Kinematic-Distance Biases in the Inner Milky Way from a Stellar-Dynamically Constrained Bar

TL;DR

This study quantifies the systematic biases that bar-driven non-circular motions imprint on kinematic-distance (KD) gas reconstructions in the inner Milky Way. By comparing axisymmetric KD inversions to a high-resolution hydrodynamic simulation within a stellar-dynamically constrained barred potential, it shows KD is reliable outside $R \gtrsim 5$ kpc but yields pronounced, quadrant-dependent artifacts inside the bar ($R \sim 0.5$–3 kpc), including arc-like overdensities and LOS-elongated cavities. The distance errors $|\Delta d|$ reach $\sim$1–2 kpc and relative errors of tens of percent, correlating with the KD geometric sensitivity $S = \left|\partial d/\partial V_{\rm LOS}^{\rm circ}\right|$ and the bar-induced streaming field via $\Delta d\simeq S\,\Delta V_{\rm LOS}$. Azimuthally averaged radial profiles reveal that these distortions systematically fill in the true inner bar depression, flattening the inferred inner disk density. The results motivate developing bar-informed KD methods or kinetic tomography to robustly recover the inner Galaxy's gas structure and streaming motions.

Abstract

We quantify how bar-driven non-circular motions bias Milky-Way gas maps inferred with the kinematic-distance (KD) method. KD reconstructions of H\,\textsc{i} and CO surveys assume circular rotation in an axisymmetric potential, an assumption that is strongly violated in the barred inner Milky Way. We use high-resolution hydrodynamical simulations of gas flow in an observationally constrained barred Milky Way potential. From a quasi-steady snapshot we generate synthetic longitude--velocity data and apply a standard axisymmetric KD inversion using the circular-speed curve derived from the $m=0$ component of the same potential. To isolate non-circular effects, we remove the near--far ambiguity by selecting, for each gas element, the KD branch closest to its true distance. We find that the KD method reproduces the gas distribution reasonably well outside the bar-dominated region ($R \gtrsim 5$~kpc), but fails systematically in the bar region ($R \sim 0.5$--3~kpc). There the KD-reconstructed face-on map exhibits anisotropic, quadrant-dependent artifacts, including arc-like overdensities and LOS-elongated low-density cavities. In azimuthally averaged profiles, these anisotropic misassignments translate into net radial mixing: the axisymmetric KD inversion substantially fills in the true bar-induced depression (hereafter, the ``bar gap'') and yields a flatter inner profile. Distance-error maps show coherent structures with $|Δd| \sim 1$--2~kpc and relative errors of several tens of percent along the bar and inner ring, coincident with zones where the KD mapping is intrinsically ill-conditioned, quantified by a large geometric sensitivity $S \equiv \left|\partial d/\partial V_{\rm LOS}^{\rm circ}\right|$. In these regions the error is well approximated to first order by $Δd \simeq S\,ΔV_{\rm LOS}$, linking KD failures directly to bar-driven streaming velocities. ...

Figures (9)

• Figure 1: (a) Face-on gas surface-density map from the barred Milky Way hydrodynamical simulation without gas self-gravity presented in Baba2025b, overlaid with stellar surface-density contours of the barred stellar component Portail+2017Sormani+2022agama. (b) Face-on molecular-gas surface-density map, $\Sigma_{\rm H_2}$, reconstructed from the Galactic CO($J$=1--0) survey of Dame+2001 using the KD method. Each $(\ell,b,v)$ voxel in the data cube is assigned to a Galactocentric position assuming an axisymmetric rotation model, and the near--far ambiguity is resolved following the procedure of NakanishiSofue2016 (see Appendix). (c) Same as panel (b), but shown over a larger radial range. The solid circle marks the Solar circle ($R=R_0$), while the dashed circle indicates the tangent-point locus. Alt Text: Three face-on maps of gas surface density in the Galactic plane. Panel (a) shows the simulated barred-galaxy gas map with stellar bar density contours. Panel (b) shows the molecular-gas map reconstructed from the Galactic carbon-monoxide J=1-0 survey using an axisymmetric KD method with near-far resolution. Panel (c) shows the same reconstruction over a larger radial range, with circles marking the Solar circle and the tangent-point locus.
• Figure 2: (a) Model circular LOS velocity field, $V_{\rm LOS}^{\rm circ}(X,Y)$, computed from the adopted axisymmetric rotation curve. The dashed circle indicates the tangent-point locus. (b) KD-sensitivity map, $S(X,Y)$, defined from the response of the circular-orbit distance to perturbations in LOS velocity. Alt Text: Two face-on maps in the Galactic plane illustrating the axisymmetric KD model. Panel (a) shows the circular line-of-sight velocity field predicted from the adopted rotation curve, with a dashed circle marking the tangent-point locus and the Sun marked by a symbol. Panel (b) shows the KD sensitivity $S$, defined as the change in inferred distance per change in line-of-sight velocity, with the same tangent-point circle overplotted.
• Figure 3: Distance dependence of (a) the circular LOS velocity $V_{\rm LOS}^{\rm circ}(\ell,d)$. and (b) the KD sensitivity $S(\ell,d)$ along the selected Galactic longitudes in the Galactic plane. Dashed vertical lines mark the tangent-point distance along each line of sight, defined as the location where $|V_{\rm LOS}^{\rm circ}(d)|$ reaches its maximum. Alt Text: Two line plots show the axisymmetric KD model versus heliocentric distance for selected Galactic longitudes in the Galactic plane. Panel (a) shows the circular line-of-sight velocity as a function of distance. Panel (b) shows the KD sensitivity $S$ as a function of distance. Dashed vertical lines mark the tangent-point distance where the absolute circular line-of-sight velocity reaches its maximum.
• Figure 4: Face-on gas distribution, LOS velocity fields, and non-circular component of the LOS velocity in the fiducial barred Milky Way simulation. All panels show the Galactic plane in Cartesian coordinates $(X,Y)$, with the Galactic center at the origin and the Sun at $(0,-R_0)$. The dotted circle shows the tangent-point locations (i.e. terminal velocity circle). (a) True gas surface density, $\Sigma_{\rm gas}(X,Y)$, obtained by vertically integrating the gas density. The bar appears as an elongated high-density feature tilted by $25^\circ$ clockwise from the $Y$-axis, accompanied by a CMZ-like nuclear ring and bar-driven spiral arms. (b) Mass-weighted mean LOS velocity field, $V_{\rm LOS}^{\rm true}(X,Y)$. Contours highlight strong streaming motions along the bar and spiral features. (c) Non-circular component of the LOS velocity, $\Delta V_{\rm LOS}(X,Y) = V_{\rm LOS}^{\rm true} - V_{\rm LOS}^{\rm circ}$, where $V_{\rm LOS}^{\rm circ}$ is the LOS velocity field predicted by the axisymmetric circular-rotation model used in the KD method. Alt Text: Three face-on maps in the Galactic plane from the fiducial hydrodynamic simulation, in Cartesian $X$ and $Y$ with the Galactic center at the origin and the Sun at $(0, -R_0)$. A dotted circle marks the tangent-point locus. Panel (a) shows the true gas surface density with an elongated bar and a central ring. Panel (b) shows the mean line-of-sight velocity field. Panel (c) shows the non-circular line-of-sight velocity component, defined as the true field minus the axisymmetric circular-rotation prediction.
• Figure 5: (a) KD-based surface-density map, $\Sigma_{\rm gas,KD}(X,Y)$, obtained by inverting synthetic longitude2013velocity data under the assumption of purely circular rotation and, for each SPH particle, selecting the KD solution (near or far) closest to its true distance. The same color scale as in Figure \ref{['fig:truemap_v2']}(a) is used, and black contours show the true surface density from Figure \ref{['fig:truemap_v2']}(a). (b) Mean KD error, $\Delta d(X,Y)$. (c) Mean KD relative error, $\epsilon_d(X,Y)$. Alt Text: Three face-on maps in the Galactic plane comparing KD reconstruction to the true simulation. Panel (a) shows the KD surface-density map, with black contours marking the true surface density. Panel (b) shows the mean distance error in kiloparsecs. Panel (c) shows the mean relative distance error, highlighting coherent, bar-related regions of over- and under-estimated distances.