Title: Discovery of a long thermonuclear X-ray burst from the ultra-compact binary 4U 1850$-$087

Abstract: We report the detection of a long X-ray burst triggered on MJD 60171.65 from the ultra-compact binary 4U 1850$-$087 by the Monitor of All-sky X-ray Image and Neutron Star Interior Composition Explorer (NICER). We analyse the NICER data observed in between MJD 60095.19$-$60177.43, including one observation covered part of the long X-ray burst tail, i.e., $0.15-3.8$ hr after the trigger. The persistent spectra are quite similar and well described by a combination of multi-color disk blackbody, with the inner temperature of 0.5 keV, and a thermally comptonized continuum with the asymptotic power-law photon index of $\Gamma\sim2.2$, and electron temperature of $kT_{\rm e}\sim20-30$ keV. The persistent fluxes were around $3.8\times10^{-10}~{\rm erg~cm^{-2}~s^{-1}}$, corresponding to a local accretion rate of $1\%~\dot{m}_{\rm Edd}$. Part of time-resolved burst spectra show a clear deviation from the blackbody model, which can be improved by considering the enhanced persistent emission due to the Poynting-Robertson drag, or the reflected disk emission illuminated by the burst. From the burst flux during the cooling tail, we estimate the burst duration, $\tau \approx 0.78$ hr, the burst fluence, $E_\mathrm{b} \approx 4.1 \times 10^{41}$ ergs, and the ignition column depth, $y_{\rm ign}\approx 3.5\times10^{10}~{\rm g~cm^{-2}}$. We propose that the long X-ray burst is powered by unstable burning of pure helium in deep layer. Moreover, we identify significant 1 keV emission lines in the burst spectra, which may originate from the surrounding disk.