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.