## Binary Stars

Visual Binaries

In the case of physically connected pairs of stars, what observers see when they plot the position angle and separation of the pair over a number of years is a curve. If followed for the whole orbital period the result would be an ellipse - this is the apparent orbit, in other words, the projection of the true orbit onto the plane of the sky. With a small telescope, hundreds of binary stars can be observed and of these the more nearby pairs offer the best chance of seeing the orbital motion over a few years. Estimates of separation can be made in terms of the diameter of the apparent disk of the brighter component which can be calculated for any telescope aperture using the Airy formula in Chapter 10. Position angle can be estimated to perhaps the nearest 5 or 10 degrees by eye by allowing the pair in question to drift through the field at high magnification with the driving motor stopped.

True (and apparent) orbits come in all shapes and sizes from circular to elongated ellipse but the tilt of the orbital plane can also vary from 90° (in which the plane is in the line of sight) to 0° in which we see the orbit face-on. To describe the real orbit fully requires seven quantities of which eccentricity, e, and inclination have just been explained. In the ellipse, the time at which the two stars are closest is called periastron (similar to perihelion when the Earth is nearest the Sun). The other values are the orbital period, P, in years (the time taken between successive arrivals by star B at the periastron point) and three values which describe the size and orientation of the orbit which are described fully in Chapter 7. The motion of star B around A follows Kepler's laws and in an exact analogy with the Solar System, the mass of both stars is related to the size of the orbit and the orbital period.

 WDS12367-0054 STF1670 2020 0°

Figure 1.3. a The visual binary 12 Lyncis. P = 706 years, e = 0.03 and orbit inclined at 2° to the plane of the sky. b y Virginis, P = 169 years, e = 0.89, inclined at 32° to the plane of the sky. The radius of the central circle indicates the Dawes limit for a 20-cm aperture. 12 Lyncis is therefore always visible in this aperture but y Virginis will close to less than 0'.'4 in early 2005 and will need at least 30 cm. At this time the position angle will change by 1 ° every five days!

Figure 1.3 gives an example of two well-known visual binaries. Contrast the orbital motion in both pairs by comparing the positions at 2000, 2010 and 2020.

To measure the total mass of both stars requires the apparent orbit to be defined as accurately as possible.

This can be done by measuring p and Q at different times, for as much of the orbit as is practical. (Long periods will mean that only a preliminary orbit can be obtained.) There are measuring techniques of various kinds which can be employed to accurately measure the relative position of B and to determine the values of p and Q. Later in this book the various methods that are available to the observer are mentioned in more detail.

For visual binaries, observations of the apparent orbit lead to the determination of the true orbit from which we can derive the sum of the masses, in terms of the solar mass, provided that the parallax is known. The astrometric satellite Hipparcos has been instrumental in providing parallaxes of high accuracy for a large number of binary stars.

Once we know the apparent orbit of a visual binary, we can, if the parallax of the system is also known, obtain the sum of the masses of the stars in the system via Kepler's third law:

where a is the semimajor axis of the apparent ellipse, and n is the parallax. Both are in arcseconds and P is in years. The mass sum is then given in units of the Sun's mass.

To obtain the individual masses requires defining the apparent orbit for each component by measuring its position with time against the background field stars. The apparent orbits are identical with the relative sizes determining the ratio of the masses, the primary star, being the most massive, traces out the smaller ellipse (see Figure 7.1 in Chapter 7). Unfortunately this method only applies to a small number of wide, nearby pairs which can be resolved photographically throughout the orbit. The apparent orbits are identical in shape, with the relative size of each orbit being inversely proportional to the mass of the star:

Combining (1.1) and (1.2) allows us to get the mass of each component.

The USNO Sixth Catalogue of Orbits2 contains more than 1700 orbits of which 1433 refer to pairs resolvable by conventional techniques. Of these orbits, about 4% are grade 1, the longest period being that of 70 Oph at

 Table 1.2. Distribution of orbit quality in the USNO Sixth Catalogue of Orbits. Grade Category Longest Number Percentage period of pairs of catalogue (years) 1 Definitive 88.38 52 3.6 2 Good 257 198 13.8 3 Reliable 522.16 292 20.4 4 Preliminary 18212.2 454 31.7 5 Indeterminate 32000 437 30.4

88.38 years. Table 1.2 shows the distribution of the five main orbit grades. Throughout this volume reference will be made to the fifth and sixth editions of this catalogue. The fifth edition is available from the USNO on CD-ROM (see the appendix) whilst the sixth is the dynamic version which is regularly updated, but a copy of this version appears on the CD-ROM accompanying this book.

### Spectroscopic Binaries

These are stars which appear single in all telescopes but turn a spectroscope on them and the spectral lines are observed to shift periodically with time due to the Doppler shift as the stars approach and then recede from the observer. The lines merge when the stars are both moving across the line of sight. There are two main types. When the stars are of similar brightness then two sets of spectral lines can be seen, particularly when one star is moving towards us and the other is moving away. These are called double-lined systems. When one star is much brighter than the other then only the spectral lines of the bright star can be seen to move periodically. This is called a single-lined system. Spectroscopic binaries have periods ranging from hours to a few tens of years. In a few rare cases they can also be resolved using speckle or ground-based interferometry. Such systems are important as they allow many characteristics of the component stars to be determined.

Astrometric Binaries

Again, these are single objects in all telescopes but reveal their duplicity by the effect that the unseen com-

panion star has on the proper motion or the transverse motion of the star against the background of fainter stars. This motion will be constant for a single star but the presence of a companion constantly pulls on the primary star and the effect is to observe the star "wobble" across the sky. This was first noticed by Bessel in the proper motion of Sirius - some 3.7'' every year and large enough to be seen by regular measurement with respect to the neighbouring stars. Bessel rightly attributed the periodic wobble of Sirius to the presence of an invisible but massive companion. In 1862 Alvan Clark saw Sirius B for the first time, thus confirming Bessel's prediction.