A precise TESS ephemeris for the short-period binary TIC-259864042

This paper presents a precise eclipse-timing analysis of TIC 259864042 (= EC 02406–6408, Gaia DR3 4647004122914240640) using eleven sectors of TESS photometry spanning 2018–2025 (7.1 yr). The system exhibits a single deep eclipse with a V-shaped profile at phase 0 and no detectable counterpart at phase 0.5. Four independent period-search methods converge to a common period agreeing to within 7 parts per million. An independent reduction with the SHERLOCK pipeline, using its own 120-second TESS photometry, confirms the same period at the same precision. A joint linear ephemeris fit gives P = 0.46048676 $\pm$ 0.0000001 d (11.059 h) and T_0 = 2458325.70381 $\pm$ 0.00002 BJD, with a residual RMS of 0.87 min across the 7.1-yr baseline. Per-sector ephemeris fits show residual medians within $\pm$0.42 min of zero, confirming that no cycle slip has occurred across the large TESS data gaps. The period is stable at the level of $\mathrm{\Delta }$BIC = +5.21 (in favour of the constant-period model); an upper limit of $\mathrm{\mid }\dot{P}\mathrm{\mid }\le 1\times {10}^{-9}$ d d${}^{-1}$ is placed on any secular period change. A PHOEBE 2.4 fit to the Sector 27 light curve yields $i={80.8}^{\circ }\pm {0.5}^{\circ }$, $R_1=0.21\pm 0.01R_{\odot }$, $R_2=0.25\pm 0.02R_{\odot }$, $q=0.49\pm 0.07$, consistent with a grazing detached geometry and a mid-M-dwarf companion. The TESS light curve alone cannot distinguish between the two temperatures 25100 K and 31000 K. The paper discusses the system in the context of the sdB eclipsing binary population, and notes that while the current data are consistent with a short-period sdB+M-dwarf architecture, a phase-resolved spectrum is needed to independently confirm the sdB identification.