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Motivated by models suggesting that the inner planet forming regions ofprotoplanetary discs are predominantly lacking in viscosity-inducingturbulence, and are possibly threaded by Hall-effect generated large-scalehorizontal magnetic fields, we examine the dynamics of the corotation region ofa low-mass planet in such an environment. The corotation torque in an inviscid,isothermal, dead zone ought to saturate, with the libration region becomingboth symmetrical and of a uniform vortensity, leading to fast inward migrationdriven by the Lindblad torques alone. However, in such a low viscositysituation, the material on librating streamlines essentially preserves itsvortensity. If there is relative radial motion between the disc gas and theplanet, the librating streamlines will no longer be symmetrical. Hence, if thegas is torqued by a large scale magnetic field so that it undergoes a netinflow or outflow past the planet, driving evolution of the vortensity andinducing asymmetry of the corotation region, the corotation torque can grow,leading to a positive torque. In this paper we treat this effect by applying asymmetry argument to the previously studied case of a migrating planet in aninviscid disc. Our results show that the corotation torque due to a laminarHall-induced magnetic field in a dead zone behaves quite differently from thatstudied previously for a viscous disc. Furthermore, the magnetic field inducedcorotation torque and the dynamical corotation torque in a low viscosity disccan be regarded as one unified effect.

Low mass planet migration in magnetically torqued dead zones - I. Static migration torque