At the time of writing astronomers, both amateur and professional, are watching with some anticipation the star known as T Coronae Borealis. 

It is a recurrent nova, hence its nickname the Blaze star, which means more fundamentally that it is a binary star system.

When you look up at the night sky, you see thousands of stars as pinpoints of light. However, observed with a telescope or even in some cases, simple binoculars, many stars reveal themselves to be double or triple star systems. In fact, binary stars make up something like 85% of the stars in the galaxy. That makes our own star the Sun atypical - which is probably quite a good thing from our perspective!

Binary systems evolve just like single stars, from gravitational instabilities within rotating molecular clouds. Eighteenth century astronomer and composer William Herschel was one of the first observers to demonstrate the existence of mutually orbiting double stars. The probability of frequent chance stellar alignments had previously been largely banished, mathematically, by John Michell (who actually predicted the existence of black holes long before Einstein came along).

Binary stars can be discovered and investigated in several ways, depending on their angular separation and the projection on the celestial sphere of their orbital plane. Whilst close binary systems may have approximately circular orbits with two stars orbiting a common centre of mass (always located at the intersection of the lines joining the two stars at any point in their orbit), the majority are in elliptical orbits. One of the most useful formulae in astronomy is the equation which relates a binary star’s orbital period T to the semi-major axis of the ellipse a; half of its longest 'diameter' (which also equates to the average orbital distance between the stars), where:

\(a³ = {G\over 4π²} T² (M + m)\)

G is the gravitational constant, with M and m being the masses of the primary and secondary components of the system. If this equation looks a lot like Johannes Kepler's third law of planetary motion, well, that's because it's basically the same, complicated only by the inclusion of a secondary mass which may be comparable to the primary object (the Sun, in Kepler's model). By measuring, visually, the ratio of the distances d_m and d_M, of the stars from the centre of mass we get an equation

\({M\over m} = {d_\text{m} \over d_\text{M}}\)

from which the respective masses of the stellar components of a system can be calculated. This is of course only possible where the angular separation of the system allows. Where a binary system is too close to be separated visually, the orbital period, semi-major axis and respective masses can be deduced spectroscopically by observing the radial velocity of the stars from the Doppler shift of lines in their spectra.

Occasionally a multiple-star system becomes evident from eclipses and periodic dips in its light curve; one such famous example is the star Algol in the constellation of Perseus. This only occurs where the orbital plane of the system is perpendicular to the celestial sphere so that the secondary star periodically moves in front of and behind the primary star creating primary and secondary minima respectively. This phenomenon usefully allows for calculation of the stars’ radii.

The presence of a secondary star may also be inferred from 'wiggles' in the proper motion of a primary star, as is the case for Sirius, which has the brightest apparent magnitude of any system in our night sky.

Perhaps the most interesting binary stars are interacting binary systems, where the two components are so close that material can pass from one to the other. Between such close pairs, there exists an inner Lagrangian point, one of a series of locations in the orbital plane where a test particle, or 'blob' of gas, feels no unbalanced gravitational force. When a star’s outermost layers fill its Roche lobe, a pear-shaped region which touches the inner Lagrangian point, stellar material may stream through to the companion star’s gravitational 'well', either colliding directly with its surface or more likely forming an accretion disc, due to conservation of angular momentum.

T Coronae Borealis, the star mentioned at the top of this discussion, is typical of interacting binaries, featuring a red giant with mass transfer onto a white dwarf, probably with a surrounding accretion disc. It appears (although unfortunately there is insufficient data to be sure) that roughly every eighty years a gravitational instability builds in the accretion disc, leading to an outburst of radiation, massively increasing the system's visual magnitude. The 'star' which is normally only visible in a small telescope becomes visible to the naked eye, the last outburst having occurred in 1946.

Binary systems come in all shapes and sizes, so to speak - featuring even orbiting neutron stars and black holes which lose gravitational potential energy (in the form of gravitational waves) by slowly spiralling towards each other.

If you are an aspiring astronomy enthusiast, the monitoring of eclipsing binaries and recurrent novae, also known dwarf novae or cataclysmic variable stars is a fascinating and exciting pursuit, made possible by the increasing availability of good quality, affordable, backyard telescopes. Useful advice can be sought from organisations like the British Astronomical Association and the American Association of Variable Star Observers.

Images

• White dwarf spiral by NASA/Tod Strohmayer (GSFC)/Dana Berry (Chandra X-Ray Observatory)
• Light curve by AAVSO, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=12084206
• T Coronae Borealis sketch by Steven L Allen - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=150043284
• Outburst by PopePompus - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=99263183