Zeeman Doppler mapping (ZDM):
facts, questions, contradictions, conjectures, errors ...


A A belief not everyone is prepared to share
B An expected surprise
C Snowdon and Everest and what this has to do with HD3980
D "Published analyses of real stars"
E Identical tests applied to 2 different codes

green A belief not everyone is prepared to share

Kochukhov & Piskunov, A&A 388, 868 (2002)

In their Fig. 3  the authors show the recovery of a single "monolithic" (i.e. structure-less) spot of 1.5 dex contrast, using the iron doublet at 6147.74 A and 6149.26 A, with 10 equidistant rotational phases, and a S/N ratio of 300. The stellar parameters were assumed to be all known. Be sure to watch this: "We have chosen the rotational velocity v sin i = 30 km/s and inclination angle i = 60 deg, which are optimal for DI."

The authors claim : "The average error of the abundance recovery was 0.04 dex" which reveals an unusual approach to an error estimate. With the spot taking up an estimated 10% of the stellar surface, and with the initial "guess" of the abundance being exactly the value for the spotless 90% of the stellar surface, there is little relevance to the globally determined 0.04 dex, with actual local discrepancies original vs. recovered attaining some estimated 0.4 dex.

Figs. 5 and 9 display the results for the reconstruction of 3 -- instead of just 1 -- monolithic, high-contrast spots. Note the washed-out spots that appear up to twice the size of the originals, with regions of under-abundances, wisps and extension towards far-lying latitudes.

A nice colour plot of the 3 spot case can be found in a lecture by O. Kochukhov (Besancon, 2014)

Based on tests with 1 and 3 monolithic spots only -- no stunning complexity of the horizontal abundance pattern (as claimed for HR3831) has been tried -- with smooth dipole-quadrupole magnetic field geometries -- not a fragmented field as in 53 Cam, see N. Piskunov, Phys. Scr. T133 (2008) 014017 -- and with angles and rotational velocities optimal for DI, the authors confidently state: "We believe that the code can be successfully applied to the imaging of global stellar magnetic fields and abundance distributions of an arbitrary complexity."

Surface cartography of the Sun and stars, Besançon, 2014   
Doppler Imaging : Exercise

Page 6 delivers a certain blow to the belief professed above:  1 spot out of 4 spots is not recovered at all, despite favourable values of v sin i, inclination and S/N ratios. Everyone would agree that the degree of complexity of the spot configuration is still rather low.

green An expected surprise

Kochukhov & al. (2004), A&A, 424, 935

The authors establish numerous examples of surface patterns which do not follow the symmetry of the dipolar magnetic topology in their abundance maps of HR3831.

On the other hand they had openly stated earlier in their paper that they were only interested in estimating the parameters of the simplest dipolar magnetic geometry and will not consider combinations of dipole and quadrupole components, since these complex topologies are poorly constrained by the available magnetic observables”.

What a surprise then to find patterns that do not follow the symmetry of an assumed, not a simultaneously or independently derived, centred dipole geometry !!

One of the most striking characteristics of these maps are the huge abundance contrasts shown for a number of chemical elements, viz. 7 dex for Ba, 6.3 dex for Na, 6.2 dex for Pr, 6.1 dex for Mn and Y, and between 4 and 5.5 dex for other metals. The maps for the 5 elements with the largest contrasts are exclusively based on single-line or dual-line inversions. No star with magnetic field and abundances determined simultaneously has ever been found to exhibit such extravagant behaviour, which could mean that the neglected magnetic field is at least partly responsible for the strikingly high-contrast abundance structures of HR 3831. Differences between observed and predicted profiles can reach and even exceed 5% of the continuum intensity in several lines of the elements C, Mg, Si and Na; note the particularly poor quality of the fit to the λ 5895.92 line of Na.

green Snowdon and Everest and what this has to do with HD3980

Just imagine a PhD student in meteorology or geophysics working on aerial photographs of a mountainous region, taken at different times and at different angles. By some more or less sophisticated method this student finds that the pressure on top of a mountain the height of Chomolungma (Mt. Everest) is just sufficient for a human being to survive. By the same method the student realises that around a mountain the height of Snowdon, the atmosphere consists of pure Xenon, leading to a pressure at the top of this mountain about equal to that on top of Chomolungma. Strangely enough, despite the moderate distance between these two fascinating mountains, the horizontal differences in pressure miraculously continue to persist, there is no air flow at all between the two regions, no mixing of the gases.

The PhD student and her supervisor from a far-away university, thrilled by their discovery, decide to submit the results to a peer-reviewed journal, offering no explanations for these strange atmospheric physics. The fact that the huge horizontal differences in pressure seem to remain stable (at least over the epoch of the observations) is imputed to some unknown effect that meteorological and geophysical theory has yet failed to detect. The empirical results -- claimed to "provide important observational constraints for modelling" but never put to scrutiny in the submitted paper -- are at the basis of the statement "This all suggests that important details are missing from the theory relating to the formation of horizontal structures".

Guess what would happen in real life if scientists tried to publish a paper of this kind. Would the paper be accepted, would these people get funding for further work in this field, would theory remain discredited forever? I am speaking of the field of meteorology and geophysics where it is impossible that such a paper would ever be accepted by any journal.

What however about astrophysics where editors and referees do not show any concern when it comes to stellar abundance spots where Si is alleged to be as abundant as hydrogen whereas at some distance away it becomes under-abundant? Would you agree that the acceptance of such a paper by a peer-reviewed journal constitutes the triumph of an insane method of empirical analysis over well-founded theoretical knowledge built up over decades and centuries by great theoreticians, including a Nobel price laureate?

green "Published analyses of real stars"

green "Identical tests applied to 2 different codes "

There is much more to come on this topic. Stay tuned.

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