We report for the first time below 1.5 keV, the detection of a secondary peak in an Eddington-limited thermonuclear X-ray burst observed by the Neutron Star Interior Composition Explorer (NICER) from the low-mass X-ray binary 4U 1608-52. Our time-resolved spectroscopy of the burst is consistent with a model consisting of a varying-temperature blackbody, and an evolving persistent flux contribution, likely attributed to the accretion process. The dip in the burst intensity before the secondary peak is also visible in the bolometric flux. Prior to the dip, the blackbody temperature reached a maximum of $approx3$ keV. Our analysis suggests that the dip and secondary peak are not related to photospheric expansion, varying circumstellar absorption, or scattering. Instead, we discuss the observation in the context of hydrodynamical instabilities, thermonuclear flame spreading models, and re-burning in the cooling tail of the burst.
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