Formation and evolution of open star clusters with the Gaia-ESO Survey

The work of this thesis has developed in the context of the study of the dynamical evolution of open star clusters, a key topic that has important implications for our understanding of cluster formation and dissolution. Almost all stars form in clusters inside giant molecular clouds, and the majority of these systems rapidly dissipate within the first 10 – 100 Myr. Several models have been proposed to understand the evolution of these systems. Such models can indeed be tested by examining the kinematic and dynamical properties of clusters covering a wide range of ages and masses. This is now possible thanks to the Gaia space mission and to the complementary ground-based spectroscopic surveys. In particular, in the thesis work I focused on the data provided by the Gaia-ESO large public spectroscopic survey (GES). GES observed Milky Way field stars, as well as a sample of 65 open clusters covering a wide age range. For those clusters GES delivered precise radial velocities, stellar parameters, and abundances, that I used to analyze the kinematic properties and investigate the dynamical evolution of some of these open clusters. I divided the work in two parts: in the first one I studied clusters with ages between 20 and 50 Myr, while in the second one I focused on clusters which older than 100 Myr. The phase between 20 and 50 Myr is an interesting phase for the early dynamical cluster evolution because the embedded phase is over (first 2 - 5 Myr) and the molecular gas of the parent cloud has been expelled (∼ 5 - 10 Myr). Thus, the OCs have already completed the process of violent relaxation predicted by the models based on stellar feedback and gas expulsion, while the tidal effects caused by outer gravitational fields have not had the time to modify the system properties since their timescales are longer (∼ 100 - 300 Myr) than the age of these clusters. Instead, determining the kinematic and dynamical properties in clusters with age until several Gyrs (i.e., ages greater than 100 Myr) is fundamental to understand how internal and external processes, such as stellar interactions or tidal shocks, affect the cluster evolution and dissipation on a longer timescale. Clusters at these ages were survived to both early gas expulsion and late tidal interactions. Therefore, they are expected to be in a virialized state. The main goal of this work is the study and comparison of the observational kinematic and dynamical properties with the predictions of the models proposed in literature for the cluster survival and disruption. The spectroscopic data provided by the Gaia-ESO Survey allowed us to obtain a list of spectroscopic candidates in the four clusters with age between 20 and 50 Myr. Using three independent spectroscopic criteria, I was able to discard the contaminant stars in each sample. Then, analyzing the radial velocity distribution and using a maximum likelihood technique, in each cluster I determined the intrinsic radial velocity dispersion and I estimated a probability to belong to the cluster for each candidate members. I found many new high-probability members that are extended across the whole area covered by Gaia-ESO Survey observations, suggesting that these clusters could be more extended than previously thought. As a final step, I estimated the total mass of each cluster and investigated the cluster dynamical state. The main new result is that the velocity dispersion measured with Gaia-ESO Survey data is about a factor two higher than that analytically derived by assuming virial equilibrium, indicating that the target clusters are supervirial and two explanations are given. The first is the residual gas expulsion scenario, which suggests that clusters became unbound after the feedback from massive stars swept out the gas. The second is that the observed velocity dispersion could be higher than the virial dispersion because most stellar systems do not fully relax, even after 20 – 30 crossing times, as shown in several new N-body simulations. Furthermore, for these four clusters a group based in Leiden independently derived the intrinsic velocity dispersion from the astrometric parameters of their members in the TGAS catalogue (Gaia DR1). Whilst the velocity dispersion measured from the RVs is higher than that measured from TGAS data, given the error on astrometric parameters, the conclusions are uncertain. On the other hand, if confirmed, the discrepancy may be due to energy equipartition or to possible anisotropy in the velocity distribution. We also mention, that our results are based on certain assumptions on the binary fraction in the investigated clusters, which also must be further investigated. Significant progress will be possible with the second Gaia data release. As mentioned, the second part of the work focused on seven clusters with ages between 100 Myr and 3.5 Gyr. Contrary to the other younger clusters, in systems with these ages the initial target selection is less affected by contaminant stars and, furthermore, the spectroscopic criteria employed to identify the contaminants cannot be applied. Therefore, for the kinematic and dynamical analysis I used the full sample of observed stars. Employing the same maximum likelihood technique, I derived the intrinsic velocity dispersion and the probability of each star to belong to the cluster. Then, using the photometry, I estimated the cluster the total mass and the half mass radius. I compared the velocity dispersions obtained with the Gaia-ESO Survey data and those under the assumption of the virial equilibrium and I found that six out seven clusters are in equilibrium, as expected from the evolution models. Instead, in one clusters the observed and the virial velocity dispersions are in agreement only within 2σ and this may be due to a higher fraction of binary stars. Further investigations will be necessary to check this result. Furthermore, I tested a theoretical scenario that describes the internal cluster evolution. I found that four out of seven clusters will never undergo core collapse due to the binary heating and they will expand until the tidal disruption. Conversely, in other three clusters the external members will expand while the central parts of these systems undergo to interior contraction that will lead to core collapse. These results are still preliminary since several theoretical and observational uncertainties still need to be addressed in a detailed way.