Spin alignment of stars in old open clusters

TL;DR

This study reveals that stars within old open clusters exhibit strong spin alignment, indicating that the initial angular momentum of their birth clouds was effectively transferred to individual stars and persisted over billions of years.

Contribution

It provides observational evidence of stellar spin alignment in old clusters and links it to the initial angular momentum conditions of the cluster-forming molecular clouds.

Findings

Stars in the clusters show strong spin alignment.

Simulations suggest at least 50% rotational kinetic energy in proto-clusters.

Angular momentum transfer from cloud to stars is efficient and long-lasting.

Abstract

Stellar clusters form by gravitational collapse of turbulent molecular clouds, with up to several thousand stars per cluster. They are thought to be the birthplace of most stars and therefore play an important role in our understanding of star formation, a fundamental problem in astrophysics. The initial conditions of the molecular cloud establish its dynamical history until the stellar cluster is born. However, the evolution of the cloud's angular momentum during cluster formation is not well understood. Current observations have suggested that turbulence scrambles the angular momentum of the cluster-forming cloud, preventing spin alignment amongst stars within a cluster. Here we use asteroseismology to measure the inclination angles of spin axes in 48 stars from the two old open clusters NGC~6791 and NGC~6819. The stars within each cluster show strong alignment. Three-dimensional hydrodynamical simulations of proto-cluster formation show that at least 50 % of the initial proto-cluster kinetic energy has to be rotational in order to obtain strong stellar-spin alignment within a cluster. Our result indicates that the global angular momentum of the cluster-forming clouds was efficiently transferred to each star and that its imprint has survived after several gigayears since the clusters formed.

Tables

Table 1. Table 1 : Global properties of NGC 6791 and NGC 6819. The total masses in units of a solar mass show that both clusters are massive, with NGC 6791 one of the most massive known in the Galaxy [ 25 , 26 ] . The size is computed in this study by means of the angular radii [ 25 , 26 ] and the distance modulus from asteroseismology [ 14 ] . Ages are based on eclipsing binaries and triple systems [ 17 , 27 ] . The galactic coordinates refer to the astronomical epoch J2000. The average mass of a core-He-burning star, M ¯ RC subscript ¯ 𝑀 RC \overline{M}_{\mathrm{RC}} , is calculated from asteroseismic scaling relations and it is comparable to that of the shell-H-burning red giants of the same cluster because of the low mass loss [ 28 ] . The total number of stars analyzed refers to the pulsating red giants whose orientation of the spin axis has been measured in this work. The corresponding 1 ​ σ 1 𝜎 1\sigma random error is shown for distance modulus and average mass of the stars.

Open cluster	NGC 6791	NGC 6819
Total mass ($M_{\odot }$)	$\sim 5000$	$\sim 2600$
Distance modulus ${\left(m-M\right)}_0$	$13.11\pm 0.06$	$11.85\pm 0.05$
Size (pc)	$\sim 10$	$\sim 7$
Age (Gyr)	$\sim 8.3$	$\sim 2.4$
Galactic coordinates	$70.0$ (long.), $+10.9$ (lat.)	$74.0$ (long.), $+8.5$ (lat.)
${\overline{M}}_{\mathrm{RC}}$ ($M_{\odot }$)	$1.15\pm 0.03$	$1.65\pm 0.04$
Stars analyzed	25	23

Equations

$$\rho (r)={\rho }_0{\left[1+{\left(\frac{r}{r_0}\right)}^2\right]}^{-1}.$$

$$\sum _{i=1}^N{\left({\vec{j}}_i\cdot \vec{z}\right)}^2={\vec{z}}^T\text{mbox}{\mathbf{J}}^T\text{mbox}\mathbf{J}\vec{z}.$$

$$\alpha =\frac{1}{N}\sum _{i=1}^N{\cos }^2{\theta }_i.$$

Full text

†† {affiliations} Laboratoire AIM Paris-Saclay, CEA/DRF — CNRS — Université Paris Diderot, IRFU/SAp Centre de Saclay, F-91191 Gif-sur-Yvette Cedex, France Instituto de Astrofísica de Canarias, E-38200 La Laguna, Tenerife, Spain Departamento de Astrofísica, Universidad de La Laguna, E-38205 La Laguna, Tenerife, Spain INAF - Osservatorio Astrofisico di Catania, Via S. Sofia 78, I-95123 Catania, Italy Space Science Institute, 4750 Walnut street Suite 205, Boulder, CO 80301, USA Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark Université Grenoble Alpes, IPAG, F-38000 Grenoble, France; CNRS, IPAG, F-38000 Grenoble, France

About half of the overall star formation in the Milky Way is occurring in the 24 most massive giant molecular clouds[1]. The star forming regions are obscured by dust, hence direct observations are limited to the infrared and radio bands[3, 2]. However, open clusters can be studied in a broad range of wavelengths because they contain small amounts of interstellar gas and dust. The great advantage of studying stars in a cluster — as opposed to field stars that often originate from dissolved small stellar systems — is that they can preserve the signature of the initial conditions of the progenitor molecular cloud.

It is believed that molecular clouds satisfying the Jeans instability undergo gravitational fragmentation in which the internal motions are strongly influenced by turbulence[4, 9]. This suggests that the angular momentum from the progenitor cloud cannot leave any significant imprint of its action on the stars born in the cluster. However, if the stars inherit the physical properties of the molecular cloud, they should to some extent reflect its average angular momentum. To investigate the angular momentum imprint, requires measurements of the space orientation of the stellar-spin axis. Previous analyses conducted on young open clusters did not find evidence of stellar-spin alignment[5].

Asteroseismology, the study of stellar oscillations, has proven to be a powerful tool to obtain model-independent information on the inclination angle of the stellar angular momentum vector, especially for red giant stars[10, 11, 7, 8]. Red giants are typically low- and intermediate-mass stars that have evolved off the main sequence of the stellar evolution. Most red giants oscillate and their oscillations can be analyzed through a Fourier frequency spectrum of their light curve. The spectrum of a red giant contains a comb-like structure of tens and sometimes more than a hundred radial and non-radial oscillation modes, most of which are mixed modes originating by the coupling between acoustic and gravity modes[12]. Each oscillation mode is identified by an angular degree l, which gives rise to a multiplet of ($2l+1$) different components through the degeneracy lifted by the stellar rotation[6]. Each rotationally split component is in turn identified by an azimuthal number, $m\leq|l|$. The dipolar ($l=1$) mixed modes are the most suited for measuring the orientation of the spin axis in red giants[13].

We have investigated 48 oscillating red giant stars, with typical masses within the range $\sim 1.1$-$1.7$ $M_{\odot}$ ($M_{\odot}$ being the mass of the Sun), that belong to the open clusters NGC 6791 and NGC 6819[14, 15, 16]. The most relevant physical properties of the two open clusters are outlined in Table 1. Both clusters are old, with NGC 6791 being one of the oldest known in our Galaxy[17], which implies that the initial molecular clouds were massive enough to ensure that the cluster evaporation time — the time it takes for all the members of a cluster to be ejected by internal stellar encounters — is well beyond the gigayear (Gyr) time scale. We used four years of time-series photometry obtained by NASA’s Kepler mission. We measure the asteroseismic properties[18, 19] of a total of about 380 rotationally split dipolar mixed modes — identified from a set of more than 3900 oscillation modes — and we use them to measure the spin-inclination angles (see Methods and Supplementary Fig. 1 for an example of the fits to the oscillation modes).

The distributions of the spin inclinations (Fig. 1), show that about $70$% of the stars in each cluster have a strong level of alignment, with a low to mid angle for NGC 6791 ($\theta\approx 30^{\circ}$ and an alignment coefficient $\alpha\simeq 0.77$) and a low angle for NGC 6819 ($\theta\approx 20^{\circ}$, $\alpha\simeq 0.74$), close to a pole-on configuration (see Methods for more details, and Supplementary Tables 1 and 2 for a list of all the results). We also notice a clear cut-off for higher angles (mid to high) in both clusters, where instead a larger number of stars would be expected if the spin vectors were uniformly (randomly) distributed in three dimensions. The binary stars identified in NGC 6819 appear to follow a similar alignment trend to that of the single star members of the cluster. The probability that the observed levels of alignment are the result of a random distribution is less than $1$ in $10^{9}$ for NGC 6791, and $1$ in $10^{7}$ for NGC 6819. Conversely, the distribution obtained for an independent sample of $36$ field red giants (not members of any cluster) shows no significant stellar-spin alignment ($\alpha\simeq 0.38$), even when considering subsamples of stars in the same evolutionary stage ($\alpha\simeq 0.41$ for shell-H-burning and $\alpha\simeq 0.35$ for core-He-burning stars, respectively, see Methods and Supplementary Table 5). In addition our reanalysis of an independent sample of main-sequence stars in NGC 6819 hinting at high spin-inclination angles from their rotational periods and projected equatorial velocities[20], reveals that their period measurements are not reliable and hence not in conflict with our low-inclination results (see Methods and Supplementary Fig. 2 and 3 for more details). In Fig. 2 we provide the spatial positions of the cluster red giants within fields of view approximately corresponding to the observed size of each cluster, as reported in Table 1. The stars appear to sample the entire field of each cluster, with a tangential distance from star to star varying from $\approx 0.1$ parsec (pc) near the center up to a few pc in the peripheral regions. This demonstrates that the spin alignment is observed across the entire clusters.

N-body simulations coupled with observations of old open clusters, aimed at reproducing their dynamical evolution, show that the stellar angular momentum can have an impact on colliding stars and on the orbital configurations of multiple stellar systems[21]. The orbital parameters of eccentricity, inclinations, and periods of multiple stellar systems are mostly influenced by tidal forces[22]. For individual stars the angular momentum typically evolves as a spin down over time[20] through either mass loss by stellar winds, magnetic braking, or tidal friction if the star is captured to form a binary. Given the average distances among the star members of an open cluster, the effect of gravitational N-body interactions on producing any significant spin alignment is negligible even for timescales of several Gyr. This is especially true for tidal forces, because their strength is a function of the inverse third power of the distance between two stars. Furthermore, using the galactic latitudes and distance moduli reported in Table 1, the heights of the two clusters from the galactic plane are $\approx 800\,$pc and $\approx 350\,$pc for NGC 6791 and NGC 6819, respectively, showing that they are located far from the most crowded regions that constitute the inner galactic disk. The position and long survival time of the two clusters therefore suggests that they experienced significantly less disruptive encounters with giant molecular clouds than other open clusters located inside the disk[23]. This means that the strong spin alignment observed in the red giants of our sample is very likely to be originating from the formation epoch of the cluster, thus preserving the signature of the early dynamical processes characterizing the progenitor molecular cloud.

For exploring this scenario we have performed three-dimensional hydrodynamical simulations of a collapsing molecular cloud leading to the formation of a proto-cluster under the action of gravitational potential[24] (see Methods for further explanations). Figure 3a shows that when considering only a turbulent velocity field, the distribution of the resulting spin inclinations resembles that of a uniform orientation in three dimensions. By introducing a global rotation as an additional initial condition and imposing a ratio of rotational kinetic energy over turbulent kinetic energy of $E_{\mathrm{rot}}/E_{\mathrm{tur}}\simeq 1$, the spin alignment produced in stars forming with masses greater than $0.7\,M_{\odot}$ becomes comparable to that found in our observations, with $\alpha\simeq 0.6$ (Fig. 3b and c). When $E_{\mathrm{rot}}/E_{\mathrm{tur}}<1$ instead, the spin alignment is only marginal (see Supplementary Table 3 for all the values we investigated). From our simulations we also observe that for stellar masses below $0.7\,M_{\odot}$ the turbulent motions still dominate over the effect of rotation even in the case $E_{\mathrm{rot}}/E_{\mathrm{tur}}\simeq 1$, thus preventing any spin alignment among stars of this low mass range. This suggests that when not enough mass from the molecular cloud is accreted into individual pre-stellar cores, the information from the cloud’s average angular momentum is lost in the stellar-spin fluctuations induced by turbulence at the scales of the forming star. A strong component of the cloud’s rotational kinetic energy, at least comparable to that of the turbulence, can therefore be responsible of efficiently aligning the spin axes within the stellar members of a cluster because the degree of alignment reflects the importance of the cloud’s average angular momentum. The two open clusters NGC 6791 and NGC 6819 could have originated through a formation process involving a compact collapsing molecular cloud giving rise to a rotating proto-cluster (Fig. 3c). During the cluster formation, stars with masses at least that of our Sun are more likely to inherit a significant fraction of the cloud’s average angular momentum with respect to stars having masses below $0.7\,M_{\odot}$. By measuring stellar spin inclinations for solar-mass stars in open clusters we can therefore constrain the initial energy budget of the progenitor molecular cloud, its global rotation, as well as the efficiency by which the cloud’s average angular momentum is transferred to the individual stellar members of the clusters. This result allows us to explore and reconstruct the dynamical evolution, structure, and geometry of galactic star forming regions that have formed stellar clusters back in times comparable to the age of our Universe.