HATS-38 b and WASP-139 b join a growing group of hot Neptunes on polar orbits

We constrain the sky-projected obliquities of two low-density hot Neptune planets, HATS-38 b and WASP-139 b, orbiting nearby G and K stars using Rossiter-McLaughlin (RM) observations with VLT/ESPRESSO, yielding $\lambda = -108_{-16}^{+11}$ deg and $-85.6_{-4.2}^{+7.7}$ deg, respectively. To model the RM effect, we use a new publicly available code, ironman, which is capable of jointly fitting transit photometry, Keplerian radial velocities, and RM effects. WASP-139 b has a residual eccentricity $e=0.103_{-0.041}^{+0.050}$ while HATS-38 b has an eccentricity of $e=0.112_{-0.070}^{+0.072}$, which is compatible with a circular orbit given our data. Using the obliquity constraints, we show that they join a growing group of hot and low-density Neptunes on polar orbits. We use long-term radial velocities to rule out companions with masses $\sim 0.3-50$ $M_J$ within $\sim10$ au. We show that the orbital architectures of the two Neptunes can be explained with high-eccentricity migration from $\gtrsim 2$ au driven by an unseen distant companion. If HATS-38b has no residual eccentricity, its polar and circular orbit can also be consistent with a primordial misalignment. Finally, we performed a hierarchical Bayesian modeling of the true obliquity distribution of Neptunes and found suggestive evidence for a higher preponderance of polar orbits of hot Neptunes compared to Jupiters. However, we note that the exact distribution is sensitive to the choice of priors, highlighting the need for additional obliquity measurements of Neptunes to robustly compare the hot Neptune obliquity distribution to Jupiters.