  In chiral magnets, localized topological magnetic whirls, magnetic skyrmions,
can be moved by spin polarized electric currents. Upon increasing the current
strength, with prospects for high-speed skyrmion motion for spintronics
applications in mind, isolated skyrmions deform away from their typical
circular shape. We analyze the influence of spin-transfer torques on the shape
of a single skyrmion, including its stability upon adiabatically increasing the
strength of the applied electric current. For rather compact skyrmions at
uniaxial anisotropies well above the critical anisotropy for domain wall
formation, we find for high current densities that the skyrmion assumes a
non-circular shape with a tail, reminiscent of a shooting star. For larger and
hence softer skyrmions close to the critical anisotropy, in turn, we observe a
critical current density above which skyrmions become unstable. We show that
above a second critical current density the shooting star solution can be
recovered also for these skyrmions.
