Some stars explode as supernovae (SNe). In particular, Type Ia Supernovae come from exploding white dwarfs in binary systems. For now, it’s not important to know how this happens. It is, however, critical to learn the consequences of this mechanism, because they too are standard candles.
(a) As with the Cepheids, we can analyze the light curve of Type Ia SNe to standardize them. Below is a set of light curves. Examine them carefully, considering quantities like light curve shape, width/timescales, relative & absolute luminosity, &c. Find a rough relation obeyed by all the Supernovae Type Ia. Note: Although the supernova light curves have many features, try to relate just one of them to the peak magnitude.
(b) Describe how you would measure the distance to a Supernova Ia.
(c) Measure the distance to SN Cornell, whose light curve is shown below.
(a) As with the Cepheids, we can analyze the light curve of Type Ia SNe to standardize them. Below is a set of light curves. Examine them carefully, considering quantities like light curve shape, width/timescales, relative & absolute luminosity, &c. Find a rough relation obeyed by all the Supernovae Type Ia. Note: Although the supernova light curves have many features, try to relate just one of them to the peak magnitude.
In all Type Ia Supernovae, the maximum ABSOLUTE magnitude reached is about -19.3. This is true for ANY Type Ia SNe. Thus:
\[M_{max}=-19.3\]
This is very useful, because they can be used as distance markers.
(b) Describe how you would measure the distance to a Supernova Ia.
This is simple using the distance modulus and a basic apparent magnitude measurement. First one would take a light curve of the SNe in question and find the maximum apparent magnitude.
Then one would apply the distance modulus.
\[m-M=5log(d)-5\]
\[d=10^{\frac{m-M+5}{5}}\]
Plugging in for a Type Ia SNe:
\[d=10^{\frac{m+19.3+5}{5}}\]
\[\boxed{d=10^{\frac{m}{5}+4.86}}\]
(c) Measure the distance to SN Cornell, whose light curve is shown below.
Looking at SN Cornell, it's apparent magnitude peaks at 7. Let's find its distance.
\[d=10^{\frac{m}{5}+4.86}\]
\[d=10^{\frac{7}{5}+4.86}\]
\[d=10^{6.86}\]
\[\boxed{d=1.8\times 10^6 pc = 1.8Mpc}\]
For reference, this is roughly equivalent to 53 Milky Way Galaxies put in a line edge to edge.
This is close, but if you look closely, you will notice that some (Yale & Brown) are shorter than the other two, they are also broader. In this we are looking for a relationship between the Full width of the light curve are the halfway point in magnitude. Lookup the Supernova Phillips Relation. 4
ReplyDeleteThe exercise is similar to the Cepheid relation problem .
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