Measuring Magnetic fields in Ultracool stars & Brown dwarfs

1. Measuring Magnetic fields inUltracool stars & Brown dwarfs Dong-hyun Lee

2. How can we measure B-field in star? • Using Zeeman Effect • The splitting of a spectral line into several components in the presence of a B-field • Stellar B-fields are usually measured through Zeeman broadening in atomic lines that have large Lande g-values • The measurement is usually carried out by comparing the profiles of magnetically sensitive & insensitive absorption lines b/w observations & model spectra • Alternate method that relies on the change in line equivalent width has been developed by Basri (1992, ApJ, 390, 622) • Both methods require the use of a polarized radiative transfer code & knowledge of the Zeeman shift for each Zeeman component in the B-field • But atomic lines vanish in the low-excitation atmospheres & among the ubiquitous molecular lines appear in the spectra of cool stars

3. How can we measure B-field in star? • Using the Wing-Ford bands of FeH(M & L spectral type) • FeH bands show a systematic growth as the star gets cooler • Model cool & rapidly rotating spectra from warmer, slowly rotating spectra utilizing an interpolation scheme based on curve-of-growth analysis • FeH features can distinguish b/w negligible, moderate, high magnetic fluxes on low-mass dwarfs, with a accuracy of about 1kG • B-fields are responsible for the generation of stellar activity • Stellar flares are observed in some of the ultracool obj.s although they seem to be different than in the solar case • Look for Zeeman broadening in molecular lines in ultracool obj.s • Strong magnetic sensitivity of the W-F band of FeH just before 1 microm is cleary demonstrated • Investigate the possibility of detecting B-fields in FeH lines of ultracool dwarfs through comparison b/w the spectrum of a star with unknow B-field can be calibrated in atomic lines

4. Wing-Ford band of FeH in Ultracool stars • Wing-Ford band of FeH in Ultracool stars • Obtain spectra that cover the wavelength region from H alpha to 1 micro m • Strong FeH absorption around 9900 Angstrom in spectra of M dwarfs • A high-resolution spectroscopic sequence of the Wing-Ford band in the spectral types M2 – L0 in <fig.1> • Amplified absorption spectrum Alpha : the optical depth scale factor A(lambda) : the normalized residual intensity at lambda C : a const. that controls the maximum absorption depth due to saturation

5. Magnetic Sensitivity in the FeH band • Magnetic Sensitivity in the FeH band • B-field measurment utilize the space quantization of the atomic angular moment J in a B-field • Sensitivity of atomic absorption lines to a B-field is approx. prop.to the Lande factor g • Magnetic splitting in atomic lines can be calculated very precisely • Molecular Zeeman effect is more complex : J vector has more quantization states due to nuclear rotation (cf. in atomic case) • Magnetic sensitivity in FeH lines would be high in transitions with very large values of J (J <= 15) • Intermediate coupling of J makes it difficult to make precise calculations for Lande factor g for molecule, and despite the efforts to understand the FeH spectrum, its coupling const.s have not yet measured and are still unknown. • FeH has an excellent potential for measuring B-fields in cool dwarfs (by observational evidence) • B-fields have been measured in early- & mid-type M dwarfs using well-understood atomic lines. In these stars, FeH band is already prominent. • Compare a spectrum of an inactive star that presumably has no measurable B-field & one of an active star with a B-field measured from atomic lines

6. Magnetic Sensitivity in the FeH band • High-resolution spectra of the inactive star GJ1227(lower line) & the active star GI873(upper line) • For comparison the sunspot spectrum is overplotted with an offset • Magnetically insensitive lines are dark gray, sensitive lines are light gray • Positions of atomic lines are marked as hatched regions

7. Detectability of B-fields on ultracool obj.s • Magnetic measurement by line ratios • One can determine line broadening due to rotation by comparison of magnetically insensitive lines to the same lines in a reference star with known rotational velocity • Zeeman signal is analyzed by comparing the shape of magnetically sensitive lines b/w the target spectrum & the reference spectrum. • One method of obtaining the magnetic signal is to employ line depth ratios b/w magnetically sensitive & insensitive lines • 2 lines should be chosen in close proximity to each other, so that differential errors in continuum placement are less of a concern • Rotation & resolution have the same effect on the line widths, the limiting resolution is the one that corresponds to the maximum rotation velocity • We identified 4 ratios of neighboring absorption features that are particularly useful to measure the magnetic flux : 2 for slow rotators & 2 for rapid rotators • For the rapid rotators, the positions are not centered on a physical absorption line, but rather on a feature that is a blend of several lines at that rotation vel. • Use the template spectra of active & inactive stars shown in <fig.5> • A linear interpolation of the observed reference spectra

8. Detectability of B-fields on ultracool obj.s • The left panels show the case of no rotation ; right panels the spectra are spun up • The top panels show the case of nonsaturated lines (alpha = 2, ~M6) ; bottom panels the FeH band is heavily saturated (alpha =16, ~L4) • The B-field increases from top to bottom in the spectra • The ratio b/w the depths of the 2 absorption features is plotted as func. Of Bf=p(3.9kG) in the small plot below each panel

9. Magnetic measurement by chi^2 fitting • Fit(solid gray line) of a linear interpolation b/w the spectra of GJ1227 & GJ873 to the spectrum of GI729 • Parameter chi^2 is calculated from the regions b/w the vertical dashed lines • Best fit is achieved for Bf=2.0kG ~50%GJ1227 & ~50% GI873