Spiral arms across stellar populations in simulations via the local dimension method

Context. The origin and nature of spiral arms remain unclear. Star forming regions and young stars are generally strongly associated to the spiral structure, but there are few quantitative predictions from simulations about the involvement of stars of different ages. Aims. We aim to quantify the interplay between spiral arms and different populations. Methods. We use a hydrodynamical simulation of an isolated disc galaxy displaying a dynamic multi-armed spiral structure. Inspired by cosmological structure metrics, we develop a new method, the local dimension, that robustly delineates arms across populations and through space and time. Results. We find that all stars, including those as old as 11Gyr, support the arms. The spiral strength decreases with stellar age up to 2Gyr-old stars and remains nearly constant for older stars. However, the scaling between arm strength and age (or velocity dispersion) depends on the strength of the global spiral structure at each time. Almost all stars formed in arms remain within them for no more than 140-180Myr, whereas old stars leave arms about three times faster. Even if the youngest populations dominate in the production of the spiral torques at early times, all populations contribute equally at later times. Conclusions. Our results highlight the power of the local dimension for studying complex spiral structures and show that all stellar populations in the disc partake in the arms. Since in our model we see spiral arms in populations with velocity dispersions up to 90km/s, which are comparable to those of the Milky Way, we predict that old Galactic populations could also exhibit spiral structure.

💡 Research Summary

This paper investigates how spiral arms in a Milky Way‑like disc galaxy involve stellar populations of different ages, using a high‑resolution isolated galaxy simulation and a novel structural diagnostic called the “local dimension” (D). The simulation (model M1_c_b from Fiteni et al. 2021) follows an isolated disc embedded in a live dark‑matter halo (M200 ≈ 10¹² M⊙) for 13 Gyr. Gas cools from a hot corona to form a stellar disc; star particles have a mass of ~9.3 × 10³ M⊙ and a softening length of 50 pc. The disc develops a weak bar briefly around 4 Gyr, but the analysis excludes the inner 4 kpc to focus on spiral structure. Snapshots are taken every 500 Myr (with some analyses at 5 Myr cadence).

The local dimension method adapts a cosmological tool for measuring the geometry of large‑scale structure. For each point on a 0.2 kpc grid, the number of particles inside concentric cylinders of radius r (0.2–2 kpc) is counted. Assuming N(<r) ∝ rᴰ, a linear fit in log‑log space yields D. To remove the effect of the exponential radial density gradient, each particle is weighted by the inverse of the azimuthally averaged surface density at its radius. In a perfectly axisymmetric disc D≈2 everywhere; filamentary overdensities such as spiral arms produce D < 2, with the strongest arms reaching D≈1.5. The authors adopt D = 1.9 as a threshold: regions with D < 1.9 are identified as spiral arms. This definition is automatic, shape‑independent, and highlights low‑contrast arm segments that are hard to see in surface‑density maps alone.

Applying this to the simulation, the authors find that at early times (5 Gyr) the disc hosts a clear two‑armed pattern plus additional weaker arms, with low D values indicating strong, narrow features. The arms weaken around 6.5 Gyr (D values cluster near 2), then become more pronounced again at 8.5 Gyr and 13 Gyr, consistent with Fourier‑mode analyses reported in earlier work.

Stellar populations are split by age: 0–0.5 Gyr, 0.5–1 Gyr, 1–2 Gyr, 2–5 Gyr, and 5–11 Gyr. Young stars (≤0.5 Gyr) trace the arms most sharply, showing the lowest D. For ages up to ~2 Gyr the median D increases roughly linearly with age, indicating that dynamically colder, younger stars support stronger, narrower arms. Beyond 2 Gyr the median D plateaus near 1.9–2.0, meaning that even old stars still reside in arm‑like overdensities, albeit with less contrast.

The authors quantify the residence time of stars within arms (the interval during which a star’s D remains below 1.9). Young stars stay in arms for an average of 140–180 Myr, while old stars (≥5 Gyr) remain only ~50 Myr, i.e., they leave arms about three times faster. This difference correlates with the increase of velocity dispersion with age; even stars with σ ≈ 90 km s⁻¹ (comparable to the Milky Way thick disc) still exhibit arm participation.

Finally, the contribution of each age bin to the non‑axisymmetric gravitational torque (τ) is measured. Early in the simulation the youngest stars generate >70 % of τ, but by the end of the run all age bins contribute roughly equally. This demonstrates that spiral arms are not a transient feature driven solely by recent star formation; instead, the entire stellar disc, regardless of age, participates in maintaining the spiral pattern.

In summary, the paper (1) introduces a robust, assumption‑free method for identifying spiral arms in particle simulations, (2) shows that stars of all ages, even those as old as 11 Gyr, are part of the spiral structure, (3) finds that arm strength declines with age up to ~2 Gyr and then stabilizes, and (4) predicts that old Galactic populations (e.g., red clump or thick‑disc stars) should exhibit detectable spiral signatures, consistent with the velocity dispersions observed in the Milky Way. These results provide a valuable framework for interpreting upcoming large‑scale spectroscopic and IFU surveys of external galaxies and for connecting Milky Way stellar kinematics to spiral structure.