# Using Supernovae to Study Cosmology

The Redshift-Distance Test

As a function of redshift, the apparent magnitude of distant objects changes under different cosmologies, for two reasons:
1. The shape of space determines how photons spread out as they move outwards (the classic 1/d2 effect)
2. The expansion history determines how the photons are redshifted.
This can be worked out under different cosmologies to derive a form akin to our regular magnitude-distance expression:

m-M = 5logdL(z) -5

where dL(z) is the luminosity distance, and depends on H0, OmegaM, OmegaL, and k. We typically plot this using the distance modulus, not the distance, though (from Carroll and Ostlie):

If we had an object of fixed brightness -- a standard candle -- we could plot its apparent magnitude as a function of distance and work out the cosmology.

Remember Type Ia supernovae: the explosion of a ~ 1.4 Msun white dwarf. These are pretty good approximations to a standard candle, and they are extremely bright. That's exactly what we want to use for the redshift-distance test.

But are SN Ia's really standard candles?

Type Ia supernovae in galaxies w/ Cepheid distances
 SN Ia Galaxy MB(max) 1937C IC 4182 -19.65 1895B NGC 5253 -19.80 1972E NGC 5253 -19.55 1981B NGC 4536 -19.29 1960F NGC 4496 -19.43 1990N NGC 4639 -19.33 1989B NGC 3627 -19.51 2011fe M101 -19.29
This translates to MB,max = -19.46 +/- 0.21. An dispersion of 0.21 magnitudes translates to a distance uncertainty of 10%. Not bad, but there are some whopping outliers. Can we do better?

Yes. It turns out that the brighter SN Ia's decline more slowly than the fainter ones. Measure how bright they are and how fast they fade, and you can make a correction. This reduces the dispersion in absolute magnitude to about 0.1 magnitudes.

But there's a significant drawback to using Type Ia SNe. You gotta find them...

## Using supernovae to study cosmology

• Take a BIG picture of the sky.
• Come back next month and take the same picture.
• Compare the two. Differences?
• If you find a possible supernova, take a spectrum of it and make sure it is a Type Ia SNe.
• Also take a spectrum of the galaxy it lives in, to find its redshift.
• Watch the supernova as it fades, so we can get its peak apparent magnitude. This is important -- you probably didn't catch it when it was at its peak, so we need to fit it to a standard light curve to derive its peak magnitude.
• Keep doing this so you have a big sample of high redshift supernovae. Then compare those supernovae to ones at lower redshift.

Some plots, courtesy of the supernovae cosmology project at LBL and the high z supernova search team at CfA:

More recent data: HST discovered supernovae, extending to higher redshift (Riess et al 2007). In this plot mu=m-M. Curvature in the data is inconsistent with models that use dust or evolution to explain faintness of high-z SNe; instead it is indicative of the "jerk" in the expansion history when lambda began to dominate and the universe went from decelerating to accelerating.