Detailed Architecture of the L 98-59 System and Confirmation of a Fifth Planet in the Habitable Zone

The L 98-59 system, identified by TESS in 2019, features three transiting exoplanets in compact orbits of 2.253, 3.691, and 7.451 days around an M3V star, with an outer 12.83-day non-transiting planet confirmed in 2021 using ESPRESSO. The planets exhibit a diverse range of sizes (0.8-1.6 R$_{\oplus}$), masses (0.5-3 M$_{\oplus}$), and likely compositions (Earth-like to possibly water-rich), prompting atmospheric characterization studies with HST and JWST. Here, we analyze 16 new TESS sectors and improve radial velocity (RV) precision of archival ESPRESSO and HARPS data using a line-by-line framework, enabling stellar activity detrending via a novel differential temperature indicator. We refine the radii of L 98-59 b, c, and d to 0.837 $\pm$ 0.019 R$_{\oplus}$, 1.329 $\pm$ 0.029 R$_{\oplus}$, 1.627 $\pm$ 0.041 R$_{\oplus}$, respectively. Combining RVs with transit timing variations (TTV) of L 98-59 c and d from TESS and JWST provides unprecedented constraints on the masses and eccentricities of the planets. We report updated masses of 0.46 $\pm$ 0.11 M$_{\oplus}$ for b, 2.00 $\pm$ 0.13 M$_{\oplus}$ for c, and 1.64 $\pm$ 0.07 M$_{\oplus}$ for d, and a minimum mass of 2.82 $\pm$ 0.19 M$_{\oplus}$ for e. We additionally confirm L 98-59\,f, a non-transiting super-Earth with a minimal mass of 2.80 $\pm$ 0.30 M$_{\oplus}$ on a 23.06-day orbit inside the Habitable Zone. The TTVs of L 98-59 c and d (<3 min, $P_{\rm TTV} = 396$ days) constrain the eccentricities of all planets to near-circular orbits ($e \lesssim 0.04$). An internal structure analysis of the transiting planets reveals increasing water-mass fractions ($f_{\rm H_{2}O}$) with orbital distance, reaching $f_{\rm H_{2}O} \approx 0.16$ for L 98-59\ d. We predict eccentricity-induced tidal heating in L 98-59 b with heat fluxes comparable to those of Io, potentially driving volcanic activity.