Physics of drifting subpulses Andrzej Szary and Joeri van Leeuwen - - PowerPoint PPT Presentation

Physics of drifting subpulses

Andrzej Szary and Joeri van Leeuwen

The Netherlands Institute for Radio Astronomy University of Zielona G´

• ra

March 27, 2018

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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.

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Neutron star magnetosphere

The force-free state (E = 0)

The Lorentz force:

• E + 1

c ( Ω × r) × B = 0

• E⊥ = −

v c × B

The plasma charge density: ρGJ = −

• Ω ·

B 2πc The co-rotation velocity:

• vcor =

c( E× B) B2

Szary & van Leeuwen (ASTRON) Drifting subpulses March 27, 2018 3 / 14

The carousel model

(Ruderman & Sutherland, 1975)

The presence

• f

the gap changes the tangential velocity within the gap and alters the corotation velocity: vcor = c(E×B)

B2

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)

x z x y x z x y x y

The electric and magnetic fields within a region of spark formation with screened acceleration (the left panel) and during the discharge (the right panel).

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Co-rotating frame of reference

The Lorentz transformation

• E ′ =

E + v c × B

x y screened unscreened co-rotating frame

Electric field across a spark forming region in the co-rotating frame of reference.

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The polar cap (electric field)

0.01 0.00 0.01 0.01 0.00 0.01 θ (rad) 0.01 0.00 0.01 θ (rad) Vmin Vmax Vmin Vmax 0.01 0.00 0.01 The electric field (the white arrows) across the polar cap for random dis- tribution of sparks. The color map corresponds to the electric potential. The electric potential of a single spark:

V ′ ∝ ln(rs)

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The polar cap (plasma velocity)

0.01 0.00 0.01 θ (rad) 0.01 0.00 0.01 θ (rad)

The plasma velocity (the white arrows) across the polar cap for random distribution of sparks.

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The ” modified”carousel model

The carousel model In parts of the polar cap sparks move faster than the corota- tion. The presence

• f

the gap changes the tangential veloc- ity within the gap. A group of localized discharges (” sparks” ) circulate around the magnetic pole of the neutron star. The ” modified” carousel model Yes it is possible. Yes, but plasma created within sparks does not exhibit any sys- tematic drift. No, sparks circulate around the point of maximum potential at the polar cap. This motion is a consequence of a drift of plasma between the sparks.

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The numerical model

neutron star setup (pulsar geometry, magnetic field configuration) calculation of open magnetic field lines and lines connected to the line of sight (a) electric potential setup (b) calculation of drift direction at the polar cap (b) and in the emission zone (c)

(a)

500 km

(c) (b)

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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).

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Thank you!

This work was financed by the Netherlands Organisation for Scientific Research (NWO) under project ” CleanMachine”(614.001.301).

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