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Algol project

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While preparing a talk about the eclipsing binary stars Algol and ε Aurigae for the Astronomical Society of Edinburgh (ASE), I had the idea of handing out comparison charts so that people could go out and estimate Algol's brightness with the naked eye. From the audience came the question whether this could not also be done with digital photography, which it can. So I have looked a bit closer into this and come up with another set of comparison stars for use in digital imaging.

Although aimed mainly at members of ASE, anyone can use the information provided here to observe Algol and then on their own or in a group draw a light curve of brightness against time. The simplest modes of observation described here are not up to a standard that would be acceptable by variable star observers, but the more advanced modes both of human-eye and digital-imaging observation should be acceptable by amateur astronomy organisations like the British Astronomical Association Variable Star Section (BAA VSS) or the American Association of Variable Star Observers (AAVSO). That said, Algol these days seems to be of little interest to serious variable star observers.

Comparison chart

Algol chart
Comparison chart for Algol. For offline use, see also the PDF version.

An essential tool in observing variable stars is a "comparison chart". This is a star chart that shows the variable itself and a number of nearby stars of known, constant brightness. The graphic shows the chart itself, and below are two lists of comparison stars with their relevant data. The PDF version of the chart includes those data; print it out and use it during your observations.

Use this chart to find the variable Algol and the comparison stars. The circle indicates a 15-degree field for use in digital photography. For naked eye observation, the comparison stars and their brightnesses are:

   α Persei  1.8     (alpha Persei)
   ζ Persei  2.8      (zeta Persei)
   ο Persei  3.8   (omicron Persei)

For digital photography, between one and six comparison stars can be used. Their colours B−V may also be used. These stars are:

      star     V     err     B−V    err
   β Persei   var          −0.050  0.001    (beta Persei)
   α Persei  1.795  0.010  +0.481  0.004   (alpha Persei)
   ν Persei  3.777  0.023  +0.425  0.005      (nu Persei)
   ι Persei  4.049  0.007  +0.595  0.007    (iota Persei)
   ω Persei  4.612  0.022  +1.115  0.006   (omega Persei)
   π Persei  4.696  0.005  +0.061  0.009      (pi Persei)
   κ Persei  3.803  0.011  +0.980  0.002   (kappa Persei)

(Data from J.C. Mermilliod 1991, Catalogue of homogeneous means in the UBV System, Institut d'Astronomie, Université de Lausanne.)

Observation

Brighter/fainter estimate by naked eye

The very simplest observation you can make of Algol is to just check whether it seems brighter or fainter than the second human-eye comparison star, ζ Persei. Of course note down the time as well as the brighter/fainter estimate.

Algol is at its brightest most of the time, clearly brighter than ζ Persei. For a few hours at intervals of just under three days, it is significantly fainter than ζ Persei. A long series of observations of this kind should allow you to determine the period - the length of time between successive brightness minima - and then to predict when minima will occur.

Quantitative brightness estimate by naked eye

The standard method to observe variable stars with the human eye is to estimate its relative brightness difference to two comparison stars, one that is brighter and one that is fainter. To do this for Algol with the chart above, first determine whether Algol is brighter or fainter than ζ Persei. If brighter, use α and ζ Persei. If fainter, use ζ and ο Persei. The result of the observation is initially noted down in the form

  A  x  V  y  B

where V stands for the variable, A and B the brighter and fainter comparison star names, and x an y are numbers to indicate where between the brightness of A and B the variable is estimated to be. For example

  α  1  V  2  ζ

would indicate that Algol is about twice as far in brightness form ζ than it is from α Persei.

Keep this original record of your observation - along with the time you made the brightness estimate. Later, to draw a light curve or to report the observation, convert the result to the magnitude scale. This conversion is a linear interpolation of the brightness between the two comparison stars. If we now use V, A and B as symbols for the magnitudes of the stars, and still use x and y for the numbers in our observing result, then:

V = (x · B + y · A) / (x + y)

or to use the example:

V = (1 · 2.8 + 2 · 1.8) / (1 + 2) = 2.133 ~ 2.1

At the end, round to the nearest 0.1 mag, which is the precision of the trained human eye.

Algol is 2.1 mag most of the time. About 10% of the time - for 9 or 10 hours every 2.9 days - it is fainter. In the middle of such a minimum it is as faint as 3.4 mag, or roughly halfway between ζ and ο Persei. A good strategy would be to look every hour, but to look every quarter hour while the variable is fainter than halfway between α and ζ Persei.

Taking digital pictures

The extraction of photometry from digital images is potentially more precise than the human eye. Here are a few points to consider when taking such images:

Photometry from digital photographs

The Citizen Sky project (http://www.citizensky.org/) has prepared a good tutorial on photometry with dSLR cameras. You will need software

  1. to convert the camera's raw data into a more common and versatile format like FITS,
  2. to stack multiple frames into a single image,
  3. to display an image, to select stars, and to measure their "instrumental magnitudes",
  4. to analyse the instrumental magnitudes of the variable and comparison stars to return the proper magnitude of the variable.

The Citizen Sky tutorial gives pointers for all these needs. Please do study these, in particular for items 1 to 3; the tutorial gives the most appropriate information for most observers. That said, I use entirely different software.

Raw data can also be converted with Dave Coffin's dcraw utility (http://www.cybercom.net/~dcoffin/dcraw/). Some Linux distributions already include it and it may only be a matter of installing the package from your distribution. I hacked the source code myself to get very original data from the conversion, but you can get the same effect with command line options to avoid unwanted scaling or colour "correction":

dcraw -r 1 1 1 1 -k 0 -S 4095 -o 0 -h -f -4

The result is 16-bit PPM format. I use my own stacking utilities (chicam, available at http://www.chiandh.me.uk/soft/) either to convert to FITS or to stack the PPM frames and write the result in FITS.

To display the result and to detect and measure stars in it I use the Starlink software collection (see http://en.wikipedia.org/wiki/Starlink_Project). This is available for Linux and Mac OS X, but this is perhaps not for the faint-hearted. I used to work for the project and my astronomer-users at work use the software; hence my computers have it installed anyway.

For the analysis I do recommend my own Photometry spread sheet. It is very much inspired by that of the Citizen Sky project. Mine is perhaps a little easier to use, it calculates the stellar coordinates with higher precision, and it adds some calculations regarding time scales. Most of all, the catalogue data have been filled in for Algol and the above six comparison stars, while the Citizen Sky original is pre-filled for ε Aurigae instead.

Single frame, one comparison star

The simplest way to use your digital camera is to take a single raw image and to measure Algol and α Persei as the comparison star. The precision of the result is not great, however. 0.05 mag is typical. Anyway, this is a bit better than the human eye can possibly be, and perhaps a lot better than the untrained eye.

The photometry software gives us the instrumental magnitudes of the variable (v) and of the comparison star (a). We also know the real brightness A of the comparison star. The brightness V of the variable then is

V = v − a + A

For example, the software might give us readings

  β Persei    -12.881 = v
  α Persei    -13.483 = a

and we have A = 1.795. Hence

V = −12.881 + 13.483 + 1.795 = 2.40

Round the result to two digits. The precision is such that quoting three digits would be overkill.

Stack of frames, colour and airmass correction

One of the advantages of digital data over observation with the human eye is that we can take many frames and average them into a single image with reduced noise. To take full advantage of this, we should also correct the frames for the camera artefacts that are captured in dark frames. And in the analysis we should correct for the colour differences between our camera's green channel and a standard Johnson V filter, and for the difference in airmass between the stars.

Airmass is a measure for the amount of air that each star has to shine through to reach our camera. A star that is lower on the horizon has higher airmass and appears more dimmed than a star further up.

All the maths is in the Photometry spread sheet. What you have to do is copy the seven instrumental magnitudes (one variable and six comparison stars) into the spread sheet, fill in the when and where of your observation, and read off the V magnitude of the variable and the precision of the result.