Force-free magnetic fields,
chemical stratifications, CP stars
(and the ApJ)
a fascinating combination


A manuscript "Zeeman Doppler maps. II: the perils of eschewing physics"


has been submitted by M.J. Stift & F. Leone for publication in the ApJ.

Today (20-07-2021), 3 reviewers, 4 reviews. 1 formal complaint and more than
4 months later, the rejection of this manuscript by the ApJ and a number of
reasons given in an Email by the Editor-in-Chief appear to show that the ApJ
is forsaking old-style editorial policies, exploring new ways to invert long-
standing roles in science. The following points made by reviewer#3 have
remained unchallenged and undisputed by both Scientific Editor and

"The point that ZDM maps generally neglect vertical chemical stratification is
well made, but no testing or evidence is provided for the impact this would
have on horizontal abundance maps."

"The authors are concerned that no physics is contained in the regularization
function, but seem to neglect that originally a major motivation for using
these functions was to avoid making assumptions about the underlying physics.
If the authors wish to propose a more physically motivated regularization
function that could be valuable. If they wish to perform more rigorous testing
of the impact of the choices in regularization function that could be useful."

"Finally the authors do not demonstrate that, if the magnetic field should be
force-free while the map is not, that it will have important impacts on the
chemical abundance map."

My comments made to the Editor-in-Chief:

Good scientific practice and simple logic require that the people neglecting
stratifications have to show that they still get meaningful results. They have
the data, we don't.

It is not up to us to carry out more testing, the burden lies on Kochukhov.
He is constantly claiming that theory is wrong, but he has never provided
the required extensive tests that would show that he can recover complex
surface structures. His is just a "belief" as stated back in 2002: "We believe
that the code can be successfully applied to the imaging of global stellar
magnetic fields and abundance distributions of an arbitrary complexity."

With the radial and the horizontal field only, and under the assumption that
there is a toroidal field, how could we ever determine the 3 components of
the magnetic vector over the stellar surface, necessary for the calculation
of the Stokes profiles? But even if there were no toroidal components, why
does the referee expect us to model profiles for some spurious magnetic
geometry that contradicts basic physics? Comparing such imaginary profiles to
profiles resulting from a force-free geometry based on a spurious radial field
map might profoundly satisfy the referee but would constitute an exercise in
futility and an incredibly stupid waste of time.

This complete inversion of roles intended by the editors of the ApJ came
somewhat as a surprise. Needless to say, my arguments have not been taken
seriously and the manuscript rejected.

Now that it is known what Science Editor, Editor-in-Chief and 2 reviewers
think about force-free fields, their importance, the neglect of these in
the ZDM literature, and what we authors are alleged to have "overlooked",
I propose a detailed discussion of the comments and appreciations due to
these experts, comparing them with rectifications and explanations made
available to editors and reviewer#3 during the review process. In addition,
I shall also dwell on the total lack of appreciation shown for novel atomic
diffusion calculations and predicted theoretical chemical stratifications.
A 26-item list of criticism of ZDM is presenting my objections from a) to z)
but here I prefer to conform to the apparently new editorial policy which
largely inverts roles, proceeding accordingly from z) to a). It's a brave
new world to which one has to adapt.


K  z)  No proof of force-free fields in CP stars ?

K  y)  Neglecting observational evidence ?

K  x)  Important impacts on maps ?

K  w)  Neglecting cool star literature ?

K  v)  No new results, no original research ?

K  u)  Dynamically evolving CP stars and acceleration of plasma ?


"The authors argue that the magnetic field must be force-free, but do not lay
out a proof of this or the assumptions necessary to reach this result. They
only discuss the solar chromosphere and provide a reference to a zip file on
a website. If this is as important as the authors suggest, clearly it needs
stronger support than one unpublished reference."

It is not necessary to "lay out a proof of this or the assumptions necessary
to reach this result"; Wikipedia would suffice.
For the rest one is faced with claims that cannot even be called "alternative
facts'. Right in the introduction we write
"While the decisive role of magnetic
fields in the outer solar layers is well recognized ..."
and in section 5 we
"It is well known that in the solar corona magnetic structures have to be
force-free, given the dominance of Maxwell stress and/or magnetic pressure over
gas pressure. Force-free fields are also prominent in the solar chromosphere
and they govern the structure of sunspots (see e.g. Tiwari 2012)."
Is referee#3
unaware of the Maxwell tensor and/or of sunspots? We then continue
"The vertical
magnetic fields of sunspots only very rarely attain values of 4 kG, so shouldn’t
the field of HD 32633 with regions of up to 17 kG field strength as derived by
Silvester et al. (2015) also qualify as force-free?"
We are giving numbers for
the field strengths, the CP stars in question have higher temperatures and lower
gravities than the sun. What else would be required to enlighten referee#3 and
to make him/her accept a "proof"?


"This argument also neglects some observational evidence for departures from
purely potential fields, notably the B star tau Sco (Donati et al. 2006),
that seems to have a significant toroidal component to its magnetic field.
While this is not a Bp star, it does seem to have a 'fossil field' similar
to Ap and Bp stars."

It would have proved wiser, had reviewer#3 not alleged that we are neglecting
"some observational evidence". The star tau Sco has a field of only about
0.5 kG, HD32633 and HD119419 instead exhibit fields far in excess of 10 and
even 20 kG. The field of the former clearly does not have to be force-free,
quite in contrast to the fields of the latter 2 stars.


"Finally the authors do not demonstrate that, if the magnetic field should be
force-free while the map is not, that it will have important impacts on the
chemical abundance map."

There is a complete lack of understanding of this point in review#4. How could
we possibly show quantitatively the difference in Stokes profiles between the
published spurious maps and the (unknown!) correct force-free maps? Figs. 4 and
5 make it clear that the effects will be large, but
a) the 3 vector components of the magnetic field cannot be recovered from
   B_r and B_h alone in the presence of a toroidal field
b) the use of incorrect formulae by Kochukhov et al. implies that the B_r
   map is spurious, too !!!


"A final less serious problem is that the manuscript neglects all ZDM and
similar Doppler mapping work done in the cool star literature. The authors
are primarily concerned with chemical spots that do not appear in cooler stars,
thus the oversight is not too serious. However, there is extensive literature
on brightness or temperature mapping (e.g. Berdyugina 2005, Living Reviews in
Solar Physics, 2, 8) as well as magnetic field mapping (e.g. Donati & Landstreet
2009, ARA&A, 47, 333) using very similar techniques. If the authors argument is
that these methods are all worthless, clearly results beyond the INVERS codes
need to be considered. If the argument is that chemical spots are somehow
exceptionally problematic, that should be made more clearly. "

Reviewer #3 apparently has not read the very first sentence of the abstract
where it is clearly stated that the article is solely dealing with ZDM of CP
stars. Otherwise he/she would have understood that we are not "neglecting"
the literature on ZDM of cool stars but that it is physically entirely
irrelevant in the context of CP stars. Are we faced with a gratuitous attempt
by reviewer#3 to discredit our analysis? May I ask, what does ZDM of cool
stars have to do with ZDM of CP stars with very strong fields and extremely
stable atmospheres? What does brightness mapping or temperature mapping have
to do with force-free fields?
In cool stars one does not have atomic diffusion
at work with resulting stratifications depending on the local magnetic field.
This is the reason why we never had a close look at ZDM of cool stars. It
would however appear to me that the problem of horizontalequilibrium in
these cool stars has never been properly addressed.


"The most serious issue for manuscript, as a main journal article, is that it
presents very little in the way of new results or original research. Nearly
all of the manuscript is spent summarizing methodology described elsewhere in
the literature, results described elsewhere in the literature, and the authors
disagreements with some of assumptions made in the methodology."

Most importantly, we are the first scientists to have looked at the force-free
condition in CP stars with strong magnetic fields, and we have shown that the
published field maps are at variance with undisputed physics, developed by a
Nobel laureate and perfectly well known to solar people, as for example ApJ
Lead Editor L. Golub. Neither O.Kochukhov nor any of the 45 or so co-authors
have discussed or at least considered force-free fields at any occasion or
time over the past 20 years!


The Editor-in-Chief personally tried -- I would claim unluckily -- to defend
the comments made in review#4, proposing the following arguments:

"The final version of this manuscript, submitted in response to this report,
included a cover note raising the point that the important novel point in
this paper is that it raises, for the first time, the importance of force
free fields in understanding the data ... The referee was not receptive to
these changes. At this point they [who?] did engage over the physics, asking
for more justification for inserting physical assumptions used in your models
[???]. In addition they raised the question of whether the use of force free
fields could be justified and if the use of this assumption makes a difference.
I should comment here that this is not a silly question. In a magnetically
dominated medium one expects that the magnetic fields will typically be
approximately force-free. This isn’t expected to be exact, or true all the
time, because very often such environments are dynamically evolving and the
acceleration of plasma will cause a significant deviation from force free
conditions. One can believe that this is a better assumption than any other,
but still be skeptical of its importance."

It must have escaped the Editor-in-Chief that all experts agree that CP star
atmospheres are extremely stable apart from the alleged occasional "mercury
weather" in some hot MgMn star. Obviously it has also gone unnoticed that the
build-up of chemical stratifications involves diffusion velocities of the order
of centimetres per second. Any casual  look at any of the numerous papers on
atomic diffusion -- up to 50 years back -- could have made him familiar with
this fact. May I add to this that all evidence points to a complete suppression
of convection by the strong magnetic fields. Does this accumulated knowledge
not entitle us to express great wonderment at the idea of dynamically evolving
CP stars with accelerated plasma that would cause significant deviations from
force-free configurations?

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