Massive Star Clusters in the Semi-Analytical Galaxy Formation Model L-Galaxies 2020

Abstract

It is established that there exists a direct link between the formation history of star cluster populations and their host galaxies. However, our lack of understanding of the assembly of star cluster populations impede our ability to use them as tracers of galaxy evolution. In this work we introduce a new variation of the L-Galaxies 2020 semi-analytic galaxy formation model that includes the formation of star clusters above 10^4 MSun and probes different physical assumptions that affect their evolution over cosmic time. We use properties of different galaxy components and localised star formation to determine the bound fraction of star formation in disks. After randomly sampling masses from an environmentally-dependent star cluster initial mass function, we assign to each object a half-mass radius, metallicity, and distance from the galaxy centre. We consider up to 2000 individual star clusters per galaxy and evolve their properties over time taking into account stellar evolution, two-body relaxation, tidal shocks, dynamical friction, and a re-positioning during galaxy mergers. Our simulation successfully reproduces several observational quantities, such as the empirical relationship between the absolute V-band magnitude of the brightest young star clusters and the host galaxy star formation rate, the mass function of young star clusters, and mean metallicities of the star cluster distributions versus galaxy masses. The simulation reveals great complexity in the z=0 star cluster population resulting from differential destruction channels and origins, including in-situ populations in the disk, a major merger-induced heated component in the halo, and accreted star clusters. Model variations point out the importance of the shape of the star cluster initial mass function, the initial distribution of half-mass radii, or the relationship between the sound speed of cold gas and the SFR.

Figures (11)

• Figure 1: Relevant prescriptions for the assembly and evolution of star clusters implemented into a modified version yates2021a of L-Galaxies 2020.0 henriques2020a.
• Figure 2: Epicyclic frequency, cold gas surface mass density, and the Toomre stability parameter as a function of galactocentric distance for disk- (blue) and bulge-dominated (red) galaxies, defined as having a bulge-to-total stellar mass ratio of $B/T < 0.2$ and $B/T \geq 0.9$, respectively. We add for comparison the value of the solar neighbourhood: we calculate $\kappa_{\mathrm{D} ,\, \odot} \approx 0.046 \, \textrm{Myr}^{-1}$, as derived from the Oort constants $A = 15.6 \, \textrm{km} \, \textrm{s}^{-1} \, \textrm{kpc}^{-1}$ and $B = -15.8 \, \textrm{km} \, \textrm{s}^{-1} \, \textrm{kpc}^{-1}$ taken from guo2023a; $\Sigma_{\mathrm{g} ,\, \odot} \approx 13 \, \textrm{M}_{\odot} \, \textrm{pc}^{-2}$ from flynn2006b; and $Q_{\mathrm{eff} ,\, \odot} \approx 1.7$binney2008a, a typical value for disks rafikov2001bleroy2008afeng2014awestfall2014a. Note that we do not calculate the Toomre stability parameter for annuli where it's surface density drops below $1 \, \textrm{M}_{\odot} \, \textrm{pc}^{-2}$ as we do not expect the formation of any star clusters at such low gaseous densities.
• Figure 3: Bound fraction of star formation, evaluated for $Q_{\mathrm{eff}} = 1.0$, as a function of angular frequency and cold gas surface density. Blue solid and gray dashed contours give the smoothed distribution (with standard deviation of $1 \, \textrm{dex}$) of all annuli of all galaxies running L-Galaxies tree-files 0-9 and 40-79 on the Millennium and Millennium-II simulations, respectively. The location of the solar neighbourhood (see \ref{['fig:annuli_frequencies_surface_density_toomre']} for details) is marked with a cross.
• Figure 4: Absolute $V$-band magnitude of the youngest and most massive star cluster versus the galaxy-averaged star formation rate. The galaxy sample is limited to disk-dominated galaxies that have a bulge-to-total stellar mass ratio of $B/T < 0.2$. We compare our results to various observations of nearby disk-dominated galaxies (see main text for details). For both the simulated data and the observations, we set an age cut of $\tau_{\mathrm{c}} \leq 0.3 \, \textrm{Gyr}$ on the star clusters. Panel A: Full observational and simulated data samples. For the simulated data, we show the 1-, 2-, and 3-$\sigma$ intervals using blue solid lines. Panel B: Same as in the first panel but colour-coding all data point by the host galaxy's stellar mass. If no stellar mass estimate is available for observational data points, we show them with gray symbols. Panel C: Same as the central panel but colour-coding the data points by the cluster formation efficiency, which is a combination of the bound fraction of star formation and the "cruel cradle effect" kruijssen2012bkruijssen2012d that takes the interaction of a proto-star cluster with its natal environment and nearby giant molecular clouds into account. Note that the two outliers, NGC 1705 and NGC 5238, are starburst galaxies and that their massive star clusters were previously classified as nuclear star clusters pechetti2020ahoyer2021a. Nuclear star clusters often exhibit complex formation histories spengler2017akacharov2018afahrion2021a and cannot easily be compared to our simulated star clusters.
• Figure 5: Estimated probability density function values of binned star cluster masses in disk- ($B/T < 0.2$; blue colour) and bulge-dominated ($B/T > 0.7$; red colour) galaxies at $z=0$. We track up to 2000.0 star clusters per galaxy, split equally between star clusters located in the disk (top row) and halo (bottom row). Host galaxies are separated into three mass bins. Additionally, we separate between young ($\tau_{\mathrm{c}} \leq 300 \, \mathrm{Myr}$; solid lines) and old ($\tau_{\mathrm{c}} > 6 \, \mathrm{Gyr}$; shaded regions) star clusters. We sample the cluster initial mass function with an initial mass of $10^{4} \, \mathrm{M}_{\odot}$ and discard star clusters with masses below $10^{3} \, \mathrm{M}_{\odot}$. The black solid line in the top left panel presents the asymptotic power-law behaviour towards $m_{\mathrm{c}} = 0$. We compare the population of simulated star clusters to the observational resulted of brown2021c. Each column shows the same data set as the location of the star clusters (disk versus halo) is not specified by the authors.