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 $L_{0.5-50\ \mathrm{keV}} = 4.9 (D/7\ \mathrm{kpc})^{2}\times10^{36}$ ergs s$^{-1}$ 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 ($R_{\rm in} \leq1.07\ R_{\mathrm{ISCO}}$). By assuming that the position of the inner disk is the Alfv\'{e}n radius, we placed an upper limit on the magnetic field strength to be $B\leq0.7(D/7\ \mathrm {kpc})\times10^{8}$ G at the poles. Given the lack of pulsations detected and position of $R_{\rm in}$, it was likely that a boundary layer region had formed between the neutron star (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 $R_{\mathrm{NS}}\leq 12.1$ km when assuming a canonical NS mass of 1.4 $M_{\odot}$.