Double stars represent one of the basic building blocks of
astronomy by permitting the determination of properties such as the masses of
stars, in some instances their distances, and other properties. The term
”double star” is actually somewhat of a misnomer because it encompasses stars
that lie near one another in space bur are not gravitationally connected. Only
our geocentric viewpoint along a certain direction makes them appear double,
called an ”optical double.” A ”binary star” on the other hand indicates a pair
of stars gravitational bound that move about a common center of gravity and
possess an orbit, generally an ellipse. The brighter of the two stars is
referred to as the primary and the fainter the secondary. If the two stars are
so close together they cannot be resolved, periodic variations in their
spectrogram indicate that the system is nevertheless binary. Such systems are
referred to as ”spectroscopic binaries.” A few binaries combine both visual and
spectroscopic observations. These systems permit a determination of the
system’s parallax independent of its trigonometric parallax and a determination
of the masses of the individual components. If the ellipse of the binary is
nearly parallel to the line of sight one of the stars either occults or
transits the other, causing decreasing the light received. Such systems are
called ”eclipsing·binaries” or ”eclipsing variables.” Sometimes either the
binary’s primary or secondary can itself be spectroscopic, and the system
morphs semantically into a triple, or more, star. I will give later examples to
illustrate these concepts and explain more carefully the nature of the system,
with the exception of eclipsing binaries. Why? Eclipsing binaries are more
complicated than other types of binaries and require practical experience to
feel comfortable with exposition of the material and its analysis. Eclipsing
variables can represent what mathematicians call ”ill-posed” problems,
discussed later, and their study involves not only mathematical prowess, but
also familiarity with the observational material. Because I have not studied
eclipsing binaries in detail it would be presumptuous of me, aside from some
general remarks, to expound on matters better explained by those who have
conducted such research. Among other references the reader can examine Irwin’s
article ”Orbit determination of eclipsing binaries” in Astronomical Techniques,
Vol. II (Ch. 24, 1962). generally an ellipse.
Notice the use of the personal pronoun ”I” in the previous
paragraph. Some authors seem abhorred by the personal pronoun and prefer
stilted phrases such as ”the writer” or ”the author”. which lead to the
intriguing question of who is the writer or author, perhaps an AI machine?
Scientific writing also seems overly addicted to the passive voice. While
indicated for many situations, overuse of the passive voice leads to a stifled
writing style that can easily become tedious. As an example an author, who
shall remain anonymous, writes ,”In 1718 it was noticed by Halley that the
positions of three bright stars....” Why not just write, ”In 1718 Halley
noticed that the positions of three bright stars...”? Fewer words and clearer
text. Also, I prefer use of the Oxford comma. ”Visual, spectroscopic, and
eclipsing binaries . . . ” clarifies that we refer to three distinct types of
binary whereas ”visual, spectroscopic and eclipsing . . . ” obfuscates the
distinction between spectroscopic and eclipsing binaries.
Astronomers use a variety of techniques to study binary
stars, some antiquated such as graphical methods, and some of more recent
vintage. I use many of the standard methods, but add: 1) impersonal weighting;
2) total least squares (TLS), also known as orthogonal regression, or mixed
least squares and total least squares (LS-TLS), developed since the 1980’s; 3)
semi-definite programming (SDP), an extension of interior point linear
programming and developed since the 1990’s.; 4) orthogonal regression, also
known as the L1 method or sometimes the errors in variables method. These three
ideas will be explained in greater detail later.
As for the instruments themselves for the study of binary
stars, many references are available. One of the best, although antiquated, is
Chauvenet’s A Manual of Spherical and Practical Astronomy, Vol. Two (1891), Petrie’s
article ”Radial Velocity Determinations” in Astronomical Techniques, Vol. II
(1962, pp. 64-67) , and Labeyrie (1970) discusses a more modern way to observe
binary stars, speckle interferometry, than the classical filar micrometer
described in Chauvenet. These techniques, while interesting, remain of
secondary importance for the determination of the orbit itself.
Regarding mathematical notation I use italics to indicate
scalars, boldface italics for vectors and matrices.
Author(s) Details
Richard L. Branham,
Jr.
Universidad Nacional de Cuyo, Argentina.
Please see the book here :- https://doi.org/10.9734/bpi/mono/978-93-88417-10-5
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