The Ca II K line in cool stars is among the strongest

emission line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...

s which originates in the star's

chromosphere A chromosphere ("sphere of color") is the second layer of a star's atmosphere, located above the photosphere and below the solar transition region and corona. The term usually refers to the Sun's chromosphere, but not exclusively. In the Su ...

. In 1957, Olin C. Wilson and M. K. Vainu Bappu reported on the remarkable correlation between the measured width of the aforementioned emission line and the

absolute visual magnitude Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it ...

of the

star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

. This is known as the Wilson–Bappu effect. The correlation is independent of spectral type and is applicable to

stellar classification In astronomy, stellar classification is the classification of stars based on their stellar spectrum, spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a Prism (optics), prism or diffraction grati ...

main sequence types G, K, and

Red giant A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses ()) in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around or ...

type M. The greater the emission band, the brighter the star, which is correlated with distance empirically. The main interest of the Wilson–Bappu effect is in its use for determining the distance of stars too remote for direct measurements. It can be studied using nearby stars, for which independent distance measurements are possible, and it can be expressed in a simple analytical form. In other words, the Wilson–Bappu effect can be calibrated with stars within 100

parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...

s from the Sun. The width of the emission core of the K line () can be measured in distant stars, so, knowing W₀ and the analytical form expressing the Wilson–Bappu effect, we can determine the

absolute magnitude Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse Logarithmic scale, logarithmic Magnitude (astronomy), astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent mag ...

of a star. The distance of a star follows immediately from the knowledge of both absolute and

apparent magnitude Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's li ...

, provided that the

interstellar reddening In astronomy, extinction is the absorption and scattering of electromagnetic radiation by dust and gas between an emitting astronomical object and the observer. Interstellar extinction was first documented as such in 1930 by Robert Julius Trumple ...

of the star is either negligible or well known. The first calibration of the Wilson–Bappu effect using distance from

Hipparcos ''Hipparcos'' was a scientific satellite of the European Space Agency (ESA), launched in 1989 and operated until 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial obj ...

parallaxes was made in 1999 by Wallerstein et al. A later work also used W₀ measurements on high-resolution spectra taken with CCD, but a smaller sample. According to the latest calibration, the relation between absolute visual magnitude (M_v) expressed in magnitudes and W₀, transformed in km/s, is the following: :

M_V=33.2-18.0 \log(W_0)

The data error, however, is quite large: about 0.5 mag, rendering the effect too imprecise to significantly improve the

cosmic distance ladder The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...

. Another limitation comes from the fact that the measurement of W₀ in distant stars is very challenging, requires long observations at big telescopes. Sometimes the emission feature in the core of the K line is affected by the

interstellar extinction In astronomy, extinction is the absorption and scattering of electromagnetic radiation by dust and gas between an emitting astronomical object and the observer. Interstellar extinction was first documented as such in 1930 by Robert Julius Trumple ...

. In these cases an accurate measurement of W₀ is not possible. The Wilson–Bappu effect is also valid for the Mg II k line. However, the Mg II k line is at 2796.34 Å in the

ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nanometer, nm (with a corresponding frequency around 30 Hertz, PHz) to 400 nm (750 Hertz, THz), shorter than that of visible light, but longer than ...

, and since the radiation at this wavelength does not reach the earth's surface it can only be observed with satellites such as the

International Ultraviolet Explorer International Ultraviolet Explorer (IUE or Explorer 57, formerly SAS-D), was the first space observatory primarily designed to take ultraviolet (UV) electromagnetic spectrum. The satellite was a collaborative project between NASA, the United K ...

. In 1977, Stencel published a spectroscopic survey that showed that the wing emission features seen in the broad wings of the K line among higher luminosity late type stars, share a correlation of line width and M_v similar to the Wilson–Bappu effect.

References

{{DEFAULTSORT:Wilson-Bappu Effect Astronomical spectroscopy