Colin Folsom (Armagh Observatory)

 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...

 For each: rotation phase, window, surface element  Determine local field  Determine strengths of components for each line  Calculate spectrum...

 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)

 Integration propagates through atmospheric layers  Surface elements are Doppler shifted and added  Gaussian instrumental profile applied  Windows and phases output separately

 Major time saving  Input and output compatible with magnetic  As similar routines as possible

 Assume horizontal homogeneity  Only need a line of surface elements rather then a disk (allows for correct v sin i and limb darkening)  Computation goes as v sin i rather then v sin i 2

 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 v sin i to independent (save a factor of a few up to > 10)

 Don’t need: line components, local field, component strengths. (but save almost no time)  Can use non-polarized radiative transfer (relatively small time saving)

 Itot 10: 10 surface elements vs 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.

 Zeeman acts as the fitting function  Preserve compatibility with regular Zeeman (easy upgrades)  Determine v sin i, microturbluence, abundances  Possibly T and logg...

 Use Levenberg Marquardt fitting algorithm:  Fast  Many parameters  Somewhat non-linear  Still can get stuck in local minima

 Conditions: 120 lines, 100 Å, 8 free parameters (vsini, microturbulence, Ca, Ti, V, Cr, Fe, Ba)  4 iterations, 41 Zeeman calls v sin i 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

 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

 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.

WindowT (K)Log g v sin i (km/s) ξ (km/s)FeTiCr Average Stdev Luca's best fit uncertainty HD comparison