New simultaneous X-ray and radio observations of the archetypal mode-switching pulsar PSR B0943+10 have been carried out with XMM-Newton and the LOFAR, LWA and Arecibo radio telescopes in November 2014. They allowed us to better constrain the X-ray spectral and variability properties of this pulsar and to detect, for the first time, the X-ray pulsations also during the X-ray-fainter mode. The combined timing and spectral analysis indicates that unpulsed non-thermal emission, likely of magnetospheric origin, and pulsed thermal emission from a small polar cap are present during both radio modes and vary in a correlated way.
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