Orbit-based structural decomposition and stellar population recovery for edge-on barred galaxies

TL;DR

This study extends orbit-based dynamical modelling to edge-on barred galaxies with BP/X-shaped bars by decomposing stellar orbits into bar, bulge, disc, and halo components and tagging them with ages and metallicities. The barred population-orbit superposition framework integrates MGE-derived potentials, NNLS orbit weights, and Voronoi-binned orbit bundles to recover component masses and 2D population maps from mock kinematic and stellar-population data. Across 12 Auriga-based edge-on mocks, the method accurately constrains mass fractions (halo ≤0.03 bias; bar/disc ≤0.15; bulge ≤0.10) and mean ages (≤1 Gyr bias) and metallicities (≤0.5 Z⊙ bias, with some exceptions), while reproducing negative age gradients in bars/discs and negative metallicity gradients in bars/bulges. The results demonstrate the feasibility of using orbit-based decompositions to study the coexistence of bars, classical bulges, and nuclear discs and to probe their formation histories with future GECKOS-like observations.

Abstract

In our previous paper, we developed an orbit-superposition method for edge-on barred galaxies and constructed a set of dynamical models based on different mock observations of three galaxies from the Auriga simulations. In this study, we adopted 12 cases with side-on bars (three simulated galaxies, each with four different projections). We decomposed these galaxies into different structures combining the kinematic and morphological properties of stellar orbits. We then compared the model-predicted components to their true counterparts in the simulations. Our models can identify (BP/X-shaped) bars, spheroidal bulges, thin discs, and spatially diffuse stellar halos. The mass fractions of bars and discs are well constrained with absolute biases of $|f_{\rm model}-f_{\rm true}|\le0.15$. We recovered the mass fractions of halos with $|f_{\rm model}-f_{\rm true}|\le0.03$. For the bulge components, 10 out of 12 cases exhibit $|f_{\rm model}-f_{\rm true}|\le0.05$, while the other two cases exhibit $|f_{\rm model}-f_{\rm true}|\le0.10$. Then, by tagging the stellar orbits with ages and metallicities, we derived the chemical properties of each structure. For the stellar ages, our models recovered the negative gradients in the bars and discs, but exhibited relatively larger uncertainties for age gradients in the bulges and halos. The mean stellar ages of all components were constrained with absolute biases $|t_{\rm model}-t_{\rm true}|\rm\lesssim1\,Gyr$. For stellar metallicities, our models reproduced the steep negative gradients of the bars and bulges, as well as all different kinds of metallicity gradients in the discs and halos. Apart from the bulge in the simulated galaxy Au-18, the mean stellar metallicities of all other components were constrained with absolute biases of $|Z_{\rm model}-Z_{\rm true}|\rm\le0.5\,Z_{\odot}$.

Figures (21)

• Figure 1: Mock stellar kinematic, age, and metallicity maps (left panels), and their corresponding error maps (right panels) for Au-23 with viewing angles, $(\theta_{\rm T},\varphi_{\rm T})=(85^\circ,50^\circ),$ with $\rm 1\,arcsec=0.2\,kpc$. From top to bottom: Mean velocity, $V$; velocity dispersion, $\sigma$; third-order, $h_3$, and fourth-order, $h_4$, Gauss-Hermite coefficients; stellar age, $t$; and stellar metallicity, $Z$. The kinematic maps and their error maps are the same as Fig. 2 of Jin2025. We note that the kinematic error maps exhibit similar statistical properties as they are generated from particle noise Tsatsi2015, but their ranges are different (as indicated by the colour bars in the right panels).
• Figure 2: Structural decomposition based on orbital properties demonstrated using Au-23-85-50 and compared with the truth. Four properties are used to decompose the galaxy: Circularity, $\lambda_z$; time-averaged radius, $R$; axis ratio, $p_{\rm orb}$, in the $x$-$y$ plane; and axis ratio, $q_{\rm orb}$, in the $x$-$z$ plane. The top panels display the true distributions while the bottom panels correspond to the model results. Left panels: Stellar orbit distributions of the entire galaxy in the $\lambda_z$--$R$ phase space. We calculate the $\rm1\,kpc$ moving average of the cold orbit fraction $f_{\rm cold}$ ($\lambda_z\ge0.8$; $\rm 1\,arcsec=0.2\,kpc$) and define the dynamical bar length, $R_{\rm bar}$, as the smallest radius where $f_{\rm cold}\ge0.5$. Orbits with $R\le R_{\rm bar}$ are classified as bar+bulge components; those with $R>R_{\rm bar}$ are categorised as disc+halo components. The values of $R_{\rm bar}$ are indicated by the blue dashed lines and the annotations. Middle panels: Stellar orbit distributions for bar and bulge components in the $\lambda_z$--$p_{\rm orb}$ phase space. Orbits with $\lambda_z\le0.5$ and $p_{\rm orb}\ge0.8$ are assigned to the bulge; other orbits constitute the bar. The boundaries between the bar and bulge are shown by the blue dashed lines. Right panels: Stellar orbit distributions for disc+halo components in the $\lambda_z$--$q_{\rm orb,in}$ phase space. Orbits with $\lambda_z\le0.5$ and $q_{\rm orb,in}\ge0.3$ are categorised as the stellar halo; while the other orbits make up the disc. The boundaries between the disc and halo are shown by the blue dashed lines.
• Figure 3: Trajectories of several representative orbits for Au-23-85-50. The first four columns display the orbital trajectories in the $x$-$y$, $x$-$z$, and $y$-$z$ planes (the bar's rotating frame), including two bar orbits and two bulge orbits, with their axis ratios $p_{\rm orb}$ and $q_{\rm orb}$ presented in the text. The fifth and sixth columns show the orbital trajectories in the $x_{\rm in}$-$y_{\rm in}$, $x_{\rm in}$-$z_{\rm in}$, and $y_{\rm in}$-$z_{\rm in}$ planes (the inertial frame), including a disc orbit and a halo orbit, with their axis ratios, $p_{\rm orb,in}$ and $q_{\rm orb,in}$, presented in the text. We note that $p_{\rm orb}$ and $q_{\rm orb}$ are calculated in the bar's rotating frame, while $\lambda_z$, $p_{\rm orb,in}$, and $q_{\rm orb,in}$ are calculated in the inertial frame.
• Figure 4: True and model-predicted probability density distributions of stellar orbits in the $\lambda_z$--$R$ phase space for different structures in Au-23. The top panels indicate the true distributions while the bottom panels represent the model results from Au-23-85-50. From left to right, the panels show the stellar orbit distributions for the bar, the bulge, the disc, and the stellar halo. The probability densities of all orbits within the data coverage ($R\le\rm50\,arcsec$) are normalised to unity, with their values indicated by the colour bar. The horizontal black dotted lines denote $\lambda_z=0$. The vertical blue dashed lines represent the true and model-predicted bar lengths, $R_{\rm bar}$, derived from orbit analysis, with their values shown in the text.
• Figure 5: Orbit bundles divided in the phase space of circularity, $\lambda_z$, versus time-averaged radius, $R$, for Au-23-85-50. The left panel represents bar orbits while the right panel is for orbits from other components, including the bulge, disc, and stellar halo. The probability densities of all orbits within the data coverage ($R\le\rm50\,arcsec$) are normalised to unity, with their values indicated by the colour bar. For each panel, orbits in $\lambda_z$--$R$ phase space are divided into different bundles by using the Voronoi binning method, with each bundle containing $\gtrsim0.5\%$ of the total orbit weight. The blue asterisks and lines indicate the centres and boundaries of Voronoi bins, respectively.