Thermal Emission and Magnetic Beaming in the Radio and X-Ray Mode-switching PSR B0943+10

PSR B0943+10 is a mode-switching radio pulsar characterized by two emission modes with different radio and X-ray properties. Previous studies, based on simple combinations of blackbody and power-law models, showed that its X-ray flux can be decomposed in a pulsed thermal plus an unpulsed nonthermal components. However, if PSR B0943+10 is a nearly aligned rotator seen pole-on, as suggested by the radio data, it is difficult to reproduce the high observed pulsed fraction unless magnetic beaming is included. In this work, we reanalyze all of the available X-ray observations of PSR B0943+10 with simultaneous radio coverage, modeling its thermal emission with polar caps covered by a magnetized hydrogen atmosphere or with a condensed iron surface. The condensed surface model provides good fits to the spectra of both pulsar modes, but, similarly to the blackbody, it cannot reproduce the observed pulse profiles, unless an additional power law with an ad hoc modulation is added. Instead, the pulse profiles and phase-resolved spectra are well described using the hydrogen atmosphere model to describe the polar cap emission plus an unpulsed power law. For the X-ray brighter state (Q-mode) we obtain a best fit with a temperature {kT}∼ 0.09 {keV}, an emitting radius R∼ 260 m, a magnetic field consistent with the value of the dipole field of 4 × 1012 G inferred from the timing parameters, and a small angle between the magnetic and spin axis, ξ = 5.° The corresponding parameters for the X-ray fainter state (B-mode) are {kT}∼ 0.08 {keV} and R ∼ 170 m.