Measuring Magnetic fields in Ultracool stars

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Measuring Magnetic fields inUltracool stars
Brown dwarfs

• Dong-hyun Lee

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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

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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

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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
  ltfig.1gt

• 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

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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 lt
  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

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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

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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 ltfig.5gt

• A linear interpolation of the observed reference
  spectra

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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 Bfp(3.9kG) in
  the small plot below each panel

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Magnetic measurement by chi2 fitting

• Fit(solid gray line) of a linear interpolation
  b/w the spectra of GJ1227 GJ873 to the spectrum
  of GI729
• Parameter chi2 is calculated from the regions
  b/w the vertical dashed lines
• Best fit is achieved for Bf2.0kG 50GJ1227
  50 GI873