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 vsini and limb darkening)

Computation goes as vsini rather then vsini2

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)

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 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.

Zeeman acts as the fitting function Preserve compatibility with regular

Zeeman(easy upgrades)

Determine vsini, 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

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

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.

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