Magnetism in High-Mass Stars
Round 1
Reviewer 1 Report
Comments for author File: 
Comments.pdf
Author Response
I wish to thank Reviewer 1 for carefully reading the manuscript and for providing constructive comments.
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The number of references is essentially a distraction, and I think could be culled more judiciously. As it stands, the reference list constitutes something like 37% of the paper, which strikes me as excessive. Admittedly, the adopted style for individual references is quite complete and takes up more space here than in other publications. But my fundamental concern is that a significant number of the references seem peripheral to the topic, or really just out of balance with their overall significance to present paper. I’ve given a few examples below.
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The style of referencing can vary from author to author. In this case, I have opted to be as exhaustive as possible since I hope that this collection of references will offer the reader a useful resource. The numbered reference format allows me to do so without affecting the readability of the main text, while the length of the Reference section is not affected by page limits. I agree with Reviewer 1 that the length of the Reference section is partially an editorial question.
I have attempted to improve the manuscript, following the list kindly provided by Reviewer 1. For example, some authors use the spin rates of compact objects to infer the efficiency of magnetic angular momentum transport in main sequence stars, thereby directly connecting topics that might otherwise seem peripheral in their details. I believe the article does not contain references that would not be warranted (or could be deemed unrelated) to describe the very rich topic of magnetism in high-mass stars.
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Would it be possible to give a brief physical explanation of why the diffusivity is so difficult to characterize?
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The discussion on Ohmic diffusion has been slightly restructured and extended.
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In Section 3.3.2, it would be helpful to comment on the extent to which the two approaches to characterizing convective expulsion are compatible with each other. Are the criteria equivalent or do they emphasize different facets of the problem?
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Section 3.3.2 has been restructured to first list the previous, simpler estimates, and then discuss the newer results. This should clarify that the new formulation supersedes the purely equipartition-based approach.
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Additional comments for consideration:
1. A bit more about referencing (not a comprehensive list)
Line 15: Since the magnetic fields of neutron stars are peripheral to the topic of magnetism in massive stars, is it necessary to have 11 references to them?
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I have reduced the number of references in the Introduction as Reviewer 1 suggested and hope to highlight this important connection in subsequent discussions of the manuscript (Section 2.3).
The physics of magnetic fields can often be applied to various objects with appropriate considerations. In this specific case, the magneto-rotational field generation for neutron stars serves as a direct example of how magnetic fields might form in non-degenerate stars. The first (recently published) works studying MRI in main sequence massive stars were largely motivated by studying the instability in other objects. In addition, massive stars are precursors of neutron stars. Thus constraints from this research field may prove highly valuable to better understand massive stars.
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Line 40: Reference 38 concerns magnetic fields in M-dwarfs. What is the specific relevance to massive stars?
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I have added "applicable to various kinds of stars" to the text to make it clearer. As advocated above, the physics of magnetic fields is universal. In the same manner, observational techniques, including polarimetry and spectral convolution and imaging are often applicable to various kinds of stars. Kochukhov's recent review (2021, A&ARew, 29, 1) discusses in great detail the background of modern spectropolarimetry, including Stokes parameters and Zeeman Doppler imaging. The physical basis is independent of the kind of star considered. Thus their Section 2 is relevant for observing magnetic fields of high-mass stars, even though their application (Section 3) focuses on low-mass stars.
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Line 118: Is it necessary to refer to the complete suite of MOBSTER papers on individual stars? Wouldn’t the initial overview paper (or maybe Papers I and II) suffice for present purposes?
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Revised the formulation of the text and reduced citations to mention the overview first paper only. Also removed the explicit mention of MOBSTER since the focus of this section is to introduce key clues and progress, independently of which specific observing campaign they result from.
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Remark: I was surprised that there’s only 1 reference (to a conference proceedings) to results from the BOB survey. I’d encourage a more inclusive approach to the observational literature beyond the results from MiMES, BinaMIcS and MOBSTER.
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Further references have been included. (I consider that the work of Fossati et al. 2016, A&A, 592, 84 is also inclusive of BOB results, thus it is not only the Morel et al. citation in the previous version of the manuscript.) The paragraph in the text primarily focuses on statistical results and is not intended to elaborate on specific observational campaigns.
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2. Miscellaneous other comments:
There’s a typo in Line 1! The manuscript is pretty clean, but would benefit from one more spell- and grammatical check.
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Thank you for catching it. Corrected.
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Line 3: on the magnetic properties = of the magnetic properties
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Corrected.
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Line 227: a few ten years = a few decades
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Corrected.
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Fig. 2 caption: it equals to the adiabatic = it equals the adiabatic OR it is equal to
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Corrected.
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Line 290: where the field spreads through = where the field spreads
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Corrected.
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Line 493: there are less metals = there are fewer metals
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Corrected.
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Line 494: This does not only apply to OB stars but also to Wolf-Rayet = This
applies not only to OB stars, but also to Wolf-Rayet
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Changed.
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Fig. 4 caption: For simplicity, the distinct … is greatly simplified = The distinct…is
greatly simplified.
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Removed "for simplicity".
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Line 73: Reference 74 concerns Theta^1 Ori C, which was introduced earlier in the paragraph. Why not mention it by name here as the first detection of a magnetic field that had previously been inferred (e.g., by references 63 – 65). However, Reference 63 is no longer thought to provide the correct interpretation of the strange line profiles. There are other observational references to infall in context of a magnetospheric model: e.g., Wade et al. 2006, A&A, 451, 195.
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Theta^1 Ori C has now been explicitly mentioned for the magnetic field detection on a chemically non-peculiar, hot, main sequence star. Reference to Wade et al. 2006, A&A, 451, 195 has been included. I wish to keep the reference to Conti's 1972 work since I believe it contributed to the clues and motivation that later led to magnetic field detection. This is in line with the general philosophy that indirect clues have been informative about the magnetic characteristics of high-mass stars.
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Line 549: Reference 285. HD 144941 is unlikely to be a double-degenerate binary. See Przybilla et al. (2021, A&A, 654A, 119).
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Reference 285 has been removed from the discussion to avoid ambiguity.
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Line 627: I didn’t understand the intent of the statement “Due to significant line broadening in high-mass stars, spectroscopy alone is insufficient to detect the Zeeman effect.” The Zeeman effect is *only* accessible by spectroscopy: what else is required? I think this statement was meant to highlight the benefits of high-resolution spectropolarimetry (e.g.,CFHT/ESPaDOnS as opposed to the VLT/FORS grism) but that’s not what it says. This point reinforces the discussion in Section 2.2 (lines 122 – 128), which describes projects that unsuccessfully searched for magnetic fields in Magellanic OB stars by using VLT/FORS2. Since this instrument has been used to successfully detect magnetism in many Galactic O-stars (e.g., the BOB survey), it seems to me that the real need is for larger apertures rather than higher spectroscopic resolution per se, though the two go hand in hand.
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The sentence in question has been removed from the Conclusions and some further clarification has been added to Section 2.2.
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Line 805: Reference 68 is incompletely specified.
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Completed.
I thank again Reviewer 1 for providing me with a clearly-written and constructive report.
Reviewer 2 Report
The work tries to summarize the current research status of the magnetism is high-mass stars in a form of a review. After a general introduction, the author gives a brief overview of observations. Then a theoretical part is presented, introducing fossil and dynamo fields concepts. In the section dedicated to modeling, different effects and their possible contribution are discussed. In the illustrative section "Roadmap ..." the phenomenological picture of the magnetic field evolution throughout the star evolution is given.
Eleven pages are dedicated to citations, which documents the aim of the work.
General comments:
The work collects a large amount of references and attempts to present an overview.
However it struggles with the task
- to comprehensibly review a large number of and achievements and publications in a restricted space.
- to combine large number of details with an overall clear picture.
Frequently, the author produces long and complex sentences, where statements are combined with uncertainties and discourses. The resulting mix between observations and contra-examples, findings and speculative(possible) scenarios does not give a clear picture. Consequently, the text becomes less readable, sometimes the sentence logic becomes unclear.
The understanding to magnetic fields in stars during their evolution is important and a clearly given presentation would be useful.
The possible effects of magnetic fields on nucleosynthesis or on change of the elemental abundance were discussed very briefly and scattered over few places in the text (e.g. in 4.4.2). These effects are of high interest in the community.
Specific comments:
Examples of vague and/or over-complicated explanations:
In Section 3.1.
As Spitzer described, ... ,which under collapse ... as a consequence. This means..
L166 some sort of kinetic energy
L170 ... in those cases ... likely best
L189 roughly by 3-4 orders ... roughly similar
L193 Although multiplicity ... thus it is not immediately evident...
L196 5 lines long difficult sentence
L213 This means ... Let us look ...
L209 However, thus far ... which could... when
L227 ... ten -> tens of
The Fig.1 - while this is a good illustration to a textbook, there is not
much context within the current work (just a ref.[149]). May have more value
when more configurations are presented for comparison.
Eq(9) T is not defined
L308 In fact ...[191] argue -> Potter et al. argues
L311 formulations starting with Nonetheless
L345 it could be instrumental to infer ... the goal of this suggestion is not clear
Fig.3 ... consider explanation of LMC, SMC and Mdot (Eq 12) and what means
Mdot scaling. The vertical axis show metalicity - is there another axis that
shows metalicity for magnetic case?
L493 ... but why metals dive the wind?
L534 In fact, the question... is not supported ... doesn't make a good sense.
L534-545 too unclear. Number of statements and expectations with unclear origins.
L547-549 So complicated formulation, that the logic of merger's origin
becomes obscured. The next sentence immediately obscures the logic of fossil
fields - ...general explanation requires solving the acquisition....
L554 and on: Section 5
While a general evolution picture is interesting, the text needs to avoid
the unclear language:
L555, L557 Let us, let us -> In the typical case of 20M star...
Phase 1 - 3x might
Phase 2A - somewhat elusive often termed, although quite certainly some
2B - most likely, possibly, unlikely, in fact could
3A - may play may be this could may preserve some of the
3B - may play, likely, could
etc. ... in total 38x expression of uncertainties over the process.
L643 ... again too complex sentence, exciting sources of discussions is
for science less important than the knowledge and discovery.
The fundamental nature of stars - the meaning of this is disputable,
one may claim, that this is already well known for 100 years, while the
origins and role of magnetic fields is a hot topic.
Book references 138, 141 are not complete
Recommendations:
It is advised to change the style to more strict, more clear. Shorter sentences are necessary. Avoid several overturns within one sentence. Some phrases (like Let us look, In fact, This means ...) should be replaced or removed. Section 5 is so stuffed with words expressing uncertainty, that the reader must pose himself a question, if all the section is just speculative. Which is probably not the aim of the author.Clear definition of conditions and cases is needed.
A paragraph, where nucleosynthesis and element abundance (possible) impacts are summarized would be useful. As the developer of MESA extensions, the author may have information to share.
Since the work is a review, a paragraph summarizing recent key observational achievements would be useful.
Author Response
I thank Reviewer 2 for carefully reading the manuscript.
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Frequently, the author produces long and complex sentences, where statements are combined with uncertainties and discourses. The resulting mix between observations and contra-examples, findings and speculative(possible) scenarios does not give a clear picture. Consequently, the text becomes less readable, sometimes the sentence logic becomes unclear.
The understanding to magnetic fields in stars during their evolution is important and a clearly given presentation would be useful.
***
The topic of magnetism in high-mass stars is still relatively young and many aspects are being debated to this day. As a result, I have attempted to collate a broad range of the existing literature in such a way that controversies, when they exist, are presented in their full complexity rather than in a one-sided fashion. I have taken the comments into account to modify the manuscript and improve its flow (as further described below). I consider that it is best to keep a balanced approach, even if it leads to more open-ended conclusions or unresolved problems in some cases. I believe this accurately represents the current state of this research field.
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The possible effects of magnetic fields on nucleosynthesis or on change of the elemental abundance were discussed very briefly and scattered over few places in the text (e.g. in 4.4.2). These effects are of high interest in the community.
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I believe this is a question that has been considered in more detail in low- and intermediate-mass stars. In particular, the impact of a magnetic field on nucleosynthesis in a high-mass star seems to be a scarcely discussed topic in the literature. I have included additional comments on the surface elemental abundances in Section 4.4.2.
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Specific comments:
Examples of vague and/or over-complicated explanations:
In Section 3.1.
As Spitzer described, ... ,which under collapse ... as a consequence. This means..
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The clarity has been improved:
"Stars could inherit some magnetic flux from the molecular cloud. The parent molecular cloud has its own magnetic field. As the cloud collapses, the magnetic field lines are compressed and the field strength increases. This amplification is a consequence of the "frozen-in" flux condition (see below)."
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L166 some sort of kinetic energy
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Removed "some sort of".
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L170 ... in those cases ... likely best
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Improved clarity:
"Several dynamo mechanisms describe a local phenomenon. Therefore, dynamo-produced fields are often characterised by length-scales that are relevant to the powering mechanism (e.g., convection). The perturbed magnetic fields can be considered as small-scale, for example, in comparison to the size of the star. "
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L189 roughly by 3-4 orders ... roughly similar
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Improved clarity:
"In high-mass stars, the nuclear-burning time-scale is much shorter than in the Sun ($\sim$ few Myr vs. $\sim$ 10 Gyr). If the Ohmic dissipation time-scale for the Sun and high-mass stars were roughly similar, any fossil field in high-mass stars should be long-lasting. Some additional mechanisms or phenomena still cannot be ruled out as potential sources of magnetic field dissipation."
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L193 Although multiplicity ... thus it is not immediately evident...
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A new sentence is started to improve readability.
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L196 5 lines long difficult sentence
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Improved:
"In general, the dissipation of fossil fields is expected to be slower than the star's evolution. The principle of the frozen-in flux condition (Alfv\'en's theorem \citep{alfven1942}) can be applied to deduce the surface magnetic field strength. The magnetic flux over a closed surface area $\mathbf{S}$ is defined as:"
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L213 This means ... Let us look ...
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Changed to:
"Dynamo fields have been proposed in several forms \citep{kulsrud2005}. For example, the induction equation for a convection and rotation-driven, so-called $\alpha$-$\Omega$ dynamo can be written as:"
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L209 However, thus far ... which could... when
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Changed to:
"These approaches often rely on stellar ages inferred from non-magnetic evolutionary models. This source of uncertainty can now be improved upon with models incorporating fossil field effects \citep{keszthelyi2020,keszthelyi2022}."
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L227 ... ten -> tens of
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Changed to:
"few decades"
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The Fig.1 - while this is a good illustration to a textbook, there is not
much context within the current work (just a ref.[149]). May have more value
when more configurations are presented for comparison.
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An additional configuration is presented now in Fig. 1, the caption has been appropriately extended, and a brief description is added to the main text.
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Eq(9) T is not defined
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It has been defined now.
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L308 In fact ...[191] argue -> Potter et al. argues
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Since "et al." makes the subject plural if it refers to the authors (which it does), the text is correct. Nonetheless, I have changed the sentence to passive form to avoid this issue.
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L311 formulations starting with Nonetheless
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Improved sentences to:
"The diffusivity, whether produced directly via Maxwell stresses or indirectly via magnetic turbulence, must be high. Indeed, it is expected that poloidal field lines could "freeze" rotation and enforce solid-body rotation \citep{ferraro1937, mestel1999,spruit1999}."
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L345 it could be instrumental to infer ... the goal of this suggestion is not clear
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Improved to:
"In recent years, it has become possible to perform multidimensional MHD simulations focusing on silicon/oxygen shell burning in massive stars \citep{varma2021}. This stage is within a few minutes of the star reaching core collapse. The rotational and magnetic properties at this stage can have a large impact on the core dynamics. For example, asphericities may aid the neutrino-driven explosion. The magnetic field might also become the seed of a subsequent dynamo action to create the neutron star's magnetic field."
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Fig.3 ... consider explanation of LMC, SMC and Mdot (Eq 12) and what means
Mdot scaling. The vertical axis show metalicity - is there another axis that
shows metalicity for magnetic case?
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Abbreviations of LMC and SMC have been included in the caption. While mass-loss rates are indeed introduced in the magnetic braking formula (Eq. 12), the physical meaning of the Mdot scaling is defined in the first sentence of the caption and in the main text. Further clarifications have been added to the text and Fig. 3 has been modified with additional text on the axes.
Presently, a comprehensive set of magnetic stellar evolution models extending to very low metallicities is not available. In our recent work (Keszthelyi et al. 2022, MNRAS, 517, 2028), we provide magnetic models at metallicities representative of the Magellanic Clouds and observe the general trend that mass-loss rates are further reduced compared to solar metallicity. The situation; however, is more complex since rotation plays an increasingly important role at lower metallicity. We hope to provide further estimates for a metallicity-dependent mass-loss quenching effect in the future.
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L493 ... but why metals dive the wind?
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The paragraph has been revised and radiative line-driving is briefly introduced with further references. Scalings are also explicitly mentioned for clarity.
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L534 In fact, the question... is not supported ... doesn't make a good sense.
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Improved clarity:
"In fact, observational evidence suggests that main sequence stellar mergers are unlikely to be responsible for generating all fossil fields in high-mass stars."
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L534-545 too unclear. Number of statements and expectations with unclear origins.
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References are provided to underpin the empirical constraints available. The expected increase in merger rates towards higher stellar masses is simply the consequence of the higher incidence rate of binarity in more massive stars. This clarification has been added to the text with additional references.
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L547-549 So complicated formulation, that the logic of merger's origin
becomes obscured. The next sentence immediately obscures the logic of fossil
fields - ...general explanation requires solving the acquisition....
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Rephrased the closing paragraph to:
"In summary, the merger of two main-sequence stars represents a possible channel to form large-scale fields in high-mass stars. However, it remains disputed whether it could be a general explanation for the origin of fossil fields in all high-mass stars. Ample observational evidence (magnetised pre-main sequence stars, randomly distributed obliquity angles, magnetised components in close binary systems) points toward the direction that fossil fields must remain from earlier stages of the star's history. Thus the exact origin of fossil fields in high-mass stars is still an unresolved problem."
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While a general evolution picture is interesting, the text needs to avoid the unclear language:
L555, L557 Let us, let us -> In the typical case of 20M star...
Phase 1 - 3x might
Phase 2A - somewhat elusive often termed, although quite certainly some
2B - most likely, possibly, unlikely, in fact could
3A - may play may be this could may preserve some of the
3B - may play, likely, could
etc. ... in total 38x expression of uncertainties over the process.
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I have revised and edited the text to improve the general flow and stylistic choices, concerning all the specific examples that were given. The language in Section 5 is chosen to be appropriate for the very uncertain overall picture of magnetic field evolution from star formation to compact objects. It would be of great importance to have more stringent constraints on this topic, but presently it remains a largely unresolved problem. Several phases of this overall picture are either hypothetical with no observational verification or only qualitatively known. Surfacing these uncertainties is important and can hopefully guide new research to solve the open questions.
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L643 ... again too complex sentence, exciting sources of discussions is
for science less important than the knowledge and discovery.
The fundamental nature of stars - the meaning of this is disputable,
one may claim, that this is already well known for 100 years, while the
origins and role of magnetic fields is a hot topic.
***
Rephrased.
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Book references 138, 141 are not complete
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References to Mestel's book [138] and the work of Goedbloed, Keppens, Poedts [141] have been completed with publisher and ISBN.
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Recommendations:
It is advised to change the style to more strict, more clear. Shorter sentences are necessary. Avoid several overturns within one sentence. Some phrases (like Let us look, In fact, This means ...) should be replaced or removed. Section 5 is so stuffed with words expressing uncertainty, that the reader must pose himself a question, if all the section is just speculative. Which is probably not the aim of the author.Clear definition of conditions and cases is needed.
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The clarity of the manuscript has been improved. The causality between sentences has also been revised and made more explicit when possible (with examples given above).
Concerning Section 5, the aim is to provide a qualitative picture of magnetic field evolution from star formation to core collapse. The emphasis is to show that magnetic fields are present in *all phases*, as it is illustrated in Figure 4. This is indeed a highly uncertain overall picture with many gaps in our knowledge of how magnetic characteristics change from one phase to another. Detailed, more quantitative discussions are presented in previous sections (Sections 3 and 4) and are now referenced more explicitly in Section 5.
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A paragraph, where nucleosynthesis and element abundance (possible) impacts are summarized would be useful. As the developer of MESA extensions, the author may have information to share.
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To my knowledge, the impact of a magnetic field on nucleosynthesis in high-mass, non-degenerate stars is largely unexplored.
The impact on (surface) chemical abundances is a complex, and partially indirect consequence of magnetism. For example, how magnetism and meridional flows interact is still not fully understood. I edited Section 4.4.2 to include some further insights.
I also rephrased "developer of extensions in MESA" to "contributor of extensions in MESA" to avoid any ambiguity.
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Since the work is a review, a paragraph summarizing recent key observational achievements would be useful.
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Section 2 provides a discussion on observational aspects, building on historical, pioneering works and presenting recent key observational achievements. In particular, Section 2.2 presents a focused summary with several new empirical findings and progress in the field. These also include various multiwavelength observations (e.g., infrared, radio, UV), spectropolarimetric follow-up studies from photometric variability, and current limitations. It is virtually impossible to summarise all new empirical findings in one paragraph as the progress over the last ~20 years has been tremendous.
