CossamDoppler : simple examples
Example 1 : "Virtual and
spurious surface structure on Ap stars"
by M.J. Stift, in IAU Symp. No.
176 Stellar Surface Structure
eds. K.G. Strassmeier and J.L. Linsky, Kluwer, Dordrecht,
p. 61-68
More than 2 decades ago, Figs. 2 and 3 of Stift's article demonstrated what happens when a very moderate magnetic field is neglected or when an incorrect magnetic field geometry is adopted in Zeeman Doppler mapping.
These results have consistently been ignored by the entire ZDM community up to the present day.
Back in 1996, the results were obtained with a code written by R.M. Fensl in Ada83. In the meantime, an independently developed new ZDM code based on Ada95 and Ada2012 takes advantage of the huge increase in computing resources over the last 20 years. Wouldn't it be instructive to see how today's results compare to those published in 1996?
For simplicity's sake we take an atomic transition that splits into a simple Zeeman triplet and a stellar atmosphere with Teff = 9000K and log g = 4.00. The magnetic geometry adopted for synthesising the phase-dependent Stokes profiles is the same as in Stift (1996), i.e. an oblique rotator with {i, α, β, γ, x2, x3} = {70.0, -90.0, 0.0, 0.0, 0.20, 0.00}. The profiles (and related files) calculated with the help of CossamMulti
./cossam_multi cossam_multi_01.inp 7020650790 7020650790
can be found here.
We first look at the example shown in the left part of Fig.2 in Stift (1996), then at the right part of Fig.2 and finally at the right part of Fig.3.
/cossam_doppler cossam_doppler_01.inp 7020650790 7020650871 > codop_01.res &
/cossam_doppler cossam_doppler_02.inp 7020650790 7020650871 > codop_02.res &
/cossam_doppler cossam_doppler_03.inp 7020650790 7020650871 > codop_03.res &
The results are stored in the following three sub-directories
702065155_dir
702065198_dir
702065248_dir
You may use auxiliary programs provided with CossamDoppler to visualise the results. Invoking
./hammer_nogrid_inv_vs_ori_diff 702065155_dir/dopimag_ham.702065155K
./hammer_nogrid_inv_vs_ori_diff 702065198_dir/dopimag_ham.702065198K
./hammer_nogrid_inv_vs_ori_diff 702065248_dir/dopimag_ham.702065248K
provides you with plots of the difference inverted abundance map minus original abundance map (in this case perfectly homogeneous over the whole stellar surface).
A complete set of files can be downloaded here.
Example 2 : A simple
abundance ring following the magnetic equator of a centred dipole
inclined by 90
degrees with respect to the rotational axis (oblique
rotator)
Convergence is not always as easy to achieve as in Example 1.
Sometimes the problem is quite ill-behaved, convergence is
slow, and the right choice of parameters (weight, step-size,
starting abundance) is not straightforward; it may involve
attempts with dozens of different combinations before you get
it right.
Warped rings resulting from non-axisymmetric magnetic
geometries are notoriously difficult to recover (see Stift
& Leone 2017), but in this simple case of an abundance
ring following a meridian of the magnetic star you can verify
yourself that CossamDoppler achieves results perfectly
comparable to what the INVERS family of codes is able to
deliver.
For this purpose there is no need to use 7 lines at 20
equidistant phases, nor do you have to push the spectral
resolution to 0.02 Angstroms. Just try this one (2 lines, 10
phases, 0.05 A) and compare the abundance errors
CossamDoppler vs. INVERS.
./cossam_doppler cossam_doppler_11.inp 7012365600 7021870909 702187240_dir/dopimag_ham.702187240J > codop_11.res &
./cossam_doppler cossam_doppler_12.inp 7012365600 7021870909 702187291_dir/dopimag_ham.702187291G > codop_12.res &
Let me explain. For each run, the rms scatter reaches a minimum at some iteration stage. If this rms scatter is still larger than what you expected or desired, restart CossamDoppler with the dopimag_ham file corresponding to this best map as the 4th argument. The program control (input) file has to be modified accordingly, usually adopting smaller weight and step size. In the present example, the 3rd run yields a final best fit to the "observed" line profiles of better than 0.1%.
Note: Counting of the individual dopimag_ham files starts in row 8 of dopimag_res.
The contents of 702187240_dir/dopimag_res.7021872408 (with the last character of dopimag_ham added for clarity):
Number of grid points : 2034A complete set of files can be downloaded here.
Sum(epsilon) : 2.372E+11
Entropy : 7.541E+00
Minimum field strength : 1250.0
Maximum field strength : 2497.1
Maximum absolute velocity : 39.94
Epsilon_total Entropy_total Chi_square_total : 2.3718E+11 7.541152E+00 3.580905E-02 7.541152E-04
Epsilon_total Entropy_total Chi_square_total : 3.2513E+11 7.503768E+00 1.013834E-02 5.368913E+00 A
Epsilon_total Entropy_total Chi_square_total : 3.0108E+11 7.473336E+00 5.021450E-03 6.415957E+00 B
Epsilon_total Entropy_total Chi_square_total : 3.2660E+11 7.437508E+00 3.361881E-03 6.729589E+00 C
Epsilon_total Entropy_total Chi_square_total : 3.1878E+11 7.427129E+00 2.939036E-03 6.808249E+00 D
Epsilon_total Entropy_total Chi_square_total : 3.2758E+11 7.412979E+00 2.594284E-03 6.866694E+00 E
Epsilon_total Entropy_total Chi_square_total : 3.2497E+11 7.408771E+00 2.459631E-03 6.890841E+00 F
Epsilon_total Entropy_total Chi_square_total : 3.2858E+11 7.402009E+00 2.302133E-03 6.917243E+00 G
Epsilon_total Entropy_total Chi_square_total : 3.2804E+11 7.398922E+00 2.216519E-03 6.932184E+00 H
Epsilon_total Entropy_total Chi_square_total : 3.2983E+11 7.394817E+00 2.124054E-03 6.947550E+00 I
Epsilon_total Entropy_total Chi_square_total : 3.3598E+11 7.370432E+00 1.683324E-03 7.015970E+00 J
Epsilon_total Entropy_total Chi_square_total : 3.3572E+11 7.371559E+00 1.692692E-03 7.015124E+00 K
