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

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 ($R \sim 0.5$–3kpc). 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. …

💡 Research Summary

This paper presents a quantitative assessment of how bar‑driven non‑circular motions in the inner Milky Way bias gas maps derived with the traditional kinematic‑distance (KD) method. The authors employ a high‑resolution smoothed‑particle hydrodynamics (SPH) simulation of interstellar gas evolving in a gravitational potential that is tightly constrained by recent made‑to‑measure (M2M) models of the Galactic bar and bulge. The potential includes a rigidly rotating bar (pattern speed Ω_b ≈ 37.5 km s⁻¹ kpc⁻¹), axisymmetric disk and halo components that reproduce the observed circular‑velocity curve, and a nuclear stellar disc/cluster. Gas physics (cooling, heating, stochastic star formation, supernova and H II region feedback) is included, and the simulation reaches a quasi‑steady state featuring offset dust‑lane streams, a CMZ‑like nuclear ring, and a characteristic depletion of gas between ≈ 1–3 kpc (the “bar gap”).

From a representative snapshot the authors place a virtual Sun at (R₀ = 8.3 kpc, V₀ = 230 km s⁻¹) and compute for each SPH particle the Galactic longitude ℓ, latitude b, line‑of‑sight velocity V_LOS, and true heliocentric distance d_true. They then generate synthetic (ℓ, b, V_LOS) data and apply a standard axisymmetric KD inversion. The KD model uses the circular‑speed curve V_c(R) derived from the m = 0 (axisymmetric) component of the same potential, assumes pure circular rotation, and adopts a fixed turbulent dispersion σ_turb = 7 km s⁻¹ to construct a Gaussian likelihood. For each line of sight the distance is taken as the maximum‑a‑posteriori (MAP) solution.

To isolate the effect of non‑circular motions, the authors deliberately remove the classic near–far ambiguity: when the KD equation yields two distance solutions for a given (ℓ, b, V_LOS), they select the branch whose KD distance is closest to the particle’s true distance. This “branch‑matching” procedure preserves the KD framework while eliminating ambiguity, allowing a clean comparison between KD‑inferred and true positions.

The results show that outside the bar‑dominated region (R ≳ 5 kpc) the KD reconstruction reproduces the true gas distribution reasonably well (≈ 70 % fidelity). Inside the bar region (0.5 ≲ R ≲ 3 kpc) the KD method fails systematically. The KD‑reconstructed face‑on map displays quadrant‑dependent artifacts: arc‑like overdensities and line‑of‑sight‑elongated low‑density cavities that have no counterpart in the true simulation. These features arise because bar‑driven streaming velocities shift the observed V_LOS away from the values expected for circular rotation, leading the KD inversion to assign gas to incorrect distances.

When azimuthally averaged, the KD map artificially fills the true bar‑gap, producing a flatter inner surface‑density profile. Distance‑error maps reveal coherent structures with absolute errors |Δd| ≈ 1–2 kpc and relative errors of several tens of percent, especially along the bar and inner ring. The authors quantify the geometric ill‑conditioning of the KD inversion by defining a sensitivity S ≡ ∂d/∂V_LOS (computed from the circular‑rotation model). Regions with large |S| coincide with the error structures, and the first‑order relation Δd ≈ S ΔV_LOS accurately predicts the magnitude and sign of the distance errors, directly linking them to the bar‑induced streaming field.

The paper also tests an alternative rotation curve derived from terminal velocities; the main conclusions remain unchanged, confirming that the bias is driven by the non‑circular flow rather than the specific choice of V_c(R).

Implications are significant: many existing 3‑D H I and CO maps of the Milky Way, as well as radial gas‑surface‑density profiles, are based on KD inversions that likely over‑estimate gas content in the inner 1–3 kpc and smooth out the genuine depletion caused by the bar. The authors argue that any study of Galactic structure, star formation, or dynamics that relies on KD‑derived gas distributions in the bar region must account for these systematic biases. Potential mitigation strategies include incorporating bar‑driven velocity fields into the distance estimator, using Bayesian frameworks with priors informed by dynamical models, or employing alternative distance tracers (e.g., maser parallaxes, Gaia astrometry) to calibrate the KD method.

In summary, the work provides a rigorous, simulation‑based demonstration that the conventional kinematic‑distance technique is fundamentally limited in the barred inner Milky Way. It quantifies the magnitude of the bias, elucidates its physical origin, and highlights the need for more sophisticated, non‑axisymmetric distance inference methods in future Galactic surveys.