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
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.
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
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