Physics of drifting subpulses Andrzej Szary and Joeri van Leeuwen The Netherlands Institute for Radio Astronomy University of Zielona G´ ora March 27, 2018 Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 1 / 14
Drifting subpulses Discovered by Drake & Craft (1968) The individual pulses consists of subpulses which, in many cases, exhibit systematic variation in position or intensity or both . Taken from ” Handbook of Pulsar Astronomy” by Lorimer & Kramer. Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 2 / 14
Neutron star magnetosphere The force-free state ( E � = 0) The Lorentz force: E + 1 � c ( � r ) × � Ω × � B = 0 E ⊥ = − � v � c × � B The plasma charge density: � Ω · � B ρ GJ = − 2 π c The co-rotation velocity: c ( � E × � B ) � v cor = B 2 Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 3 / 14
The carousel model (Ruderman & Sutherland, 1975) The presence of the gap changes the tangential velocity within the gap and alters the corotation velocity: v cor = c ( E × B ) B 2 A group of localized discharges (” sparks” ) cir- culate around the magnetic pole of the neu- tron star. The carousel model can explain variety of pulsar data (e.g., Gil & Sendyk 2000; Gil & Mitra 2001; Gil et al. 2003; Weltevrede et al. 2006, 2007; Herfindal & Rankin 2007; Rankin & Wright 2008; Herfindal & Rankin 2009), ... . Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 4 / 14
The carousel model problems (Ruderman & Sutherland, 1975) In parts of the polar cap sparks move faster than the corotation (is it possible in plasma starved region?). For the non-dipolar structure of surface magnetic field the magnetic axis may be may be beyond the polar cap. The E × B drift is around the rotation axis not the magnetic axis! ” ... the carousel model is yet an heuristic model that provides frustratingly little physical insight.” (Rankin & Rosen 2014) Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 5 / 14
Spark forming region (Szary & van Leeuwen, 2017) y y x x y x z z x x The electric and magnetic fields within a region of spark formation with screened acceleration ( the left panel ) and during the discharge ( the right panel ). Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 6 / 14
Co-rotating frame of reference The Lorentz transformation E + � v E ′ = � � c × � B y x screened unscreened co-rotating frame Electric field across a spark forming region in the co-rotating frame of reference. Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 7 / 14
The polar cap (electric field) 0.01 0.00 0.01 0.01 0.01 θ (rad) The electric field (the 0.00 0.00 white arrows) across the polar cap for random dis- tribution of sparks. The color map corresponds to 0.01 0.01 the electric potential. The electric potential of V max V min V max a single spark: V min V ′ ∝ ln( r s ) 0.01 0.00 0.01 θ (rad) Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 8 / 14
The polar cap (plasma velocity) 0.01 θ (rad) 0.00 0.01 0.01 0.00 0.01 θ (rad) The plasma velocity (the white arrows) across the polar cap for random distribution of sparks. Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 9 / 14
The ” modified”carousel model The carousel model The ” modified” carousel model In parts of the polar cap sparks move faster than the corota- Yes it is possible. tion . Yes, but plasma created within sparks does not exhibit any sys- The presence of the gap tematic drift. changes the tangential veloc- ity within the gap. No , sparks circulate around the point of maximum potential at A group of localized discharges the polar cap. This motion is a (” sparks” ) circulate around the consequence of a drift of plasma magnetic pole of the neutron between the sparks. star. Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 10 / 14
The numerical model (c) neutron star setup (pulsar (a) geometry, magnetic field configuration) calculation of open magnetic field lines and lines connected to 500 km the line of sight (a) (b) electric potential setup (b) calculation of drift direction at the polar cap (b) and in the emission zone (c) Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 11 / 14
Bi-drifting phenomenon in PSR J0815+0939 Simulations using the Dutch national supercomputer Cartesius Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 12 / 14
Conclusions (Szary & van Leeuwen 2017, ApJ, 845, 95) The discharging regions, i.e. sparks, rotate around the point of maximum potential at the polar cap. The subpulses rotate around the magnetic axis (radio emission at higher altitudes) . The ” modified”carousel model provides physical insight into the polar cap region (surface magnetic field, electric potential variation) . Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 13 / 14
Thank you! This work was financed by the Netherlands Organisation for Scientific Research (NWO) under project ” CleanMachine”(614.001.301). Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 14 / 14
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