When the Jeans don't fit: How stellar feedback drives stellar kinematics and complicates dynamical modeling in low-mass galaxies

In low-mass galaxies, stellar feedback can drive gas outflows that generate non-equilibrium fluctuations in the gravitational potential. Using cosmological zoom-in baryonic simulations from the Feedback in Realistic Environments (FIRE) project, we investigate how these fluctuations affect stellar kinematics and the reliability of Jeans dynamical modeling in low-mass galaxies. We find that stellar velocity dispersion and anisotropy profiles fluctuate significantly over the course of galaxies' starburst cycles. We therefore predict an observable correlation between star formation rate and stellar kinematics: dwarf galaxies with higher recent star formation rates should have systemically higher stellar velocity dispersions. This prediction provides an observational test of the role of stellar feedback in regulating both stellar and dark-matter densities in dwarf galaxies. We find that Jeans modeling, which treats galaxies as virialized systems in dynamical equilibrium, overestimates a galaxy's dynamical mass during periods of post-starburst gas outflow and underestimates it during periods of net inflow. Short-timescale potential fluctuations lead to typical errors of $\sim 20\%$ in dynamical mass estimates, even if full 3-dimensional stellar kinematics -- including the orbital anisotropy -- are known exactly. When orbital anisotropy is $\textit{not}$ known a priori, typical mass errors arising from non-equilibrium fluctuations in the potential are larger than those arising from the mass-anisotropy degeneracy. However, Jeans modeling alone $\textit{cannot}$ reliably constrain the orbital anisotropy, and problematically, it often favors anisotropy models that do not reflect the true profile. If galaxies completely lose their gas and cease forming stars, fluctuations in the potential subside, and Jeans modeling becomes much more reliable.