Sky & Telescope - December 2020 - 64

Backyard Science

Photometry Made Easy
Differential photometry is the "sweet spot" for amateur
astronomers, and my preferred method for as long as I have
been doing photometry. This technique measures a star's
brightness relative to a nearby comparison star of known
magnitude. For many observing programs, you can ignore
atmospheric extinction and transforming instrumental
magnitudes into standard magnitudes. Best of all, differential
photometry is a great way to get started doing photometry.
Visiting the American Association of Variable Star Observers (AAVSO) observer page (aavso.org/observers), you'll
ﬁnd extensive advice about choosing variable star observing
programs. Fair warning: It can be overwhelming! But as an
example, let's focus on just one star, one of my favorites: XX
Cygni. It's a pulsating SX Phe star, with a 3.23-hour period
and an amplitude of 0.85 magnitude, and it varies enough to
see visually in a telescope. You can observe an entire cycle or
more in just one night, and for northern observers, it's high in
the sky in summer through late autumn. (A fast variable during the winter months is BL Camelopardis.)
Making a series of variable star observations is just like
making sub-exposures for a stacked deep-sky image. For this
work, you can use a CCD or CMOS camera (including DSLR
and mirrorless models). Be sure to take matching dark and
ﬂat frames, or use library master darks and ﬂats to calibrate
the images. On each image, extract the instrumental magnitudes of the variable (V), the comparison star (C1), and the
"check" star that serves as a second comparison (C2). (The
XX Cygni ﬁgure on page 61 shows the AAVSO star chart and
an image from a time series.)
Enter the time each image was made, along with the V,
C1, and C2 magnitudes into a spreadsheet program. To ﬁnd
differential magnitude, place the difference between the
variable and comparison star in one column and the difference between the check star and the comp star in the other.
When you plot them on a graph, the XX Cygni plot rises and

Comp

Check

p BATCH PROCESSING Every serious photometry program includes
batch processing to measure many images with just a few clicks. This
window shows the Stars tab of the Magnitude Measurement Tool in AIP4WIN. Here you mark the star you intend to perform photometric measurements on (V), the comparison star, (C1), and the check star (C2). This
tool computes the exact time of mid-exposure in each image, converts
it into Heliocentric Julian Date (the standard time format for photometric
data), adds the air mass, saves the instrumental magnitudes of the stars,
and writes it in formats favored by the AAVSO and other institutions.

XX Cygni

u FINAL CURVE The repeating cycle of the
star's brightness variability becomes clear after
graphing the value for XX Cygni in a series of
B, V, and R images. This observing campaign
spanned roughly 6 hours, resulting in 135 magnitude measurements with each filter.

DECEMBER 2 02 0 * SK Y & TELESCOPE

12.6

2455371.70
(4:48)

2455371.75
(6:00)

2455371.80
(7:12)

2455371.85
(8:24)

2455371.90
(9:36)

Heliocentric Julian Date (Universal Time)

2455371.95
(10:48)

2455372.00
(12:00)

X X CYG NI G R A PH: LE A H TISCIONE / S&T

June 23, 2010

B
V
R

Apparent Magnitude

number of pixels inside the aperture radius and ﬁnds the sum
of those pixels. Next, it surveys all the pixels in the annulus.
The average value of the annulus pixels is close to the sky
brightness, though not exactly because the annulus often
includes a few faint stars. The program may take the median
value of the annulus pixels, or it may apply a more complex
algorithm to ﬁnd an accurate sky brightness.
The computer's ﬁnal step in the process is to subtract the
light from the background sky. The trick is this: The computer
found the total pixel value in the aperture (star plus sky) and
also counted the number of pixels in the aperture. It multiplies the sky background value by the number of aperture
pixels, then subtracts the sky total from the star plus sky
total. The result is the total pixel value of
the star image with no sky light.
11.4
Our end goal isn't a brightness in pixel
values, but rather a brightness in the
11.6
logarithmic scale of stellar magnitudes.
The magnitude equation m = -2.5 log10
11.8
(S)+Z, converts the linear pixel value sum
to an instrumental magnitude, m. In the
12.0
equation, S is the signal, the sum of star
pixels, and Z is the zero-point constant.
12.2
The zero-point constant is determined
by observing standard stars to produce a
12.4
reasonable apparent magnitude value.

http://www.aavso.org/observers

Sky & Telescope - December 2020

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