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Astronomical Observatory: Cool Images

Astr212 Project: Light curve of variable star FM Cas

Contents:
The picture above is a star field containing our project star, FM CAS. The white arrow points to the star. FM CAS is a Cepheid variable star, an interesting class of stars that allows us to determine distance using just magnitude and brightness.

Our project sought to measure the distance to FM CAS. By observing the star frequently we can determine the period of variability, which can reveal its absolute magnitude and distance.

Discovery of Cepheids
The very first Cepheid Variable found was Delta Cephei (named according to the constellation it is a part of), discovered by John Gooricke in the 1780s. This discovery earned him the Copley Medal of the Royal Society in 1784. Unfortunately, Goodricke caught pneumonia while observing DCephei and died at the age of 21. The potential of this discovery was not fully realized, however, until Henrietta Leavitt appeared on the scene in the late 1800s. Leavitt volunteered at the Harvard College Observatory in 1895, concentrating her efforts on an intense study of variable stars in the Small Megellanic Cloud. In 1912, Leavitt realized that the relationship between the apparent magnitudes and periods of variability was clearly linear.
(History of Women in Astronomy)

Interesting Facts about Cepheids

  • These types of stars are most commonly found in open star clusters.
  • The mass of a Cepheid variable is anywhere from 5 to 20 solar masses (that is, 5 to 20-times the mass of our sun).
  • Cepheid variables can have periods anywhere from 1 to 50 days. FM CAS has a period of approximately 5.8 days (Fourier Coefficient Website).
  • They can be measured at distances of up to 20 million light years, and can have temperatures ranging from 6000-8000 Kelvin.
  • The brightest Cepheids have an absolute magnitude of approximately -6 magnitudes.
  • The light curve of Cepheid variables resembles a shark fin. It has rises sharply, and then the rate it falls is a lot slower.

Cepheid Variables are Important

  • Cepheid variables are giants and super giants that are unstable. The stars are continuously expanding and contracting, when they are too large, gravity pulls them inward, and when they are too small, the gas has more pressure on it, so it pushes outward.
  • Due to the change in size, the temperature varies. The brightness is a function of surface temperature to the fourth power, so the brightness changes much more compared to the size of the star.
  • The distance to far away objects in the sky often have to be found using stepping stones, by comparing objects of a known distance to the change in distance to a farther object. Cepheid variables are a starting point for finding the distance to other objects.
  • After the period and apparent magnitudes are measured by observation, the period-luminosity, found by Leavitt, gives us the absolute magnitude of the star. Using the inverse-square law the distance to the star can be found.
  • This gives us a primary stepping stone to find the distances to far away galaxies. This is a very accurate way to find distances because it is just one step away, not multiple, like other ways of calculating distances. This accuracy means, Cepheids are very important for astronomical calculations.

Observing Log

    Date Time Description
    30 Sep 2002 10:35PM Clear until 10:50 (immediately after FM CAS was found), at which time it became overcast.
    07 Oct 2002 11:30PM Clear. Found FM CAS; by the time the camera was appropriately focused, it became overcast.
    09 Oct 2002 11:50PM Slightly hazy. Found FM CAS; took pictures, but FM CAS was not in field of view. No time to correct, as the telescope had to be shared equally.
    14 Oct 2002 10:46PM Clear, waxing gib. moon. Took 10 (good)lights and 3 darks with 8 sec. exposures in clear filter.
    28 Oct 2002 10:40PM Clear, no moon. Took 10 good lights and 3 darks with 8 sec. exposures in clear filter.
    04 Nov 2002 7:50PM Slightly hazy, no moon. Had trouble getting the camera to focus well. Took 10 lights and 3 darks with 8 sec. exposures in clear filter.
    08 Nov 2002 7:50PM Quite hazy, crescent moon. Again, troubles with focusing the camera and frost on the lens. Took 10 lights and 4 darks with 8 sec. exposures in clear filter.
    12 Nov 2002 9:30PM Thin layer of clouds. Located FM CAS, but before pictures could be taken, it became overcast...once again.

Processing:
We took all of the pictures from each night and condensed them down into one. We did this using CCD Soft to reduce the good images. There were bad pictures due to frost, the camera out of focus, the camera not fully aligned on FM CAS and other complications. Each of the pictures were reduced by subtracting the darks to remove any noise from the camera. The background and range were adjusted to show clarity in the picture. The photographs were then aligned by CCD Soft and added together. This process was done for each of the days that data was collected.

Calculations:
We used CCD Soft fits files to compare the magnitudes of a known star that was always in our pictures, with FM CAS. The known star we used was SAO 21238. This star has a constant magnitude, so plotting the difference between it, and F M CAS, on different days, will show the light curve of FM CAS.

We used excel to plot these differences in magnitudes versus time, in days wrapped around into the known period of 5.8 days (see chart below). The average brightness is used. The period of FM CAS is 5.8 days, it has an absolute magnitude of about -4 and an apparent magnitude of 9.1.

We found that the distance to FM CAS is 4100pc. This does not agree with Hipparcos catalog. They both say that the distance to FM CAS is 10000pc using a parallax of 0.1 milliarcseconds (SIMBAD). Due to poor weather conditions and strenuous time constraints, solid data was difficult to obtain.

Variability Chart: FMCas light curve

Our observed data does not correspond to other verified reports. This is largely due to a limited number of observations, caused by frequent cloud cover.

Plot of FM CAS that shows variability correctly, with the characteristic "shark fin" shape.

Orientation & Scale:
North is to the left and east is down. The angular dimensions are 12.75 by 8.5 arcminutes (765 by 510 arcseconds).

Location:
RA: 00h14m53s, +56deg13'10". FM-CAS can be found in the Cassiopeia constellation.  

Related Links:

Team: Elise Crull , Matthew Koop, Maggie Leonard

 

 

 

 

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