Ellipsoidal Variables
Ellipsoidal Variables (el)¶
Ellipsoidal variables are close binary systems where one or both stars are tidally distorted into an ellipsoidal shape by their companion's gravity. As the distorted star orbits, its projected area changes, producing smooth, low-amplitude brightness variations at twice the orbital frequency — even without eclipses.
Classification and numbers¶
- Supertypes
- variable
- periodic
- sinusoidal
- Occurrence rate: common, about 104 expected in ZTF data
Description¶
In a close binary system, the gravitational field of the companion distorts the primary star into a roughly ellipsoidal (egg-like) shape elongated toward the companion. As the system orbits, the observer sees varying cross-sections of the distorted star, producing a smooth photometric modulation. The key signature is that the period of the brightness variation is half the orbital period, since the star presents its largest cross-section twice per orbit (at quadratures).
Ellipsoidal variations are often seen in systems containing a compact object (white dwarf, neutron star, or black hole) where the companion star is close to filling its Roche lobe but not yet transferring mass. They are also common in close detached binaries with evolved (giant or subgiant) components.
Light curve characteristics¶
- periodic variable
- period range: 0.1-100 days (half the orbital period)
- amplitude: typically small, 0.01-0.3 mag; increases with mass ratio and Roche lobe filling factor
- light curve shape:
- smooth, nearly sinusoidal with two maxima and two minima per orbital period
- minima may be unequal (gravity darkening on the side facing the companion)
- maxima are typically equal or nearly equal
- no flat-bottomed eclipses (distinguishes from eclipsing binaries)
Distinguishing ellipsoidal from similar classes¶
| Feature | Ellipsoidal | W UMa (EW) | Sinusoidal (rotation) |
|---|---|---|---|
| Cause | Tidal distortion | Eclipses + tidal | Starspots |
| Eclipses | None | Two per orbit | None |
| Minima per orbit | Two (equal-ish) | Two (may differ) | One |
| Period relation | P_phot = P_orb / 2 | P_phot = P_orb | P_phot = P_rot |
| Amplitude | Small (< 0.3 mag) | Moderate (< 0.75 mag) | Small (< 0.2 mag) |
Astrophysical sources of ellipsoidal variability¶
- Pre-cataclysmic variables: detached white dwarf + main sequence systems near Roche lobe overflow
- Low-mass X-ray binaries: neutron star or black hole with a Roche-lobe-filling companion
- Red giant binaries: evolved stars in close binaries with significant tidal distortion
- sdB + WD binaries: hot subdwarfs with close white dwarf companions (e.g., KPD 1930+2752)
- Heartbeat stars: eccentric binaries showing tidal distortion pulses near periastron passage
Other characteristics and selection methods¶
- Radial velocity measurements confirm the binary nature and give mass constraints
- May show reflection effects (irradiation of one face by a hot companion) in addition to ellipsoidal modulation
- Doppler boosting can add a small asymmetry to the light curve in very close systems
- Systems near Roche lobe overflow may transition to mass transfer (cataclysmic variable or X-ray binary)
References and further reading:¶
- Morris, S. L., 1985, ApJ 295 143, The Ellipsoidal Variable Stars
- Gomel et al., 2021, MNRAS 501 2822, Search for compact object candidates from LAMOST time-domain survey arxiv:2010.13791
- Green et al., 2023, MNRAS 522 29, A Systematic Search for Close Binary Stars in the ZTF Survey arxiv:2304.03791