SOLAR POLARIZATION 5 ASP Conference Series, Vol. 405, c 2009 S. V. Berdyugina, K. N. Nagendra, and R. Ramelli, eds. Observations of Magnetic Fields on Late-type Stars and Brown Dwarfs C. M. Johns–Krull Rice University, Dept. of Physics & Astronomy, 6100 Main St., Houston, TX 77005, USA Abstract. Magnetic fields produce activity on the Sun and cool stars. Ac- tivity itself involves both the dynamo production of magnetic fields and the magnetic heating of the outer atmosphere of these objects which produces the radiative signatures of activity. On cool pre-main sequence stars, magnetic fields truncate circumstellar disks and direct accreting disk material near the poles of the central star. In the past several years, measurements of the magnetic field strength and constraints on the field geometry have become available for a num- ber of low mass stars and brown dwarfs. Much of the recent observational effort has centered on TTauri stars, due to the importance of strong stellar fields in explaining this stage of star formation, and on very low mass stars and brown dwarfs where measurements of traditional activity indicators suggest sharp differences in field production and/or heating efficiency compared to what is observed in slightly higher mass stars. It is important to note that a complete picture of the fields on these objects requires both spectropolarimetric and Zee- man broadening measurements made in non-polarized light. Here, I will review the techniques for measuring the magnetic field properties of cool stars and the general trends that have emerged from these observations. 1. Introduction Magnetic fields on the surface of cool stars are thought to be the link between dynamo activity within the star and a host of observed phenomena at an above their surfaces including: the appearance of starspots; heating of chromospheres, transition regions, and coronae; the channeling of accreting disk material onto the surface of pre-main sequence stars; and possibly the launching of vigorous outflows in young stars. None of these processes is well understood. One avenue to constrain and better understand these phenomena is to obtain actual mea- surements of the stellar fields. However, this can be challenging since many of the stars which are expected to show large field strengths and magnetic filling factors also are rapidly rotating, making the expected magnetic broadening of spectral lines difficult to detect in the presence of rotational line broadening. On the other hand, with the advent of high resolution infrared (IR) spectrometers, better analysis techniques, and the promise of new magnetic field diagnostics, we can now measure accurate surface magnetic parameters for a large sample of active stars including dwarfs, pre-main sequence stars (PMS), and just recently, brown dwarfs. In the area of stellar activity, these new observations will allow us to separate the coupled questions of dynamo generation of fields and the resulting magnetic heating they produce in the outer atmosphere. In the case of pre-main sequence 485 486 Johns–Krull stars, these observations allow us to test current theories of magnetospheric accretion and disk locking, which affects the rotational evolution of young stars. This in turn may feedback on the dynamo generation of these fields. Field measurements on both PMS and low mass main sequence stars provide tests of emerging dymano models for fully convective stars. Virtually all measurements of stellar magnetic fields make use of the Zeeman effect. In this review, measurements based on Zeeman broadening of magneti- cally sensitive lines observed in intensity spectra are discussed. When an atom is in a magnetic field, different projections of the total orbital angular momentum are no longer degenerate, shifting the energy levels taking part in the transition. In the simple Zeeman effect, a spectral line splits into 3 components: 2 σ compo- nents split to either side of the nominal line center and 1 unshifted π component. This both broadens the spectral line and causes (partially) saturated lines to in- crease their total opacity resulting in an increase in line equivalent width. This equivalent width effect has been used by a number of authors to infer the mean magnetic field strength, i.e., the product of the field strength, B, and the filling factor, f, of magnetic regions (Basri et al. 1992; Basri & Marcy 1994; Rueedi et al. 1997; Guenther et al. 1999). However, great care must be taken to determine accurate Teff values for stars when using this technique since the temperature has a strong effect on line equivalent widths. The wavelength shift of a given σ component is given by ∆λ = kλ2gB; where k is a constant, g is the Land´e-g value of the specific transition, B is the strength of the magnetic field, and λ is the wavelength of the transition. One thing to note from this equation is the λ2 dependence of the Zeeman effect. Compared with the λ dependence of Doppler line broadening mechanisms, we see that observations in the IR are generally more sensitive to the presence of magnetic fields than optical observations. For most studies of main sequence stars, the observed line profile can be expressed as F (λ) = FB(λ)∗f +FQ(λ)∗(1−f); where FB is the spectrum formed in magnetic regions, FQ is the spectrum formed in non-magnetic regions, and f is the flux weighted surface filling factor of magnetic regions. The magnetic spectrum, FB, differs from the spectrum in the quiet region not only due to Zee- man broadening of the line, but also because magnetic fields affect atmospheric structure, causing changes in both line strength and continuum intensity at the surface. Most studies assume that the magnetic atmosphere is in fact the same as the quiet atmosphere; a point we will return to later. If the stellar magnetic field is very strong, the splitting of the σ components is a substantial fraction of the line width, and it is easy to see the σ components sticking out on either side of a magnetically sensitive line (e.g., Fig. 1). In this case, it is relatively straightforward to measure the magnetic field strength, B, from the splitting, and the depth of the σ components relative to the π component gives the filling factor, f. Differences in the atmospheres of the magnetic and quiet regions pri- marily affect the value of f. If the splitting is a small fraction of the intrinsic line width, then the resulting observed profile is only subtly different from the profile produced by a star with no magnetic field and more complicated model- ing is required to be sure all possible non-magnetic sources (e.g., rotation and pressure broadening) have been properly constrained. Measuring circular polarization in magnetically sensitive lines is perhaps the most direct means of detecting magnetic fields on stellar surfaces, but it is Magnetic Fields on Late-type Stars 487 also subject to several limitations. When viewed along the axis of a magnetic field, the Zeeman σ components are circularly polarized, but with opposite he- licity; and the π component(s) is(are) absent. The helicity of the σ components reverses as the polarity of the field reverses. Thus, on a star like the Sun that typically displays equal amounts of + and − polarity fields on its surface, the net polarization is very small. If one magnetic polarity does dominate the visible surface of the star (such as in a dipolar field geometry), net circular polariza- tion is present in Zeeman sensitive lines. This can be measured in the Stokes V profile, or as wavelength shift between the line observed through right- and left- circular polarizers. The magnitude of the shift represents the surface averaged line of sight component of the magnetic field (which on the Sun is typically less than 4 G even though individual magnetic elements on the solar surface range from ∼ 1.5 kG in plage to ∼ 3.0 kG in spots). Thus, polarization measurements supply information on the geometry of the stellar magnetic field, though polarity cancellation means that substantial portion of the magnetic flux can be missed by polarization measurements alone. 2. Main Sequence Stars Measuring magnetic fields on late type main sequence stars proved to be chal- lenging using optical diagnostics. Improvements in analysis techniques invariably resulted in a reduction of the measured field strengths. An excellent discussion of this history is given by Valenti et al. (1995). Saar & Linsky (1985) first advo- cated using IR lines for field measurements on cool stars, and Saar (1994, 1996) and Valenti et al. (1995) produced many reliable field measurements for G and K stars. These results showed that the field strength on these stars appeared to be set by pressure equilibrium with the surrounding photospheric gas, and that it was the filling factor of the magnetic regions that correlated with rotation rate and typical signatures of “activity.” These initial results suggested that the strongest fields should be found on the dMe stars, as the early observations of Saar & Linsky (1985) also suggested. Johns–Krull & Valenti (1996) used high resolution high signal-to-noise optical spectra to measure the magnetic field on the flare stars EV Lac and GJ 729. Figure 1 shows the spectrum of EV Lac along with several inactive comparison stars. This figure clearly shows the presence of Zeeman split σ components on either side of the Land´e g = 2.5 Fe i line at 8468.4 A.˚ The magnetic field is even more clear in the ratio plot shown in the top panel of Fig. 1. Dividing the active star by an inactive template of the same spectral type removes the TiO lines for which the line data is uncertain.