Hacking Zeeman
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Transcript of Hacking Zeeman
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Colin Folsom(Armagh Observatory)
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Read input Calculate line components (Zeeman splitting) Calculate continuum opacity (per window, per
atmospheric layer) Calculate line to continuum ratio (window, layer,
line) Calculate spectrum from each stellar surface
element...
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For each: rotation phase, window, surface element Determine local field Determine strengths of components for each
line Calculate spectrum ...
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For each: phase, window, surface element, layer For each component of each line:
Calculate Voight profile, at each point in wavelength, with polarization information(Humlicek, 1982 algorithm)
For each point in wavelength, perform radiative transfer, for 4 Stokes parameters(Martin & Wickramasinghe, 1979; Landstreet ,1988; Wade et al., 2001)
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Integration propagates through atmospheric layers
Surface elements are Doppler shifted and added Gaussian instrumental profile
applied Windows and phases output
separately
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Major time saving Input and output compatible with
magnetic As similar routines as possible
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Assume horizontal homogeneity Only need a line of surface elements
rather then a disk (allows for correct vsini and limb darkening)
Computation goes as vsini rather then vsini2
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Skip separate Voight profiles for different components (save a factor of a few)
Voight profiles of one line at one layer are the same for all surface elements (only angle of emergent flux differs)
Go from proportional to vsini to independent(save a factor of a few up to > 10)
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Don’t need: line components, local field, component strengths. (but save almost no time)
Can use non-polarized radiative transfer(relatively small time saving)
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Itot 10: 10 surface elements vs 1001 Voight profile vs. a few 100 (per line, layer, window and
phase) 133 lines (60 Å) in 5 sec vs. 849 sec Identical non-magnetic results, down to
machine precision.
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Zeeman acts as the fitting function Preserve compatibility with regular
Zeeman(easy upgrades)
Determine vsini, microturbluence, abundances
Possibly T and logg...
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Use Levenberg Marquardt fitting algorithm: Fast Many parameters Somewhat non-linear
Still can get stuck in local minima
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Conditions: 120 lines, 100 Å, 8 free parameters(vsini, microturbulence, Ca, Ti, V, Cr, Fe, Ba)
4 iterations, 41 Zeeman calls
vsini 10.9 km/s
ξ 2.3 km/s
Ca -6.13
Ti -6.98
V -7.68
Cr -6.19
Fe -4.55
Ba -9.44
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Repeat this process for several windows Averages Standard deviations Discrepancies
Check result are sensible Parameters are constrained Inaccurate atomic data is not a (serious)
problem
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Interpolating on a grid of model atmospheres
Constrain T by excitation potentials And logg by ionization balance
Test results of throwing everything in Calculate new abundance specific
models, e.g. ATLAS12.
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Window T (K) Log gvsini
(km/s) ξ (km/s) Fe Ti Cr4400 9156 3.48 10.7 2.2 -4.564 -7.094 -4500 10080 4.18 10.8 2.3 -4.146 -6.484 -5.6454600 10005 4.23 10.4 2.2 -4.141 -6.631 -5.6585000 9420 3.67 10.5 2.6 -4.407 -6.959 -5.9715200 9363 3.51 10.7 2.4 -4.431 -7.034 -6.0165400 9291 3.52 10.4 2.7 -4.464 -7.184 -6.011
Average 9552 3.77 10.58 2.40 -4.36 -6.90 -5.86Stdev 356 0.32 0.16 0.19 0.16 0.25 0.17Luca's best fit 9382 3.78 10 1.9 -4.3 -6.86 -6.01uncertainty 200 0.2 0.5 0.2 0.07 0.04 0.07
HD 73666 comparison