Research

Globular cluster formation scenarios



Different formation scenarios

Young massive cluster NGC 3603. Image credits: NASA, ESA, R. O'Connell (University of Virginia), F. Paresce (National Institute for Astrophysics, Bologna, Italy), E. Young (Universities Space Research Association/Ames Research Center), the WFC3 Science Oversight Committee, and the Hubble Heritage Team (STScI/AURA). One of the biggest mysteries still unsolved in astrophysics is: How did globular clusters (GCs) form? These roughly spherical collections of stars tightly bound by gravity are of typical ages as old as (>)10 Gyrs, which means that they were formed around the same time as the galaxies they orbit. Only recently have we attained a high enough computational resolution, given their small scales compared to their host galaxies, to start answering this question. However, a reliable picture of their formation is yet not completely clear, and different formation scenarios could coexist.

For instance, one proposed mechanism is that they could be formed in their own dark matter (DM) minihalos, such as galaxies, but due to lack of observational constraints and poor data in the outskirts of GCs (where possible amounts of DM may still exist), this scenario remains considerably unexplored. Other possible formation scenarios include GCs as relics of young massive clusters formed in the high-redshift Universe, or being debris of past galaxy mergers or being simply formed in-situ along with their host. All these possibilities have arguments in favor and against them, with particular GCs being more or less likely to cope with the predictions of each scenario. Therefore, it is more arguable that these star clusters probably arose from more than a single formation channel.



Globular clusters embedded in dark matter

I have explored the formation scenario where GCs are formed inside their own DM mini-halos with the help of numerical N-body simulations performed by my collaborator, Pierre Boldrini. I have provided evidence that the existence of a DM mini-halo initially helps to shield the GC from tidal effects from its host galaxy.

Dark matter shield: Velocity dispersion map of DM particles for a GC embedded in DM, projected in the X vs. Y plane and centered in the center of mass of the GC system. We display the last six pericenters of its orbit, where the tidal effects are stronger. The extension of bound GC stars and bound DM particles are highlighted as dotted and dashed green lines, respectively, while the theoretical tidal radius is displayed as a solid green circle. The maps are color-coded logarithmically from blue (lower dispersion) to red (higher dispersion). The centers of Fornax and of the GC are represented as a thick green cross and a plus sign, respectively. For this cluster, we notice that the empirical tidal radius, well traced by the blue region, remains always larger than the bound stars radii. This argues in favor of the dynamical presence of a dark matter shield. This figure uses data from Vitral & Boldrini 2022.

This is because the dark extra mass triggers a tidal radius growth that allows the mini-halo to act as a protective shield against tidal stripping, being itself stripped beforehand the stars. As a consequence, tidal effects such as inflation of the stellar velocity dispersion, development of prominent tidal tails, ellipticity increase and diffusion of the stellar distribution profile are generally much milder in clusters that are embedded in DM.

Dark matter impact on tidal tails: Stellar distribution (and respective zoom in) of a GC for the case where it was originally embedded in a DM mini-halo (right) and where it was devoid of it (left). This video highlights more prominent tails in the DM-free case, while clusters formed inside DM mini-halos present a more compact stellar envelope. Hence, the dark matter shield (see image above) has the effect of delaying the formation of tidal tails. This video uses data from Vitral & Boldrini 2022.

Integrals of motion: Evolution of simulated clusters in the integrals of motion (IOM) space, in particular, the E × LZ diagram. Their positions in this diagram are scattered in a sequential color-map, starting from the same point in white at t = 0, and ending in darker tones (green for GCs originally formed in DM mini-halos, and red for clusters devoid of DM). The last snapshot is marked by a cross, for each cluster. This plot highlights a bimodal evolutionary distribution of clusters originally embedded in dark matter (moving towards lower energies) and those who were not (moving only slightly towards higher energies), and more importantly, it shows that clusters originally embedded in DM move significantly in IOM space, such that their association with past merger events through this diagram is not reliable. This figure uses data from Vitral & Boldrini 2022.


I have helped to show that GCs formed in DM mini-halos move significantly in integrals of motion (IOM) space due to their more intense energy loss from dynamical friction. Hence the association of such clusters with past merger events by using the IOM method is not reliable.

Furthermore, this energy loss shifts the GC population formed in DM mini-halos to lower regions of the E × LZ diagram, creating a clear bimodal evolutionary distribution that can help to evaluate if the existence of a DM mini-halo is likely .

In Vitral & Boldrini 2022, we have also provided a general parametric form that describes the mass profiles of DM mini-halos (stripped or not) that embed GCs, which can be used in Jeans mass-modeling searches for DM in GCs. This form follows a Zhao (1996) αβγ model, with fixed α = 2 and β = 5, such as in the the classic Plummer (1911) model: $$M_{\bullet}(r) = \displaystyle{\frac{4 \pi \, a^{3 - \gamma} \, \rho_0}{3 - \gamma}} \, \displaystyle{\left[ 1 + \left( \frac{a}{r} \right)^{2} \right]^{(\gamma - 3)/2}} \ ,$$ where ρ0 is a scaling factor, a the scale radius, γ ∈ (0,3) an inner slope, and r the distance to the cluster's center.