Simultaneous NICER and NuSTAR Observations of the Ultra-compact X-ray Binary 4U 1543-624

We present the first joint NuSTAR and NICER observations of the ultra-compact X-ray binary (UCXB) 4U 1543$-$624 obtained in 2020 April. The source was at a luminosity of $L_{0.5-50\ $\mathrm{k}\mathrm{e}\mathrm{V}$} = 4.9 (D/7
$\mathrm{k}\mathrm{p}\mathrm{c}$)^{2}\times10^{36}$ergss$^{-1}$ and showed evidence of reflected emission in the form of an O VIII line, Fe K line, and Compton hump within the spectrum. We used a full reflection model, known as xillverCO, that is tailored for the atypical abundances found in UCXBs, to account for the reflected emission. We tested the emission radii of the O and Fe line components and conclude that they originate from a common disk radius in the innermost region of the accretion disk ($R_{\mathrm{i}\mathrm{n}}\le 1.07R_{\mathrm{I}\mathrm{S}\mathrm{C}\mathrm{O}}$). Assuming that the compact accretor is a neutron star (NS) and the position of the inner disk is the Alfv'{e}n radius, we placed an upper limit on the magnetic field strength to be $B\le 0.7(D\mathrm{/}7\mathrm{k}\mathrm{p}\mathrm{c})\times {10}^8$ G at the poles. Given the lack of pulsations detected and position of $R_{\mathrm{i}\mathrm{n}}$, it was likely that a boundary layer region had formed between the NS surface and inner edge of the accretion disk with an extent of 1.2 km. This implies a maximum radius of the neutron star accretor of $R_{\mathrm{N}\mathrm{S}}\le 12.1$ km when assuming a canonical NS mass of 1.4 $M_{\odot }$.