Star cluster disruption by giant molecular clouds

We investigate encounters between giant molecular clouds (GMCs) and star clusters. We propose a single expression for the energy gain of a cluster due to an encounter with a GMC, valid for all encounter distances and GMC properties. This relation is verified with N ‐body simulations of cluster–GMC encounters, where the GMC is represented by a moving analytical potential. Excellent agreement is found between the simulations and the analytical work for fractional energy gains of Δ E /| E 0 | < 10 , where | E 0 | is the initial total cluster energy. The fractional mass loss from the cluster scales with the fractional energy gain as (Δ M / M 0 ) = f (Δ E /| E 0 |) , where f ≃ 0.25 . This is because a fraction 1 − f of the injected energy goes to the velocities of escaping stars, that are higher than the escape velocity. We therefore suggest that the disruption time of clusters, t dis , is best defined as the time needed to bring the cluster mass to zero, instead of the time needed to inject the initial cluster energy. We derive an expression for t dis based on the mass loss from the simulations, taking into account the effect of gravitational focusing by the GMC. Assuming spatially homogeneous distributions of clusters and GMCs with a relative velocity dispersion of σ cn , we find that clusters lose most of their mass in relatively close encounters with high relative velocities (∼2σ cn ) . The disruption time depends on the cluster mass ( M c ) and half‐mass radius ( r h ) as t dis = 2.0  S ( M c /10 4  M ⊙ )(3.75 pc/ r h ) 3 Gyr , with S ≡ 1 for the solar neighbourhood and S scales with the surface density of individual GMCs (Σ n ) and the global GMC density (ρ n ) as S ∝ (Σ n ρ n ) −1 . Combined with the observed relation between r h and M c , that is, r h ∝ M λ c , t dis depends on M c as t dis ∝ M γ c . The index γ is then defined as γ= 1 − 3λ . The observed shallow relation between cluster radius and mass (e.g. λ≃ 0.1 ), makes the value of the index γ= 0.7 similar to that found from observations and from simulations of clusters dissolving in tidal fields (γ≃ 0.62) . The constant of 2.0 Gyr, which is the disruption time of a 10 4 M ⊙ cluster in the solar neighbourhood, is about a factor of 3.5 shorter than that found from earlier simulations of clusters dissolving under the combined effect of Galactic tidal field and stellar evolution. It is somewhat higher than the observationally determined value of 1.3 Gyr. It suggests, however, that the combined effect of tidal field and encounters with GMCs can explain the lack of old open clusters in the solar neighbourhood. GMC encounters can also explain the (very) short disruption time that was observed for star clusters in the central region of M51, since there ρ n is an order of magnitude higher than that in the solar neighbourhood.