Wilson-Bappu effect
Encyclopedia
The Ca II K line in cool stars is among the strongest absorption lines. A small emission, which originates in the chromosphere
, is present in its core. 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
of the star
. This is known as the Wilson–Bappu effect. The correlation is independent of spectral type and applicable to stars of type
G, K, and M
. The wider the absorption, the brighter the star.
The main interest of the Wilson–Bappu effect resides in its potential as a distance indicator, which is a consequence of the following facts:
The first calibration of the Wilson–Bappu effect using distance from Hipparcos
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(W0)
But the dispersion of the data-points about this relationship, is quite large: about 0.5 mag, rendering the effect too imprecise to significantly improve the cosmic distance ladder
. 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 line. 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 and, since the radiation at this wavelength does not reach the earth suface, it can only be observed with ultraviolet satellites, such as the International Ultraviolet Explorer
.
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 Mv similar to the Wilson–Bappu effect.
Chromosphere
The chromosphere is a thin layer of the Sun's atmosphere just above the photosphere, roughly 2,000 kilometers deep....
, is present in its core. In 1957, Olin C. Wilson
Olin Chaddock Wilson
Olin Chaddock Wilson was an American astronomer best known for his work as a stellar spectroscopist.Born in San Francisco, CA as the son of a lawyer, Wilson showed an interest in physics at an early age...
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
Absolute magnitude is the measure of a celestial object's intrinsic brightness. it is also the apparent magnitude a star would have if it were 32.6 light years away from Earth...
of the star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
. This is known as the Wilson–Bappu effect. The correlation is independent of spectral type and applicable to stars of type
Stellar classification
In astronomy, stellar classification is a classification of stars based on their spectral characteristics. The spectral class of a star is a designated class of a star describing the ionization of its chromosphere, what atomic excitations are most prominent in the light, giving an objective measure...
G, K, and M
Red giant
A red giant is a luminous giant star of low or intermediate mass in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower...
. The wider the absorption, the brighter the star.
The main interest of the Wilson–Bappu effect resides in its potential as a distance indicator, which is a consequence of the following facts:
- the Wilson–Bappu effect 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 pc from the Sun;
- the width of the emission core of the K line ( W0 ) can be measured in distant stars;
- knowing W0 and the analytical form expressing the Wilson–Bappu effect, we can determine the absolute magnitude of a star
- the distance of a star follows immediately from the knowledge of both absolute and apparent magnitude, provided that the interstellar reddening of the star is either negligible or well known.
The first calibration of the Wilson–Bappu effect using distance from Hipparcos
Hipparcos
Hipparcos was a scientific mission of the European Space Agency , launched in 1989 and operated between 1989 and 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial objects on the sky...
parallaxes was made in 1999 by Wallerstein et al. A later work also used W0 measurements on high-resolution spectra taken with CCD
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...
, 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(W0)
But the dispersion of the data-points about this relationship, is quite large: about 0.5 mag, rendering the effect too imprecise to significantly improve the cosmic distance ladder
Cosmic distance ladder
The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are "close enough" to Earth...
. 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 line. 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 and, since the radiation at this wavelength does not reach the earth suface, it can only be observed with ultraviolet satellites, such as the International Ultraviolet Explorer
International Ultraviolet Explorer
The International Ultraviolet Explorer was an astronomical observatory satellite primarily designed to take ultraviolet spectra. The satellite was a collaborative project between NASA, the UK Science Research Council and the European Space Agency...
.
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 Mv similar to the Wilson–Bappu effect.