A star cluster’s motion can tell more than one kind of age

What does a cluster’s age measure?

Stars form inside turbulent gas clouds, but their birth and their assembly into recognizable clusters need not happen simultaneously. A cluster can also begin expanding while some of its stars are still forming. Asking how old it is therefore requires deciding which event to date.

Astronomers commonly estimate stellar ages by comparing stars’ brightnesses and temperatures with models of stellar evolution, a technique called isochrone fitting. Another approach uses positions and velocities to reconstruct earlier configurations. These motion-based estimates, called dynamical ages, are increasingly practical thanks to measurements from the European Space Agency’s Gaia mission.

But what do those estimates actually measure? Isabella Armstrong, Alison Sills and Claude Cournoyer-Cloutier investigate that question in an arXiv preprint whose submission record reports acceptance for publication in The Astrophysical Journal. Their study is a numerical experiment, not a new measurement of an observed cluster.

Rewinding a history that is already known

The researchers used a simulation beginning with a gas cloud containing 20,000 times the Sun’s mass. Its initial evolution included gas dynamics, magnetic fields, star formation, stellar gravity and feedback from stars. By 4.45 million years, the simulation had formed 4,658 stars and reached gas expulsion. The team then followed stellar gravitational interactions until 20 million years.

At that endpoint, they identified stellar groups and concentrated on two: a mostly gravitationally bound cluster containing 4,184 stars, and a mostly unbound group containing 92. Bound stars remain held together by gravity; unbound stars can disperse. Both systems nevertheless showed signs of expansion.

The simulation supplies something observations cannot: the stars’ actual formation times and subsequent histories. The researchers used each group’s median stellar age as a stand-in for an isochronal age, rather than fitting synthetic observations to stellar models.

They compared five dynamical methods. Three rewind the whole group and seek its most compact reconstructed configuration, using different mathematical measures of size. Two instead calculate when individual stars would have passed closest to a moving cluster center, then summarize those individual times.

All five reconstructions assume constant stellar velocities. That assumption simplifies the rewind, but it is not how the simulated stars actually evolve under gravity.

Different selections produce different clocks

The three size-based methods failed to recover stellar ages reliably in the mostly bound cluster. Stars orbiting within a gravitationally bound system cannot generally have their histories reconstructed by extending their current motions backward along straight lines. Even a detectable expansion signal did not make the whole cluster suitable for this approach.

For the mostly unbound group, size-based ages increased broadly with elapsed time. However, they generally indicated younger ages than the median stellar age. The covariance-based methods more closely traced the onset of expansion than the group’s actual minimum size.

One example makes the distinction concrete. Using one size measure, the unbound group really was smallest about 2.16 million years after the simulation began. Its reconstructed minimum typically fell near 2.72 million years, close to its expansion onset at about 2.76 million years. These are milestones within this simulated cloud, not universal timescales for star formation.

The two individual-star methods also differed. The evaporation method emphasizes stars with the oldest reconstructed departure histories. In these tests, it supplied an upper limit on the median stellar age, rather than the closest estimate of that age.

The closest-approach method instead takes the median traceback time of selected outward-moving stars whose reconstructed paths enter the cluster’s half-mass radius. It best followed the median stellar age in both systems. Its success in the mostly bound cluster depended on using a suitable outward-moving subset, not on rewinding every member successfully.

Promising, but not a universal calibration

The comparison supports matching the method to the question: expansion history and typical stellar birth time are different targets.

Its limits matter. The analysis follows two groups from one simulated cloud, without observational measurement errors or a Galactic gravitational potential. Membership is unusually well controlled because every star’s origin is known. Real surveys must distinguish members from unrelated stars, handle binaries and measure a cluster’s bulk motion accurately.

The study also warns that unusual motion does not necessarily mean a star is an interloper: genuine members can have their velocities altered by interactions. The median closest-approach method is therefore a promising age proxy for expanding systems, but these simulations do not establish its accuracy for every real cluster.