Visual binary

A visual binary consists of two stars, usually of a different brightness.

If the primary is too bright, relative to the companion, this can cause a glare making it difficult to resolve the two components.

[2] However, it is possible to resolve the system if observations of the brighter star show it to wobble about a centre of mass.

[3] In general, a visual binary can be resolved into two stars with a telescope if their centres are separated by a value greater than or equal to one arcsecond, but with modern professional telescopes, interferometry, or space-based equipment, stars can be resolved at closer distances.

For a visual binary system, measurements taken need to specify, in arc-seconds, the apparent angular separation on the sky and the position angle – which is the angle measured eastward from North in degrees – of the companion star relative to the primary star.

Taken over a period of time, the apparent relative orbit of the visual binary system will appear on the celestial sphere.

The study of visual binaries reveals useful stellar characteristics: masses, densities, surface temperatures, luminosity, and rotation rates.

The trigonometric parallax provides a direct method of calculating a star's mass.

This will not apply to the visual binary systems, but it does form the basis of an indirect method called the dynamical parallax.

[5] In order to use this method of calculating distance, two measurements are made of a star, one each at opposite sides of the Earth's orbit about the Sun.

These masses are used to re-calculate the separation distance, and the process is repeated a number of times, with accuracies as high as 5% being achieved.

A more sophisticated calculation factors in a star's loss of mass over time.

[5] Spectroscopic parallax is another commonly used method for determining the distance to a binary system.

No parallax is measured, the word is simply used to place emphasis on the fact that the distance is being estimated.

The star is then assigned a position on the Hertzsprung-Russel diagram based on where it is in its life-cycle.

[7] The two stars orbiting each other, as well as their centre of mass, must obey Kepler's laws.

This means that the orbit is an ellipse with the centre of mass at one of the two foci (Kepler's 1st law) and the orbital motion satisfies the fact that a line joining the star to the centre of mass sweeps out equal areas over equal time intervals (Kepler's 2nd law).

[8] Kepler's 3rd Law can be stated as follows: "The square of the orbital period of a planet is directly proportional to the cube of its semi-major axis."

[9] To arrive at Newton's version of Kepler's 3rd law we can start by considering Newton's 2nd law which states: "The net force acting on an object is proportional to the objects mass and resultant acceleration."

would form a line starting from opposite directions and joining at the centre of mass.

Now we can substitute this expression into one of the equations describing the force on the stars and rearrange for

to find an expression relating the position of one star to the masses of both and the separation between them.

Before applying Kepler's 3rd Law, the inclination of the orbit of the visual binary must be taken into account.

Relative to an observer on Earth, the orbital plane will usually be tilted.

Kepler's 3rd law still holds but with a constant of proportionality that changes with respect to the elliptical apparent orbit.

[12] The inclination of the orbit can be determined by measuring the separation between the primary star and the apparent focus.

We re-write it in terms of the observable quantities such that From this equation we obtain the sum of the masses involved in the binary system.

In both cases, the absolute difference in spectral class seems ordinarily to be related to the disparity between the components...2.

With some exceptions, the spectra of the components of double stars are so related to each other that they conform to the Hertzsprung-Russell configuration of the stars..." An interesting case for visual binaries occurs when one or both components are located above or below the Main-Sequence.

The study of binaries is useful here because, unlike with single stars, it is possible to determine which reason is the case.