that you can actually burn material rather than when
it gets on the surface, that you actually burn it on the way in.
So you have hydrogen coming from a star, burning
as it reaches the surface of the star, and essentially being
created as helium.
And that allows you to essentially make the star grow
heavier and heavier over time.
PAUL: But if the white dwarf is growing heavier and heavier,
I mean, we've known that the degeneracy pressure is
wholly atop these electrons moving at relativistic speeds because
of the uncertainty principle, but I wonder if there's a limit to that.
I'm of course, not the first person to wonder about this.
The famous Indian astrophysicist, Chandrasekhar, cycles
was worrying about this in the 1930s.
Let's see what his calculation came out as.
OK, let's do the calculation.
Can you really pile more and more matter onto the surface of a white dwarf
without something nasty happening to it?
Is there a limit to how hard this degeneracy pressure,
this quantum mechanical electron pressure, can push back?
Well from our calculation earlier, we derive the radius over white dwarf
by balancing the downward force of gravity
against the upward force of the degeneracy pressure.
And this gets us some clue right away.
You see it depends on the mass of the white dwarf to the one over 1/3 power.
So one over the cube root of the white dwarf mass.
So this means that as the white dwarf becomes more massive,
the radius become smaller.
Not very fast.
You could increase this 8 times, this is only half in size.
So this would seem to imply that white dwarfs can
survive almost any amount of mass.
As the mass gets bigger, the white dwarf gets smaller,
but as the white dwarf gets smaller, its quantum mechanical pressure
gets bigger and bigger.
And so you just end up with very, very small very, very dense white dwarfs
without limit to their mass.
So end of story.
Well no, of course.
And to explain why it's not the end of the story, of we're
going to have to make a little detour into what makes a star stable.
