Eclipsing and Spectroscopic Binaries

When a binary's orbit is seen nearly edge-on, the stars eclipse one another and their light shifts in wavelength as they orbit; combining these effects yields the masses and radii of stars with extraordinary precision.

Definition

A spectroscopic binary is one identified by the periodic shift of its spectral lines due to orbital motion, and an eclipsing binary is one in which the stars periodically pass in front of each other from our viewpoint, causing measurable dips in brightness.

Scope

The topic covers spectroscopic binaries detected by the periodic Doppler shifts of their spectral lines, eclipsing binaries whose brightness dips as one star passes in front of the other, the analysis of light curves and radial-velocity curves, and the determination of accurate stellar masses, radii, and temperatures from systems where both effects are observed.

Core questions

• How are spectroscopic binaries detected?
• What causes the brightness dips in an eclipsing binary?
• How do eclipses and radial velocities together give stellar radii and masses?
• Why are detached eclipsing binaries so valuable?

Key concepts

• radial-velocity curve
• mass function
• double-lined binary
• light curve
• primary and secondary eclipse
• orbital inclination
• fundamental stellar parameters

Key theories

Radial velocities and the mass function

Orbital motion shifts a star's spectral lines back and forth by the Doppler effect; the amplitude and shape of the radial-velocity curve constrain the masses through the spectroscopic mass function, and a double-lined system yields the mass ratio directly.

Light-curve analysis of eclipses

The depths, durations, and shapes of the eclipses in the light curve, combined with the orbital velocities, yield the stars' relative radii, temperatures, and orbital inclination; a detached double-lined eclipsing binary gives absolute masses and radii to a few percent.

Mechanisms

As the stars orbit, their motion toward and away from us shifts their spectral lines, tracing radial-velocity curves; when the orbit is nearly edge-on, each star periodically blocks the other, producing eclipses whose timing and depth reveal the stars' sizes and the inclination. Together these break the degeneracies that limit other methods, delivering absolute masses and radii.

Clinical relevance

Detached eclipsing binaries provide the most accurate fundamental stellar parameters available and are benchmarks against which stellar evolution models are tested; they also serve as precise distance indicators to nearby galaxies, anchoring rungs of the cosmic distance ladder.

History

Goodricke explained the variability of Algol as eclipses by an unseen companion in the eighteenth century, Russell and Shapley developed methods to extract orbital elements from eclipse light curves in the early twentieth century, and Kopal and later workers refined the modeling now used to derive precise stellar parameters.

Key figures

• Henry Norris Russell
• Harlow Shapley
• John Goodricke
• Zdenek Kopal

Seminal works

• torres2010
• russell1912

Frequently asked questions

What is the star Algol an example of?

Algol is the prototype eclipsing binary: its regular dimming, noticeable to the naked eye, is caused by a fainter companion star periodically passing in front of the brighter one, a phenomenon first correctly explained as an eclipse by John Goodricke.

Why are eclipsing binaries that are also spectroscopic so useful?

Spectroscopy gives the stars' velocities and the eclipses fix the orbital inclination and relative sizes; combining them removes the usual unknown of how the orbit is tilted, allowing astronomers to determine the absolute masses and radii of both stars with high precision.