Multi-resolution kinematic modelling of nearby galaxies: a demonstration using MHONGOOSE observations

TL;DR

The paper tackles the challenge of robustly extracting galaxy kinematics by combining HI data from multiple spatial resolutions. It introduces radial weighting functions derived from mock analyses and an adaptive Gaussian smoothing scheme to merge five resolution levels into self-consistent geometric and kinematic profiles, demonstrated on two MHONGOOSE galaxies. The approach yields smoother, more physically plausible inclination and position-angle profiles and rotation curves that extend further in radius than any single-resolution analysis, reducing central beam-smearing artifacts. This method enhances the reliability of dynamical mass inferences from HI kinematics and provides a pathway to optimally exploit information-rich, multi-resolution observations.

Abstract

We present a novel method of combining kinematic models obtained at multiple spatial resolution levels in a self-consistent manner. The MHONGOOSE survey has mapped atomic hydrogen emission in $30$ nearby dwarf and spiral galaxies. Each galaxy is imaged at multiple resolution levels with unprecedented dynamic range in spatial resolution (from $\sim 10''$ to $ 90''$) and HI sensitivity, with the latter varying by almost a factor of $30$ across all resolution scales. We use radial weighting functions to combine kinematic models from all resolution levels. The weights are derived from the residuals of model fits to a set of observations of synthetic model galaxies with known rotation curves and geometries. We obtain combined (weighted and smoothed) inclination and position angle profiles for each galaxy. These suppress the sharp, often unphysical radial fluctuations arising in single-resolution profiles. We then fit the rotation speed and velocity dispersion profiles at each resolution level with the geometric profiles fixed to the combined profiles, finally combining these using the same weighting and smoothing approach. The combined rotation curves utilise all of the available information and have smaller typical systematic errors compared to those obtained using a single resolution level, particularly near the centres and outer edges of models. This initial demonstration is promising; there is scope to further refine the process to use such information-rich observations to their full potential.

Figures (8)

• Figure 1: MHONGOOSE H i$\mathrm{S}/\mathrm{N}=3$ contours at different resolution levels overlaid onto DECaLS grz band images of J1106-14 (left) and J0309-41 (right). The contours are colour-coded according to the respective column density colour bars. These contours, in order from smallest to largest, are derived from the r05_t0 (light blue), r10_t0 (purple), r15_t0 (pink), r05_t60 (orange), and r10_t90 (yellow) resolution levels. The values within the colour bars represent the beam major axis lengths for each resolution level. Concentric ellipses are included in the bottom left to represent the beam for each resolution, and a physical scale bar is included in the bottom right.
• Figure 2: Best-fitting tilted ring models returned by $^\mathrm{3D}$barolo for J1106-14 at the r10_t90 (left column), r15_t0 (middle column), and r05_t0 (right column) resolution levels. The rotational (first row) and residual ($V_\mathrm{res} = V_\mathrm{rot} - V_\mathrm{model}$; second row) velocity maps are shown, along with profiles of the rotation speed (third row), velocity dispersion (fourth row), inclination (fifth row), and position angle (sixth row) as a function of radius. In the $V_\mathrm{rot}$ maps, the black cross and purple star indicate the dynamical centre positions as estimated by $^\mathrm{3D}$barolo and given by the stellar light, respectively. The green line represents the zero isovelocity contour. All maps span the same angular region, and all profiles are displayed with the same radial limits. The shaded regions in the rotation speed and dispersion panels represent the uncertainties on these parameters returned by $^\mathrm{3D}$barolo.
• Figure 3: Calculation of radial weighting functions for J1106-14 across resolution levels: r05_t0 (light blue), r10_t0 (purple), r15_t0 (pink), r05_t60 (orange), and r10_t90 (yellow) from left to right. The top row shows the fractional deviation of the rotation curve obtained by $^\mathrm{3D}$barolo from the true curve for a range of mock galaxy geometries and kinematic configurations, with the average fractional residuals shown in black. The bottom row shows the resultant normalised weighting functions, derived from the inverse of the above residuals. These weighting functions represent the weighting per data point, accounting for the radial sampling frequency of data at each resolution level.
• Figure 4: The application of our methodology to mock datacubes with known profiles. The coloured lines show the difference between the known profiles and those obtained from running $^\mathrm{3D}$barolo's two-stage fitting routine (with Bézier interpolation for the inclination and position angle profiles) on the 15 mock datacubes generated at each resolution level: r05_t0 (dotted line; light blue), r10_t0 (solid line; purple), r15_t0 (dashed line; pink), r05_t60 (dash-dot line; orange), and r10_t90 (dash-double-dot line; yellow). The heavy black lines show the difference between the known profiles and those obtained via our combined smoothing method. The top left, bottom left, top right, and bottom right panels show the inclination, position angle, rotation speed, and velocity dispersion profiles, respectively. The vertical dashes in the top left panel mark the radii at which the data for each resolution level independently start and end.
• Figure 5: Demonstration of our multi-resolution approach for J1106–14 (left) and J0309–41 (right). The top row shows the per data point weighting functions used in the smoothing, with the second row displaying the width of the Gaussian kernel as a function of radius. The dashed black $s(r)$ profile shows the kernel widths used to smooth the inclination, position angle, and velocity dispersion profiles, while the grey solid profile represents those used to smooth the combined rotation curve. The third and fourth rows present the inclination and position angle profiles obtained by independently fitting each resolution level (data points correspond to Stage 1 fits from $^\mathrm{3D}$barolo; lines show profiles after Stage 2), alongside the combined, smoothed profiles shown by a heavy black line. The bottom two rows display the rotation curves and velocity dispersion profiles derived from each resolution level independently (coloured lines), using the combined inclination and position angle profiles. The smoothed curves, calculated using the same weighting functions, are shown in black, with shaded regions indicating the asymmetric uncertainty ranges. The double-sided arrows plotted in the $v_\mathrm{rot}$ panels represent the beam major axis lengths for each resolution level. The colour coding, linestyles, and marker styles used are as follows: r05_t0 (dotted line; circle markers; light blue), r10_t0 (solid line; triangle markers; purple), r15_t0 (dashed line; diamond markers; pink), r05_t60 (dash-dot line; 'X' markers; orange), and r10_t90 (dash-double-dot line; star markers; yellow).