Magma oceans and enhanced volcanism on TRAPPIST-1 planets due to induction heating

Low-mass M stars are plentiful in the Universe and often host small, rocky planets detectable with current instrumentation. These stars host magnetic fields, some of which have been observed to exceed a few hundred gauss. Recently, seven small planets have been discovered orbiting the ultra-cool M dwarf TRAPPIST-1, which has an observed magnetic field of 600 G. We suggest electromagnetic induction heating as an energy source inside these planets. If the stellar rotation and magnetic dipole axes are inclined with respect to each other, induction heating can melt the upper mantle and enormously increase volcanic activity, sometimes producing a magma ocean below the planetary surface. We show that induction heating leads the four innermost TRAPPIST-1 planets, one of which is in the habitable zone, either to evolve towards a molten mantle planet, or to experience increased outgassing and volcanic activity, while the three outermost planets remain mostly unaffected.