Peer review of: Determining the rotation direction in pulsars (2019)

Reviewers' comments:  

 

Reviewer #1 (Remarks to the Author):  

 

Pulsars provide valuable tools to probe ISM magnetic fields via Faraday rotation measures (RMs) and 
to test general relativity. In previous observational studies, the contribution of the pulsar 
magnetosphere’s plasma to the RM has been assumed to be negligible. This paper focuses on the 
effect of the rotation of the pulsar magnetosphere, whereby mechanical-optical rotation (MOR) 
adds an additional term to the rotation of the pulsar emission’s polarisation position angle as it 
propagates through the gyrotropic medium (and is dependent on the pulsar’s rotational frequency). 
Assuming the commonly adopted electron-positron plasma (accounting for relativistic-quantum 
effects in addition) the MOR term can vary from 0 to proportional to ω√(ω-ω_cl) or ω^-2, depending 
on the observing frequency ω. If this effect can be detected observationally, then the MOR 
contribution can be determined and the rotation direction of the pulsar may be deduced.  



There are only a few works focussed on investigating the effect on the rotation of the polarisation 
position angle of the pulsar’s emission as it propagates through the pulsar magnetosphere, and 
these previous literature works have been referenced and discussed appropriately. It seems that a 
thorough analytical derivation of the MOR effect has been done, and an analysis of the results 
presented, which is novel. The level of detail provided for the derivation in the methods section 
should provide an independent researcher with enough information to reproduce the work. 
Therefore, the claims made in the paper appear convincing. Moreover, the significance and impact 
of the results are stated without exaggeration.  

 

I believe that the paper will be of interest to (at least) both plasma physicists and pulsar 
astronomers. The rotation of the polarisation angle due to MOR stated here can be tested 
observationally, enabling further studies and information about the pulsar magnetosphere to be 
gleaned. Therefore, the paper will influence and inform studies in this area.  

 

 

Perhaps a simple simulation that propagates the polarisation position angle through the pulsar 
magnetosphere and the ISM with the MOR + Faraday rotation effects (i.e. integrated along the 
entire line-of-sight) would have strengthened the conclusions drawn for the low-frequency 
wavelength scaling deviation section. For instance, if the polarisation angle after traversing the 

magnetosphere (at point Q) is not constant with lambda, or does not follow the lambda^2 
dependency, how will the polarisation position angles be observed after propagating through the 
ISM? A remark as to the expected relative contributions of the MOR effect in the magnetosphere vs 
the Faraday rotation in the ISM could prove useful and strengthen the conclusions drawn. For 
instance, assume that a nearby pulsar is observed, what function does the rotation of the observed 
polarisation position angles with frequency follow? If the polarisation angle vs lambda^2 may not be 
observed, it may affect the measurement of the observed RM? For instance, using the method of 
RM-synthesis (Brentjens & de Bruyn 2005; 
https://ui.adsabs.harvard.edu/#abs/2005A&A...441.1217B) to measure RMs may not be successful 
in this case because the lambda^2 law is assumed. I don’t think this has been observed as yet. Also, 
note that there appears to be little evidence that high- and low-frequency RM measurements differ 
for a pulsar set as a whole (Sobey et al. 2019; 
https://ui.adsabs.harvard.edu/#abs/2019MNRAS.484.3646S). Although, evidence for 
magnetospheric effects on the radiation of radio pulsars has been seen in phase-resolved RM studies 
at higher frequencies (Ilie et al. 2019; https://ui.adsabs.harvard.edu/#abs/2019MNRAS.483.2778I).  


Some additional brief comments:  

 

— The pulsar beam geometry has traditionally been estimated using the rotating vector model 
(RVM; Radhakrishnan and Cooke, 1969). Perhaps it would be useful to the conclusions of this paper 
to note that the RVM method is not able to distinguish the direction of rotation?  

 

— k || B will evolve as the wave propagates through the magnetosphere. Do you expect this to 
affect the results obtained in any way?  

 

— Table 1: The typical rotational frequency for a pulsar used in Table 1 is not a particularly 
representative number for the known pulsar population. For slow pulsars, the median \Omega is 
~1.3 s^-1 and for millisecond pulsars it is ~200 s^-1. In addition, a comment clearly stating the effect 
of \Omega on the results would also be helpful for observational pulsar astronomers, e.g., if there a 
marked difference between `slow’ pulsars and MSPs.  

 

— Reference 19: Perhaps a more recent and pulsar-specific reference would be better suited here, 
e.g., Han et al. 2018; https://ui.adsabs.harvard.edu/#abs/2018ApJS..234...11H  

 

— Figure 1: Perhaps B and \alpha should also be included/labelled.  
 

It would be desirable to include the source code (or interactive interface) used to produce the plot in 
Figure 3. This would be useful for others to input pulsar- and ISM- specific parameters to see the 
effect expected in particular cases. However, this is not essential to this paper.  


The manuscript is clearly written, although copyediting is advised to correct the grammar in some 
instances. I do not think that the manuscript could be shortened as it already succinctly describes 
the work and results. The title may be somewhat misleading, as the paper does not answer the 
question "Do pulsars rotate clockwise or counterclockwise?", but provides a possible method to 
determine this.  



Reviewer #2 (Remarks to the Author):  

 

The paper suggests a rotation-dependent intramagnetospheric contribution  

to Faraday rotation in pulsar radiation as a way to determine the sign of pulsar's omega*b.  

The claims are novel/original and may be of interest to pulsarists, however, I am somewhat skeptical 
about the claims and the way they have been presented.  

 

In short, the problems with the paper are that  

1) observational detection of the  

suggested effects (the mode jump at the cutoff frequency and the nonquadratic  

nu dependence) is unlikely, because we observe all sorts of strange  

polarization phenomena at several radio frequencies. The manuscript is  

strangely silent about the observed multitude of various polarization effects.  

2) the paper is about how ray propagation affects the polarization angle (PA) -  

recently a fairly active subject of study in radio pulsars, but the reference to recent works  

on this subject is sparse.  

3) I am not sure about parameters used in the model. It seems that near surface  

plasma density is used instead of a lower value in a higher-altitude region  

where the emission and propagation effects actually take place.  

In general the paper seems suspicious in that too little reference is made to  

recent theoretical works on the PA distortions, despite several of them describe  

nu-dependent or rotationally-driven effects. Equally poor is discussion of observed  

pulsar polarization and realistic prospects for detectability.  

 

More specifically:  

1) Some nu-dependent orthogonal PA transitions are observed to occur at higher frequencies  

(eg. in D-type pulsars above 1 GHz, Young and Rankin 2012, fig. 3 in Dyks 2019)  

and the orthogonal modes are observed to disappear or appear in profiles here and there. It  

may be hard to discern these various observed changes of mode amount ratio from your cutoff  

frequency effect. Moreover, smooth non-interstellar changes of PA are also  

observed at different frequencies, as is recognized when  

they occur within limited pulse longitude interval (see eg. the PA loop of B1933+16, Mitra et  

al. 2016; also see Ilie et al. 2019). These phenomena, often  

interpreted in terms of mode coupling at limiting polarization radius,  

may be hard to distinguish from your nonquadratic effect.  

With the plenty of complex polarization effects observed, it seems there is very low chance  

to detect or isolate the effects that you propose.  

 

2) Faraday rotation is the propagation-induced change of PA, and changes of  

pulsar's PA have recently been studied quite thoroughly.  

The nu-dependent change of observed PA may result from the nu-dependent  

emission altitude (Blaskiewicz et al. 1991, Dyks 2008),  

nu-dependent refraction (Barnard & Arons 1986, Lyubarskii & Petrova 1998),  

longitudinal currents in polar tube (Hibschman and Arons 2001),  

"adiabatic walking" below polarization limiting radius (PLR) (Cheng &  

Ruderman 1979), nu-dependent mode coupling at the PLR (Petrova & Lyubarskii  

2000). The manuscript contains little reference to these previous works.  

For example, Petrova & Lyubarskii (2000) follow the ray polarization in the  

presence of rotation and find the PA modifications shown in their Fig 6.  

Do these distortions have anything to do with your Faraday rotation?  

I mean that peculiar radio pulsar polarization effects are usually interpreted in terms  

of polarization-limiting-radius mode coupling effects. The models include  

the birefringent/dispersive plasma properties along with the rotation,  

which is essentially what you do. The reader therefore expects a discussion of how your  

approach/results fit in the context of those typically applied for understanding pulsar  

polarization.  

Is your non-quadratic Faraday rotation dependent on pulse longitude (place in  

the profile?). Or do you mean phase-averaged PA when showing figure such as Fig. 2?  

 

3) On p.4 line 91 the cutoff frequency is estimated to 100 MHz using plasma  

parameters in "table 1".  

The magnetic field seems very high in table 1 especially that the caption  

says "typical plasma parameters in ... pulsars' magnetosphere".  

The value of 10^12 Gauss seems appropriate to neutron star surface rather  

than to "magnetosphere". The radio emission is believed to originate from  

say 50 Rns above the surface, and the Farady rotation may occur in even  

weaker B at higher altitude. Assuming that B (and plasma density) drops as r^-3,  

should the cutoff frequency be at least 50 times lower than the number you  

give? Well below the observed radio range? Or do I miss something?  

 

Minor points:  

p.1, l. 25+, the first paragraph can safely be skipped in a paper on pulsar  

polarization. Instead it would be of much higher value to relate your work  

to other studies of pulsar polarization.  

p.3, l. 61, "whether it is rotating clockwise or counterclockwise"  

I understand that the model can tell the sign Omega_dot_B and this is the  

meaning of clockwise and counterclockwise. I doubt this (i.e. the meaning of clockwise and  

counterclockwise) is clear for every reader.  

p.3, l. 70 "when the obliquity alpha = 0 in Fig. 1"  

I am not sure if this is the best reference to the figure: neither alpha is marked  

nor tilt is zero in Fig. 1.  

p.4, l. 91 and other spots: does "s^-1" mean Hz or rad*Hz?  

The factor of 2pi makes some difference / is not quite negligible in the  

estimates.  

The same ambiguity is for the capital Omega, eg. in Table 1.  

It is especially so given that Omega is usually understood as 2pi/P in most pulsar  

papers. Please define the quantities or anyhow make them (and units) unambiguous.  

p. 8, l. 182 "operator A" should be "Q"?  

p. 11, l. 242, missing 2 in the denominator of Delta_phi?