Since our CMD doesn't have a main sequence on it, we couldn't use that to get the distance. So instead, we went out and tried to learn about the horizontal-branch stars, because we see them on our CMD --- (here's our CMD again for reference):
We found our first
astronomical research paper that told us that
the horizontal branch should have a magnitude of about 0.5 if it's
at a distance of 10 parsecs (33 light-years). So we each measured
the magnitude of our horizontal branch stars --- Marbella measured
V=15 for the HB while Marvin got V=14.8 for the HB. The
difference between the observed magnitude and the magnitude if it
were at 10 parsecs is called the distance modulus, so for
Marbella it's DM = 15 - 0.5 = 14.5, and for Marvin it's DM = 14.8 -
0.5 = 14.3. There's a formula that relates the distance modulus
(DM) to the distance:
distance (in parsecs) =
100.2*(DM+5)
so Marbella got a distance of about
7940 pc while Marvin got about 7240 pc. So one way to state our
result for the distance is this:
M5's distance is 7600 +/- 350 pc. (do you know
why we rounded off the numbers?)
We know our distance is
at least as uncertain as the spread in these two values, and it's
probably even more uncertain because we had to assume the
horizontal-branch stars have a known magnitude. But, we dug
around in the astronomical literature and found some recent values
(for instance,
here,
here,
and
here)
for M5's distance modulus that range from about 14.35 to about 14.70,
so we agree with their work. Does that mean we're right? Or
they're right?
How far is 7000-8000 parsecs, anyway? Well, it's the same as about 23,000 to 26,000 light-years if that helps. But in other terms, it's like the distance from the Sun's neighborhood to the center of the Galaxy --- is that a coincidence?
Next we worked to determine the age of M5. We used the Yale Isochrones for this part of the project. They show what a group of stars at 10 parsecs looks like in the CMD for a series of ages. Here is an animation of the isochrones as the group of stars ages --- if you cannot see the animation, if it doesn't work for some reason, here is a page with some isochrones of different ages to look at...
Since we'd already determined the distance modulus, we knew that we must line up the V=0 magnitude on the isochrone with the V=14.5 (about) magnitude on M5 --- we also knew that the colors have to line up (that's why we made the B-V axes the same on these plots). So all we had to do was print out a bunch of isochrones on transparencies, and lay them on top of our cluster until we got one with the right shape.
Just eyeballing the isochrones, it seemed obvious that M5 must be
older than a few billion years old. So we printed out isochrones from
9 billion years old and older on transparencies, lined them up (using
our distance modulus values) on the M5 CMD and looked for a good
fit. We did this for a while, trying different ages, coming back to
ones we'd looked at before ... trying to make different parts of the
diagram fit ... it took a while to settle on an answer.
Even though Marvin and Marbella had slightly different distance
modulus values, they both settled on the 11-billion-year-old isochrone
as the best fit:
We agreed, though, that the isochrones from 9 billion years old to
about 13 billion years old all fit pretty well. So we decided the
best way to state our determination of the age is:
M5's age is 11 +/- 2 billion years.
Again, we dug up some recent values from other astronomers (like
here and
here)
--- they find ages for M5 that range from about 10 to about
14.5 billion years, so again we agree well with other astronomers.