Astronomy 122 Honors, Fall 2009
Long Period (Mira) Variable Stars
The objects of the exercise are to:
1. appreciate that the sky is not unchanging;
2. examine directly part of the way in which most stars die;
3. explore how scientific data are acquired and used.
To these ends, you will look at the variations of a "long-period
variable" (LPV) star, otherwise known (after the first discovered)
as a "Mira" variable. We will discuss them in class. Mira
variables are dying stars with dead carbon-oxygen cores that are
ascending the giant branch for the second time. The stars have
lost their equilibria and pulsate, changing their brightnesses over
periods of 100 to 1000 days. They are in this state for 100,000 or
so years. At the same time they are losing matter through massive
winds, and will eventually lose their entire outer envelopes,
nearly exposing their old nuclear-burning cores. At the end, they
will produce "planetary nebulae" that are seen as shells of gas
surrounding the hot cores that will die as "white dwarfs."
The observations were secured with a now-defunct camera system
called "Stardial" that is mounted on the roof of the Astronomy
Building and that took a digital picture of the sky every 15
minutes throughout the night. The field of view is about 9 degrees
wide (about twice that of the bowl of the Big Dipper); the camera
is pointed toward the celestial meridian about 5 degrees south of
the celestial equator (at a declination of 5 degrees south). Each
picture has been indexed and posted on the Web under "Stardial,"
and presented so that north is to the right and east is up. The
system was in operation from July of 1996 and to August 2006, and
all the observations have been archived for your use.
Your job is to construct a "light curve" for your star
in which you make a graph of magnitude plotted against time.
Magnitude measurements are to be made using the oldest device, the
human eye. Accompanying these notes are prepared images called
"finding charts" of two fields of view. One contains a variable
star known as T Virginis (in the
constellation Virgo). The other contains two variable stars, S Virginis and V
Virginis. You may pick any of the three stars to work on.
Click on the star's name to bring up an image. Each image shows
the variable star (labelled "S", "T", or "V") and several
"comparison stars" whose magnitudes have been pre-measured. Each
magnitude is given to a tenth of a unit, but the decimal points
have been left out to avoid confusion with stars; for example, 97
means 9.7, etc. (Technical detail: To minimize color differences,
the fundamental reference star against which the other comparison
stars were measured is always a late G or a K star. Since Stardial
is a red-sensitive camera, the variable, which is cool and red,
will appear brighter than it would to the eye, and your magnitudes
will be lower than they would be were you using your eye at the
telescope.)
Your data are on a link called Stardial, which you
can also find on the Astronomy Department's home page. Go to it
and read the introduction about how stardial works. You do not
have to absorb it all, just read to get a feel for the system. The
images are organized by date and also by position around the sky
from west to east according to the field of view's right
ascension (see Measuring the Sky or
Appendix 1 of your textbook). Right ascension is an angle around
the sky to the east of the Vernal Equinox measured in time units
rather than degrees, where "one hour" = 15 degrees, and so on. T
Virginis is found in the field with the right ascension of 12 hours
and 15 minutes, or 1215. S and V Virginis are found at 13 hours 30
minutes, or 1330. You may pick any year with available data.
To find images for measurement do the
following:
1. Go to Stardial's main menu.
2. Click on "Data."
3. Click on "Archive via the Web."
4. Click on "jpg" (the format used for the images).
5. Scroll down and click on "RA" (for right ascension mode).
6. Scroll down until you find your chosen field (the one that
contains your variable star), either "1215" or "1330."
7. Pick any year. On the left will be a list of dates with
month and day (mmdd, 0117 = January 17, 0225 = February 25, etc.).
On the right will be a date of posting and the file size in
kilobytes. The camera took pictures whether clear or cloudy.
Cloudy nights were automatically set to "6K" or so. These are
useless. Clear nights are "25K" or so. These are the ones to use.
You must still examine them (compare several), as some will still
be taken under partly cloudy or murky conditions. You are looking
for the better nights.
Interpolating between comparison stars on the
finding chart, make an eye estimate of the magnitude of your star
(to a tenth of a unit) for each observing night. You should have
10 observations spaced throughout your observing season. (Note
that you might have to go into the previous year to fulfill the
whole season of visibility.) This is actually the way variable
stars are examined, except that professionally, electronic
measuring devices are used; generations of amateurs, however, have
made useful observations employing the "naked eye" technique at the
telescope.
As you make your observations, record your data in a table and then
plot your data on a graph with the date on the bottom axis (the
x-axis) and the magnitude INCREASING DOWNWARD (so fainter is down)
on the side (the y-axis). When you plot your observations on your
graph, you will see that the points do not exactly follow a smooth
path. Draw the best smooth curve that you can through your
observations as is done in the accompanying sample
.
No measuring device is perfect, and all measurements necessarily
contain errors. The deviations of your points from the smooth
curve you have drawn indicate your typical "error of measurement,"
which should always be cited. Estimate your typical errors from
the graph before turning it in. There are formal ways of assigning
errors; you need only make your best estimate.
Reports are due on Wednesday, December 2. Include:
1. a TABLE of measurements that includes the date and the
magnitude;
2. a GRAPH with magnitudes increasing downward;
3. your ERROR ESTIMATE (the
size of a typical error);
4. and a brief STATEMENT about the behavior of your star.
This should be fun; as you proceed, you do not know what your star
is going to do; you are looking into the unknown.