In-flight energy calibration of the space-borne Compton polarimeter POLAR
POLAR is a compact wide-field space-borne detector for precise measurements of the linear polarisation of hard X-rays emitted by transient sources in the energy range from 50 keV to 500 keV. It consists of a 40$\times$40 array of plastic scintillator bars used as a detection material. The bars are grouped in 25 detector modules. The energy range sensitivity of POLAR is optimized to match with the prompt emission photons from the gamma-ray bursts (GRBs). Polarization measurements of the prompt emission would probe source geometries, emission mechanisms and magnetic structures in GRB jets. The instrument can also detect hard X-rays from solar flares and be used for precise measurement of their polarisation. POLAR was launched into a low Earth orbit on-board the Chinese space-lab TG-2 on September 15th, 2016. To achieve high accuracies in polarisation measurements it is essential to assure both before and during the flight a precise energy calibration. Such calibrations are performed with four low activity $^{22}$Na radioactive sources placed inside the instrument. Energy conversion factors are related to Compton edge positions from the collinear annihilation photons from the sources. This paper presents main principles of the in-flight calibration, describes studies of the method based on Monte Carlo simulations and its laboratory verification and finally provides some observation results based on the in-flight data analysis.