Roughly half of the stars that we see
are members of multiple star systems. An inspection of any field of stars with
even a modest telescope will reveal numerous "close pairs" of stars. It was once
thought that this closeness was the result of coincident alignment. While some
are no more than "chance alignments" (example Albireo (beta Cygni)) it is now
understood that stars can orbit each other as part of a common system. Indeed,
the observations over decades of binary stars helps confirm in our minds an assumption
that we made earlier - that the laws of physics operating on earth also operate
for distant star systems.
What Good are Binary Stars?
Binary stars are our "laboratories" in which we can learn about:
the masses of stars
the sizes of stars
the subtleties of stellar surfaces
Types of Binary Systems
1. Visual Binaries
both components visible (for
a fascinating example click here to "visit" Gliese 623
- the image used as background to the title page of this lecture)
long orbital periods (hundreds
of years)
61 Cygni for example consists
of two stars separated by approximately 30" and has an orbital period of 722
years.
2. Astrometric Binaries
only one component visible
detected by "wobble" in the proper
motion of the visible component. The Flash movie shown below greatly exaggerates
such motion. The curved line along which the same stellar image has been placed
simulates the view an astronomer might put together of this star by observing
it for many decades.
example: Barnard's Star
3. Spectroscopic Binaries
Systems that appear as a single star
but which show variations in their spectra which can be attributed to the presence
of more than one component. Spectroscopic binaries are subdivided into two categories:
3a. Double-Line Spectroscopic Binaries
These are systems in which the spectrum of the "star" actually appears
as two spectra "sandwiched" together. As the individual stars move to and
away from the earth the astronomer sees the lines of each star shifted in
opposite directions. This allows one to determine such things as the eccentricity
of the orbits and the mass ratio of the stars.
animation showing the back
and forth shifting of the spectral lines. In a real spetrum these two
sets will be superimposed.
Often only one spectrum is visible. This is especially so when the component
stars are of much different luminosity. Still, in a manner analogous to that
of the astrometric binary, the nature of these systems is revealed by the
periodic back-and-forth shifting of the spectral lines in the stellar spectrum.
4. Eclipsing Binaries
Occasionally, if the orbit is aligned properly with respect to earth, an
eclipse will occur. When this happens the binary system is considered to be
an eclipsing binary. All of the previous cases could also be eclipsing binaries.
A famous example of an eclipsing binary system is Algol (a Persei).
The study of binary star systems remains
an integral part of fundamental stellar astronomy. By applying Kepler's and Newton's
laws to the analysis of binary star orbits it is possible to determine the mass
and basic dimensions of stars. This is our most direct and accurate way of determining
stellar masses. Recall Kepler's 3rd law in Newtonian form:
where M1 and M2 are the masses of the components measured in solar masses, P is
the orbital period in years, R is the average orbital separation between the centers
of the stars measured in AU. For an example application of this click
here.
Computer Models of Binary Systems
With the advent of modern computers
it is now possible for an astronomer to "model" a binary system. Modeling is one
of the most common tools in science. Essentially, maudlin consists of creating
a possible binary system (in the computer) and then predicting how this system
would appear. We can, for example, produce a binary system and then predict how
the light and velocity of each component would appear during the course of a complete
cycle of the system. By comparing observation and theory we can try to infer what
is really happening. For example, here are computer models generated for a number
of star systems:
Algol:
the "demon" star in Perseus which "winks" with a period of 2.867315 days.
On the basis of this model we think that Algol consists of stars with masses
3.7 and 0.81 solar masses separated by 14 solar radii. As you can, tidal forces
are extreme in this system and the stars are not spherical.
TY
Boo is from a very strange class of binary stars called "W Ursa Majoris
Stars". These stars actually touch and may be in the process of coalescing.
TY Boo has an orbital period of 0.317146 days.
SAO
20517 is a faint, cool star in Cassiopeia. It was found to be variable
during a study conducted by the author on another star, HD 219634. Subsequent
observations at both The King's University College Observatory and The Dominion
Astrophysical Observatory are beginning to reveal the nature of this system.
A very tentative model suggests that the system consists of a pair of late-type
(K5 or later) giants with a combined mass between 5 to 10 solar masses. The
period for this star system is 15.8336 days and the stars are in an "over-contact"
configuration. Shown in this figure is the photometric and radial velocity
data amassed to date. One of the things that makes this system interesting
is its possible identification with an as yet unidentified X-Ray source detected
by the Einstein orbiting observatory.
An Example: A Case Study of
HD174853
HD174853 is a double-lined
eclipsing binary system of type B8Vnn. The first analysis of the spectroscopic
variation in this system was carried out by Hube in the early 1970's. The first
complete light curve (photometric analysis) was carried out by Martin and Hube
in the fall of 1990. The system consists of two apparently similar stars that
orbit each other with a period of 1.391113 days. The orbits are circular and
the short period would suggest that they are synchronous. The radial velocity
and light curves are as follows.
V filter LIght Curve for HD174853 . Solid line represents
a computer model fit to the data.
When one analyzes data such as these
you must resort to powerful computer models. The Wilson- Devinney code is one
of the most sophisticated and commonly used computer models. The following analysis
was done using the WD code run on a PC computer.
When using this program the computer "constructs" models of the stars as they
would appear to us from earth. A lot of very fancy physics is done to calculate
the light each star would emit, the effect of tidal distortion on each star
and whether or not eclipses are occurring. The "game" the astronomer plays is
to modify the parameters he/she uses to describe this system until the computer
produces a light/radial velocity curve that fits (in a statistical sense) with
the data. This may take several hundred "iterations" to accomplish. The analysis
of such a star system can often consume many hours of computing time.
What we learned about HD 174853 (and hopefully about all B8V stars) is
summarized in the following table.
Also of interest is the publication
procedure that an astronomer (any scholar) submits to. Here is a copy of the
first page of the referee's report for our paper on HD174853.
Even I write and get my "term
papers" corrected! Writing and re-writing is just part of doing good scholarship.
Time
toTake a Quiz!
If you are ready, click on "Big Al"
to take a 20 question multiple choice quiz. It should take about 10 minutes and
provide you
with an evaluation of your comprehension of the past 6 lectures. Don't forget
to "register" the quiz so that I have a record that you have completed it. Seeds:
Chp10; pgs 185-198 Kaufmann:
Chp19; pgs 355-361
Time
toTake a Quiz! 
Seeds:
Chp10; pgs 185-198
