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Cepheid Variables

Cepheid Variables as Distance Indicator

This is a research project suitable for undergraduate Astronomy and Physics students. It was put together by Dr Helmut Jerjen from the Research School of Astronomy and Astrophysics at the Australian National University. Please send me an e-mail if you are planning to do this project. I would be delighted to hear more about your own results. Enjoy and have fun!
INTRODUCTION

CEPHEID VARIABLE STARS: A Cepheid variable or Cepheid is a member of a particular class of very luminous, massive variable stars with pulsation periods of 1-70 days. The namesake and prototype of these variables is the star Delta Cephei, discovered by John Goodricke in 1784.

STANDARD CANDLE: Because of the tight correlation between periodicity and luminosity, an empirical law discovered and stated by Henrietta Swan Leavitt in 1908, a Cepheid variable can be used as a standard candle to determine distances to galaxies. Since the period-luminosity relation can be calibrated with great precision using the nearest Cepheid stars observed in the Milky Way, the distances derived with this method are among the most accurate available to astronomers.

PL-RELATION: The relationship between a Cepheid's period P (in days), and its absolute magnitude (e.g. in V magnitude) has been empirically derived by many astronomers throughout the Twentieth Century. The relationship is calibrated using data collected from Cepheids whose distances are determined by other means. The accuracy of the period-luminosity relationship has remained essentially unchanged since the calibration given in 1968 by Allan Sandage and Gustav Tammann. More recent notable calibration was published by Feast & Catchpole in 1997. Using data from the Hipparcos astrometry satellite, the latter authors calculated the distances to many Galactic Cepheids via trigonometric parallax. The resultant period-luminosity relationship was:

PROJECT

  • Your colleague, Dr Patrick Tisserand, from the European Southern Observatory requests your help. Working under all sorts of atmospheric conditions, he monitored a Cepheid star using various telescopes across the world over a period of 96 hours. The images are available here. He asks you to establish a light curve and other parameters of that star to find out where it is located in the universe.
  • Browse through the 68 CCD fits images he sent you, using ds9 and locate the Cepheid variable. It is at the centre of the CCD (x=101, y=101). Load 4 files into ds9 and blink between the images to see possible flux variations. What else do you notice that might me important for the data analysis?
  • The names of the CCD images reflect the Julian dates when the data was taken. Record the accurate date/time(in seconds) for each image.
  • Use the IRAF command imexam or qphot to measure the flux of the Cepheid star (I_CV) on each CCD image. Important: because you are working in a crowded field, you need to set the radius of the aperture for the photometry in a way that you can avoid measuring fluxes from neighbouring stars. Does it matter if you only measure a fraction of the light from the Cepheid star to avoid neighbouring stars? Explain your answer. Once you decided on a suitable aperture radius, go and edit the "rimexam" parameter file by writing in IRAF "epar rimexam" -> change parameters if necessary -> quit with ":q" (or "epar qphot" when working with that command).
  • Record the flux of the Cepheid using the aperture of your choice and compute the instrumental magnitude in all 68 frames [m_CV = -2.5 Log(I_CV)] and plot the results vs Julian date. How does the light curve look? What is the mean magnitude and the scatter in the data?
  • Something must be wrong and you have an idea what the problem could be. As the CCD images were obtained under all sorts of atmospheric conditions not all the data is photometric. Some of the measured fluxes must have been affected by cirrus and clouds.
  • You can solve this problem by comparing the flux from the Cepheid with that of another star in the same field. Choose a second (bright) star in the field that is NOT variable. The flux from that star, I_CS, shall serve in the following as zero point for the differential photometry.
  • Go back and record the flux of the control star using the same aperture and compute the instrumental magnitudes in all 68 frames [m_CS = -2.5 Log(I_CS)].
  • Plot m_CV-m_CS as a function of time. How does the light curve of the Cepheid look now when compared with the control star. It should look something like this. Use a computer program to fit a suitable analytical function at the observed data. Determine the duration of the pulsation cycle and the average brightness.
  • In the meantime, Patrick photometrically calibrated the first CCD image (ceph_2451894.64542.fits). He informed you that the bright star at the postion x=103.5, y=172.5 has a V-band magnitude of 14.8. Use this information to calibrate the time series of the Cepheid.
  • Use the PL relation to estimate the absolute V magnitude for your Cepheid.
  • Estimate the distance to the Cepheid star and therefore to its host galaxy. What galaxy could it be?
  • Discuss your results within the context of other people's distances reported in publications ( ADS) .
  • What are effects not taken into account in our experiment (2nd and 3rd order effects) and how could the experiment be improved? What about Galactic extinction?


    Data credit: HJ thanks Patrick Tisserant for providing the exquisite set of CCD images from the EROS data base.
    Image credits: ESA - "http://sci.esa.int/science-e-media/img/20/cepheid-variables.jpg"
    Comments and feedback: jerjen@mso.anu.edu.au
    Last update: April, 2010