Spun-Up Rotation-Powered Magnetized White Dwarfs in Close Binaries as Possible Gamma-ray Sources: Signatures of Pulsed Modulation from AE Aquarii and AR Scorpii in Fermi-LAT Data

Round 1

Reviewer 1 Report (Previous Reviewer 2)

The paper have no observational motivation.

The paper contains numerous mistakes and misleading statements, here I presented a few of them:

The motivation of the paper is based on the Whiple observations, which was rulouted by observations of MAGIC team, which is much more precise and accurate.

Authors do estimations (6) and (7) and get dV\sim 1.e12 [V] (I get value for the same parameters order of magnitude smaller), OK, but they put AR Sco on figure 4 above line with potential 1.e20!!!

On the Fig 6 I can see grow of the electric potential beyond light cylinder radius, It is contradict to energy conservation low...

So, I can't recommend the paper for publication.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

In the manuscript "Spun-Up Magnetized White Dwarfs as Possible Gamma-Ray Sources: Signatures of Pulsed Emission from AE Aquarii and AR Scorpii in Fermi-LAT Data, Meintjes et al. discuss the possibility of periodic
pulsar-like gamma-ray emission from the white dwarfs in AE Aquarii and
AR Scorpii.

The paper is suitable for publication after correction of figures. Namely,
figures are technically of low quality, especially Figs. 7, 8, 9b, 10b,
11a, 12a, 14, 16a,  where it is very difficult to read inscriptions.

Also the English should be checked and in particular references.
Examples of misprints are:

l 156: by by --> by
l 318: braking --> breaking?
ll 3332-334: The distribution ... have been determined--> The distribution ... has been determined; or:
The distributions ... have been determined
l 337: the that distribution --> that the distribution
l 358. the fact magnetospheric --> the fact that magnetospheric
l 358: to double --> to the double
l440-441: had hadronic?
l 534: Lobato  , --> Lobato,
l 546: Caiazzo  ., --> Caiazzo,
l 549: J.D. Jackson --> Jackson, J.D.
l 550: Hillas  , --> Hillas,
l 554: J. Becker & J. Trumper --> Becker, J. & Trumper, J.,

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Please see the attachment

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report (New Reviewer)

In this paper, the authors presented a comprehensive study of rotation-powered white dwarf pulsars, with the focus on two sources, namely AE Aquarii and AR Scorpii. They presented theoretical models for WD pulsars based on the standard neutron star pulsar models. They also searched for pulsations using the Fermi LAT data. The paper is well written. Nonetheless, I have several comments. The paper should be acceptable for publication in Galaxies if they are properly addressed.

 

My major comment is that the pulsed gamma-ray detections with Fermi-LAT for both sources are at most marginal. The authors should not claim “We report the detection of pulsed gamma-ray emission …” in the abstract and elsewhere in the paper. Instead, they should be very cautious of claiming such a detection. This would not affect the overall structure and significance of the paper.

 

My relatively minor comment is that the WD pulsar theory has been developed and applied to some other candidates. The electric potential, particle acceleration, curvature radiation and inverse Compton scattering as well as pair production in strong magnetic field for WD pulsars have been studied in 

https://ui.adsabs.harvard.edu/abs/2005ApJ...631L.143Z/abstract.

The theory was applied to GCRT J1745-3009. These should be commented in the paper. 

 

Another comment is the use of “Spun-up Magnetized White Dwarfs” in the title. I do not see discussion of spin up due to accretion or any other processes. All the formulae used in the paper are related to magnetic dipolar spin down of the WD pulsar. Maybe “Spin-up” was a typo and should be “Spin-down”?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (Previous Reviewer 2)

The authors removed obviouse mistakes but the paper still suffer from numerous over ones. In general the paper is strongly fragmented and did not have a general logical conection.

For example in the paper we can see strenth of the magnetic field from 1.e6 till 1.e9 G without explanation which one should be used.

Authors have to explain how to spin up the WD with so high magnetic field and realistic accretion rates in low mass binary system.

Equation 17 presented in the dimensional form but left and right parts are dimensionally different. So the following equations impossible to check.

Authors speculate that the pi+- can produce pairs which can explain X-ray emission, but did not compare with upper limit on the flux in TeV energy band from pi0 decay. 

Detection by Fermi/LAT on the level 2 sigma is not enough. We can say something if we have >5 sigma!

Authors claim about fast cooling of normal component of velocity in the strong magnetic field and completely ignore this emission in the following analisys.

 

Reviewer 3 Report (New Reviewer)

The revised paper is fine. I have no further comments.

Reviewer 4 Report (New Reviewer)

The authors have properly addressed my concerns. The paper is now acceptable for publication. 

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

This is an interesting paper worthy of further exploration and certainly suitable for publication in Galaxies. The authors discuss the possibility of high energy emission from fast-spinning WD pulsars has been evaluated based on the results of recent findings from two non-accreting fast-spinning white dwarfs in close binaries, i.e. AE Aquarii and AR Scorpii. In fact, several theoretical and observational works regarding very magnetic, massive, and fast WDs have been published in the last few years (see Caiazzo et al. 2021, Cáceres et al. 2017, Borges et al. 2020). In addition, these sources may be the missing link to support a recent claim made in Malheiro et al. (2012) and Coelho & Malheiro (2012, 2014) that some of the anomalous X-ray pulsars (AXPs) that spin with period of ~10 s could be very massive, magnetic, and fast WDs that resulted from WDs mergers. Furthermore, the Zwicky Transient Facility is currently discovering large numbers of very fast-spinning WDs. In addition, CTA and LSST will discover many of these sources. Also, these fast-spinning WDs have been confirmed by the recent results of the Sloan Digital Sky Survey (SDSS) (see the recently observed isolated WD with a rotation period of $70.32$s in Kilic et al 2021). It is important to highlight the author's participation in several of these discoveries. This contribution has much merit of being published in the special issue proposed by Galaxies.

Reviewer 2 Report

Authors refer on the speculative observation data, 2\sigma significance in the HE/VHE astrophysics it is level of noise and not significant (we need >>5 \sigma). MAGIC see nothing and reference on the older low quality observations is not feasible.

More serious mistakes began from very beginning of the section 2, which is inconsistent with logic of the authors after Eq14.

Please compare a logic presented in the paper and the logic in the papers like:

https://ui.adsabs.harvard.edu/abs/1984ApJ...283..694K/abstract

https://ui.adsabs.harvard.edu/abs/2006ApJ...648L..51S/abstract

https://ui.adsabs.harvard.edu/abs/1984ARA%26A..22..425H/abstract

Please compare synchrotron  and inverce Compton  losses.

The paper contains numerous physical inconsistencies. I can't recommend it for the  publication.

Reviewer 3 Report

This paper deals with particle acceleration in fast-spinning white dwarfs. The topic is relevant to the special issue of "Galaxies" which aim is to "to review the current state of the art and to explore the potential advances in high-density compact objects, high-energy astrophysics, and multi-messenger observations.".

The first two sections of the paper present a review of observation and theory of non-thermal emissions from fast-spinning white dwarfs. The third section appears to present new results. As such it seems to me that the scope of the paper is ill-defined. Although the authors present the first two sections as "a brief discussion", it appears to cover more than two third of the paper.

The theoretical review, Sec 2, appears somewhat unclear, unstructured, and sometimes contradictory. Most equations have issues, ranging from typos to apparent contradictions with other equations. Many results are introduced with the words "it has been shown.." cutting short derivations and creating what occasionnally resembles a patchwork of equations without clear pedagogical strategy (even considering this is a review) and they sometimes lack internal consistency. Some references are missing or not relevant. Notations and units are not very consistent throughout.

Section 3 seems to present new results. Although not familiar with FERMI/LAT analysis, the description of methodology seems limited and results are quoted without confidence level (at least not clearly).

Due to these several important issues, I consider that this paper requires important restructuring and corrections to the point that is warrants submitting a new paper with different scope, aim and structure. This is why I recommend rejection.

Below is a more detailed list of remarks and suggestions.


*** Introduction
p1 : l23 : missing references, what "high energy studies" ?
l75 : charge -> charged

*** Section 2
This section should be sub-divided into sub-sections, in my opinion. Lines starting with "---" below suggest such divisions.
Perhaps the general geometry of the problem should be introduced.
--- Single-particle energetics in vacuum magnetosphere
eq 3 : "q" not introduced
eq 4 : Consistency of units and notations w.r.t. following equations : Volt cm-1 , Vm-1 ?
eq 6 : what is theta ? Is it still magnetic inclination ? More generally this equations is given without deduction nor reference. The preceding affirmation "E is not perpendicular to B" is also neither derived nor referenced.
p4 : notion of polar cap has not been introduced
eq 7 : ">> 0" does not seem relevant here. What do we compare this quantity to ?
eq 8 : what is "emf" ? Where is the factor 300 coming from ? The authors conclude from this rough estimate that extreme acceleration is possible (see below) but the potential drop of Eq 8 is several orders of magnitude larger than the numbers given in eq 10 below. These two equations are somewhat contradicting, and certainly no conclusion can be drawn from 8 since 10 places an upper limit on the potential drop (being calculated all the way to the light cylinder, contrary to 8).
l122 : The comparison with the Crab nebula is misleading here, because the way it is put it suggests a comparison with the Crab pulsar. But VHE emissions from the nebula are understood as coming from the termination shock of the pulsar wind (e.g. Kennel and Coroniti 1984), not the pulsar itself which can't produce such high energies in most models although its potential drop is much larger than what is calculated in eq 10 with figures of AE Aquarii.
eq 9 : unclear from which reference this equation is taken. The logical link with the above derivation is also unclear: is it the same quantity as in Eq. 7 ?
In the paragraph above, B_* is given in centimeters, while the electric field of Eq. 9 is called a "potential".

--- Particle extraction  
l123 : in this paragraph, sentence "Magnetic field lines are very nearly equipotentials so that charges can flow along them" : I do not see the relevance of this sentence: why is this important? This is all the more puzzling that the whole discussion above was about the fact that field lines along which particles flow and are accelerated are precisely not equipotentials, which leads to acceleration.
eq14 and paragraphs above and below: The authors explain that the structure of the magnetosphere is "essentially a vacuum" above a thin atmosphere the height of which is given by Eq. 14. This comes after the authors have explained that the electric fields in vacuum are so strong that they will "pull charges from the surface", see eq 5, and that they form a "corotating force-free magnetosphere" (thus full of plasma with charge density given by 12). These statements contradict each other. However the conclusions made by authors in this paragraph is that vacuum computations hold in the magnetosphere above the thin atmosphere, which implies that the considerations on vacuum potential drop are essentially valid. This is a dangerous oversimplification as is well-known in the pulsar literature (starting with articles cited by the authors, such as e.g. Arons and Scharlemann 1979).

--- Pair cascades (after l132)
Overall, this part implicitely deals with the fundamental concept of death line, which is however not mentionned.

Paragraph starting with "It has been shown [31] that the region above the polar caps can be a site of e+/- production" : the reference given deals only with pulsars and therefore does not show directly that these considerations can apply in the context of white dwarfs. The work of adaptation has however been done in [33].

In the same paragraph "average radius" is rather a characteristic radius in the vicinity of the polar cap.

"... a necessary condition for pair avalanche in the accelerator is that chi = 1/15 << 1" : the condition is rather chi > 1/15, which is actually consistent with eq 18.

eq 17 : this equation is given without explanations. However it derives from eq 16 and from the subsequent discussion on curvature radiation, so derivation could be easily made.
eq 20 and 21 : fiducial period is 1 sec, why ? Besides it is curious that h still appears on the rhs of eq. 21 instead of being substituted with eq. 20.
eq 22 : this estimate seems to assume no radiation reaction. However, as is well-known in the context of pulsar magnetospheres, the dynamics of electrons with such high Lorentz factors is usually limited by radiation reaction (see e.g. Vigano 2014, Eq 36, http://arxiv.org/abs/1411.5836).

*** Section 3 :
This sections seems to present new results, although it is not very clearly said.
Although interesting, the methododology of the analysis is not clearly described, and comparisons with previously published observations would deserve to be further developped, in my opinion.
Importantly, results are quoted without error bars or confidence level.

Figures : labels and captions are too small to be readable.