  L 98-59 (TIC 307210830, TOI-175) is a nearby M3 dwarf around which TESS
revealed three terrestrial-sized transiting planets (0.80, 1.35, 1.57 Earth
radii) in a compact configuration with orbital periods shorter than 7.5 days.
Here we aim to measure the masses of the known transiting planets in this
system using precise radial velocity (RV) measurements taken with the HARPS
spectrograph. We consider both trained and untrained Gaussian process
regression models of stellar activity to simultaneously model the RV data with
the planetary signals. Our RV analysis is then supplemented with dynamical
simulations to provide strong constraints on the planets' orbital
eccentricities by requiring long-term stability. We measure the planet masses
of the two outermost planets to be $2.46\pm 0.31$ and $2.26\pm 0.50$ Earth
masses which confirms their bulk terrestrial compositions. We are able to place
an upper limit on the mass of the smallest, innermost planet of $<0.98$ Earth
masses with 95% confidence. Our RV plus dynamical stability analysis places
strong constraints on the orbital eccentricities and reveals that each planet's
orbit likely has $e<0.1$ to ensure a dynamically stable system. The L 98-59
compact system of three likely rocky planets offers a unique laboratory for
studies of planet formation, dynamical stability, and comparative atmospheric
planetology. Continued RV monitoring will help refine the characterization of
the innermost planet and potentially reveal additional planets in the system at
wider separations.
