Highly polarized components of integrated pulse profiles
aa r X i v : . [ a s t r o - ph . H E ] A ug MNRAS , 1–9 (0000) Preprint 14 October 2018 Compiled using MNRAS L A TEX style file v3.0
Highly polarized components of integrated pulse profiles
P. F. Wang ⋆ and J. L. Han National Astronomical Observatories, Chinese Academy of Sciences. A20 Datun Road, Chaoyang District, Beijing 100012, China
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Highly polarized components of pulse profiles are investigated by analyzing observationaldata and simulating the emission processes. The highly polarized components appear at theleading or trailing part of a pulse profile, which preferably have a flat spectrum and a flatpolarization angle curve compared with the low polarized components. By considering theemission processes and propagation effects, we simulate the distributions of wave modes andfractional linear polarization within the entire pulsar emission beam. We show that the highlypolarized components can appear at the leading, central, and/or trailing parts of pulse profilesin the models, depending on pulsar geometry. The depolarization is caused by orthogonalmodes or scattering. When a sight line cuts across pulsar emission beam with a small im-pact angle, the detected highly polarized component will be of the O mode, and have a flatpolarization angle curve and/or a flat spectrum as observed. Otherwise, the highly polarizedcomponent will be of the X mode and have a steep polarization angle curve.
Key words: pulsars: general – polarization – acceleration of particles
Integrated pulse profiles are obtained by integrating tensof thousands of individual pulses. Features of pulse pro-files have been investigated to understand the geometry andphysical processes within pulsar magnetosphere (e.g. Rankin1983; Lyne & Manchester 1988; Kramer et al. 1994; Noutsos et al.2015). Integrated pulse profiles generally comprise several com-ponents, and are characterized by diverse polarization fea-tures, including prominent linear polarization, ‘S’-shaped po-larization angle curves, single sign or sign reversals of circu-lar polarization. Some integrated pulse profiles are highly po-larized for the whole pulse, even 100% polarized such as PSRB1259-63 and B1823-13. These pulsars are generally youngand have very high spin-down luminosity ˙ E and flat spectrum(Qiao et al. 1995; von Hoensbroech et al. 1998; Crawford et al.2001; Weltevrede & Johnston 2008). Some pulsars have highlylinearly polarized leading or trailing components, for exam-ple, the leading components of PSRs B0355+54 and B0450+55(Lyne & Manchester 1988; von Hoensbroech & Xilouris 1997;Gould & Lyne 1998), and the trailing components of PSRs B1650-38 and B1931+24 (Karastergiou et al. 2005; Han et al. 2009).von Hoensbroech et al. (1998) noticed that the highly polarizedleading component of PSR B0355+54 has a flat spectrum and be-comes increasingly prominent at higher frequencies. The highly po-larized trailing component of PSR B2224+65 has a flat polarizationangle curve (Mitra & Rankin 2011). ⋆ E-mail: [email protected]
Theoretical efforts have been made to understand various po-larization features. In general, pulsar polarizations are closely re-lated to the emission processes of the relativistic particles stream-ing along the curved magnetic field lines (e.g. Blaskiewicz et al.1991; Wang et al. 2012), the propagation effects within pulsarmagnetosphere (e.g. Barnard & Arons 1986; Wang et al. 2010;Beskin & Philippov 2012), and the scattering within the interstel-lar medium (Li & Han 2003). However, these investigations havebeen conducted separately on each aspect, rarely done jointly.Curvature radiation which serves as one of the most proba-ble mechanisms for pulsar emission can produce highly polar-ized emission (Gangadhara 2010; Wang et al. 2012). Propaga-tion effects are succeeded in demonstrating the interaction ofthe ordinary (O) and extra-ordinary (X) modes within pulsarmagnetosphere and can lead to diverse depolarization features(Cheng & Ruderman 1979; Barnard & Arons 1986; Wang et al.2010; Beskin & Philippov 2012), though initial ratios for bothmodes are uncertain. Propagation effects within the interstellarmedium need to be investigated further. Recently, we investigatedthe emission processes jointly with propagation effects (Wang et al.2014, 2015), which provides us a new opportunity to understandthe highly polarized components, because distributions of the X-mode and O-mode within pulsar magnetosphere are related to thedepolarization across pulsar emission beam by considering the re-fraction and corotation effects. Emission can be highly depolarizedin some beam regions where both modes have comparable inten-sities, but dominated by one mode in other regions and hence theresulting profile can be highly polarized.In this paper, we summarize observations for highly polarizedcomponents of integrated pulse profiles in literature and then theo- c (cid:13) P. F. Wang and J. L. Han
Figure 1.
Highly polarized leading component of PSR J1048-5832 and trailing component of J2225+6535 at three frequencies to show their frequencyevolution. The solid lines stand for the total intensities, the dashed and dashed-dotted lines represent the linear and circular polarizations, respectively. Theposition angle curves are shown by dotted lines at the upper part of each panel. The polarization data are collected from literature as listed in Table 1. retically explain them by modeling emission and propagation pro-cesses. In Section 2, we analyze various features for highly polar-ized components of observed pulsar profiles. In Section 3, we sim-ulate polarized pulsar beams and pulse profiles by considering theemission processes and propagation effects. Discussions and con-clusions are given in Section 4.
The highly polarized components of integrated pulse profiles ex-hibit diverse polarization features. To demonstrate the properties, asample of 78 pulsars is collected from literatures, as listed in Ta-ble 1. Among them, 20 pulsars have highly polarized leading com-ponents, 11 pulsars have highly polarized trailing components, fourmillisecond pulsars have both highly polarized leading and/or trail-ing components, and 43 pulsars are highly polarized for the wholepulse profile. The fractional linear polarization is larger than 70%for highly polarized components or the whole profile for these pul-sars at more than one frequency.
Multi-frequency observations demonstrate that pulsar flux densitygenerally decreases with frequency, following a power-law spec-trum (e.g. Sieber 1973). Different components for a given pulsarcould evolve differently with frequency. For example, the relative spectra for the leading and trailing components are diverse for theconal double pulsars (Wang et al. 2001). The highly polarized com-ponents also show frequency evolution. Fig. 1 shows the polar-ized pulse profiles at three frequencies for two pulsars, J1048-5832and J2225+6535. PSR J1048-5832 exhibits highly polarized lead-ing component with polarization degree approaching 100%. At 692MHz, the peak intensity of the highly polarized leading componentis weaker than the low polarized trailing component. As observa-tion frequency increases, the highly polarized leading componentgradually dominates, as shown by the profiles of 1369 and 3068MHz. Similar features have been seen from PSRs J0358+5413,J0454+5543, J1057-5226IP, J1825-0935MP and J1844+1454. Incontrast, PSR J2225+6535 is an example for highly polarized trail-ing component, which becomes dominant as observation frequencyincreases. Similar cases can be found from PSRs J0601-0527,J0922+0638 and J1539-5626.Figs. 2 and 3 quantitatively demonstrate the frequency evo-lution of the peak intensity ratios, I HiP / I LowP , of the highly po-larized components with respect to the low polarized ones at a se-ries of frequencies, see data in Tables A1 and A2 in the Appendix.Clearly, I HiP / I LowP generally increases with frequency for highlypolarized leading or trailing components, and can be described bya power-law, though the power-law indices vary from 0.35 to 1.79for different pulsars. We conclude that the highly polarized compo-nents exhibit a flatter spectrum than the low polarized components,regardless of its location at the leading or trailing phase.
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MNRAS000 , 1–9 (0000) ighly polarized components of pulsars Table 1.
Highly polarized components of 78 pulsars in literature.PSR Jname Bname Period DM Polarization Features References(s) ( cm − pc )J0014+4746 B0011+47 1.24069 30.8 Leading 31, 70, 86J0358+5413 B0355+54 0.15638 57.1 Leading, Flat Spec., Orth. Modes 8, 9, 16, 20, 24, 26, 30, 31, 34, 77, 81J0454+5543 B0450+55 0.34072 14.5 Leading, Flat Spec., Flat PA 16, 20, 30, 31, 81J0814+7429 B0809+74 1.29224 5.7 Leading, Orth. Modes 1, 9, 30, 31, 44, 58, 78, 88J0942-5657 B0941-56 0.80812 159.7 Leading 23, 33, 69, 90J0954-5430 0.47283 200.3 Leading 69, 90J1048-5832 B1046-58 0.12367 129.1 Leading, Flat Spec. 23, 56, 59, 69, 76, 89, 90J1057-5226IP B1055-52 0.19710 30.1 Leading, Flat Spec. 4, 6, 12, 16, 29, 69, 72, 77, 89, 90J1112-6103 0.06496 599.1 Leading, Scattering 69, 89, 90J1341-6220 B1338-62 0.19333 717.3 Leading, Scattering 23, 39, 59, 60, 69, 90J1410-6132 0.05005 960.0 Leading, Scattering 68, 69, 89, 90J1453-6413 B1449-64 0.17948 71.0 Leading, Flat PA, Orth. Modes 5, 6, 7, 29, 54, 59, 69, 71, 81, 90J1730-3350 B1727-33 0.13946 259.0 Leading, Scattering 31, 39, 59, 69, 89, 90J1805+0306 B1802+03 0.21871 80.8 Leading, Flat PA 31, 38J1823-3106 B1820-31 0.28405 50.2 Leading 21, 31J1825-0935MP B1822-09 0.76900 19.3 Leading, Flat Spec., Orth. Modes 7, 9, 24, 29, 30, 31, 49, 61, 63, 65, 73, 77J1844+1454 B1842+14 0.37546 41.4 Leading, Flat Spec., Flat PA 17, 31, 38, 54, 65, 74, 77, 81, 90J1849+2423 0.27564 62.2 Leading 70J1937+2544 B1935+25 0.20098 53.2 Leading, Flat PA 31, 38, 63, 70, 81, 90J2008+2513 0.58919 60.5 Leading, Orth. Modes 70J0601-0527 B0559-05 0.39596 80.5 Trailing, Flat Spec., Flat PA 20, 23, 31, 34, 54, 69, 90J0922+0638 B0919+06 0.43062 27.2 Trailing, Flat Spec., Orth. Modes 13, 19, 24, 29–31, 38, 49, 54, 5962, 65, 74, 81, 90J1401-6357 B1358-63 0.84278 98.0 Trailing 21, 23, 29J1539-5626 B1535-56 0.24339 175.8 Trailing, Flat Spec., Flat PA 23, 56, 59, 69, 90J1548-5607 0.17093 315.5 Trailing 69, 90J1653-3838 B1650-38 0.30503 207.2 Trailing 56, 69, 90J1739-1313 1.21569 58.2 Trailing 69, 90J1808-3249 0.36491 147.3 Trailing 56, 69, 90J1933+2421 B1931+24 0.81369 106.0 Trailing 31, 70J2013+3845 B2011+38 0.23019 238.2 Trailing, Flat PA 31, 81J2225+6535 B2224+65 0.68254 36.0 Trailing, Flat Spec., Flat PA 9, 16, 31, 77, 86, 88J0737-3039A 0.02269 48.9 MSP, Leading&Trailing 47, 55, 57, 82Flat PA, Orth. ModJ1012+5307 0.00525 9.0 MSP, Trailing, Flat PA 35, 37, 70, 88J1022+1001 0.01645 10.2 MSP, Trailing 35–37, 46, 48, 52, 80, 84, 85, 87, 88J1300+1240 B1257+12 0.00621 10.1 MSP, Leading 35, 70J0108-1431 0.80756 2.3 Whole 33, 69, 90J0134-2937 0.13696 21.8 Whole 33, 65, 69, 71, 90J0139+5814 B0136+57 0.27245 73.7 Whole 16, 20, 30, 31, 81, 86, 88J0538+2817 0.14315 39.5 Whole 30, 81J0543+2329 B0540+23 0.24597 77.7 Whole, Pol. dec. with freq. 9, 10, 17, 19, 24, 30, 31, 38, 4953, 63, 65, 69, 74, 77, 81, 90J0614+2229 B0611+22 0.33495 96.9 Whole, Strong CP 10, 16, 19, 31, 34, 38, 53, 63, 65, 69, 74J0630-2834 B0628-28 1.24441 34.4 Whole 5, 6, 7, 9, 16, 29, 31, 34, 54, 59, 65, 69, 81, 90J0631+1036 0.28780 125.3 Whole 27, 69, 75, 89, 90J0659+1414 B0656+14 0.38489 13.9 Whole 17, 31, 38, 40, 53, 59, 63, 64, 69, 7475, 81, 89, 90J0742-2822 B0740-28 0.16676 73.7 Whole 6, 7, 9, 16, 24, 29–31, 33, 49, 54, 5961, 69, 71, 75, 77, 81, 83, 89, 90J0835-4510 B0833-45 0.08932 67.9 Whole, Strong CP 2, 3, 5–7, 11, 29, 43, 54, 59, 6169, 71, 76, 81, 89, 90J0901-4624 0.44199 198.8 Whole, Strong CP 69, 90J0905-5127 0.34628 196.4 Whole 69, 90J0908-4913 B0906-49 0.10675 180.3 Whole, Inter Pulse 21, 23, 32, 59, 66, 69, 76, 89, 90J1015-5719 0.13988 278.7 Whole 60, 69, 90J1028-5819 0.09140 96.5 Whole 67, 69, 89J1057-5226MP B1055-52 0.19710 30.1 Whole 4, 6, 12, 16, 29, 69, 72,77, 89, 90J1105-6107 0.06319 271.0 Whole 39, 60, 69, 89, 90MNRAS , 1–9 (0000) P. F. Wang and J. L. Han
Table 1.
Highly polarized components differ from low polarized compo-nents also in polarization angle curves. Table 2 summarizes thegradients of polarization angle curves for 35 pulsars extracted fromTable 1. The highly polarized components generally have flat po-larization angle curves. For example, the gradient of polarizationangle curve for the highly polarized trailing component of PSR J2225+6535 in Fig. 1 approximates to be -0.1 at 325MHz, but itis -3.7 for the low polarized leading component (Mitra & Rankin2011). The gradient is 2.4 for the highly polarized leading com-ponent of PSR J1844+1454 at 1.4GHz, but 17.0 for low polarizedtrailing component (Johnston et al. 2005). The large difference forthe gradients can also be found for PSRs J0454+5543, J1453-6413,J1805+0306, J1937+2544 and J0601-0527, as listed in Table 2. Itimplies that the highly polarized emission of these pulsars might
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MNRAS000 , 1–9 (0000) ighly polarized components of pulsars Figure 2.
The frequency evolution for the peak intensity ratio of the highlypolarized leading components for six pulsars with respect to the low polar-ized trailing ones. The intensity ratios are listed in Table A1, which can bedescribed by a power-law as I HiP / I LowP ∼ a ν k . Figure 3.
Same as Fig. 2 but for the highly polarized trailing componentsfor four pulsars. Data are listed in Table A2. be generated from the beam regions well away from the magneticmeridional plane.However, the highly polarized emission of some pulsars mightalso be produced near the meridional plane, e.g. J0942-5657 andJ1933+2421. Both of them have very steep polarization anglecurves with gradients of 14.2 and 9.4 for the highly polarized com-ponents. Gradients for low polarized components of many pulsarsare hard to determine due to various reasons as noted in the fifthcolumn of Table 2.As shown in Fig. 4, the gradients of polarization angle curvesfor the highly polarized components are concentrated near 0.0. Thegradients for the low polarized components have fewer data but arewidely distributed. We therefore conclude that the highly polarizedemission tends to have a flat polarization angle curve.
Table 2.
Gradients of polarization curves for the highly polarized and lowpolarized components. References are numbered in Table A1.
PSR Hi. Pol. Comp. Freq. ∆ PA/ ∆ φ ∆ PA/ ∆ φ Ref.(GHz) High Pol. Comp. Low Pol. Comp.J0454+5543 Leading 1.41 − . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . . ± . − . ± . − . ± . . ± . . ± . − . ± . − . ± . − . ± . Orth. Modes 31J0814+7429 Leading 1.41 − . ± . Orth. Modes 30J1825-0935 Leading 0.691 . ± . Orth. Modes 63J2008+2513 Leading 0.774 . ± . Orth. Modes 70J0922+0638 Trailing 0.692 . ± . Orth. Modes 90J1112-6103 Leading 1.5 − . ± . Scattering 693.0 − . ± . - 69J1341-6220 Leading 1.5 . ± . Scattering 603.0 . ± . - 60J1410-6132 Leading 1.5 . ± . Scattering 693.1 . ± . - 68J1730-3350 Leading 1.5 − . ± . Scattering 693.0 − . ± . - 69J0014+4746 Leading 0.774 − . ± . − . ± . . ± . . ± . . ± . . ± . . ± . Mixed 69J1048-5832 Leading 1.369 . ± . Mixed 90J1823-3106 Leading 1.4 − . ± . Mixed 31J1401-6357 Trailing 0.955 . ± . Mixed 29J1739-1313 Trailing 1.377 . ± . Mixed 90J2013+3845 Trailing 1.408 − . ± . Mixed 31J1849+2423 Leading 0.774 − . ± . Weak Pol. 70J1539-5626 Trailing 1.5 . ± . Weak Pol. 69J1548-5607 Trailing 1.4 . ± . Weak Pol. 90J1653-3838 Trailing 1.377 . ± . Weak Pol. 90J1808-3249 Trailing 1.377 − . ± . Weak Pol. 90J1933+2421 Trailing 0.774 . ± . Weak Pol. 70J0737-3039A MSP-Leading 1.4 . ± . Orth. Modes 82MSP-Trailing 1.4 . ± . - 82J1012+5307 MSP-Trailing 0.774 − . ± . Mixed 70J1022+1001 MSP-Trailing 1.3 . ± . . ± . . ± . Weak Pol. 70Note: Gradients of polarization angle curves for the low polarized components are hard to determinedue to various reasons as listed in the fifth column.
Figure 4.
Histograms for absolute values of gradients of the polarization an-gle curves for highly polarized and low polarized components. The gradientvalues are listed in Table 2.MNRAS , 1–9 (0000)
P. F. Wang and J. L. Han
There are two mechanisms for depolarization of pulsar profiles:orthogonally polarized radiation and scattering within the inter-stellar medium. Single pulse observations (e.g. Stinebring et al.1984a,b) show the orthogonal modes of pulsar emission, andhighly polarized components of integrated profiles are generallyof one mode. The orthogonal modes often depolarize the inte-grated profiles and lead to low polarized components, as shownfor PSRs J0814+7429 and J0922+0638 by Stinebring et al. (1984a)and Ramachandran et al. (2002). PSRs J0358+5413, J1825-0935and J2008+2513 also show orthogonal modes and have depolarizedtrailing components, as listed in Table 2.Scattering during the propagation of pulsed emission in the in-terstellar medium can also cause depolarization at the trailing partsof profiles and result in a flat polarization angle curve (Li & Han2003). For example, PSR J1112-6103 has a dispersion measureof 599.1 and has two highly polarized components at 3.1GHz(Weltevrede & Johnston 2008). But at frequencies below 1.5GHz,the effect of scattering becomes very significant and causes depo-larization in the trailing part. The polarization angle curves are alsoflattened, as indicated by the gradient values in Table 2. The otherthree pulsars, PSRs J1341-6220, J1410-6132 and J1730-3350 showsimilar polarization profiles due to scattering.Millisecond pulsars exhibit highly polarized components asthe normal pulsars. PSR J0737-3039A is an orthogonal rotator andhas an inter-pulse. The leading part of the main pulse and the trail-ing part of the interpulse are highly linearly polarized with a nearlyconstant position angle. The gradient of polarization angle curveis near 0.0 as listed in Table 2. Orthogonal modes might happenat the trailing part of the main pulse and the leading part of theinterpulse (Guillemot et al. 2013). PSR J1012+5307 is an alignedrotator and has emission at almost all rotation phases. The trailingpart of the brightest component and all the other components arehighly linearly polarized (Stairs et al. 1999; Han et al. 2009). Theswing of polarization angle is nearly flat at all these phases. PSRsJ1022+1001 and J1300+1240 show similar polarization features.
It can be summarized from observations that the highly polarizedcomponents preferably have a flat spectrum and a flat polarizationangle curve. Orthogonal modes and scattering could cause depolar-ization. Millisecond pulsars exhibit similarly highly polarized com-ponents as the normal pulsars. After we analyze literature data touncover these features for highly polarized components, we herecarry out numerical simulations of emission processes and propa-gation effects to understand the polarization.
In general, pulsar magnetosphere is assumed to be an dipole, B = B ⋆ ( R ⋆ r ) [3ˆ r (ˆ r · ˆ m ) − ˆ m ] , (1)here R ⋆ and B ⋆ represent neutron star radius and the magnetic fieldon its surface, ˆ r and ˆ m are the unit vectors along r and the mag-netic dipole moment. The magnetic axis inclines to the rotation axisby an inclination angle α . It rotates freely in space. Relativisticparticles with a Lorentz factor of γ are produced by the sparking Figure 5.
The distributions of wave modes and fractional linear polarizationwithin simulated pulsar emission beam. The upper panels are plotted forthe X-mode and O-mode intensities, I X and I O . The bottom panel showsthe degree of linear polarization. Seven density patches labeled as a , b , c , d , e , f and g are shown in the figure and their locations are listed inTable 3. Example sight lines at ζ = 31 o and o from the rotation axisof a neutron star are indicated by the dashed lines. Other pulsar parametersused for simulations are the inclination angle of the magnetic axis from therotation axis α = 30 o and pulsar period P = 1 s . Relativistic particles areassumed to have a Lorentz factor of γ = 500 , and emit at 1.4GHz. processes above the polar cap. They stream out along the curvedmagnetic field lines and co-rotate with pulsar magnetosphere. Asinfluenced by the perpendicular acceleration, relativistic particleswill produce curvature radiation. The radiation field E ( t ) and itsFourier components E ( ω ) can be calculated by using circular pathapproximation (Wang et al. 2012). Curvature radiation at a givenposition of pulsar magnetosphere actually contains the contribu-tions from all the nearby field lines within a /γ cone around thetangential direction. The polarization patterns of emission cones arefurther distorted by rotation effects, as demonstrated by Wang et al.(2012).In general, there are four wave modes (two transverseand two longitudinal) in the plasma of pulsar magnetosphere(Beskin & Philippov 2012). Two modes are damped at large dis-tances from the neutron star in the magnetosphere. Only the X-mode and superluminous O-mode, hereafter the O-mode, can es-cape from the magnetosphere to be observed. Immediately afterthe waves are generated in the emission region, they are coupledto the local X-mode and O-mode to propagate outwards. Withinthe /γ emission cone, both components have comparable intensi-ties and propagate separately. The X-mode component propagatesin a straight line, while the O-mode component suffers refraction MNRAS000
The distributions of wave modes and fractional linear polarizationwithin simulated pulsar emission beam. The upper panels are plotted forthe X-mode and O-mode intensities, I X and I O . The bottom panel showsthe degree of linear polarization. Seven density patches labeled as a , b , c , d , e , f and g are shown in the figure and their locations are listed inTable 3. Example sight lines at ζ = 31 o and o from the rotation axisof a neutron star are indicated by the dashed lines. Other pulsar parametersused for simulations are the inclination angle of the magnetic axis from therotation axis α = 30 o and pulsar period P = 1 s . Relativistic particles areassumed to have a Lorentz factor of γ = 500 , and emit at 1.4GHz. processes above the polar cap. They stream out along the curvedmagnetic field lines and co-rotate with pulsar magnetosphere. Asinfluenced by the perpendicular acceleration, relativistic particleswill produce curvature radiation. The radiation field E ( t ) and itsFourier components E ( ω ) can be calculated by using circular pathapproximation (Wang et al. 2012). Curvature radiation at a givenposition of pulsar magnetosphere actually contains the contribu-tions from all the nearby field lines within a /γ cone around thetangential direction. The polarization patterns of emission cones arefurther distorted by rotation effects, as demonstrated by Wang et al.(2012).In general, there are four wave modes (two transverseand two longitudinal) in the plasma of pulsar magnetosphere(Beskin & Philippov 2012). Two modes are damped at large dis-tances from the neutron star in the magnetosphere. Only the X-mode and superluminous O-mode, hereafter the O-mode, can es-cape from the magnetosphere to be observed. Immediately afterthe waves are generated in the emission region, they are coupledto the local X-mode and O-mode to propagate outwards. Withinthe /γ emission cone, both components have comparable intensi-ties and propagate separately. The X-mode component propagatesin a straight line, while the O-mode component suffers refraction MNRAS000 , 1–9 (0000) ighly polarized components of pulsars Table 3.
Assumed seven density patches within a pulsar emission beam.Here, θ i and φ i represent the peak positions for the Gaussian densitypatches in the magnetic colatitude θ and azimuth φ directions within rangesof < θ i < and − o < φ i < o . σ θ and σ φ represent the widthof Gaussian distribution of the density distribution of particles.Index θ i φ i ( o ) σ θ σ φ ( o ) a b c d e f g (Barnard & Arons 1986). Hence, both mode components are sepa-rated (Wang et al. 2014). The detectable emission at a given posi-tion consists of incoherent superposition of X-mode and O-modecomponents coming from discrete emission regions. Both modecomponents experience ‘adiabatic walking’, wave mode coupling,and cyclotron absorption (Wang et al. 2010; Beskin & Philippov2012).These emission processes and propagation effects have beenconsidered jointly by Wang et al. (2014) for four particle densitymodels in the form of uniformity, cone, core and patches. Wedemonstrated that refraction and co-rotation significantly affectpulsar polarizations. Refraction bends O-mode emission towardsthe outer part of pulsar emission beam, and causes the separationof both modes. Co-rotation will lead to different ratios for bothmodes at different parts of pulsar emission beam. Investigations onthe influences of both effects have been extended to a wide rangeof frequencies, and succeeded in demonstrating the frequency de-pendence of pulsar linear polarization (Wang et al. 2015).Based on our previous studies (Wang et al. 2012, 2014, 2015),we here simulate the curvature radiation processes and propaga-tion effects, but focus mainly on the distribution of highly polarizedemission regions within pulsar emission beam. Fig. 5 represents avery typical case for the distributions of wave modes and fractionallinear polarization, based on an uniform density model demon-strated in Wang et al. (2014). It shows that the intensity distribu-tions for both modes are quite different. The X-mode components, I X , are stronger at the two sides of pulsar beam in the ζ direction,as shown in the top left panel of Fig. 5, while I O are stronger atthe two sides of pulsar beam in the ϕ direction, as shown in thetop right panel of Fig. 5. Here, ζ is the sight line angle, i.e., theangle between sight line and the rotation axis, ϕ represents the ro-tation phase. Depolarization is caused by two modes. Some regionsin emission beam is dominated by one mode that can be highly po-larized. The depolarization leads the distribution of fractional linearpolarization | I X − I O | / | I X + I O | to be quadruple. It implies that thehighly polarized emission could be produced at four parts of pulsaremission beam, i.e., the leading (O-mode), trailing (O-mode), top(X-mode) and bottom (X-mode) parts of the beam.In order to demonstrate the formation of highly polarized com-ponents, seven density patches ( a , b , c , d , e , f and g ) are simulatedas listed in Table 3. As shown in the bottom panel of Fig. 5, patches a and d are dominated by the O-mode emission, while patch f by the X-mode. The emission from these regions should have alarge fraction of linear polarization. However, emission from den-sity patches b , c and e have both the X and O modes with compa- Figure 6.
Pulse profiles resulting from the cut of density patches ( a , b ) and( c , d ) to explain the highly polarized leading and trailing components, de-pending on the available density patches in the emission region. The soldlines represent the total intensity, the dashed and dotted lines are for the lin-ear polarization and polarization angle curves. The wave modes are markednear the polarization angle curves. rable intensity, hence the observed emission from these regions isdepolarized. When a sight line has a small impact angle, β , i.e., ζ − α , cut-ting across pulsar emission beam, it will detect emissions from thedensity patches a , b , c and d in Fig. 5. The resulting pulse pro-files are shown in Fig. 6, depending on the available density patchcombinations, for example ( a , b ) or ( c , d ). We can conclude fromsimulations that:1) The highly polarized components can be generated from theleading (patch a ) and the trailing (patch d ) parts of pulsar emissionbeam, both of which are dominated by the O-mode.2) The highly polarized components have a flat polarizationangle curve, because density patches a and d are away from themeridional plan of ϕ = 0 o .3) The low polarized components exhibit orthogonal modes,and the emission from the X and O modes has comparable intensity.Orthogonal mode jump happens when one mode dominates overthe other, as shown by the polarization angle curves.In addition, the simulations predict that the highly polarizedcomponents are more likely to be generated at the leading parts ofpulse profiles, because the highly polarized leading part of pulsaremission beam is broader than the trailing one (see Fig.5) due torotation-induced asymmetry. Highly polarized components wouldhave a flatter spectrum than the low polarized components, becausethe beam regions further away from the magnetic axis tend to havea flat spectrum according to Lyne & Manchester (1988), while thedetailed spectrum behavior is not modeled in our simulations. When a sight line has a large impact angle to cut across the pulsaremission beam, it will detect emission from density patches e , f and g in Fig. 5. The resulting pulse profiles are shown in Fig. 7 fordifferent patch combinations ( e , f ), ( f , g ) or ( e , f , g ) for availabledensity distributions of particles. Highly polarized components canappear at the leading, central or trailing part of pulse profiles. Theseprofiles have similar features as those in Fig. 6, but differences areas following.1) The highly polarized component from the bottom part, i.e., MNRAS , 1–9 (0000)
P. F. Wang and J. L. Han
Figure 7.
Same as Fig. 6 but for density patch combinations of ( e , f ), ( f , g ) and ( e , f , g ). density patch f , of pulsar emission beam is dominated by the X-mode, rather than the O-mode.2) Highly polarized component has a steeper polarization an-gle curve, because the component is generated near the merid-ional plane, where the polarization angle has the maximum rateof change approximating ( dP A/dϕ ) max = sin α/ sin β . The gra-dient is inversely proportional to the impact angle β .3) Highly polarized component may have a similar spectrumto the low polarized components, since all components are gener-ated at comparable distances from the magnetic axis.In summary, joint simulations of emission processes and prop-agation effects demonstrate that highly polarized components canbe produced at the leading, central and trailing parts of pulse pro-files. The properties of emission components, polarization anglecurve, mode characteristic and spectrum, depend on pulsar geome-try and the density patches of radiating particles. In this paper, we have investigated the highly polarized componentsof integrated pulse profiles observationally and theoretically. Wefound from observational data that:(i) Highly polarized components of pulsar profiles have a flat-ter spectrum than the low polarized components, regardless of theirlocations at the leading or trailing phase;(ii) Highly polarized components tend to have a flat polariza-tion angle curve, though a small fraction of pulsars have very steeppolarization angle curves;(iii) Highly polarized components generally have one mode,while the low polarized components often show orthogonal modes;(iv) Significant scattering will cause depolarization at the trail-ing parts of pulse profiles and result in flat polarization anglecurves;(v) Millisecond pulsars can have highly polarized componentsas normal pulsars. We simulated emission processes and propagation effectswithin pulsar magnetosphere, and found that highly polarized emis-sion could be produced at the leading (O-mode), trailing (O-mode),top (X-mode) and bottom (X-mode) parts of pulsar emission beam.When a sight line cuts across the beam with different impact angles,the detected highly polarized components have different properties,depending on the specific geometry and available density patchesof the radiating particles:(i) Highly polarized component generated from the leading ortrailing part of pulsar emission beam is of the O-mode, and has aflat polarization angle curve;(ii) Highly polarized component generated from the top or bot-tom part of pulsar emission beam is of the X-mode, and has a steeppolarization angle curve.In the observational aspect, polarization observations at mul-tiple frequencies are important to reveal the frequency depen-dencies of intensities and polarization degrees of the compo-nents. The polarization observations should have higher signal tonoise ratio and time resolution. For example, PSR J1048-5832 ap-peared to have one component at 1.44GHz due to limited timeresolution (Qiao et al. 1995), but it is clearly resolved to twocomponents by the recent polarization observations at 1.5GHz(Weltevrede & Johnston 2008), which show clearly the gradientdifferences of polarization angle curves between the highly polar-ized and low polarized components. In addition, single pulse ob-servations can help to identify the wave modes and depolarizationprocesses (Stinebring et al. 1984a,b).In the theoretical aspect, our simulations here represent thefurther development of joint researches on the emission processesand propagation effects (Wang et al. 2014) and focus mainly onthe properties for the highly polarized components within the wavemode separated magnetosphere. Note, however that in our currentcalculations, the magnetic field is assumed to be a rotating dipolefor an empty magnetosphere. Radiation correction is neglected, andthe effect of loaded plasma on magnetic fields is not yet incorpo-rated. Furthermore, the energy and density distributions of relativis-tic particles are assumed to follow a simple model. Therefore, theconclusions and predictions under these assumptions may be al-tered if more complicated pulsar magnetosphere is considered.
ACKNOWLEDGEMENTS
This work has been supported by the National Natural ScienceFoundation of China (11403043, 11473034 and 11273029), and theStrategic Priority Research Programme “The Emergence of Cos-mological Structures” of the Chinese Academy of Sciences (GrantNo. XDB09010200).
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APPENDIX A: PEAK INTENSITY RATIOS FOR HIGHLYAND LOW POLARIZED COMPONENTS
Tables A1 and A2 list the peak intensity ratios, I HiP / I LowP , of thehighly polarized components at the leading and trailing part of pro-files with respect to the low polarized components at a series offrequencies.
MNRAS , 1–9 (0000) P. F. Wang and J. L. Han
Table A1.
The ratios for peak intensities of highly polarized leading com-ponents, I HiP , with respect to low polarized ones, I LowP , at a series offrequencies. References are numbered in Table A1.PSR Freq.(GHz) I HiP / I LowP
ReferencesJ0358+5413 0.234 < . < . . ± .
16, 310.610 . ± . . ± . . ± . . ± . . ± . . ± .
9, 202.65 . ± .
8, 94.85 . ± .
30, 34, 818.7 . ± . . ± .
24, 30, 3432.0 > . . ± . . ± .
16, 310.610 . ± . . ± . . ± .
30, 311.642 . ± . . ± . . ± .
30, 81J1048-5832 0.692 . ± . . ± . . ± . . ± . . ± .
56, 906.387 . ± . . ± .
59, 90J1057-5226IP 0.17 . ± . . ± . . ± .
6, 120.64 . ± . . ± . . ± . . ± .
4, 72, 901.5 . ± . . ± .
69, 90J1825-0935MP 0.243 . ± . . ± .
65, 73, 770.408 . ± . . ± . . ± .
63, 650.925 . ± . . ± . . ± .
30, 49, 61, 651.612 . ± . . ± .
61, 63, 654.85 . ± . . ± . < .
65, 900.325 < .
65, 77, 900.408 < . . ± . . ± .
65, 900.925 . ± . . ± .
17, 31, 3854, 65, 741.642 . ± . . ± .
65, 90Note: The highly polarized components of PSR J0358+5413 andJ1844+1454 are confused with the corresponding low polarized componentsat frequencies smaller than 0.408 and 0.61GHz.
Table A2.
Same as Table A1 but for highly polarized trailing components.PSR Freq.(GHz) I HiP / I LowP
ReferencesJ0601-0527 0.243 . ± . . ± . . ± . . ± . . ± . . ± . . ± .
31, 54, 901.5 . ± . . ± . . ± . . ± . . ± . . ± . . ± .
65, 900.322 . ± .
62, 65, 900.43 . ± . . ± .
65, 90J1539-5626 0.692 . ± . . ± . . ± . . ± .
56, 69, 906.2 . ± . . ± .
59, 90J2225+6535 0.15 . ± . . ± . . ± . . ± .
16, 310.61 . ± . . ± . . ± . . ± . . ± . . ± .000