The recent detection of a large polarization degree in the optical emission
of an isolated neutron star led to the suggestion that this has been the first
evidence of vacuum polarization in a strong magnetic field, an effect predicted
by quantum electrodynamics but never observed before. This claim was challanged
in a paper by Capparelli, Maiani & Polosa (2017), according to whom a much
higher polarization degree would be necessary to positively identify vacuum
polarization. Here we show that their conclusions are biased by several
inadequate assumptions and have no impact on the original claim.Comment: 10 pages, 2 figure

Caniulef, D. Gonzalez

Mignani, R. P.

Taverna, R.

Testa, V.

Turolla, R.

Wu, K.

Zane, S.

English

arXiv

The recent detection of a large polarization degree in the optical emission of an isolated neutron star led to the suggestion that this has been the first evidence of vacuum polarization in a strong magnetic field, an effect predicted by quantum electrodynamics but never observed before. This claim was challanged in a paper by Capparelli, Maiani & Polosa (2017), according to whom a much higher polarization degree would be necessary to positively identify vacuum polarization. Here we show that their conclusions are biased by several inadequate assumptions and have no impact on the original claim

Turolla,, R

Zane, S

Taverna, R

Gonzalez, D

Mignani, R

Testa, V

Wu, K

UCL Discovery

A Comment on “A note on polarized light from Magnetars:QED effects and axion-like particles” by L.M. Capparelli, L.Maiani and A.D. PolosaR. Turolla1,2, S. Zane2, R. Taverna1, D. González Caniulef2, R.P. Mignani3,4, V. Testa5,K. Wu2Received ; accepted1Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131Padova, Italy2Mullard Space Science Laboratory, University College London, Holmbury St. Mary,Dorking, Surrey, RH5 6NT, UK3INAF-Istituto di Astrofisica Spaziale e Fisica Cosmica Milano, via E. Bassini 15,20133, Milano, Italy4Janusz Gil Institute of Astronomy, University of Zielona Gòra, Lubuska 2, 65-265,Zielona Gòra, Poland5INAF-Astronomical Observatory of Rome, via Frascati 33, I-00078, Monte PorzioCatone, ItalyarXiv:1706.02505v1  [astro-ph.HE]  8 Jun 2017– 2 –AbstractThe recent detection of a large polarization degree in the optical emissionof an isolated neutron star led to the suggestion that this has been the firstevidence of vacuum polarization in a strong magnetic field, an effect predictedby quantum electrodynamics but never observed before. This claim was chal-langed in a paper by Capparelli, Maiani & Polosa (2017), according to whom amuch higher polarization degree would be necessary to positively identify vac-uum polarization. Here we show that their conclusions are biased by severalinadequate assumptions and have no impact on the original claim.Subject headings: polarization — sources (individual): RX J1856.5-3754 —stars:magnetic fields — stars: neutron– 3 –1. IntroductionIn a recent paper, Capparelli, Maiani & Polosa (2017) presented some considerationsin connection with the discovery of a relatively high linear polarization degree (∼ 16%)in the optical emission of the isolated neutron star (NS) RX J1856.5-3754 (hereafterRX J1856; Mignani et al. 2017). Specifically, they expressed some criticism on theinterpretation of the measured polarization as the first evidence for vacuum birefringence,as stated by Mignani et al. (2017).According to quantum electrodynamics (QED), photons propagate in a stronglymagnetized vacuum in two normal polarization modes, the ordinary (O) and extraordinary(X) one, with different refractive indices and this strongly influences the polarizationproperties of the observed radiation (e.g. Heyl & Shaviv 2000, 2002; Harding & Lai 2006;Taverna et al. 2015; González Caniulef et al. 2016). This effect has been searched for butnever observed in terrestrial laboratories (e.g the PVLAS experiment; della Valle et al.2014). The main point raised by Capparelli, Maiani & Polosa (2017) is that the observedpolarization degree in RX J1856 would be not high enough to provide an unambiguoussignature of vacuum birefringence. According to their calculation, in fact, the maximumvalue of the polarization degree, neglecting vacuum birefringence, is ∼ 40%, whileaccounting for QED effects it should be close to 100%. Hence their conclusion thatthe measured value is too small to support the presence of vacuum birefringence in themagnetosphere of RX J1856.Here we show that their conclusions are incorrect because of the oversimplifiedtreatment of the magnetic field around the neutron star they use. Besides, their approachin computing the phase-averaged polarization observables appears flawed and theconstraints set by the observed values of the star parameters, the surface magnetic fieldand the pulsed fraction, are not accounted for.– 4 –2. Magnetic field topologyCapparelli, Maiani & Polosa (2017) considered a simplified magnetic fieldconfiguration in which the magnetic field vectors are tangent to the meridians of the starsurface. This assumption works well to illustrate how the photon electric field directionchanges as the radiation propagates in the magnetized vacuum around the source (asshown in their figure 1). However, as also they themselves note, the external field of anNS is most likely a core-centered dipole, and this seems indeed the case for RX J1856, asrecently discussed by Popov, Taverna & Turolla (2017). Actually, while meridional fieldlines well approximate the dipolar ones far from the star, the agreement becomes worseand worse closer to the star surface, where radiation is emitted. In assessing the maximumobserved value of the polarization degree in the absence of vacuum birefringence (QED-offcase), Capparelli, Maiani & Polosa (2017) keep to this unrealistic approximation (seetheir footnote 2) and get a value . 40% for photons initially 100% polarized in the Xmode. We stress that the magnetic field topology is key in computing the observablepolarization signal (in the QED-off limit). Since the magnetic configuration assumedby Capparelli, Maiani & Polosa (2017) is much more uniform than the dipolar one,this produces an overestimate of the polarization degree. This can be clearly seen infigure 1 which shows the magnetic field over the star surface (projected on the planeperpendicular to the line of sight, LOS) for both magnetic configurations. The meridionalmagnetic field configuration is indeed more organized/uniform than that of the dipolarfield, so that the expected polarization degree in the absence of QED effects is higher forthe meridional field.This can be explained by the fact that the Stokes parameters associated to eachphoton have to be rotated around the LOS in order to be all referred to the sameframe (the polarimeter frame) before they are summed together to obtain the overallpolarization signal (see Taverna et al. 2015, for further details). Since the rotation angle– 5 –α is indeed the angle between the projection of the local B-field perpendicular to theLOS at the emission point and the polarimeter reference axis, it becomes clear that theconfiguration of the magnetic field on the star surface strongly influences the observedpolarization degree when QED effects are neglected. In particular a narrow range ofvariation for the angle α over the star surface translates into a larger polarization degreeat the observer.To better assess this point, we recomputed the polarization observables with ourray-tracing code using a setup similar to that adopted by Capparelli, Maiani & Polosa(2017), i.e. meridional field and 100% polarized blackbody photons, obtaining a valueof the polarization degree in the QED-off limit of ∼ 50% for the most favourableviewing geometry, much higher than that for a dipolar field, ∼ 13% for the same photoninput. This is clearly illustrated in figure 2 which shows the observed phase-averagedpolarization degree ΠL as a function of the two geometrical angles ξ and χ, the magneticaxis and the LOS, respectively, make with the rotation axis.The value of ∼ 40% reported by Capparelli, Maiani & Polosa (2017) as the upperlimit for the observed polarization degree in the absence of QED effects is stronglyaffected by their oversimplified treatment of the star magnetic field, has no physicalbasis, and cannot be compared with the results discussed in Mignani et al. (2017). As aconsequence, their statement that the measure of ΠL ∼ 16% in RX J1856 is insufficientto infer vacuum birefringence is devoid of any meaning.3. Phase-average of the Stokes parametersThe definition adopted by Capparelli, Maiani & Polosa (2017) for the polarizationdegree is unclear. The polarization degree considered in Mignani et al. (2017) is definedin terms of the (normalized) Stokes parameters Q and U as ΠL =√Q2 + U2. The– 6 –Fig. 1.— Magnetic field distribution over the star surface projected on the plane per-pendicular to the LOS for both a meridional field (left-hand panel) and a dipolar field(right-hand panel).Fig. 2.— Contour plot of the phase-averaged polarization degree ΠL (see text) in theabsence of QED effects for the meridional (left-hand panel) and dipolar (right-hand panel)magnetic field configurations, as a function of the geometrical angles χ (between the LOSand the rotation axis) and ξ (between the magnetic and the rotation axes).– 7 –FORS2 instrument used in the polarimetric observation measures the Stokes parametersof the collected radiation. Due to the limit on the time resolution imposed by theexposure duration, only an average of the polarized signal over the rotational phase canbe obtained. Since the Stokes parameters are additive, the phase-averaged polarizationdegree can be obtained only by averaging the Stokes parameters before computingthe polarization observables, a fact Capparelli, Maiani & Polosa (2017) completelyneglect. Indeed, the effect of phase-averaging over the star rotation is that of an effectivedepolarization, and this holds also when QED effects are accounted for (as shown inTaverna et al. 2015; González Caniulef et al. 2016). As a key example, one may considerthe configuration shown in figure 1 of Capparelli, Maiani & Polosa (2017), and set the starspin axis along the LOS. After a full rotation of the star, a polarimeter collects photonswith electric field pointing in different directions. This reduces the polarization degreedown to zero (even using the simplified meridional configuration for the magnetic field),despite the fact that a phase-resolved polarization measurement gives, instead, 100%.This means that the phase-averaged polarization degree as measured at infinity stronglydepends on the viewing geometry and the observed signal in the presence of vacuumbirefringence is not necessary 100% polarized. In particular, it attains a maximum whenthe phase-averaging effects are less important, i.e. in the case of an orthogonal rotatorseen perpendicularly to the rotation axis.4. Constraints on the star viewing geometry and magnetic fieldIn order to observe the maximum polarization degree Capparelli, Maiani & Polosa(2017) consider the case of the LOS perpendicular to the star magnetic axis. We pointout that, actually, this is not entirely true. In fact, the angle between the LOS and themagnetic axis depend in general on the rotational phase (Taverna et al. 2015; GonzálezCaniulef et al. 2016). Hence, as illustrated in the previous section, the only geometrical– 8 –configuration which allows to observe the maximum polarization degree turns out to bethat in which both the LOS and the magnetic axis are orthogonal to the spin axis ofthe star. This is also shown in the contour plots of figure 2 above, as well as in thoseshown in Mignani et al. (2017), where the maximum polarization degree is attained atthe top-left corner.However, observations place several constraints on the geometrical angles χ andξ for RX J1856. In particular the pair (χ , ξ) must be compatible with the observedpulsed fraction in the X-rays (∼ 1.2%; Tiengo & Mereghetti 2007). This was accountedfor in Mignani et al. (2017). In addition, also on the basis of spectral observations, afurther constraint was placed by Ho (2007), forcing χ and ξ to vary in narrow ranges, i.e.χ ≈ 20◦– 45◦ and ξ . 6◦. Including these constraints, it becomes clear that the viewingconfiguration which gives the maximum polarization degree (i.e. χ = 90◦, ξ = 0◦) is ruledout by observations.Capparelli, Maiani & Polosa (2017) note that a 16% polarization degree may indeedbe the maximum value attainable in the case the surface radiation is not 100% polarized.Since in this situation the estimate of the polarization degree at the emission may beuncertain, they claim that “only very high degrees of linear polarization (& 50%) wouldbe the indisputable footprint of QED birefringence effects”. However, Mignani et al.(2017) have clearly shown that, once all the available observational constraints areaccounted for, a 16% polarization degree is indeed sufficient for a strong statement on thepresence of QED effects even considering the worst case of surface blackbody radiation100% polarized in the extraordinary mode.Furthermore, Capparelli, Maiani & Polosa (2017) consider the source as a magnetarcandidate, with a surface magnetic field B ∼ 1014 G. This is incorrect, since RX J1856belong to the neutron star class known as the XDINSs (see e.g. Turolla 2009, for areview), and its spin-down magnetic field is ∼ 1013 G, one order of magnitude lower (van– 9 –Kerkwijk & Kaplan 2008). Besides the effects on the polarization observables, this mayalso impact on their analysis on axion-like particle effects on the polarization signal.5. ConclusionsCapparelli, Maiani & Polosa (2017) state “Finally, even if we assume that everysingle point of the star emits polarized light, then a degree of polarization of 16% maybe reached in the absence of QED effects just by a favourable orientation of the magneticaxis of the star with respect to the observation line, as is also evident from some modelsanalyzed in Mignani et al. (2017).” However, by performing a careful analysis (i.e. takinga dipolar magnetic field on the star surface, computing the polarization observables fromphase-averaged Stokes parameters and accounting for the geometrical constraints givenby the observations), we showed that the minimum polarization degree sufficient for aconclusive claim about vacuum birefringence effects for RX J1856 is indeed much lowerthan the maximum polarization attainable, which is not 40% but rather . 14%. Hence,the claim put forward by Capparelli, Maiani & Polosa (2017) is totally unjustified.DGC acknowledges a Becas-Chile CONICYT Fellowship (No. 72150555).– 10 –REFERENCESCapparelli, L.M., Maiani, L., Polosa, A.D. 2017, preprint (arXiv:1705.01540)della Valle, F. et al. 2014, Phys Rev. D 90, 092003González Caniulef D., Zane S., Taverna R., Turolla R., Wu K., 2016, MNRAS, 459, 3585Harding, A.K., Lai, D. Reports on Progress in Physics, 69, 2631Heyl J.S., Shaviv N.J., 2000, MNRAS, 311, 555Heyl J.S., Shaviv N.J., 2002, Phys. Rev. D, 66, 023002Ho W. C. G., 2007, MNRAS, 380, 71Mignani, R.P., Testa, V., Gonzàlez Caniulef, D., Taverna, R., Turolla, R., Zane, S., Wu,K. 2017, MNRAS, 465, 492Popov, S.B., Taverna, R., Turolla, R. 2017, MNRAS, 464, 4390Taverna, R., Turolla, R., González Caniulef, D., Zane, S. 2015, MNRAS, 454, 3254Tiengo, A., Mereghetti, S. 2007, ApJ, 657, L101Turolla, R. 2009, Astrophysics and Space Science Library, 357, 141van Kerkwijk, M.H., Kaplan, D.L. 2008, ApJ, 673, L16This manuscript was prepared with the AAS LATEX macros v5.2.

A Comment on "A note on polarized light from Magnetars: QED effects and axion-like particles" by L.M. Capparelli, L. Maiani and A.D. Polosa

A Comment on "A note on polarized light from Magnetars: QED effects and
  axion-like particles" by L.M. Capparelli, L. Maiani and A.D. Polosa

A Comment on "A note on polarized light from Magnetars: QED effects and axion-like particles" by L.M. Capparelli, L. Maiani and A.D. Polosa

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