Figure 1 gives a clear example of the correspondence between surface brightness and magnetic flux density on the Sun. Relations between these two values were provided, e.g., by Ortiz et al. (2002). They determine contrasts of active region faculae and the network as a function of heliocentric angle and magnetogram signal. Although this information is not available in spatially unresolved observations of other stars, it can be very helpful for the analysis of stellar variability from high quality photometric data, e.g., from the CoRoT or Kepler satellites.
The correspondence between chromospheric Ca ii K emission and magnetic fields for the solar surface was investigated by Schrijver et al. (1989). Figure 10 shows that a close relation exists between the field strength and Ca ii emission in solar surface observations:et al., 1989). Schrijver (1990) found a relation between C iv and magnetic flux density of the form et al., 1995; Hall, 2008).
X-ray observations are available for the Sun and many stars. A close relation between magnetic flux and X-ray spectral radiance was shown by Pevtsov et al. (2003) (see also Güdel, 2004). The relation holds for solar quiet regions, active regions, and disk-integrated measurements of very active stars and covers more than ten orders of magnitude in both parameters (see Figure 11). The relation is approximated by
Emission of radiation at radio wavelengths is indicative of ionized atmospheres that in many cases are related to stellar magnetic activity. Radio emission can be generated by different processes leading to characteristic signatures of radio emission; for an overview see Güdel (2002). The close correlation between radio and X-ray emission (the Güdel–Benz relation; Benz and Güdel, 1994) shows that radio and X-ray emission are generated by the same or at least correlated processes. The relation holds for quiescent and active emission of the Sun and a wide variety of stars. In very low-mass stars or brown dwarfs, however, Berger et al. (2005) showed that this relation is violated with objects that are overluminous at radio wavelengths.
Depending on the emission process, or on the question whether the emitting electrons are relativistic or not, radio emission has characteristic properties that can allow the determination of magnetic fields (see Güdel, 2002). The gyrofrequency, or cyclotron frequency, in a magnetic field is
Coherent emission, in particular electron cyclotron maser emission, can be a reliable tracer of the magnetic field strength because it is emitted mostly at the fundamental and the second harmonic of . Detection of radio emission at a given frequency indicates the presence of magnetic field corresponding to that frequency, for example the detection of 8.5 GHz radio emission indicates a field of strength (see, e.g., Hallinan et al., 2008).
Living Rev. Solar Phys. 8, (2012), 1
This work is licensed under a Creative Commons License.