We report measurements of the linear polarization degree (PD) and angle (PA) for hard X-ray emission from the Crab pulsar and wind nebula. Measurements were made with the XL-Calibur (similar to 15-80 keV) balloon-borne Compton-scattering polarimeter in July 2024. The polarization parameters are determined using a Bayesian analysis of Stokes parameters obtained from X-ray scattering angles. Well-constrained (similar to 8.5 sigma) results are obtained for the polarization of the similar to 19-64 keV signal integrated over all pulsar phases: PD = (25.1 +/- 2.9) per cent and PA = (129.8 +/- 3.2)degrees. In the off-pulse (nebula-dominated) phase range, the PD is constrained at similar to 4.5 sigma and is compatible with the phase-integrated result. The PA of the nebular hard X-ray emission aligns with that measured by IXPE in the 2-8 keV band for the toroidal inner region of the pulsar wind nebula, where the hard X-rays predominantly originate. For the main pulsar peak, PD = (32.8(-28.5)(+18.2)) per cent and PA = (156.0 +/- 21.7)degrees, while for the second peak (inter-pulse), PD = (0.0(-0.0)(+33.6)) per cent and PA = (154.5 +/- 34.5)degrees. A low level of polarization in the pulsar peaks likely does not favour emission originating from the inner regions of the pulsar magnetosphere. Discriminating between Crab pulsar emission models will require deeper observations, e.g. with a satellite-borne hard X-ray polarimeter.

The balloon-borne hard X-ray polarimetry mission XL-Calibur observed the black hole X-ray binary (BHXRB) Cygnus X-1 (Cyg X-1) during its nearly 6 day long-duration balloon flight from Sweden to Canada in 2024 July. The XL-Calibur observations allowed us to derive the most precise constraints to date of the polarization degree (PD) and polarization angle (PA) of the hard X-ray emission from a BHXRB. XL-Calibur observed Cyg X-1 in the hard state and measured a similar to 19-64 keV PD of ( 5.0-3.0+2.7 )% (equivalent to an upper limit, at the 99% level, of 11.1%) at a PA of -28 degrees +/- 17 degrees, with an 8.7% chance probability of detecting larger PDs than the one observed, given an unpolarized signal. The XL-Calibur results are thus comparable to the 2-8 keV PD and PA found by Imaging X-ray Polarimetry Explorer (IXPE), with a similar agreement between the hard X-ray PA and the radio jet direction. We also discuss the implications of our polarization measurements in the context of models describing the origin of the broadband X-ray and gamma-ray emission, to which XL-Calibur provides independent constraints on any proposed emission modeling.

XL-Calibur is a balloon-borne Compton polarimeter for X-rays in the ∼15–80 keV range. Using an X-ray mirror with a 12 m focal length for collecting photons onto a beryllium scattering rod surrounded by CZT detectors, a minimum-detectable polarization as low as ∼3% is expected during a 24-hour on-target observation of a 1 Crab source at 45° elevation. Systematic effects alter the reconstructed polarization as the mirror focal spot moves across the beryllium scatterer, due to pointing offsets, mechanical misalignment or deformation of the carbon-fiber truss supporting the mirror and the polarimeter. Unaddressed, this can give rise to a spurious polarization signal for an unpolarized flux, or a change in reconstructed polarization fraction and angle for a polarized flux. Using bench-marked Monte-Carlo simulations and an accurate mirror point-spread function characterized at synchrotron beam-lines, systematic effects are quantified, and mitigation strategies discussed. By recalculating the scattering site for a shifted beam, systematic errors can be reduced from several tens of percent to the few-percent level for any shift within the scattering element. The treatment of these systematic effects will be important for any polarimetric instrument where a focused X-ray beam is impinging on a scattering element surrounded by counting detectors.