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Colour — Magnitude Diagram

How to create of a colour-magnitude (CMD) diagram which is a photometric equivalent of the Hertzsprung-Russel diagram.

Open cluster M 67

Open cluster M 67 is an old galactic cluster with a differently evolved stars which covers wide range of colour indexes. All stars are approximately same old, but due to its different initial masses and the fact that heavy stars gets older quickly, we are observing the cluster members in different stages of evolution.

Sample Data

A sample data are available as munipack-data-m67.tar.gz. Use commands

$ cd /tmp
$ tar zxf munipack-data-m67.tar.gz

to unpack it to a desired directory. We will assume that the sample data are unpacked to /tmp directory as /tmp/munipack-data-m67.

The sample data has been acquired at MonteBoo Observatory by group of author's students "Hrošátka". The flat-fields by ChM. Quality of the observation is poor due to a light pollution by our urban neighbourhood.

Data Processing

To get CMD, follow these points:

  1. Prepare images for photometric corrections as describes Photometric Corrections Tutorial.
    $ munipack dark -o d7.fits d7_*.fits
    $ munipack dark -o d30.fits d30_*.fits
    
    $ munipack flat -o fB.fits -dark d7.fits flat_*B.fits
    $ munipack flat -o fV.fits -dark d7.fits flat_*V.fits
    $ munipack flat -o fR.fits -dark d7.fits flat_*R.fits
    
    $ munipack phcorr -dark d30.fits -flat fB.fits m67_*B.fits
    $ munipack phcorr -dark d30.fits -flat fV.fits m67_*V.fits
    $ munipack phcorr -dark d30.fits -flat fR.fits m67_*R.fits
    
  2. Stars detection and photometry
    $ munipack find -th 10 -f 6 m67_*.fits
    $ munipack aphot m67_*.fits
    
    Warnings like:
    Object at coordinates:   739.055908       94.7188416    
      Are you sure your bad pixel thresholds are all right?
      If so, then you need a larger outer sky radius.
               8          20        1762   84700.0000       3.39999995E+38
    
    are reported for stars near of border (when aperture lie outsdie of image) and can be safety ignored.
  3. Search an astrometric catalogue (required for astrometric calibration)
    $ munipack cone -r 0.2 132.8 11.8
    
  4. Astrometry calibration of all images
    $ munipack astrometry -c cone.fits m67_*.fits
    
  5. Sum of all images
    $ munipack kombine --rcen 132.8304 --dcen 11.7771 -o m67_B.fits m67_*B.fits
    $ munipack kombine --rcen 132.8304 --dcen 11.7771 -o m67_V.fits m67_*V.fits
    $ munipack kombine --rcen 132.8304 --dcen 11.7771 -o m67_R.fits m67_*R.fits
    
  6. Aperture photometry of final frames
    $ munipack find -th 10 -f 6 m67_?.fits
    $ munipack aphot m67_?.fits
    

The files M67_*_MAG.fits contains the table:

α [J2000]δ [J2000]instrumental magnitudestd. deviation
132.822830111.75628057.62841.00036

To match and visualise data, topcat (part of Virtual Observatory software) can be recommended.

Determination of Properties of M67

One can be easy compared with models tabulated in the article Theoretical isochrones from models with new radiative opacities, Bertelli G., Bressan A., Chiosi C., Fagotto F., Nasi E, Astron. Astrophys. Suppl. Ser. 106, 275 (1994) tables can be downloaded here: ftp://cdsarc.u-strasbg.fr/pub/cats/J/A+AS/106/275

M67cmd.png
Colour - magnitude diagram for M 67. The star track for 10 Gyr, Z=0.0080, Y=0.25 and 1 kpc.

The models can be easy plotted and one can determine basic astrophysical characteristics of M 67 open cluster:

Notes

This is the outline of the real method used to determine the parameters of clusters in astrophysics. The fitting of the main sequence and the turning point gives an age estimation, at least as wishful thinking.

The presented method is focused on use of Munipack. Therefore we are ignoring some astrophysical difficulties:

See Also

Photometry calibration, Photometric System Transformation, Photometry Format.