We present a detailed, broadband X-ray spectral analysis of the ULX pulsar NGC 7793 P13, a known super-Eddington source, utilizing data from the $XMM$-$Newton$, $NuSTAR$ and $Chandra$ observatories. The broadband $XMM$-$Newton+NuSTAR$ spectrum of P13 is qualitatively similar to the rest of the ULX sample with broadband coverage, suggesting that additional ULXs in the known population may host neutron star accretors. Through time-averaged, phase-resolved and multi-epoch studies, we find that two non-pulsed thermal blackbody components with temperatures $sim$0.5 and $sim$1.5 keV are required to fit the data below 10 keV, in addition to a third continuum component which extends to higher energies and is associated with the pulsed emission from the accretion column. The characteristic radii of the thermal components appear to be similar, and are too large to be associated with the neutron star itself, so the need for two components likely indicates the accretion flow outside the magnetosphere is complex. We suggest a scenario in which the thick inner disc expected for super-Eddington accretion begins to form, but is terminated by the neutron stars magnetic field soon after its onset, implying a limit of $B lesssim 6 times 10^{12}$ G for the dipolar component of the central neutron stars magnetic field. Evidence of similar termination of the disc in other sources may offer a further means of identifying additional neutron star ULXs. Finally, we examine the spectrum exhibited by P13 during one of its unusual off states. These data require both a hard powerlaw component, suggesting residual accretion onto the neutron star, and emission from a thermal plasma, which we argue is likely associated with the P13 system.
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