Axisymmetric Jeans modelling systematically overestimates the circular speed in the inner Milky Way

Abstract

We quantify systematic biases in rotation curves inferred from steady, axisymmetric Jeans modelling when the underlying stellar velocity field is non-axisymmetric. Using a high-resolution $N$-body/hydrodynamic simulation of an isolated Milky Way-like disk galaxy, we construct mock stellar-kinematic measurements for two observer azimuths relative to the bar. One observer is placed at a Solar-like viewing angle of $25^\circ$ from the bar major axis, and the other at $115^\circ$. For each configuration, we analyse multiple snapshots and compare the Jeans-inferred circular-speed curve, $V_{\rm c,Jeans}(R)$, with a reference axisymmetric circular-speed curve, $V_{\rm c,axi}(R)$, defined from the azimuthally averaged ($m=0$) component of the gravitational field. The Jeans analysis is performed in a wedge-shaped mock observational volume that mimics limited sky coverage. For the $25^\circ$ configuration, the mean azimuthal streaming is typically higher than the azimuthally averaged expectation by $\approx 10$--$15~\mathrm{km\,s^{-1}}$, which leads to an average overestimate of the axisymmetrically defined circular speed by $\approx 4\%$ ($\approx 10~\mathrm{km\,s^{-1}}$) in the inner disk. Across snapshots, the mean offset corresponds to a $\sim 1.5$--$2\sigma$ systematic deviation of $V_{\rm c,Jeans}$ from $V_{\rm c,axi}$. For the $115^\circ$ configuration, the bias reverses sign and $V_{\rm c,Jeans}$ tends to underestimate $V_{\rm c,axi}$. Under the usual spherical approximation, a $\approx 4\%$ bias in $V_{\rm c}$ corresponds to an $\approx 8\%$ bias in the enclosed dynamical mass at fixed radius. These results imply that steady, axisymmetric Jeans modelling of Milky Way stellar kinematics can overestimate the axisymmetrically defined circular-speed curve at the percent level unless non-axisymmetric streaming is modelled explicitly or included in the error budget.