Ages and Distance of Clusters

The write-up is very complete.  Use the online version in order to grab the
color-magnitude diagrams for the clusters (M45, M11, M25, M44, M67, or NGC 6791),
the standard HR Diagram, the distance graph, and the age graph.  The technique
is very much like the Method 2 for the Pleiades lab.

Make sure you are aligning the corrected B-V scales (the ones with the
subscripts).  Once you have overlayed the standard HR Diagram onto the
color-magnitude diagram and have aligned the (B-V)o scales, then you may
only move vertically.  After finding a match to the ZAMS, read off the graph
these three items

1.  The comparison between the vertical scales.  Use the 0.0 on the M scale
on the HR and find where it falls on the m scale of the CMD.  This is a
direct measurement of distance modulus.

2.  The color index of the cluster turn-off point.

3.  The offset between the (B-V) and (B-V)o scales on the CMD.  This is
called color excess.

Do these measurements at the same time and you'll find the lab goes quickly
and the results are more reliable.

Gas and dust have two important effects:

1.  The starlight is dimmed.  This causes us to measure an apparent
magnitude greater (dimmer) than we would if the dust weren't there.  To
correct for this, we would have to make the apparent magnitude less
(brighter) by some factor that accounts for the dust.  We think the stars
are farther away than they actually are.

2.  The starlight is reddened.  We are measuring color index, i.e., blue
magnitude - visual magnitude (B-V).  Redder stars have larger B-V values.
So the stars we measure all have larger B-V values than they should, if dust
didn't exist.  To correct for this we will subtract an amount from the B-V's
to get a value unaffected by dust.  If we used the observed B-V's, we would
not get a satisfactory alignment of the Main Sequence.  But the reddening is
a function of the dust between here and the stars in the cluster and has
nothing to do with the stars themselves.  Thus all of the stars in a
particular cluster have the same amount of reddening.