Let's now turn to use of supernovae as a standard candle to measure distances in
cosmology. This is today one of the most powerful
tools in the observation of cosmology arsenal, to measure distances or
cosmological scales. We keep using the term, standard candle.
And this is where it comes from. Actually, there used to be such a thing
as standard candle. And such standard candles ostensibly had
the same brightness. Now, a supernova is a lot brighter than a
candle, but the same concept applies. So if, somehow, a supernova or something
else has a constant luminosity. If we put it at different distances from
us, its brightness will decline according to inverse square law or rather, the
relativistic version thereof. So if we can measure relative brightness
of the standard candle, at two different distances.
We can derive, what's the ratio of their luminosity distance.
Similarly, if we have objects of a standard size, like a ruler is always the
same size, and observe it at the different distances from us, the ratio of
the angle, or diameters will be, equal to the ratio of the angular diameter
distances. So we could use, standard rulers, to
determine relative distances to objects we'ere looking at.
So how are the supernovae playing this? They are certainly very bright, can be
seen very far away which makes them useful for cosmological tools and, turns
out, they can be actually standardized. Now, there are 2 different kinds of
supernovae, and both can be used, although one of them is much more useful
than the other. First, there's so called supernovae of
type 1A. They correspond to detonating white dwarf
stars, which have accreted too much material for their own good, either from
their companion or by merging with another white dwarf, which causes
instability and explosion. They're pretty good standard candles
already, and they can be made even better using a trick that I'll show you.
We use their light curves. Brightness is a function of time to put
them to a standard. The other type of supernovae are type 2.
Those are very massive stars that are at the end of their life.
And explode, because their core collapses.
Now, they have a much larger spread of luminosities.
And that will not make them good standard candle.
However, they can be used in a slightly different test called expanding
photosphere method which is similar to the Baade-Wesselink method that we
mentioned earlier when we were talking about pulsating stars.
And thus they can be used as an independent check to those measurements
made with supernovae type 1A. So here is schematically shown, the
difference between, average light curves of the supernovae of 2 kind.
In both cases, their brightness increases, as the star explodes, and then
declines. But the, the shape of the light curve is
different, because it's powered by slightly different physical mechanism.
Supernova classification is actually a little more intricate business.
There are these 2 basic channels. Either massive stars at the end of their
life that exploded because they, no longer produced nuclear reactions in
their core or white dwarfs that are pushed over their stability limit by an,
an additional accretion. They come in many different varieties.
In terms of spectra and so on but they still are, these 2 basic mechanisms,
although they can manifest themselves, in a broader fundamentalogical sense.
So type 1a Supernovae are believed to come, from detonating white dwarfs, and
I'll tell you why that is in a moment. A white dwarf Is a low mass star that has
shed its envelopes. Its at the end of its life.
It, its core just slowly cooling down they are not making energy in the around
there are not thermal nuclear reactions in the core.
But, sometimes or often they can be in binary systems since majority of the
stars in binary systems and if the binary is close enough and their companion, Is
not yet, white dwarf. The gravitational field of a white dwarf
can, pull the outer envelopes of the companion, and accrete, on the surface of
it. Once the, mass of the white dwarf crosses
the so called Chandrasekhar limit, which is the highest mass a white dwarf can
have, and be stable collapse, due to the generousity pressure.
The star explodes. Another way of dumping more matter on it
is if there is a binary white dwarf. And they lose energy by emitting
gravitational waves. They spiral in as the two stars merge.
You get something that's twice a big as then what's sustainable.
As the two stars merge, the effect is the same.
So, we're pretty sure that type 1A suprenovae come from detonating light
force, although this is not yet a 100% certain.
The reasons why we think this is the case is as follows.
There are no hydrogen lines in the explosions of type 1A supernovae. Meaing
they have shed all of their envelopes, so it has to be an old stellar remnant which
would be just like a white dwarf. There are also strong lines of silicon,
which means that nuclear burning in the progenitor has to have reached at least
that stage. Second, they are seen in all kinds of
galaxies, elliptical as well as spiral. Young massive stars That are responsible
for type 2 explosions, are only found, in star forming regions that is like discs
or spiral galaxies. But not in all stellar populations like
bulges or ellipticals. Type 1A supernovae are seen in all
environments, so they have to come from some kind of old progenitor and white
dwarfs, fit that bill. Furthermore, they do have remarkably
similar set of properties, unlike type 2s which suggests that there is single
projenitor mechanism. Their lightcurves are powered by the
radioactive decay of an isotope of mik nickel.
It's about one solar mass worth of radioactive nickel.
However, this is an explosion of the whole star.
And that, by definition, is a very messy business.
We can model supernova explosions in super computers but that is still not a
perfectly well solved problem. This is a very complex phenomenon of
nature. And,
can you imagine it would be kind of hard to standardize an explosion.
So how is it possible that these are standard candles? There is an empirical
relationship between the shapes of light curves of these supernovae, and their
peak luminosity. And it goes in the sense that those that
are intrinsically more luminous are also slower in decaying.
Since the light curves have similar shape, they can be parameterized by a
stretch factor. 1 can be stretched into another, and then
they can be shfited vertically. When you do this, the following happens.
Here we show on the top, a set of actual light curves of, some type 1A supernovea.
And the second panel shows what happens when we normalize them and correct them
with the stretch factor. Suddenly, they all seem to fit this one
universal shape. It turns out that, by doing this, we can
standardize the peak luminosity of a type 1A supernova to 10% or even slightly
better, which is plenty good enough for cosmological purposes.
Note again, that we have to calibrate this, standard luminosity, using
distances to galaxies that were measured in some other way.
Say, with cephates. There aren't very many of those, maybe 20
or so, that have both cephate measurements, and supernovae.
A very similar, result can be obtained by looking not only at the shape of the
light curve, but also behavior of different colors.
The more luminous supernova, tend to be decaying slower, but also, have,
systematically different colors. Either way, supernova, or type 1A can be
standardized, so their peak brightness is nearly constant to within 10%.
And that's what makes them really useful, as cosmological tool.
Not just for the measurement of Hubble constant, but also other cosmological
parameters. And for example they have played a key
role in the Recent confirmation of the existence of the dark energy.
Here is an example of a supernova 1A Hubble diagram, corrected for the stretch
factor and so on. The scatter is remarkably small.
What's plotted here is the distance, luminosity distance in formal distance
modules, raises the redshift. And it's as good a Hubble diagram as
you'll ever Hope to get. Now the other kind of Supernovae type IIs
can still be used using, with a different trick.
This is so called Expanding Photosphere Method.
An interesting thing about this method, it's based on physical reasoning and, in
principle, does not require messy calibrations.
However, it is model-dependent. And that more in compensates for the
other benefits. It is very similar in principle to the
Baade-Wesselink method we used for pulsating stars.
This uses type II supernovae and it can be cross checked with Cepheids to see how
well it works. The physical basis behind this method is
that supernova photospheres Will emit light in a way that's not too different
from the blackbody radiation, according to Stefan Boltzmann law.
So if you can measure temperature, and if you can measure the radius of the
photosphere, then you can immediately derive luminosity.
From luminosity and observed apparent brightness, you can find the distance.
So this is how it works. The angular diamater, of the expanding
photosphere is the ratio of its physical diameter, and the distance.
And that can be, folded through Stefan-Boltzmann formula, as shown, as
shown here, except that there is an extra fudge factor, it's inserted to account
for the deviations, of the, real supernova spectra from the black.
Body. This is where, theory comes in, that's
where the modeling comes in. Just like with [UNKNOWN] method, we can
figure out the radius from observing the velocity of the expanding photo-sphere,
from the moment of the explosion, as a function of time.
It is probably as good approximation as any, to assume that the initial radius is
about zero. Because it is certainly much smaller,
than, radii of the expanding supernovae shells.
Now we have everything we need. We can simply solve for the distance.
But again, there is model dependance. An expanding, shell, of a stellar
explosion, is not exactly in equilibrium, and spectrum is not exactly that one of
the black body. So modeling has to be done to,
to connect the two. Next we will talk about what's really the
first definitive measurement of the Hubble's constant, using Hubble's Space
Tell.