Hard X-ray polarimetry in the stratosphere

X-rays are routinely used to study compact astrophysical objects, such as black hole binaries and neutron stars. Too small and distant to be directly imaged, information on source geometry and high-energy emission mechanisms is instead derived from spectral and timing measurements. Although spectacular advances have been made, results are often model dependent with interpretation subject to degeneracies which cannot be resolved. X-ray polarimetry provides an independent source diagnostic. Two new observables describe the high-energy emission - the linear polarisation fraction and the linear polarisation angle. One of the highlights of astrophysics in the 2020-2030 decade will be establishing X-ray polarimetry as a new window into the high-energy Universe. Methods allowing X-ray polarimetry in the hard X-ray band $\sim$10-200 keV are currently being explored by balloon-borne instruments operated in the stratosphere at an altitude of $\sim$40 km. I will review two complementary approaches used for hard X-ray polarimetry: the PoGO+ mission, which flew from Esrange to Canada in summer 2016, making observations of the Crab pulsar and black-hole binary Cygnus X-1; and the X-Calibur mission which observed the accreting neutron star, GX301-2, during a flight from Antarctica at the end of 2018. The second generation of balloon-borne hard X-ray polarimetry is provided by an upgraded version of X-Calibur, "XL-Calibur". The design and expected performance of this mission will also be presented.