Previous studiesDispersion relation and natural wave modes in pulsarmagnetosphere.(Melrose&Stoneham1977,Arons&Barnard1986v0nHoensbroaechet al.1998,Lyubaskii1998, Melroseetal.1999)SpecialPropagation effectsAdiabatic Walking (Cheng &Ruderman 1979)Wavemode coupling (orlimiting-polarization effect)(Cheng&Ruderman1979,Petr0va2000,2006)Circularization (Cheng & Ruderman 1979)RefractiveeffectofO-mode(Melrose1979,Allen&Melrose1982,Barnard&Arons1986,Lyubarskii&Petrova1998.Weltevredeetal.2003.Fussell&Luo2004)Cvclotron absorption(Luo&Melrose2001.2006.Fusselletal.2003)
Previous studies • Dispersion relation and natural wave modes in pulsar magnetosphere. (Melrose & Stoneham 1977, Arons & Barnard 1986, von Hoensbroaech et al. 1998, Lyubaskii 1998, Melrose et al. 1999) • Special Propagation effects – Adiabatic Walking (Cheng & Ruderman 1979) – Wave mode coupling (or limiting-polarization effect) (Cheng & Ruderman 1979, Petrova 2000, 2006) – Circularization (Cheng & Ruderman 1979) – Refractive effect of O-mode (Melrose 1979, Allen & Melrose 1982, Barnard & Arons 1986, Lyubarskii & Petrova 1998, Weltevrede et al. 2003, Fussell & Luo 2004) – Cyclotron absorption (Luo & Melrose 2001, 2006, Fussell et al. 2003)
Dispersion relation and natural wave modes in pulsarmagnetosphereB=00 limit (Tsytovitch & Kaplan 1972;Arons & Barnard 1986)Cyclotronfrequency>>wavefrequencyDon't considerQEDeffectin dielectrictensor.BTwo naturalwavemodesordinary mode,or O-mode1+fnPolanizedink-Bn2 = Nca = 1+ f, cos2 0BO-modeplanew?fn=-w23(1-nβcos 0)2extraordinary mode, or E-modePolarizedperpendiculartok-Bplanen2=1E-modeIn the real case, the two modes are elliptically polarized
B=∞ limit (Tsytovitch & Kaplan 1972; Arons & Barnard 1986) – Cyclotron frequency >> wave frequency – Don’t consider QED effect in dielectric tensor. Two natural wave modes – ordinary mode, or O-mode – extraordinary mode, or E-mode Polarized in k-B plane Polarized perpendicular to k-B plane Dispersion relation and natural wave modes in pulsar magnetosphere k B k B O-mode E-mode In the real case, the two modes are elliptically polarized
Dispersion relation and natural wave modes in pulsarmagnetosphereB-oo limit02nc2k2c2kz=0(0)2DispersionrelationofO-mode302(1 -βck/0)2IntheplasmarestframeInthelabframesubluminous O-mode21/Bcose.m//o=X-modesubluminous O-mode1/cose.superluminous O-modex-mode/w=1/cospg(/)-3/2/β+1/(cos8)superluminous O-mo0.51.5020.51.5o21(@p/w)-3/2ap/w
Dispersion relation and natural wave modes in pulsar magnetosphere Dispersion relation of O-mode In the plasma rest frame In the lab frame B=∞ limit
Propagation effects:Adiabatic walking电场垂直磁场The polarization direction follows方向方向Bfield in adiabatic conditionBEOEPPA-30eiepe8-60PB5010020050010002000S/R*△k/2-ΦBsin20mAdiabaticTad》1i0m+Φgcos20mCondition-UONMake the finalPAdifferentfrom the initial emission
Propagation effects：Adiabatic walking • The polarization direction follows B⊥ field in adiabatic condition • Make the final PA different from the initial emission B⊥ E φB φPA 垂直磁场 方向 电场 方向 Adiabatic Non - Adiabatic Adiabatic Condition
Refractive effect of O-modeMelrose1979,Allen&Melrose1982,Barnard&Arons1986,Lyubarskii&Petrova1998,Weltevredeetal.2003,Fussell&Luo2004)Only happens when wavefrequency is close to proper plasma frequency,nearthe emission height. n is not so close to unity.Refractiondirection dependsonthedensitygradient...Can cause the separation of naturalwaves.=>OPMphenomenon.IsubluminousO-mode2(Melrose1979.Allen&Melrose1982)m/yo=uOutwarddensitydecreasecausesraymodedeviationawayfrommagneticaxis,superluminous O-modewhich maywidentheemissionbeamw./w=1/cosggwidth（(Lyubarskii&Petroya1998)10.51.52OTherefractioninducedwavemodeap/wcouplingmay cause CP with signreversal(Petrova&Lyubarskii2000)
Refractive effect of O-mode • Only happens when wave frequency is close to proper plasma frequency, near the emission height. n is not so close to unity. • Refraction direction depends on the density gradient. • Can cause the separation of natural waves, => OPM phenomenon. (Melrose 1979, Allen & Melrose 1982) • Outward density decrease causes ray deviation away from magnetic axis, which may widen the emission beam width. (Lyubarskii & Petrova 1998) • The refraction induced wave mode coupling may cause CP with sign reversal (Petrova & Lyubarskii 2000) (Melrose 1979, Allen & Melrose 1982, Barnard & Arons 1986, Lyubarskii & Petrova 1998, Weltevrede et al. 2003, Fussell & Luo 2004)