Sky & Telescope - June 2019 - 37

and Beyond
Selecting the Targets
Some of the closely merged 6th-magnitude stars I observed
resembled the elongated image representing stars at the Sparrow limit (bottom image, see sidebar). Others, which had
components of unequal magnitudes (Δ mag ≤ 1.0), presented
ovate or peanut-shaped images. These forms can also be distinguished (as opposed to resolved) since:
* One can infer two stars are involved by the irregularity of
the image.
* The shape of the ﬁrst diffraction ring usually mimics the
inequality of the merged stars and provides a recognizable
signature.
* The fainter star of the image generally points toward the
requisite position angle.

where r is the resolution of a telescope, 4.56″ is
Dawes' empirically derived constant, and a is the
aperture of the telescope in inches. If a is given in
millimeters, the constant is 116″.
Double stars are just separated if they meet the
Rayleigh criterion. In this scenario, the centers of the
two stars' Airy disks (the bright central source of the
star's diffraction pattern) are exactly one disk radius
apart. The more stringent Dawes criterion was developed from "ﬁve and thirty" years of observations and
embodies Dawes' concept of resolution. The centers
of the Airy disks at the Dawes limit are separated by
about 0.84-disk radii, as shown in the middle panel.
J. B. Sidgwick's Amateur Astronomer's Handbook
describes overlapping stars with separations closer
t SIMULATING DOUBLE STARS In order to describe what close
double stars look like through a telescope, simulations such as the
one at left can be generated. The top panel shows two Airy disks,
fully separated. The middle panel is representative of the Dawes
limit, while the bottom panel simulates the Sparrow limit.

So, in addition to establishing a personal Dawes' limit for
my telescopes (a 3½-inch and a 7-inch), I also addressed a
lower limit of distinguishability. I included this feature, hoping to bring attention to the practice of claiming a Dawes'
limit resolution for an elongated shape (meaning the stars
aren't resolved at all) that in fact falls within the purview
of the Sparrow criterion. I observed stars with separations
progressively smaller than the conventional Dawes' limit, to
a point where I could no longer detect any elongation, and
recorded the components' separation (ﬁfth column in the
tables overleaf). There was nothing to measure; everything
was subjective and limited to speciﬁc telescopes. In the end, I
chose 18 sixth-magnitude double stars, each meeting at least
some of the speciﬁcs mentioned.

than the Dawes limit. These appear in the eyepiece as a single elongated star with no drop of
light intensity (see bottom image). Sidgwick adds
that the normal eye can detect this elongation
when the separation is more than about r/2. This
leads to the Sparrow criterion, which describes
the appearance of the merged stars as prolate or
rodlike, with centers about 0.78-disk radii apart.
This form shows no notching and the stars can't be
considered resolved. The separation of the stars in
arcseconds where the elongation can no longer be
visually detected with a given telescope comprises
the Sparrow limit.
SOURCES
I relied on the U.S. Naval Observatory (USNO) for double
star data. The ephemerides of the Sixth Catalog of Orbits
of Visual Binary Stars (https://is.gd/usno_orb6) generally
matched those data provided by the Washington Double
Star Catalog (https://is.gd/usno_wds), but there were
exceptions.

sk yandtele scope.com * J U N E 2 019

https://www.is.gd/usno_orb6 https://www.is.gd/usno_wds http://www.skyandtelescope.com

Sky & Telescope - June 2019

Table of Contents for the Digital Edition of Sky & Telescope - June 2019