2 Methodology of Magnetic Field Measurements

Magnetic fields are not directly visible. Their effects on the observable world are manifold, but all we can hope to measure are the consequences the presence of a magnetic field has on any properties that are accessible to observation. A particularly useful indicator of stellar magnetic activity, for example, is the non-thermal emission generated through magnetic heating (for a review, see Hall, 2008Jump To The Next Citation Point). Non-thermal emission is an example for indicators of magnetism that I will call indirect in the following. Indirect indicators require an additional mechanism to provide evidence for magnetic fields, and it is often difficult to entirely rule out alternative mechanisms as a source for its presence. For example, non-thermal emission may be generated by acoustic heating mechanisms so that the detectability cannot be translated into a magnetic field strength without further knowledge (Narain and Ulmschneider, 1996). Nevertheless, there is ample evidence that indirect indicators like chromospheric Ca or coronal X-ray emission are reliable tracers of magnetic flux density at least in sun-like stars (Schrijver et al., 1989Jump To The Next Citation Point; Pevtsov et al., 2003Jump To The Next Citation Point). For the following, an observable is called direct if its detection or amplitude necessarily implies the presence of a magnetic field.

The most successfully employed mechanism for direct detection of stellar magnetic fields is the Zeeman effect (Zeeman, 1897). Different approaches to use the Zeeman effect for magnetic field measurements and resulting field determinations are discussed and build the main part of the following chapters. Another mechanism that appears similar to the Zeeman effect and has been used in solar magnetic field measurements is the Hanle effect (Hanle, 1924). The Hanle effect describes how selective level population can be modified by a magnetic field (Landi Degl’Innocenti and Landolfi, 2004; Trujillo Bueno, 2006). It can be used to measure tangled, very small-scale fields of up to a few hundred Gauss but requires a very detailed understanding of atomic level population and three-dimensional scattering processes (Trujillo Bueno et al., 2004). This level of detail cannot yet be achieved in stellar observations and the Hanle effect could so far not be used to detect magnetic fields in stars other than the Sun.

Observations of magnetically induced emission, i.e., indirect magnetic field diagnostics, provide a wealth of information on stellar magnetic activity that is often easier accessible than direct field measurements. For reviews on observations of coronal emission, chromospheric emission, and starspots the reader is referred to the reviews by Güdel (2002Jump To The Next Citation Point, 2004Jump To The Next Citation Point), Berdyugina (2005), and Hall (2008Jump To The Next Citation Point). In this article, the main consequences of indirect observations for our picture of stellar magnetism will be discussed only briefly in Section 2.3.

 2.1 Zeeman effect
  2.1.1 Absorption lines in a magnetic field
  2.1.2 Polarization of Zeeman components
  2.1.3 The Stokes vectors
  2.1.4 Reconstruction of stellar magnetic fields from Stokes vectors
  Integrated field measurements
  Reconstruction of the magnetic vector field
  2.1.5 Field, flux, and filling factor
  2.1.6 Equivalent widths
  2.1.7 Doppler Imaging
  2.1.8 Least Squares Deconvolution
 2.2 Broad band polarization
 2.3 Indirect diagnostics
  Intensity contrast
  Chromospheric emission
  X-ray emission
  Radio emission

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