One of the most exciting research areas of astrophysics today is binary star systems. With the single star picture nearly complete, the mystique of binary star systems has attracted researchers at an increasing rate. Binary star systems, or binaries, are defined as two stars gravitationally bound in orbits about a common centre of mass. Binary stars were first observed by William Herschel, between 1782 and 1821, who was searching for double stars; stars located at nearly the same position in the night sky. By the end of the next century William and his son John had discovered nearly 11,000 double stars.

Many of these 11,000 doubles turned out to be binary star systems. Today it is known that over half of the stars in the night sky are in fact binaries or multiple star systems.

It is not exactly known how binaries form; though there is extensive research in this field and we shall come back to this later. However, there is much known and further research into, other fields of study of binary star systems. The areas we shall look at in this paper are stellar mass determination using binary stars, close binary star systems, accretion disks, exploding binaries, black holes, neutron stars, bursters and binary pulsars. But first we must look at how it is possible to detect binaries and how they are consequently classified.

The methods used to detect binaries from orbital data vary ‘depending on the geometry of the system, its distance from the observer, and the relative masses and luminosity’s of each component’. (Carroll and Ostlie: 201). Therefore we have positional, brightness and spectroscopic measurements, which all lead to various classifications of binary stars.

Positional measurements result in optical doubles, visual binaries and astrometric binaries. An optical double is not a true binary as they are merely two or more stars that lie along the same line of sight, therefore not all are gravitationally bound and therefore do not fit the definition of a binary star system.

Visual binaries on the other hand, are true binaries and are gravitationally bound. A visual binary system is one where each star can be resolved independently and the motion of each member observed. Because of restrictions in observation technology it is usually only stars with relatively large separations that can be seen as visual binaries, and these systems tend to have rather long orbital periods, due to Kepler’s Third Law.

The last classification due to positional measurements is astrometric binaries. Sometimes we are unable to resolve independently the stars of a binary system due to one star being significantly brighter than the other is. The existence of the dimmer star is shown through observing the oscillatory motion of the brighter star. Newton’s First Law along with these oscillations, requires there to be another mass present.

Further to positional measurements, we have brightness measurements, which yield only one classification of binary, the eclipsing binary. Only a very small amount of binaries are eclipsing binaries and they occur when the orbital plane of the system is nearly edge-on to the line of sight. This results in one of the stars periodically passing directly in front of the other, giving a partial or total eclipse.

The above diagram shows the light curve of an eclipsing binary system. The deeper trough on the left of the diagram is a result of the primary eclipse, while the secondary eclipse causes the shallower trough. Deeper analysis of the results in the diagram can give the effective temperature and radii of both the stars in the system, the usefulness of which we will discuss later.

The last technique we shall discuss is spectroscopic measurements that give rise to the classifications of spectrum binaries and spectroscopic binaries. If a star appears to be single and spectroscopic measurements are taken, it may be shown that two different spectral classes are present, indicating that there are in fact two stars present. This is called a spectrum binary and it is necessary for the two stars to be of near equal brightness.

The last classification of a binary star system is a spectroscopic binary, the most common type of binary star, and it is somewhat related to the spectrum binary. It is not always clear that two different sets of spectral lines are present when an analysis is taken, due to either the faintness of one set of lines or both stars having similar sets of lines. Due to the way in which the stars orbit each other, moving back and forth along our line of sight, alternating Doppler shifts of red and blue will appear in the spectral lines. We can then read from these new measurements to tell us that the star is in fact a binary, specifically a spectroscopic binary.

A binary star system usually fits into more than one of the classifications in this section and can therefore provide a wealth of stellar information, like radii, temperature, but most importantly, binaries are the primary source of data on stellar masses.

In this section we shall look at how we can measure stellar masses from certain binary systems and other parameters. The mass of a star can only be measured by observing it’s gravitational effect on other objects according to Kepler’s Third Law:

P² = 4p²a³/ G(m₁+m₂)

Where P is the time taken for one orbit and a is the semimajor axis.

Therefore the mass of a star can only be measured directly if it is in a binary star system. There are three classifications of binaries which can provide us with such a measurement and these are: ‘visual binaries combined with stellar parallax information; visual binaries for which radial velocities are available over a complete orbit; and eclipsing, double-line, spectroscopic binaries’ (Carroll and Ostlie: 205).

The measurement of mass using a visual binary is fraught with complications and errors. Firstly the angular separation of the stars must be greater than the ‘resolution limit imposed by local seeing conditions and the fundamental diffraction limitation of the Rayleigh criterion’ (Carroll and Ostlie: 205), in order for us to determine the orbital characteristics of each star.

What we can see is only the apparent orbit, which is a projection of the true orbit onto the celestial sphere. It is possible to find the true orbit from the projected orbit through a complicated procedure that can produce very large errors. Though, if given a well determined true orbit, using trigonometric parallax, it is easy to find values of a and P, which in turn can be used to find the sum of the masses of the stars using Kepler’s Third Law.

To find the individual masses we have to recall that both of the stars are orbiting their common centre of mass. Therefore, their masses are inversely proportional to their distances giving us the ratio:

m₁/m₂ = R₂/R₁

From our knowledge of the sum of the masses and the ratio of the two masses it is possible to calculate the individual masses of each star.

Even if the distance to the stars from the earth cannot be calculated using parallax techniques, it is still possible to determine the individual masses of the stars in visual binary systems using detailed radial velocity data. We can achieve this by ‘the projection of velocity vectors onto the line of sight, combined with information about the stars’ positions and the orientation of their orbits, provides a means of determining the semimajor axes of the ellipses, as required by Kepler’s Third Law’ (Carroll and Ostlie: 208).

In reality only a few stellar masses are found using visual binaries and the above two methods. Instead, the large majority of stellar mass determinations, using binary star systems, are obtained from eclipsing, spectroscopic binaries. Though, as we shall find, it is also possible to calculate the stars’ radii and the ratio of their effective temperatures when working with such systems.

As we mentioned earlier, for eclipsing binaries to be seen on earth the orbital system must be nearly edge-on to the line of sight, i.e. the angle of inclination must be nearly ninety degrees for the eclipse to be visible from earth. Therefore the inclination being known and the period easily calculated from the light curve (see figure1); all that we now require in determining the masses is the semi-major axis.

Earlier we stated that in a spectroscopic binary each stars movement along our line of sight would cause red or blue shifts in the observed wavelengths of the spectra lines due to the Doppler effect:

Dl = (v/c)l

Where Dl is the change in a lines wavelength l, c is the velocity of light, and v is the velocity of the relevant star.

These types of binary systems usually have near-circular orbits, therefore we can then obtain the semi-major axis from the equation:

a = Dv_maxP/2p

Where Dv_max is the maximum apparent relative velocity of the two stars which can be seen on the diagram below.

Substituting Equ.4 for a in Equ.1 we can show that the sum of the masses can be calculated from the following equation:

(m₁+m₂) = Dv_maxP/2pG

The ratio of the masses can be calculated from the ratio of the stars’ individual maximum radial velocities, hence from which we can calculate the individual masses of the stars in conjunction with Equ.5:

m₁/m₂ = |(Dv_max)₂|/|(Dv_max)₁|

Unfortunately this is not the full picture as it is possible for a binary system that has a deviation from the line of sight to be viewed as an eclipsing binary, as long as it is small. This adds a small sinusoidal factor to Equ.4, which now becomes:

a = Dv_max/2psini

Where i is the angle of inclination.

This in turn causes a change to the sum of the masses equation and results in the individual mass equations being as follows:

m₁sin³i = (Dv_max)₂[(Dv_max)₁+(Dv_max)₂]²P/2pG

m₂sin³i = (Dv_max)₁[(Dv_max)₁+(Dv_max)₂]²P/2pG

Now that we know how to calculate the individual masses of stars we shall at how to calculate stellar radii and ratios of effective temperatures. We shall first look at stellar radii, which is easily calculated for those stars in an eclipsing spectroscopic binary system. We assume in this calculation that i=90 degrees, the semi-major axis of the smaller star’s orbit is much larger than either stellar radius, and that both stars travel in near-circular orbits. From this we can say that approximately the distances measured in the eclipse are perpendicular to our line of sight and therefore virtually a straight line over the distances that we measure.

Knowing the relative velocity of the two stars is v=v_s+v_l (where v_s and v_l are the velocities of the smaller and larger stars respectively); we can easily see from the basic physical equation, velocity is equal to distance divided by time, that the radius of the small star is just:

r_s = v(t_b-t_a)/2

And that the radius of the larger star is simply:

r_l = v(t_c-t_a)/2 = r_s+[v(t_c-t_b)/2]

If we consider the amount of light received during an eclipse and compare it with the amount of light when both stars are visible; it is possible to obtain the ratio of effective temperatures of the two stars in the binary system using their light curve. Though for this to work we have to treat each star as a blackbody radiator such that the radiative flux F_r is directly proportional to the effective temperature raised to the power four, T_e⁴.

When both stars are fully visible, the amount of light (B_o) is given by the equation:

B_o = k(pr_l²F_rl + pr_s²F_rs)

At the primary and secondary minima, the equations for the amount of light detected are respectively given by:

B_p = kpr_l²F_rl

Bs = k(pr_l² – pr_s²)F_rl + kpr_s²F_rs

Taking ratios of the primary and secondary minima, we can show using the above equations that:

(B_o-B_p)/(B_o-B_s) = F_rs/F_rl = (T_es/T_el)⁴

Thus we have a simple way of measuring the ratio of temperatures in a binary star system.

In this section we have looked at some of the ways of measuring the most important physical characteristics of stars. It is through these techniques that physicists were first able to work out the mass, size and temperature of the stars in our night sky, and from which they could build a bigger pictures and try to answer more underlying questions.

Most binary star systems are so far apart that the impact they have on each other is negligible. They are bound only gently by gravity and evolve independently, isolated from each other. A few though are close binary star systems which are defined as being systems that have a separation of roughly equal to that of the diameter of the larger star. At this distance gravity has significant effect causing one or both stars to deform into an egg of teardrop shape. Also they may start to pulsate, whereupon the oscillations will be damped, leading to loss of energy by the system. Eventually the system will reach a point, due to the loss of orbit and rotational kinetic energy, where its angular momentum is at a minimum. The result of which is circular orbits and synchronous rotation, though the latter may not be the case if either star were a white dwarf or a neutron star.

We shall concentrate on the morphology of the stars and the loss of the mass that can occur after a certain point. Due to the mechanics of the system, i.e. the lagrangian of the system, there are many equipotential points that all together form equipotential surfaces or contours, as the diagram below shows.

A French mathematician, Edouard Roche, discovered these equipotential surfaces and that the appearance of a binary star system depends on which equipotential surfaces are filled by the stars. Roche found that one of these surfaces formed a figure of eight, which he called the critical surface, and each loop, which makes up the figure of eight, is today called a Roche lobe. The point where the Roche lobes touch is called the inner lagrangian point, a point at which the gravity and the rotation of each star cancel each other out.

The extent of how the stars in a close binary system fill their Roche lobes can be classified in four different ways. If both stars’ surfaces are well contained within their own Roche lobes, they are said to be detached.

At a point during the evolution of the system, one of the stars, the secondary star, will complete its main sequence phase and expand as a red giant, filling and then going beyond its Roche lobe. When this occurs mass is exchanged, with the secondary star giving mass to the primary star via the inner lagrangian point. This system is called a semi-detached binary, and mass transfer will continue until the red giant has shrunk back within its Roche lobe once again. An interesting result of this is that the least massive star may become the more massive star, and therefore the more dominant of the pair.

If both stars fill their Roche lobes at the same time then the result is a contact binary, so named as the stars actually touch one another. This situation is unlikely to occur as both stars are more likely to overflow their Roche lobes which results in what is called an over-contact binary which has a common envelope of gas surrounding it.

Of the above classifications the most interesting one is semi-detached binaries as they lead to phenomena such as accretion disks, which we shall look at in detail in the next section. Taking the case of two stars of equal mass, we can make a rough estimate for the mass transfer rate that occurs in semi-detached binaries.

If we assume that the gas escapes from the secondary star via the circular opening of radius x in the above diagram, which has an area of A=px², travelling at a velocity v. As Mass = density X volume, i.e. M=rV, taking small increments on both sides we get:

dM = r.dV

Now

dV = A.dy

Where y is the distance along the axis which the mass is travelling. Thus dividing both side by small increments of time we get:

dM/dt = rA.(dy/dt) = rvA

Now using a little geometry and the equation for the thermal velocity of gas particles we get:

x = (Rd)^1/2

v_rms = (3kT/m)^1/2

Thus, a rough estimate for the mass transfer rate from one star to another in a semidetached binary system is:

dM/dt = pRd.r(3kT/m)^1/2

When mass transfer occurs in a system it changes the mass ratio m₂/m₁. This change causes a redistribution of the angular momentum of the system, which in turn affects the separation of the stars and the orbital period of the system.

The equations that describe the consequence of mass transfer on the separation of a binary star system and its angular frequency are as follows, and are derived on Pages 704-706 of Carroll and Ostlie:

(1/a).(da/dt) = 2(dm1/dt).(m₁-m₂/m₁.m₂)

(1/w).(dw/dt) = -(3/2).(1/a).(da/dt)

Where a is the semimajor axis, and w the angular momentum, of the system. From the last equation it is easy to see that if the orbital separation decreases, the angular frequency will increase, and vice-versa.

We shall look at the importance of mass transfer more when we study its effect in creating accretion disks. For now we shall look at the complicated history of close binary star systems and the many possible variations that arise depending on the initial separation of the two stars and their masses, one of which gives us details of how mass transfer was first discovered. An example of the possible evolution of a close binary star system is shown in the diagram below.

Algol’s, that is Arabic for demon, are a class of binary star systems containing main sequence or sub-giant stars. They provided the first evidence for the discovery of two very important phenomena in astronomy, the first of which was the measurement of brightness variations which lead to the discovery of eclipsing binaries, something we have discussed already. The second phenomena arose from the following contradiction; astronomers had calculated that the more massive star of the pair was the one still on the main sequence, while the secondary, less massive star was filling its Roche lobe and was a red giant. This totally went against the theory that more massive stars evolve more rapidly and the problem became known as the Algol Paradox.

To resolve the paradox, the process of mass transfer was theorised by Zlenek Kopal at the University of Manchester and others. They predicted that the secondary, less massive star was at one time the more massive star until it reached the end of it’s main sequence whereupon it started to expand, overflowing it’s Roche lobe. Matter was then transferred to what was the less massive star until became the more massive star by the time the other star had shed enough matter to once again be contained within it’s Roche lobe as a red giant.

Other types of close binaries are RS Canum Venaticorum and BY Draconis Stars which are studied for their magnetic properties, which are similar to that of the sun and include star-spots and flares. Also studied for their magnetic properties are W Ursae Majoris Contact Systems. These systems are in fact over-contact systems as they share a common gaseous envelope. It is thought that ‘the drag of magnetic braking may cause these binaries to coalesce into single stars’ (Carroll and Ostlie: 709).

There are many classes of long-period binaries. There are pairs that interact which include z Aurigae Systems, VV Cephei Systems and Symbiotic Binaries. And there are pairs that do not which include Barium and S-Star Binaries.

The interacting long-period binaries systems usually contain a giant star along with a hot companion, if it is an Aurigae or Cephei system, or a dwarf or low-mass main-sequence star in the case of Symbiotic Binaries. The Barium and S-Star where at one time themselves interacting binaries but now they consist of giant star along with what is thought to be white dwarf companions, yet this is difficult to be sure of as they are considerable cooler. These latter systems are important for studying mass loss in evolved stars and nucleosynthesis.

Finally, we have Post-Common Envelope Binaries, which consist of a white dwarf or a sub-dwarf along with a cooler secondary star. They are thought to have passed through the common envelope phase and are studied for the insight that they give into short-lived stages of stellar evolution.

Later we shall look more in-depth at white dwarfs in semi-detached binaries and at neutron stars and black holes in binary systems. Now though we shall look at one of the more fascinating phenomena of binary stars, accretion disks, which will lead us into the above two topics.

Due to the orbital motion of a semi-detached binary, mass that is being transferred from the secondary star may not fall directly onto the primary star. This usually happens if the primary star’s radius is less than 5% of the binary separation and instead, causes the mass stream to go into orbit around the primary star. It is this thin ring of swirling mass, in the orbital plane that is called an accretion disk.

Figure 13. An accretion for a b Lyrae binary star system (Kaufmann: 395)

The mass stream slowly falls inward to the primary star as it loses kinetic energy, which is converted into thermal energy through the viscosity of the disk material. Thus, the closer to the primary star the mass stream gets, the hotter its material becomes and the higher is the frequency of the radiation produced. An accretion disk around a neutron star is known to get hot enough to emit X-rays, therefore becoming an X-ray source detectable by X-ray telescopes on satellites or rockets in orbit around the earth.

We can calculate an estimate for the temperature of the gas in an accretion disk by making a few basic assumptions about the gas, such as: in the disk it acts as a blackbody radiator; it travels in circular Keplerian orbits; it’s mass is relatively small and so it only feels the gravitational attraction of the primary star; the inward radial velocity is small in comparison to its orbital velocity. The equation for the total energy, kinetic and potential, of mass m of gas, orbiting the primary star of mass M₁, is given by:

E = -GM₁m/2r

Here r is the distance of the mass m from the centre of the primary star. As the gas orbits closer to the star its total energy decreases, while its temperature raises, and eventually it is radiated away by the blackbody.

If we take a small section of the disk dr, we know that the amount of mass entering this section of the disk is equal to the amount that is leaving it. This means that there must be an energy difference dE that has been radiated by the mass over the distance dr, if the law of conservation of energy is to be maintained. Thus, the change in luminosity of the disk, dL_ring, of width dr is:

dL_ring = GM₁.(dM/dt).dr/2r²

Where m=(dM/dt).t is the amount of mass in the section dr of the disk and dL_ring.t = dE. Now using the Stefan-Boltzmann equation it is possible to show that :

dL_ring = 4prsT⁴dr = GM₁.(dM/dt).dr/2r²

Solving for T we get:

T = [GM₁.(dM/dt)/8psr³]^1/4

This is only a rough estimate that can be made more accurate by taking account of other factors that were ignored in the above derivation. When r = R, the radius of the primary star, then T is said to be T_disk, the characteristic temperature of the disk. This is not the maximum temperature of the disk, which is approximately half of T_disk. This is because of the errors in the model that arise due to assuming that the maximum is at r = R, when it is in fact at r = (49/36)R. Therefore the model does not account for the sudden drop in temperature that occurs near to the surface of the primary star, as can be seen in the diagram below.

Taking the radius of the primary star to be R and by integrating equ.26 from r = R to r = infinity, we can also find the luminosity of the disk which is:

L_disk = GM₁.(dM/dt)/2R

The radius of the disk is also obtainable from calculating where the mass stream from the secondary star will enter into a circular orbit around the primary. The actual disk radius is approximately twice that of the radius of the circle calculated, this is because of the conservation of angular momentum results in matter spreading outwards, as well as spiralling inwards, when the mass stream enters its orbital plane around the primary star.

Prove of accretion disks and measurements of their properties have been obtained from brightness measurements on certain eclipsing semi-detached binary systems. One such system is cataclysmic variables, which contain a white dwarf star and a late main sequence star. In a cataclysmic variable the light from the accretion disk around the white dwarf dominates and so large changes in brightness can be measured, which include the detection of dwarf nova.

If the primary component of a semi-detached binary star system is a white dwarf then ‘the result might be a dwarf nova, a classical nova, or a supernova, in order of brilliance’ (Carroll and Ostlie: 710). Classical and dwarf novae, unlike supernovae, reoccur again and again in the same system, with long intervals between each outburst. Both occur cataclysmically and result in and increase in brightness of over ten times the original value for dwarf novae, and up to a million times for classical novae.

Although dwarf novae were first observed in 1885, the process by which they occurred remained unknown until 1974. This was when Brain Warner of the University of Cape Town, gave the explanation that a dwarf nova was the observable result of the brightening of the accretion disk around a white dwarf. Due to the fact that visible wavelengths are observed about a day before those in the ultraviolet region, it is thought that the cause of dwarf novae is a sudden dramatic increase in the radial velocity of the mass in the disk. Starting in the cooler, outer edges of the disk the mass spirals inwards getting hotter and hotter, and thus emitting ever shorter wavelengths of light, but at a faster rate than usual which causes the increase in brightness.

The theoretical predictions of the process of a dwarf nova match the observational results. Unknown though is the reason for the sudden increase in matter transfer through the disk. General explanations are that either the mass transfer rate from the secondary star is unstable, or the disk stores up matter over a regular time period before releasing it in one go when it becomes to unstable.

Classical novae on the other hand are better understood than their dwarf novae counterparts. A classical nova results also from accretion, but here it is a build up of hydrogen on the outer-surface of the white dwarf, which then explodes, that causes the sudden brightness of the system. This happens because the hydrogen gets compressed into a dense layer and its temperature rises as more gas is added from the accreting secondary star. Eventually it reaches a temperature of around 10⁷K at which hydrogen ignites, covering the white dwarf’s surface in a thermonuclear explosion.

The sudden brightening of the star by up to a factor of 10⁶ will then slowly decline over what could be a period of several months, as the hydrogen burns off or is ejected into space. Eventually the burning stops as the temperature falls and the process can start over again.

The final type of novae that has been observed from close binary star systems containing white dwarfs is a Type Ia supernova. As this is a paper on binary star systems we shall not delve into the classification details of supernovae. What is important here is how the accretion in this system results in such a catastrophic event, which unlike dwarf novae or classical novae ends the life of the star.

The established model for such a supernova is an accreting carbon-oxygen white dwarf that eventually approaches the Chandrasekhar limit at around 1.3 to 1.4 solar masses, whereupon carbon burning will occur at its core. The carbon burning turns into a runaway process similar to that of a helium flash. This happens due to the matter in the white dwarf is degenerate, which means the increase in temperature is not offset by a corresponding increase in pressure; thus the temperature continues to rise unhindered. Eventually the temperature gets to high for the degeneracy of the electrons to be sustainable, thus causing a rapid explosion of pressure of great magnitude throughout the star, tearing it apart.

After a supernova has occurred either a neutron star or a black hole remains in place of the white dwarf. This binary system will otherwise remain intact unless its gravitationally bound state is broken by the loss of over half its mass in the supernova explosion. If what remains is still in a semi-detached system it will become a vast emitter x-rays as matter spirals down from the companion star into the deep gravitational potential well of the neutron star or black hole. Due to the rapid rotation of a neutron star in such a system, the accreting matter is funnelled onto the star’s polar regions; thus the x-rays are emitted in two opposite beams from the North and South poles as can be seen in Figure16 below.

Neutron star binaries are not all created by the above method. Some accreting white dwarfs collapse into a neutron star without exploding into a supernova, though this is not theoretically understood. Others may be isolated at first, but then tidal capture other stars that are close by due to a chance encounter.

Accreting neutron star binary systems produce a similar phenomenon to that of classical nova, called bursters. Bursters are named so after a sudden burst of x-ray emission from a neutron star well above its usual low level, that lasts for around ten seconds. The phenomenon is thought to be caused by a layer of gas that builds up around the star due to the neutron star’s weak magnetic field, which is unable to funnel it into its Polar Regions. The layer of gas is made up of mainly hydrogen which when it crashes to the surface of the star is converted into helium under the great pressures and temperatures that prevail there. Eventually the temperature is right to ignite the helium layer that consequentially builds up; this explosion is what we observe in the form of x-rays.

Black holes thought to be in close binary systems give the most satisfying evidence that black holes themselves do exist, because from their own very nature we are unable to observe them directly. What we are able to observe though is the x-rays emitted by matter falling into a compact object that could be either a black hole or a neutron star in a close binary system. Though, if it is calculated that the mass of the binary x-ray source is greater than 3 solar masses then it is probably a black hole. If it is greater than 5 solar masses then it is almost certainly a black hole.

In the early 1970’s and x-ray satellite telescope called Uhuru was launched and soon after it found the first possible candidate for a black hole, the x-ray source called Cygnus X-1. This x-ray source neither pulsated or, but flickered at times of around 10 milliseconds. From this information it was calculated that Cygnus X-1 had to be smaller than the earth and therefore a compact object. From further photometric investigation of absorption lines showed that Cygnus X-1 was in fact part of a binary star system along with a supergiant star, whose mass was calculated to be 30 solar masses. From the observed wobbling of the supergiant star it was then calculated that the mass of Cygnus X-1 was greater than 6 solar masses, leaving us with the view that it could only be a black hole.

The flickering in the x-ray source form Cygnus X-1 is thought to be caused by hot spots of gas on the inner edge of the accretion disk that surrounds the black hole. At this point the gas is of course very hot with temperatures of around 2 million Kelvin. The accretion disk itself is a donought in shape as this is though to be more stable than a flat surface, a computer-generated image can be seen below.

As with neutron stars, black holes are not only formed due to a type Ia supernova. It is also believed that a white dwarf or a neutron star could collapse into a black hole if it accreted enough material to push it over three solar masses. Also, it is thought that it may be possible for two neutron stars, in a binary system, to eventually radiate enough gravitational potential energy to merge and collapse into a black hole.

Anthony Hewish, who was awarded the Nobel Prize for Physics for his work, discovered the first binary pulsar system at Cambridge in 1967. Such a system’s binary characteristic is observed from the rate of change of the period of the pulsation as the stars rotate around their common centre of mass. The change in the period is due to the Doppler shifts of the observed x-rays as the pulsar moves away form us, and then back again.

One interesting property of x-ray binary pulsars may occur if the two x-ray emission regions of the pulsating secondary star lie on the orbiting plane of the primary star. If the orbital period of the primary star coincides with that of the pulse period, subsequently substantial heating of the surface of the primary star will result. Calculations have been made that predict the temperature of the irradiated region for an F-type star to be of the order of 22,000K, significantly larger then the typical 7,000K on the

Pulsating x-ray binaries are important as they give us the best possible estimates for neutron star masses. This is due to the regulatory of the number of pulses per orbital period that makes them equivalent to a clock. The beginning and end of an orbit can be easily figured out from the Doppler shifts in the x-rays that occur because of the motion of the pulsar in the binary orbit, similar to radio pulsars. From the pulse period, its distance and a velocity curve of the primary star, it is possible to calculate the combined mass of the primary and secondary stars. With other data form photometry, the ratio of the stellar masses can be found and the individual masses then calculated. It is usually found that the mass of a neutron star is less than two solar masses.

In 1974, Russell A. Hulse and Joseph H. Taylor, JR. using a radio telescope in Puerto Rico discovered a new type of binary pulsar. This new pulsar was given the name PSR 1913+16 and was calculated to contain two compact objects of around 10 Km in radius, with masses similar to that of the sun and separated by only a distance several times that from the earth to the moon. Also, it was found to have relativistic properties, orbiting at 10^-3 the speed of light with an orbital period of 7 3/4 hours.

The importance of PSR 1913+16 is its great deviation from Newton’s Laws. The relativistic shift of 4 degrees per year in its orbit is much greater than the 43 seconds of arc per century of Mercury. This gave astrophysicists the best opportunity to date to indirectly prove Einstein’s Theory of General Relativity.

Einstein’s theory predicted that binary system should lose energy due to the radiation of gravitational waves. As a consequence the orbital period of the pulsar should decline with time as the two stars rotate around the centre of gravity faster and faster in an increasingly tighter orbit. Over sufficient time Taylor managed to measure the decrease in orbit time to be 75 millionths of a second per year, accurate to within half of one percent of the theoretical value. For this work and the discovery of PSR 1913+16, Hulse and Taylor were awarded the Nobel Prize for Physics in 1993.

Gravitational waves have still to be directly proven to exist and the quest to do so is proving to be as tough as detecting the neutrino for astrophysicists. The work by Hulse and Taylor was a huge leap forward and hopefully soon gravitational waves will be observed by one of the many experiments currently running to do so.

The formation of binary or multiple star systems has only recently become a popular field of study amongst observational astrophysicists, the reason being twofold. Now that single star formation is generally understood, multiple star formation is the more usual occurrence in our universe. This, along with increased observation technology to view pre-main sequence (PMS) systems, has led to extended interest into this field of study over the last 10 years. During this period most of the PMS systems that we know of have been discovered and are being increasingly observed, pushing back the boundaries of our understanding of such systems. Our increased knowledge of early binary system evolution has given theorists much improved ideas of how binary star systems might be formed. Soon it is hoped to observe the formation of such a system and this seems quite feasible as at least 50% of stars in binary systems are thought to be PMS.

We have already mentioned tidal capture earlier as one possible method of binary star system formation. Other theorised methods include ‘fission of a protostar, independent bound condensations, cloud fragmentation’ (Mathieu 1994: 511). Today, fission of a protostar and tidal capture are ruled out, except in very-high density stellar environments. The favourite of the remaining theories is dynamic gas cloud fragmentation.

There are various ideas within the theory of fragmentation of a gas cloud relative to the time of the cloud’s collapse. These are ‘1. prompt fragmentation of a cloud, after which the fragments collapse to form star, 2. fragmentation during cloud collapse, and 3. fragmentation of disks composed of infallen material’ (Mathieu 1994: 511). After fragmentation there is a gap in the theory to the point of the observed PMS binary systems. Unfortunately, none of the hypotheses have been calculated through to this point on the evolutionary scale, therefore we lack the knowledge of how a PMS binary system may become an isolated system, away form the area of its formation.

Overall, it is widely believed that there is another step between the theorised formation of binary star systems and the observed PMS phase. It is hoped that in the not to distant future that further increase in observational technology, in combination with more calculations by theorists, will result in the early evolution of binary and multiple star systems to be generally understood.

When I set out to write this dissertation I aimed to giver the reader a basic overview of binary star systems and an insight into what I believe are some of the more interesting areas of this field of study. What I did not realise then is the breadth and depth of this subject is so great, yet interesting, and surely has an area that can stimulate the intellectual curiosity of any reader. In the first half of the paper I tried to concentrate on detection of such systems and stellar mass measurement. While the latter half has been taken up by, mass transfer, system disruption and an area of up to date research.

We have learnt how binary stars are detected, classified and how their masses are calculated. Also, we have studied various interesting and spectacular phenomena such as accretion disks, various novae, bursters and binary pulsars. Finally we have learnt of attempts to observe gravitational waves and the ongoing search for the knowledge of how binary star systems were formed.

I have managed to keep the mathematics to what I believe is a minimum and decided on placing it all in the text, and not in an appendix. I felt that this was needed to explain certain phenomena, especially those involving mass calculations. Placing them in appendices instead, I felt, would have resulted in a loss of continuous flow for the reader.

I certainly enjoyed the research for this piece of work and hope the reader has enjoyed the result. The work on binary star systems is far from over for both theoretical and observational astrophysicists. I will especially watch with interest, over the coming years, for the bridge that will fill the gap in our knowledge of the formation and the early evolution of binary star systems and the news that a gravitational wave has at last been observed.

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