Variable stars are an exciting and dynamic aspect of astronomy. Whereas
most events in the lives of stars take incredibly long times (as compared to
that of the human life), variable stars can change dramatically in a very short
period of time. Variables are often studied, because the different types
provide us with a wealth of information about the lives, structure, and
distances to the stars. The primary focus of this project was searching for
new variable stars and determining their periods. In particular we
concentrated on pulsating variable stars in the Northeast Arm of the Small
Magellanic Cloud (SMC).
The Magellanic Clouds are small irregular galaxies that can only be seen
from the Southern Hemisphere. There are two Magellanic Clouds, creatively
named Large (LMC) and Small (SMC), that are companions to our Milky
Way Galaxy. They are much smaller than our Milky Way Galaxy, only about 7
kiloparsecs and 3 kpc in diameter (1 parsec = 3.26 light years), with very low
masses, only about 20 billion solar masses for the LMC and about 10% of that
for the SMC (for comparison our Milky Way is about 25 kpc in diameter, with a
mass of roughly 2x1011 solar masses) (Seeds, 1997). The Magellanic
clouds are very close to us, only about 50-60 kpc away, so they have been very
widely studied. Because they are so close to our Milky Way, the SMC in
particular, is currently in the process of being ripped apart by tidal forces,
and will eventually merge with the Milky Way. Studies of variable stars in
both the LMC and SMC form the basis for distance calibrations to other galaxies
much farther away.
In general a variable star is any star that changes brightness over a
relatively short period of time. There are two primary classifications of
variable stars: extrinsic, and intrinsic variables. Extrinsic variables are
geometric variables such as eclipsing binary systems, and rotating stars. In
these systems only the geometry of the two stars or the rotation of a star
causes the variation in the light. Intrinsic variables, on the other hand,
have light variations due to the physical structure/nature of the star itself.
(Zeilik, 1992 and AAVSO, 1997)
Intrinsic variables are further divided into two categories: pulsating
stars, and cataclysmic (eruptive, or explosive) stars. Pulsating stars are
those that undergo periodic expansion and contraction of their outer
atmospheres. These include classes of stars such as Cepheids, RR Lyrae stars,
RV Tauri stars, Delta Scuti stars, and Mira stars. Cataclysmic/eruptive
variables exhibit sudden and dramatic changes in their brightness. They
include Supernovae, Novae, and Dwarf Novae. There are other star types, such
as T Tauri stars, flare stars, and magnetic stars, that do not fit nicely into
either of these categories. (Zeilik, 1992)
Our study primarily focuses on identifying stars belonging to the second
group of variables, intrinsic. In particular, Cepheids and RR Lyrae stars were
being sought. As was mentioned before, Cepheids and RR Lyrae stars are
variable due to a physical change in the structure of the star causing its
envelope to expand and contract at regular intervals. Actually all stars,
including our sun, pulsate to some extent, but like our sun the pulsations in
most normal stars are very small in magnitude and are quickly damped out by
other factors. But in these types of stars, the combination of the temperature
and luminosity (power output) are such that instead of being damped out, the
normal pulsations are greatly amplified.
Stars are divided in to groups called Spectral Classes, based on their
temperatures and spectral characteristics. Spectral Classes are labeled by a
combination of a letter and number. The main classes are labeled with a
letter: O, B, A, F, G, K, M (with O being the hottest, down to M being the
coolest). Subclasses of these are given numbers 0 - 9 (0 are early types, 9
are late types). Our sun, a yellow star, is in the Spectral Class G2, whereas
Sirius A, a blue-white star (the brightest star in the night sky),is in the
Spectral Class A1.
By creating a graph, called a Hertzsprung-Russell (H-R) Diagram, of the
spectral class of a star (or its temperature) vs. its luminosity (power
output, or brightness), the resulting plot shows a line of stars passing
diagonally through the plot from one corner to the other (Figure 1). This line of stars is called
the Main Sequence, these are "normal" or "average" stars.
Other stars lie off the main sequence to the two opposite corners, these stars
are at various states in evolution, most are old, dying stars that have evolved
off the Main Sequence, but a few are young stars about to enter onto the Main
Sequence.
In H-R Diagrams (Figure 1) the
temperature of a star decreases as you move from left to right across the
horizontal (x) axis. So in the upper left corner the large, blue-white (hot)
stars are located, whereas the small, red (cool) stars are found in the lower
right corner. Our sun, being a yellow star of roughly average size, and
brightness, is situated in about the middle of the H-R Diagram along the Main
sequence.
On the H-R Diagram, there is a grouping of stars in the upper right corner
above the Main Sequence (Figure 1). This
group of stars represent old, "large" stars that have begun to fuse
Helium in their cores, these stars include Betelgeuse, Antares, and Mira.
These stars have interesting properties. Many are unstable and pulsate, some
erratically, while others very regularly. Cepheids and RR Lyraes are only two
types of these unstable stars, there actually are many other types of pulsating
stars. Most are found along an area that passes diagonally through the H-R
Diagram from upper right to lower left and lies primarily above the Main
Sequence (Figure 2). This
"Instability Strip" marks the region where the temperatures and
luminosities provide a perfect combination to enhance the pulsation.
The stars pulsate because the star itself is not in hydrostatic
equilibrium; in other words the force of gravity acting inward is not quite
balanced by the interior pressure from fusion acting outward. The star expands
due to an increase in the interior gas pressure, and owing to momentum
overshoots the hydrostatic equilibrium point; at this time gravity takes over
causing the star to contract. As the star contracts it once again overshoots
the equilibrium point, again owing to momentum. After the star contracts past
equilibrium the gas pressure builds up and ultimately causes the star to expand
again, repeating the process. (Zeilik, 1992)
In most normal stars energy is dissipated during the pulsation (this can
be thought of as similar to frictional losses) and eventually the star returns
to equilibrium due to the damping. In pulsating stars there is a mechanism in
place that replenishes the dissipated energy causing the star to continue to
pulsate. This pulsation mechanism is He+ ion. Simply put, a layer
of He+ found in the outer envelope of these stars, at just the right
depth and of the right thickness, becomes transparent to the outward flux of
radiative energy when the stars expands out past equilibrium, and opaque to
this same energy when the star contracts in past equilibrium. This provides a
valve to control the flux of energy and to drive the pulsations. (Zeilik,
1992)
The periods of pulsation of Cepheids and RR Lyrae stars are essentially a
function of their densities - the longer the period the more massive the star
is, and due to the mass-luminosity relationship, the more massive stars are the
more luminous stars (Seeds, 1997). Due to this fact, these stars can be used
to very accurately measure distances to star clusters and galaxies. In order
to get a distance the apparent magnitude (brightness) of the star, and the
period of its pulsation must be known very precisely. Once these are known the
absolute magnitude (actual brightness, luminosity) of the star and thus its
distance can be calculated. The larger the known number of these stars in a
cluster, the more accurate the distance to the cluster can be calculated. But,
the primary purpose of the project is just to concentrate on accurately
calculating the periods of known variables, and to find more of these types of
variables in the SMC. Other astronomers can then use our findings to more
accurately calculate the distance to the SMC, and thus to other galaxies.
The field that we are studying is roughly 1x1.3 deg. area centered on
RA = 1h02m Dec = -71o30' (epoch 1975). It
covers the area from the Northeast Arm of the SMC out into the lower star
density region of the "inner halo". This region includes the
foreground globular cluster NGC 362 and the SMC cluster NGC 361. (Figure 3)
We are basing some of our project on data collected during an earlier
photographic study (Smith et al, 1992) of the same region. This region has
been broken up into five fields, each of which was covered in a single Charged
Coupled Device (CCD) frame (one frame for each forth of the total region -
Northeast, Northwest, Southeast, and Southwest; and a separate frame for only
NGC 362 and the immediate surrounding area) (Figure 4). Each field was
photographed twice in two different wavelengths: visual (yellow-green), and
blue. The actual data images that we are using were taken over several years,
1992-1994, at Cerro Tololo Inter-American Observatory in La Serena, Chile.
These raw images then had to be reduced and combined to produce the actual
working data files. Two programs were utilized to process the images: IRAF
and DAOPHOT. IRAF was used to combine, view, and label images. DAOPHOT did
the actual counting and identification of stars, then flagged stars whose
brightness changed more than a certain amount between several images. These
stars were then observed using IRAF and identified as known variables,
suspected variables, possible new variables, or due to some type of noise in
the image. This was a very time consuming job, considering there were
(roughly) over 7000 stars per frame, roughly 100 were identified as variable
candidates, and of the 100 maybe about half were actually identified as known
or suspected variables. Detailed records needed to be kept of each known or
suspected variable found, including which field it was found on, and the
identification number it was assigned.
To date we have finished the first two runs (September and October, 1992).
From these we have identified several variables that have very well known
periods and light curves. We compiled a list of the Julian Dates (JDs) of each
image, and the individual magnitudes of each of these stars on the images.
Using this list we created some preliminary light curves to check the accuracy
and quality of our data (Figures 5 and 6).
This project has a long way to go before completion. There are some
technical computing problems that need to be solved before the image reduction
can be completed for the 1993 and 1994 runs, along with all of the NGC 362
fields. These problems primarily include offsets and rotations between images
of the same field. Once the computing problems are solved star counts still
will need to be made on the 1993 and 1994 runs, and on all of the NGC 362
fields. More extensive databases, one for each known, suspected, and new
variable, must be created to contain all of the relevant magnitudes and JDs.
There is still a lot of work to be done, but all in all it is manageable,
especially after the computer problems are fixed.
E-mail to stark @ astro.psu.edu
