TheCa II K line in cool stars is a strong photospheric absorption line that exhibits anemission line at its core originating in the star'schromosphere. In 1957,Olin C. Wilson andM. K. Vainu Bappu reported on the remarkable correlation between the measured width of this emission core and theabsolute magnitude of thestar.[1] This relationship is now known as theWilson–Bappu effect. The correlation is independent of spectral type and is applicable tostellar classification main sequence typesG,K, andRed giant type M. The greater the emission band width, the brighter the star, which provides an empirical correlation with distance.
The Wilson–Bappu effect elicited some interest in the past for its potential as astandard candle. The method can be calibrated using nearby stars for which independent distance measurements are available, allowing the relationship to be expressed in a simple analytical form. Historically, the Wilson–Bappu effect was calibrated using stars within 100parsecs from the Sun.
Once calibrated, the width of the emission core (W0) of the K line can be measured in distant stars. From W0 and the analytical expression of the Wilson–Bappu effect, it is possible to determine theabsolute magnitude of the star. The distance then follows immediately from knowledge of both absolute andapparent magnitude, provided that theinterstellar reddening is either negligible or well known.
The first calibration of the Wilson–Bappu effect using distances fromHipparcos parallaxes was made in 1999 by Wallerstein et al.[2] A later work also used W0 measurements on high-resolution spectra taken withCCD detectors, though with a smaller sample.
According to the latest calibration, the relation between absolute visual magnitude (Mv) expressed in magnitudes and W0, expressed in km/s, is:
The observational uncertainty is quite large, with typical errors of about 0.5 magnitudes. This renders the effect too imprecise to significantly improve thecosmic distance ladder. Another limitation stems from the fact that measuring W0 in distant stars is very challenging and requires long observations with large telescopes. Furthermore, the emission feature in the core of the K line can be affected byinterstellar extinction. In such cases, accurate measurement of W0 is not possible.
The Wilson–Bappu effect is also valid for the Mg II k line.[4] However, since the Mg II k line lies at 2796.34 Å in theultraviolet, and radiation at this wavelength does not reach Earth's surface, it can only be observed with space-based instruments such as theInternational Ultraviolet Explorer.
In 1977, Stencel published a spectroscopic survey showing that the wing emission features seen in the broad wings of the K line among higher-luminosity late-type stars share a correlation between line width and Mv similar to the Wilson–Bappu effect.[5]