Stellar spin in young star clusters: comparison between simulations and observations

TL;DR

This study investigates the origin of the initial stellar spin distributions in very young clusters by pairing high-resolution MHD simulations of star-cluster formation with observational rotation-period data for clusters $\lesssim15$ Myr old. The simulations explore how cloud properties, via parameters $\alpha_{\mathrm{vir}}$, $\mathcal{M}$, and $\zeta$, shape the $P_{\mathrm{rot}}$–$M_\star$ relation and reveal a high-mass break driven by runaway accretion. A key finding is that simulated stars rotate far faster than observed due to their $\lesssim1$ Myr ages; quantifying the discrepancy requires rescaling angular momentum by $f_{\Delta L}$ values of roughly $78\%$–$94\%$, implying $80$–$95\%$ of the initial angular momentum must be shed in the first $0.1$–$1$ Myr. The results underscore that angular-momentum evolution is dominated by the earliest phases of cluster formation and that incorporating detailed star–disc coupling and wind/magnetic braking is essential to reproduce the observed spin distributions across young clusters.

Abstract

The angular momentum evolution of stars is crucial for understanding the formation and evolution of stars and star clusters. Using high-resolution magnetohydrodynamical (MHD) simulations of star formation in clouds with different physical properties, we study the initial distribution of stellar rotation periods in young clusters. We compare these results with observations of young Galactic clusters. Simulations qualitatively reproduce the observed trend of increasing rotation period with stellar mass. Additionally, simulations with lower virial parameter (ratio of turbulence to gravity) or solenoidal turbulence driving produce period-mass distributions that more closely match the observed ones. These simulations also recover the break in the mass-period relation. However, the break appears at higher masses than in observations and is absent in the youngest simulated clusters. This suggests that the emergence of the break is an important diagnostic of angular momentum evolution during the earliest stages of cluster formation. The simulations yield stars that rotate about an order of magnitude faster than those observed. This discrepancy mainly reflects the earlier evolutionary stage of the simulations, while unresolved physical interactions between stars and discs might also contribute. This conclusion is supported by simulations showing a significant period increase within 0.1-1 Myr. We quantify the required angular-momentum loss by rescaling simulated rotation periods to match observations, finding that 80-95% of the initial angular momentum must be removed within the first Myr. Our results highlight that understanding the earliest stages of star cluster formation is fundamental to addressing the angular momentum problem.

Figures (6)

• Figure 1: Stellar rotation period vs. stellar mass for the numerical simulations listed in Tab. \ref{['tab:tab sim']} (panel numbers correspond to simulation numbers). Stars are coloured according to their age, as defined in Sec. \ref{['sec:sim']} and indicated in the colour map. All simulations show the overall trend of longer periods at higher masses; several setups (e.g. 1, 4, and 5) also exhibit a high-mass break after which stars start to rotate faster. This break is interpreted as runaway accretion driving spin-up of massive stars. Simulations with younger stars, e.g. lighter colours, instead do not show evidence of the break. The break in stellar rotation vs. mass is also observed in young star clusters, albeit at lower stellar masses.
• Figure 2: Stellar rotation period as a function of stellar mass for all analysed clusters listed in Tab. \ref{['tab:tab cl']} (panel numbers correspond to cluster IDs). Stellar masses are derived via interpolation of PARSEC isochrones. Clusters included in the comparison with numerical simulations are marked with green labels. A broad dispersion in rotation periods is evident at young ages, which progressively narrows in older clusters (e.g. NGC 2422), indicating that the early diversity in stellar spins converges with time. Most clusters also show a characteristic break at the high-mass end, beyond which rotation periods decrease; this feature is particularly prominent in Blanco 1.
• Figure 3: Updated. Stellar rotation period vs. stellar mass for the simulations shown in Fig. \ref{['fig:sim']} (Tab. \ref{['tab:tab sim']}) together with the observations shown in Fig. \ref{['fig:all clusters']} (Tab. \ref{['tab:tab cl']}). Observations and simulations are displayed with different markers, and colour-coded by stellar/cluster age. Simulations reproduce the increasing period–mass trend at low masses but are typically faster than observations by roughly an order of magnitude, likely due to the age mismatch between very young simulated stars ($\lesssim1\,\mathrm{Myr}$) and older observed populations ($1-15\,\mathrm{Myr}$). Certain setups (e.g. compressive driving in panel, lower $\alpha_\mathrm{vir}$) exhibit a better agreement with the data in terms of period-mass values, spread in periods, with the high-mass break in simulations occurring at higher masses than observed.
• Figure 4: Stellar rotation period versus age for simulations and observations. Simulated stars are shown as circles, colour-coded by stellar mass. Observed clusters are represented by boxplots, where boxes and whiskers indicate the interquartile range (IQR) and 1.5 times the IQR, respectively, and horizontal lines mark the median period values. In all simulation setups, rotation periods increase with stellar age, indicating that stars spin down during the first $0.1$–$1\,\mathrm{Myr}$. On average, the oldest stars in each simulation rotate about an order of magnitude more slowly than the youngest ones, implying substantial angular-momentum loss at early times, consistent with the discussion in Sec. \ref{['sec:discussion']}.
• Figure 5: Same as Fig. \ref{['fig:sim comparison']} but including only clusters younger than $15\,\mathrm{Myr}$, after scaling simulated periods to best match the observational distributions. The inset reports the best-fit angular-momentum loss fraction $f_{\Delta L}$ (and uncertainty) and the corresponding $-\ln(\mathrm{PLR})$. The fits imply $\sim78$–$94\%$ angular-momentum must be lost between the $\sim0.1-1\,\mathrm{Myr}$ of the simulations and the few-$\mathrm{Myr}$-old observed clusters, with $\alpha_\mathrm{vir}=0.125$ (panel 7) and solenoidal driving (panel 5) setups providing the best overall matches.