Eclipsing binary

An eclipsing binary is a binary star oriented so that one component passes in front of the other as seen by the observer. The changing blocked light produces repeated minima in the light curve. Eclipse depths depend on surface brightness and size as well as on the geometry, while durations constrain stellar radii relative to orbital separation and the orbital inclination.

When both components also have measured Doppler shifts, their velocity amplitudes supply a binary mass ratio and orbital scale. Combining these with the eclipse geometry can determine individual masses and stellar radii, providing direct tests of stellar structure. A deeper eclipse usually means more light was hidden; it does not by itself identify the more massive component.

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Central eclipse contact-radius relations ( $R_{L} \pm R_{S} = a sin (π T_{\pm} / P)$ )

For a circular edge-on eclipsing binary with central passage, define

T_{+} = t_{4} - t_{1}

between external contacts and

T_{-} = t_{3} - t_{2}

between internal contacts, with

R_{L} \geq R_{S}

. The projected separation from conjunction is

a ∣ sin [2 π (t - t_{c}) / P] ∣

. At contact it equals

R_{L} + R_{S}

or

R_{L} - R_{S}

, proving the title formula. Taking half the sum and difference recovers the radii. When durations are small compared with

P

, this becomes

R_{L, S} = v_{rel} (T_{+} \pm T_{-}) /4

with

v_{rel} = 2 πa / P

. A nonzero impact parameter changes the contact chords.

Eclipsing-binary distance ( $d = R / θ$ for angular radius $θ$ )

For a detached double-lined binary, radial velocities supply an orbital length scale times

sin i

, while eclipse geometry supplies inclination and relative radii. Together they determine physical stellar radii. Comparing them with angular radii from a calibrated surface-brightness/colour relation gives distance. The orbital scale is geometric, but the angular-radius calibration, extinction and third light add astrophysical assumptions.^[ref]

Algol variable

An Algol variable is an eclipsing binary with well-separated eclipse minima and relatively little variation between eclipses. This light-curve classification includes detached systems as well as interacting Algol binaries; it does not by itself imply Roche-lobe overflow.

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