List of Figures

View Image Figure 1:
Images of the Sun taken with the SOHO (ESA & NASA) satellite. Cool sunspots appear as dark areas in the visible light image (left). They correspond to magnetic areas seen as black or white areas in the magnetogram (right; black and white show magnetic areas of different polarity). The magnetic field is arranged in spot groups of opposite polarity.
View Image Figure 2:
Schematic view of Zeeman splitting. (a) The upper level in the example is split into three levels producing three spectral lines that are separated. (b) Polarization of the π and σ components.
View Image Figure 3:
Three examples of simplified field geometries and their signals in Stokes I, V, and Q or U if the field is perpendicular to the line of sight (transverse field). Blue, green, and red lines show the line profiles of individual Zeeman components σblue, π, and σred, respectively. The black line is the sum of the three, that means the line that will be observable. In the Stokes I panel, the magenta line shows how the line would appear with zero magnetic field. Rotational Doppler effects are ignored in these examples.
View Image Figure 4:
Three examples of simplified field geometries and their signals in Stokes I, V, and Q or U if the field is tangential to the line of sight (longitudinal field). Colored lines like in Figure 3. Rotational Doppler effects are ignored in these examples.
View Image Figure 5:
The net polarization of a weak line is zero, and its equivalent width remains constant if a magnetic field is applied. In contrast, the net polarization of a saturated line in a transverse magnetic field is nonzero, and the equivalent width of a saturated line becomes larger in a magnetic field (from Mullan and Bell, 1976, after Leroy, 1962; reproduced by permission of the AAS).
View Image Figure 6:
(a) Surface image consisting of two magnetic spots with 8 kG radial field of opposite polarity, and (b) reconstructions involving all four Stokes parameters and (c) involving only Stokes I and V (from Kochukhov and Piskunov, 2002, reprinted with permission ESO).
View Image Figure 7:
Removed figure post-publication due to copyright restrictions. Springer did not grant permission to reuse material “in a work to be published on an Open Access Website”. Field reconstructions shown in a flattened polar projection with parallels drawn as concentric circles every 30° down to a latitude of –30°. Bold circle and central dot denote equator and visible pole, respectivey. Black and white code field intensities of 1000 G and –1000 G. Reconstructions of a synthetic dipole field (left panel) are shown assuming unconstrained field structure (center panel) and linear combination of force-free fields (right panel) (from Donati, 2001).
View Image Figure 8:
Six spot star simulations for a star observed under an inclination angle of i = 30°. The data set includes Stokes V profiles at 10 evenly spaced phases. The original images is shown in the left two columns. The next two columns show the optimal reconstruction followed by reconstructions with noise levels increased to 5 × 10–5 (S/N = 20 000) and 1.25 × 10–4 (S/N = 8000) (from Donati and Brown, 1997, reprinted with permission ESO).
View Image Figure 9:
Stokes V plotted vs. the derivative of Stokes I (weak field approximation). The linear relation shows that the star has a magnetic field, and from the slope of the relation magnetic field strengths on the order of 2 kG are derived for the two configurations (reprinted with permission from Bagnulo et al., 2002,  ESO).
View Image Figure 10:
Ca ii K core wing intensity ratio vs. absolute value of the magnetic flux density from resolved solar surface observations after degradation of the resolution to 14.4” × 14.4” (from Schrijver et al., 1989, reproduced by permission of the AAS).
View Image Figure 11:
X-ray spectral radiance vs. total unsigned magnetic flux for solar and stellar observations. Dots: Quiet Sun. Squares: X-ray bright points. Diamonds: Solar active regions. Pluses: Solar disk averages. Crosses: G, K, and M dwarfs. Circles: T Tauri stars. Solid line: Power-law approximation 1.15 LX ∝ Φ (from Pevtsov et al., 2003, reproduced by permission of the AAS).
View Image Figure 12:
CES spectra of 59 Vir with uncertainties overplotted by best-fit solutions. Solid blue lines represent the overall best-fit solutions, dash-dotted red lines are other solutions shown for comparison. Residuals drawn below the fits visualize differences between measured and calculated line profiles, scaled by factor 100. The purple error bar to the right shows σi. Green lines indicate the difference between overall best-fit and the comparison model, i.e., the change in line shape due the presence of magnetic flux (other fit parameters vary freely). Top: Model with identical temperature for magnetic and non-magnetic regions; best-fit: Bf  = 500 G (solid blue), comparison: Bf  = 0 G (dash-dotted red). Bottom: Best fit for model with different temperatures for magnetic and non-magnetic regions; Bf  = 120 G (blue solid), comparison: solution from upper panel (Bf  = 500 G, same temperatures, red dashed line) (from Anderson et al., 2010, reprinted with permission ESO).
View Image Figure 13:
2 χ-maps for 59 Vir solutions (see Figure 12). Left panel: Solution using the same atmospheres for magnetic and non-magnetic regions; Center panel: the same using cool magnetic regions; Right panel: the same for warm magnetic regions (from Anderson et al., 2010, reprinted with permission ESO).
View Image Figure 14:
Magnetic field measurements in active M dwarfs. Left: Spectra of the flare star EV Lac and the inactive star Gl 725B in the vicinity of the magnetically sensitive Fe i line at 8468.4 Å. Right: The spectrum of EV Lac divided by the inactive star Gl 725B (solid histogram). The dashed line shows a single field fit to the data (missing the line wings), the dashed-dot line show a fit allowing a distribution of magnetic fields (from Johns-Krull and Valenti, 2000).
View Image Figure 15:
Magnetic field measurement using the empirical method of Reiners and Basri (2006). The black histogram shows the spectrum of Gl 729. The red and blue lines are scaled spectra of the active star EV Lac and the inactive star GJ 1002, respectively. The green line is an interpolation between the red (Bf  = 3.9 kG) and blue (0 kG) lines yielding a field strength of Bf  = 2.2 kG for Gl 729 (from Reiners and Basri, 2007, reproduced by permission of the AAS).
View Image Figure 16:
Measurements of M dwarf average magnetic fields from integrated light measurements. Data are given in Table 2. Limits are indicated by arrows, and multiple measurements of the same star are connected with vertical lines.
View Image Figure 17:
Measurements of pre-main sequence and young brown dwarf magnetic fields from integrated light measurements. Data are given in Table 3. Limits are indicated by arrows, and multiple measurements of the same star are connected with vertical lines.
View Image Figure 18:
Left panel: Rotation-activity relation showing the normalized X-ray luminosity as a function of Rossby number. Right panel: Empirical turnover time chosen to minimize the scatter in the rotation-activity relation (from Pizzolato et al., 2003, reprinted with permission ESO).
View Image Figure 19:
Magnetic fields as a function of Rossby number. Crosses are sun-like stars Saar (1996a, 2001), circles are M-type of spectral class M6 and earlier (see Reiners et al., 2009a). For the latter, no period measurements are available and Rossby numbers are upper limits (they may shift to the left hand side in the figure). The black crosses and circles follow the rotation-activity relation known from activity indicators. Red squares are objects of spectral type M7 – M9 (Reiners and Basri, 2010) that do not seem to follow this trend (τconv = 70 d was assumed for this sample).
View Image Figure 20:
Normalized Hα luminosity as a function of Bf . Filled black circles: Early-/mid-M type stars of spectral type M0 – M6; blue triangles: spectral type M7; green stars: spectral type M8; red upside down triangles: spectral type M9.
View Image Figure 21:
Estimated average magnetic fields as a function of equatorial rotational velocity. Equatorial velocities are calculated for stars with measured rotation periods in Noyes et al. (1984) and Donahue et al. (1996). Average fields are estimated from the relation given in the text.
View Image Figure 22:
Three-color composite of EUV images of the Sun obtained by the Solar Dynamics Observatory during the Great Eruption of August 1, 2010. White lines show a model of the Sun’s complex magnetic field based on an extrapolation for the full-sphere magnetic field (from Schrijver and Title, 2011).
View Image Figure 23:
Properties of the large-scale magnetic geometries of cool stars (Donati, 2011) as a function of rotation period and stellar mass. Symbol size indicates magnetic densities with the smallest symbols corresponding to mean large-scale field strengths of 3 G and the largest symbols to 1.5 kG. Symbol shapes depict different degrees of axisymmetry of the reconstructed magnetic field (from decagons for purely axisymmetric fields to sharp stars for purely non-axisymmetric fields). Colors illustrate field configuration (dark blue for purely toroidal fields, dark red for purely poloidal fields, intermediate colors for intermediate configurations). Full, dashed, and dash-dot lines trace lines of equal Rossby number Ro = 1, 0.1, and 0.01, respectively (from Donati, 2011, reproduced by permission of Cambridge University Press).
View Image Figure 24:
Measurements of M dwarf magnetic fields from Stokes I and Stokes V. Top panel: Average magnetic field – Open symbols: measurements from Stokes I; Filled symbols: measurements from Stokes V. Center panel: Ratio between Stokes V and Stokes I measurements. Bottom panel: Ratio between magnetic energies detected in Stokes V and Stokes I. Circles show objects more massive than 0.4 M ⊙, stars show objects less massive than that.
View Image Figure 25:
Magnetic energy density in the dynamo vs. a function of density and bolometric flux (both in units of J m–3) according to Christensen et al. (2009). The scale on the right shows r.m.s. field strength at the dynamo surface. Blue: T Tauri stars; red: old M dwarfs. Black lines show the rescaled fit from Christensen et al. (2009) with 3σ uncertainties (solid and dashed lines, respectively). The stellar field is enlarged in the inset. Brown and grey ellipses indicate predicted locations of a brown dwarf with 1500 K surface temperature and an extrasolar planet with seven Jupiter masses, respectively (from Christensen et al., 2009).