a) Light curves (i.e. brightness time series) are often useful in studying time-variable phenomena in astrophysics. Below are a set of light curves of Cepheid Variables. Using plotting and fitting programs if necessary, find a rough relation obeyed by all the Cepheids. This relationship should relate the brightness (magnitude) of the Cepheid with another property. In other words, your relationship should have the form \(M_V = A*feature+M_0\), where A and \(M_0\) are variables you should find.
We can use these light curves to determine the period and the \(M_V\) (mean magnitude) and of each Cepheid.
Ashley:
- period: 50 days
- \(M_V\): -5.7
Moiya:
- period: 15 days
- \(M_V\): -4.4
J Arbanus:
- period: 20 days
- \(M_V\): -4.8
Yutong:
- period: 100 days
- \(M_V\): -6.2
Graphing \(M_V\) vs. period appears to give us a logarithmic relationship:
So we graph \(M_V\) vs. log(period) and get a best-fit line:
A = -2.17 and \(M_0\) = 1.925, where the "feature" is log(period):
\(M_V = -2.17log(period)-1.925\)
b) Describe how you would measure the distance to a Cepheid.
Based on the light curve, we should know the apparent magnitude of the Cepheid. We can then plug that into the equation from question 2:
\(d = D*10^{0.2(m-M)}\) where D = 10pc
c) Below is an image of a Cepheid Variable in the Large Magellanic Cloud. Determine its period, mean absolute magnitude, and distance.
The period is the distance between the two peaks, which is approximately 5 weeks or 35 days.
We can calculate the mean absolute magnitude using the equation from part a.
\(M_V = -2.17log(35)-1.925 = -5.28\)
Using this absolute magnitude, we can calculate the distance using the equation from part b, where m is the mean apparent magnitude of 15.6 and M is the mean absolute magnitude of -5.28.
\(d = 10*10^{0.2(15.6+5.28)} = 1.5 * 10^5pc \rightarrow 150kpc\)
Excellent!
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