Binary Stars
Dr. K. Y. Michael WONG
Department of Physics, The Hong Kong University of Science and Technology
Introduction
When you watch the twinkling stars in the night sky, you may think that they are
lonely objects in the infinite space. Yet astronomers tell us that a majority of stars in
fact come in pairs. Stars which exist in pairs are called binary stars.
Sirius
Take the example of Sirius (天狼星), which is the brightest star visible in the night. In
Hong Kong, it is easily visible shortly after sunset in winter, as shown in Fig. 1.
Astronomers have traced its trajectory in the sky for years, and found that it is
wobbling leftward and rightward along its path, as shown in Fig. 2. This is contrary to
the prediction of Newton’s first law, which states that an isolated object should move
uniformly along a straight line. Indeed, modern astronomical observations reveal that
the star has a faint companion, which is believed to be a white dwarf. The bright and
more massive star is called Sirius A, and the faint and lighter white dwarf is called
Sirius B.
(Fig. 1: Sirius (twinkle star symbol) as seen from Hong Kong in the direction of ESE
at 9 pm, 1 January. It is the major star in the constellation Canis Major (meaning the
big dog), with Sirius located at the neck (or collar) of the dog.)
Fig. 2: The dancing motion of Sirius A and Sirius B from 1910
to 1990.
The dancing motion of Sirius resembles what we see in ballroom dancing. Imagine a
gentleman in black tuxedo embracing a lady in white dress, circling gracefully on the
floor. When the lights are switched off, we can only see the trajectory of the white
dress, which wobbles leftward and rightward as the lady is carried forward from one
side of the dancing floor to the other. Though we may not see the gentleman in black,
we can easily infer that the lady has a partner.
For the dancing partners, the spinning motion is maintained by the force acted through
their holding arms. Without this force, the partners would fly apart. This is the
centripetal force which maintains the circular motion of the partners. If the partners
spin faster than their arms can hold, they would break apart eventually. Hence by
observing how fast they spin, we will know how tight they hold each other.
Binary Stars
Let us extend this analogy to the binary stars. The force holding the binary stars
together is the gravitational force, which is determined by the masses of the stars.
Two observations can reveal how large this force is, and hence can provide
information about the mass of the binary stars. First, we should observe the distance
between them. If the distance is large, we can guess that the force that keeps the
bonding of the partners intact should be large. Second, we should observe the period
of their dancing motion around each other. If the period is short, then the stars are
spinning fast around each other, and the force that keeps the bonding of the partners
intact is large. In fact, using Newton’s laws of motion and Newton’s law of universal
gravitation, we can derive the generalized form of Kepler’s law, which states that the
total mass of the binary stars is directly proportional to the cube of the average
distance between them, and inversely proportional to the square of the period.
Arguably, binary stars provide the only direct way to measure the masses of stars. It is
true that we can obtain much information from the starlight collected from telescopes.
We can analyse the chemical composition, the surface temperature, the velocity and
the distance, and so on. However, none of these directly reveals the masses of stars.
To measure their masses, we must see their gravitational forces in action. The dancing
motion of the binary stars provides the opportunity.
Compact objects
More recently, binary stars play another significant role in the discovery of many
compact objects. These refer to stellar objects with extremely high densities, which
may be white dwarfs, neutron stars or black holes, all of them have masses of the
order of one to ten times the solar mass, compressed to sizes comparable to the
diameters of the Earth, a metropolitan city, and Hong Kong Island respectively. They
are difficult to be detected optically because of their small sizes. However, compact
objects are much more easily discovered when they are members of binary systems.
The recent discovery of Sirius B, a white dwarf, illustrates the usefulness of binary
stars.
X-ray source and Black hole
Another example is the first discovery of a black hole in Cygnus X-1, an X-ray source
in the Cygnus constellation. It contains a very large and bright star and an invisible
partner orbiting each other. How do we know that the partner is a black hole? We
know it from the observation that Cygnus X-1 is a strong X-ray source. The best
explanation is that matter from the bright star has been blown off from its surface and
falls towards the black hole, due to its extremely strong gravity. As matter falls, it
develops a spiral motion, similar to the whirlpool of water flowing out of a sink, as
shown in Fig. 3. This turbulent motion is so violent that X-rays are emitted.
Furthermore, from the orbital period of the binary system, we know that the mass of
the compact object is about 6 times the solar mass. Since astrophysical principles tell
us that white dwarfs and neutron stars cannot be so massive, the compact object is
most likely a black hole.
Fig. 3: The generation of X-rays when a compact object (e.g. a black hole) is a member of a binary
system. Matter from the companion star is attracted to the compact object, and flows violently in a
whirlpool.
Binary Pulsar
A further example, important to both astrophysics and fundamental physics, is the
discovery of the first binary system containing a pair of pulsars in 1974 by Hulse and
Taylor. They called it PSR 1913 + 16 (PSR stands for pulsar, and 1913 + 16 specifies
the pulsar's position in the sky). It is widely accepted that pulsars are in fact rapidly
spinning neutron stars, radiating out electromagnetic waves which appear as pulses to
an observer. The pulses from one of the two pulsars are directed towards the Earth.
(In this case, the neutron star remains invisible optically because of its small size, but
becomes detectable because of the pulses observed by radio astronomy.)
How do we know that the pulsar is a member of a binary system? A very important
property of pulsars is that their pulse periods are so regular that they effectively have
the same precision as the atomic clocks. Hulse and Taylor observed that the pulse
periods from PSR 1913 + 16 grew longer and then grew shorter regularly every 7.75
hours. This reminded them of the Doppler effect, in which the periods of waves from
a moving source are lengthened when it is receding from the observer, and are
shortened when it is approaching the observer. Hence the periodic changes indicate
that the pulsar is orbiting in a binary system with a period of 7.75 hours.
Binary Pulsar and Gravitational Waves
An even more exciting discovery followed. After a long time of observation, Hulse
and Taylor found that both the radius and orbital period of the binary system were
decreasing and the speed of rotation was increasing. They associated this observation
with the energy loss due to gravitational waves. According to Einstein’s general
theory of relativity, moving massive objects create disturbances in their surroundings,
which can propagate outwards in the form of waves called gravitational waves. This is
generated in a way similar to moving electric charges that creates disturbances, which
can propagate outwards in the form of electromagnetic waves, in the electric field
surrounding them. Since Einstein predicted its existence, there was so far no
observational confirmation. Pulsars are sufficiently compact and hence can generate
noticeable effects of gravitational wave emission when they rotate in a tightly bound
binary system, as shown in Fig. 4. This provides the first strong evidence of the
existence of gravitational waves. In 1993, Hulse and Taylor won the Nobel Prize in
Physics for their work in binary pulsars.
(Fig. 4: The radiation of gravitational waves from a pair of pulsars in a binary
system.)
References:

M. A. Seeds, Foundations of Astronomy, Seventh Edition, Chapters 9 and 14
(Brooks/Cole, Thomson Learning, Pacific Grove, CA, 2003).

S. Hawking, A Brief History of Time, Chapter 6 (Bantam Press, London,
1988).

J. M. Weisberg, J. H. Taylor and L. A. Fowler, Gravitational Waves from an
Orbiting Pulsar, Scientific American OCT 74, 1981.
[About the author: Dr. K. Y. Michael WONG received his BSc degree in Physics
from the University of Hong Kong, and PhD degree in Physics from the University of
California, Los Angeles. He did postdoctoral research at the Imperial College and the
University of Oxford. He is presently an Associate Professor in Physics in the Hong
Kong University of Science and Technology. His research interest is in theoretical
physics.]
Keywords:
Binary stars, centripetal force, black holes, pulsars, Doppler effect, gravitational
waves, white dwarf, turbulent motion, Kepler’s laws, Stellar Objects, Binary Pulsar,
general theory of relativity, Newton’s law of universal gravitation.
Related Topics in the syllabus:
Newton’s first law of motion, gravity, gravitational force, period, electromagnetic
wave, mass.
Extensions (from the syllabus):
Bring out ideas:
Warm-up discussion:
o
Based on the paragraph, what do these physical principles mean:
(a) Newton's laws of motion,
(b) Newton's law of universal gravitation,
(c) conservation of linear momentum,
(d) conservation of energy, and
(e) Doppler effect.
Explain how the following physical principles are applied in the study
of binary stars:
o
What does Kepler’s law mean? By Kepler’s law, try to guess how does
the period of PSR 1913 + 16 change if the orbital radius is doubled?
Also, what if the masses of the pulsars are doubled?
o
Consider the X-ray emission of Cygnus X-1. Explain how energy is
converted to various forms and finally to X-rays which reach an
observer on Earth.
Points for further discussion:
o
Consider a pair of ice-skaters in a Winter Olympic figure-skating event.
Compare their motion of dancing in circles with those of the binary
star. How does the motion depend on the masses of the skaters, the
mass ratio of the skaters, the holding force of the skaters’ arms, and the
distance between the skaters. In what ways are skating and binary stars
similar?
o
Besides binary stars, suggest other cases of astronomical observations
where the motion of the celestial objects can provide information about
their masses.
o
Matter flow towards the black hole of Cygnus X-1 in the form of a
whirlpool. Suggest examples of whirlpool motion from your daily life
at home. Identify the common factors in causing the whirlpool motion.
o
What is the major property of black hole? Based on the reason you
mentioned, try to guess a reason why black hole is invisible (i.e. you
cannot see them through optical telescope)?
o
What is Doppler effect? By Doppler effect, describe the sound you will
hear when a horning ambulance is approaching you, then leaving you
when you stand stationary?
o
The article compares the propagation of gravitational waves with that
of electromagnetic waves. Suggest examples of disturbances
propagating as waves from daily life.
Activities:
o
Access the Website http://www.phys.ust.hk/genphys/press/presshkust.htm to download the software “Simulation of Eclipsing Binary
System”. It displays the orbits of the binary stars, and describes how
the light intensity changes when one star is possibly moving in front of
the other (that is, eclipsing the other). Set “iteration number” to 1,500
so that the simulation is sufficiently slow. Set “eccentricity” to 0 so
that the binary stars have a circular orbit. Change the masses of the two
stars and the distances between the stars and observe their effects on
the orbit and the light curve. Change “eccentricity” to nonzero values
and observe elliptical orbits as well.
Related Web Sites:
o
Physics 1993
The Nobel Prize of Physics in 1993 went to two physicists who
discovered a new type of pulsar and this discovery has opened up new
possibilities for the study of gravitation.
http://www.nobel.se/physics/laureates/1993/
o
PSR 1913+16
In 1993, the Nobel Prize in Physics was awarded to Russell Hulse and
Joseph Taylor of Princeton University for their 1974 discovery of a
pulsar, designated PSR1913+16, in a binary system, in orbit with
another star around a common center of mass.
http://astrosun.tn.cornell.edu/courses/astro201/
psr1913.htm
o
科景 Sciscape： “天文學家發現最短週期的雙子星系” (Chinese
version only)
Astronomers in Finland have discovered a stellar binary system in
which the two stars are orbiting around each other every 5 minutes.
This object sets the record as the fastest known binary and beats the
previous record-holder by 5 minutes.
http://www.sciscape.org/news_detail.php?news_id=682
o
New Scientist - “Nano-pulses reveal the power of pulsars”
Astronomers made the discovery by performing a detailed analysis of
radio emissions from the Crab Pulsar, a powerful source at the centre
of the Crab Nebula. They found sub-pluses within the emission lasting
just two nanoseconds each. The existence of these nanosecond pulses
is consistent with just one of a handful of competing theories about the
inner workings of pulsars.
http://www.newscientist.com/news/news.jsp?id=ns99993499
o
New Scientist - “Star cluster puzzle revealed by Chandra”
The Chandra space observatory has revealed that an enigmatic star
cluster 6000 light years from Earth is immersed in a mysterious cloud
of high-energy electrons. The cluster of stars has an X-ray spectrum
indicating that its surrounding gas cloud is filled with extremely highenergy electrons moving through a magnetic field. These high-energy
particles are normally associated with supernova explosions or the
neutron stars they leave behind, but not star clusters.
http://www.newscientist.com/news/news.jsp?id=ns99993207
o
New Scientist - “Hubble snaps Little Ghost nebula”
The glowing remains of a dying star have been captured by the Hubble
Space Telescope. The new image clearly shows the end-stage red giant
star expelling its outer layers into space.
http://www.newscientist.com/news/news.jsp?id=ns99993033
o
牛頓科學網 - “哈伯望遠鏡發現宇宙時鐘” (Chinese version only)
The Hubble Space Telescope had found the oldest stars in our galaxy.
These old stars enabled us to estimate the age of the universe.
http://www.newton.com.tw/news/news_detail.asp?id=
{405BABA2-C9AF-4179-A02F-48C23854E87F}&class=天文現場
o
牛頓科學網 - “噴流觸發超新星爆發” (Chinese version only)
By analyzing the observation of a supernova in the nearby radio-galaxy
3C 78, scientists suggested that jets might trigger supernova explosions.
http://www.newton.com.tw/news/news_detail.asp?id=
{9DA935C5-4093-40A4-83F2-8E19A531E136}&class=天文現場
Further readings:

科學人：中文版，2002 年 6 月號，p.58-68，“時空漣漪”，講述探測重力
波的最新情況。

科學人：中文版，2002 年 6 月號，p.69-71，“重力波天文學的來臨”，簡
述全球重力波觀察的最新情況。

科學人：中文版，2003 年 1 月號，p.110-120，“恆星相撞非奇事”，講述
恆星相撞的研究。