Astro 15 Assignment 3
Henry Breslin
1.​ Introduction
Color-Magnitude Diagrams (CMDs) are one of the most powerful tools in observational
astronomy for studying stellar populations. By plotting a star's brightness against its color (a
proxy for temperature), a CMD reveals the evolutionary state of stars within a population.
Distinct features emerge in CMDs of coeval populations: the main sequence traces
hydrogen-burning stars, the red giant branch traces post-main-sequence evolution, and the
horizontal branch traces core helium-burning stars.
Theoretical isochrones, curves representing the predicted positions of stars of a single age
and metallicity in the CMD, provide a way to extract physical properties from observational data.
By matching the shape and position of an isochrone to observed stellar populations, we can
estimate both the age and the distance of our observed galaxy.
2.​ Data Analysis:
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To analyze the stellar populations within the assigned galaxy (Catalog 12), data
containing stellar positions and photometry was analyzed in MATLAB. Before constructing the
Color-Magnitude Diagram (CMD), it was necessary to correct the raw F606W and F814W
magnitudes for Milky Way dust extinction. The corrected magnitudes were calculated by
subtracting the provided extinction values from the raw apparent magnitudes. This one done by
subtracting the extinction factor for each color from the given value.
Using these corrected values, a CMD was generated by plotting the apparent F814W
magnitude on the vertical axis against the color index (F606W - F814W) on the horizontal axis.
Per standard astronomical convention, the y-axis was inverted so that brighter stars (lower
numerical magnitude values) appear at the top of the plot. In order to properly isolate the main
sequence stars from the noise data was selectively removed to create a plot that resembles what
the main sequence should likely look like. This was done by creating boxes that would remove
data. There was not a specific algorithm used for this; rather, I selected the data that I believed
was noise based off of previously examined CMDs. Of the original 2698 data points, 1907 noisy
data points were removed in order to create this clean main line sequence.
3.​ Identification of Key Stellar Populations:
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Figure 1: CMD Prior to Data Clean
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Figure 1 shows the CMD diagram for Catalog 12 prior to any noise being removed. The
majority of the removed points were in the region with a magnitude of greater than 25 and a
color of below 0.8.
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Figure 2: CMD After to Data Removal
Figure 2 shows the data set after the noisy data was removed. The main sequence is more
apparent.
The two key stellar populations that seem to be present in catalog 12 appear to be the
main sequence and a small region of red giant stars. It is very difficult to tell with high
confidence that what appears to be the red giant section is not a branch of the main sequence.
Due to the slight red shift and increase in luminosity, it seems likely that this group is the red
giant branch. The main sequence appears to be located between 0.5 and 1.5 in color magnitude
and above a magnitude of 21. The red giant branch appears to be located between 0.5 and 0.7 for
color magnitude and between 19 and 21 for brightness.
No clear horizontal branch is visible in the CMD for Catalog 12. A horizontal branch
would be expected to appear as a roughly horizontal feature at constant magnitude extending
blueward of the red giant branch. It may be that the galaxy contained in catalog is not old enough
for the red giant stars to evolve into the horizontal branch.
4.​ Age and Distance Estimation via Isochrone Fitting
Figure 3: Main Sequence of data set plotted against Dartmouth Stellar Isochrones
Figure 4: Main Sequence plotted against the best fitting Dartmouth Stellar Isochrone at different
distances.
To estimate the age and distance of the galaxy, the observational CMD was compared
against Dartmouth theoretical isochrones. To facilitate a clear comparison, an "empirical ridge
line" was calculated using a pathfinding algorithm (moving median) to cleanly trace the center of
the observed Main Sequence and the base of the red giant branch, effectively filtering out
background noise and photometric scatter. Clause Opus 4.7 was used to help create this moving
average algorithm.
Theoretical isochrones for 1 Gyr, 5 Gyr, and 13 Gyr populations were overlaid onto the
empirical ridge line at varying distance moduli (40 kpc, 45 kpc, and 50 kpc).
The morphological shape of the Main Sequence turn-off is the primary indicator of stellar age.
The 1 Gyr and 5 Gyr isochrones fail to replicate the sharp bend observed in the empirical data at
F814W = 26.5. The 13 Gyr isochrone, however, perfectly traces the lower Main Sequence,
cleanly follows the turn-off point, and accurately maps the base of the subgiant/Red Giant
branch. This indicates a very old, mature stellar population.
By evaluating the vertical shift required to align the absolute magnitudes of the 13 Gyr
theoretical isochrone with the apparent magnitudes of the empirical ridge line, a distance of
approximately 45 kpc provides the best fit. At this distance modulus, the theoretical Main
Sequence and the observed data are tightly aligned.
5.​ Limitations
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I believe that the primary limitation in this report is caused by the amount of noise
contained within the dataset. While correction methods were applied to attempt to correct for
these it is difficult to tell how successful they were. I was able to match the mainline sequence to
a theoretical isochrone with an age of 13 Gyr and a distance of 45 pc, however due to the amount
of data points that were removed I do not feel that this report can confidently conclude that this is
the isochrone that fits this galaxy the best. There is a possibility that there could have been a
significant amount of real data that was located in the removed data points that could have
significantly altered isochrone which would best match this data.
The Dartmouth isochrones used assume a specific metallicity. If the true metallicity of the
population differs significantly from the assumed value, both the age and distance estimates
could shift. A full analysis would involve varying metallicity as an additional free parameter.
Appendix:
Matlab Code: