An Outer Giant Excites and Constrains the Orbit of $π$ Mensae d

RESUMO

The nearby $\pi$ Mensae system contains the eccentric giant planet b on a 5.7 yr orbit, the 6.27 day transiting sub-Neptune c, and a candidate planet d on a 123 day orbit between them. Published estimates place the eccentricity of d between approximately 0.2 and 0.4. We reanalyze 772 published velocities with three-Keplerian fits and explore three-dimensional b-d dynamics with N-body integrations. The high-eccentricity solution persists when the phase or apsidal prior is widened; exact importance reweighting to a population-informed Beta eccentricity prior gives $e_{d}=0.378^{+0.050}_{-0.049}$. In 20 kyr integrations, 84.5% of configurations near the prograde and retrograde coplanar endpoints survive, compared with 21.3% across $60^\circ \leq I_{bd} < 120^\circ$; stellar collisions dominate the failures. Secular forcing by b moves 53 of 62 one-Myr survivors initialized with $e_{d} \leq 0.1$ into $0.3 \leq e_{d} \leq 0.5$. Representative b+d configurations remain viable for 100 Myr, whereas controls with c and general relativity retain fewer systems. The outer giant can therefore excite the observed eccentricity of d while constraining its viable orbit toward prograde or retrograde near-coplanar configurations.