Sky & Telescope - December 2020 - 65

star times the extinction coefficient from the instrumental
magnitude. That gives the star's magnitude at zero air mass
- outside Earth's atmosphere. Extinction coefficients at high
altitude observatories are smaller than those in humid, hazy,
and low-altitude continental observing sites, which also often
change from night to night.

Transformation to Standard Magnitude

p ASSEMBLED DATA Magnitude data from variable star measurements
are submitted to organizations such as the AAVSO and other institutions
that collect, curate, and serve variable star data to astronomers both
amateur and professional. The data in this form was used to produce the
light curve on the facing page.

falls while the check star plot remains flat. The beauty of this
method is that atmospheric extinction is nearly the same for
all three stars and cancels out.
For some historical context, search online for "astronomy
XX Cygni" to learn how the Harvard astronomer Harlow Shapley made light curves for this star in 1914 and 1915, and see
how many other astronomers have studied its slowly changing
period of variation.

Correcting Atmospheric Extinction
We Earth-bound observers view stars through our planet's
atmosphere: It acts as a filter, blocking fractions of the star's
light at different wavelengths. The loss is called extinction. In
differential photometry, the V star, C1, and C2 suffer nearly
equal extinction, so it largely cancels out. However, if your
goal is to obtain an accurate magnitude for a star, you must
measure the extinction every night and compensate for it.
Astronomers call the depth of atmosphere between the target and the telescope air mass. Straight overhead, the air mass
equals 1, or one atmospheric thickness. At 45° from the zenith,
starlight passes through 1.4 air masses, and at 60° the air mass
reaches 2. Photometrists prefer to avoid working through an
air mass greater than 2.5. Many camera-control programs
embed the computed air mass in each image's FITS header.
The observing procedure to measure extinction is simple:
As the evening progresses, you measure the instrumental
magnitudes of two stars, one rising and the other setting. As
the eastern star rises, it brightens; stars in the west dim as
they set. Performing this measurement once an hour is often
enough. At the end of the night, plot a graph of instrumental magnitude versus the air mass. On a clear night, the
plot should be a straight line. The slope of a best-fitting line
through the points tells you how much extinction occurs for
each air mass - the extinction coefficient - which is typically around 0.2 magnitudes per air mass for a V filter. Corrections get a bit more complicated for very red and very blue
stars, where you may encounter non-linear effects.
To correct for extinction, you subtract the air mass of the

Quite often the goal in photometry is to produce a standard
magnitude that can then be compared directly to the magnitudes measured at any other observatory with any other
telescope and camera. Just as correcting for atmospheric
extinction removes the effects of a star's location in your sky,
transformation to the standard magnitude system corrects
the instrumental signature of your telescope and camera.
But even though you may be using a set of Johnson-Cousins
UBVRI or Sloan filters, minor variations in the filters you use,
or the wavelength sensitivity of your camera's sensor, will
introduce small mismatches.
The solution is similar to that for atmospheric extinction:
Observe a set of diverse standard stars that have carefully
determined U, V, B, R, and I (or Sloan) magnitudes, then determine linear equations that transform your extinction-corrected instrumental magnitudes to the standard system. You
first determine the transform coefficients and zero-point for
each filter you are using. To do this, image one of several open
clusters (such as M67 or M11) or standard fields, then extract
the instrumental magnitudes. The AAVSO provides complete
instructions and software for recording standard fields, as well
as generating coefficient values and applying transforms.

Get Involved
You'll want to get your feet wet with an observing program
of differential photometry as you gain confidence in your
newfound knowledge of this rewarding branch of astronomy.
Photometry is an excellent pursuit on bright moonlit nights.
As you get deeper into it, every night offers an opportunity to
find something quite unexpected, as well as the satisfaction of
knowing that you're making a real contribution to astronomy.

¢ RICHARD BERRY is a long-time telescope maker, astrophotographer, and member of the AAVSO.
FURTHER READING:
The Handbook of Astronomical Image Processing by Richard Berry
willbell.com/aip/index.htm). Written for amaand James Burnell (willbell.com/aip/index.htm
teur astronomers and includes a copy of AIP4WIN PC software.
The Sky Is Your Laboratory: Advanced Astronomy Projects for
Amateurs by Robert Buchheim (https://is.gd/skylab). Advice and
projects on observing and performing photometry.
To Measure the Sky: An Introduction to Observational Astronomy
by Frederick R. Chromey (https://is.gd/measurethesky). An
undergraduate college astronomy laboratory textbook.
The AAVSO Guide to CCD Photometry (aavso.org/ccd-cameraphotometry-guide). A practical guide to getting started.
sk yandtelescope.org * DECEMBER 2 02 0

65


http://www.willbell.com/aip/index.htm https://www.is.gd/skylab https://www.is.gd/measurethesky http://www.aavso.org/ccd-camera-photometry-guide http://www.aavso.org/ccd-camera-photometry-guide http://www.skyandtelescope.org

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