Dr. K. Y. Michael WONG
Department of Physics, The Hong Kong University of Science and Technology

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.

Take the example of Sirius, 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 (orange line) and Sirius B (red line) 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.

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.

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 a mass of the order of one to ten times the solar mass, compressed to sizes comparable to the diameters of the Earth, Washington DC or 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.

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.)

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.

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.)