Sky & Telescope - December 2020 - 62

Backyard Science

correct non-uniformities in the chip and the telescope optics.
The resulting calibrated image consists of millions of pixels
corrected for the sensor's quirks and foibles. Each pixel in the
image becomes a reasonably faithful record of the light that
fell on the corresponding photodiode at the focus of your
telescope. Photometrists refer to properly calibrated images as
"science frames."

C = 104

V = XX Cyg
K = 106

Astronomers Use Filters
Color is integral to astronomy. The eye sees a narrow range of
wavelengths centered at 555 nanometers, in the yellow/green,
but stars radiate over a wide range of wavelengths depending
on their energy output, temperature, and chemistry. To limit
what wavelengths the camera sees, we place carefully deﬁned
color ﬁlters ahead of the image sensor.
Color ﬁlter photometry gave birth to one of the most powerful tools astronomers use: the Hertzsprung-Russell diagram. The
diagram shows the absolute magnitude, measured through a
V-ﬁlter, against the color, measured via the difference between
V-ﬁlter and B-ﬁlter magnitudes, for a range of stars. By plotting
an individual star on this diagram, you can glean its relative
redness or blueness, clues to its temperature and spectral class.
Color photometry reveals which stars are main sequence, blue
giants, red giants, red dwarfs, and white dwarfs, and where our
Sun ﬁts among them.

Measuring Magnitudes
So you have a science image ﬁlled with stars. How do you
extract the magnitude of a star from an image? Fortunately,
most good astronomical image-processing software includes
tools to measure the magnitudes of stars. After loading your
image into your preferred program, the ﬁrst task is setting
the radii of the measurement tool that you will use to extract
magnitude measurements. You can use any star for this. The
tool typically has three radius settings. The innermost is the
q APERTURE IS KEY To measure a star's brightness, we measure a star
as well as the surrounding sky. The area inside the inner ring or aperture
measures the combined sky plus star brightness, while the middle and
outer rings define a "donut" or annulus of the sky by itself. Software then
subtracts the annulus measurements from the aperture to produce the
total pixel sum and the instrumental magnitude of the target star.

p DIFFERENTIAL PHOTOMETRY XX Cygni (center) is a variable with a
3.23-hour period that you can easily monitor throughout an entire cycle
in a single evening. The two circled stars at upper right and lower left are
the comparison star and "check" star (see page 64). If the photometry has
been done correctly, the variable will change while the others do not.

aperture. This should be set to ﬁt tightly around the star you
are studying but without cutting off its edges, ideally containing at least 90% of the target stars light. The aperture contains the combined light of the star and its sky background.
The second and third radii deﬁne an annulus (or "donut") of
sky surrounding the star image. The inner radius of the annulus must be larger than the aperture radius, leaving a gap. The
outer annulus radius should be big enough to include a good
amount of sky, but small enough to exclude any nearby bright
stars. The annulus is used to measure the sky brightness.
q APERTURE ADJUSTMENTS Users of AIP4WIN can use the Curve
of Growth tab in the Photometric Analysis tool to fine-tune the aperture
radius setting. This graph displays the instrumental magnitude of the star
image versus the radius of the aperture. If the aperture is set too small,
it doesn't measure all of the star's light. If the aperture is set too large, it
includes unnecessary sky. In this example, the instrumental magnitude
becomes asymptotic at 4.0 pixels, meaning a 4-pixel aperture radius is
the proper radius setting for this star.

Aperture
Annulus

DECEMBER 2 02 0 * SK Y & TELESCOPE

Sky & Telescope - December 2020

Table of Contents for the Digital Edition of Sky & Telescope - December 2020