Abstract
Metallicities of the Milky Way globular cluster (GC) system are interpreted within the framework of a closed box model of chemical evolution. Model age-metallicity relations normalised to the Sun are compared with an observed age-metallicity relation constructed from literature data for the Galactic globular clusters and solar neighbourhood dwarf stars. One branch of the GC age-metallicity relation is seen to form a natural extension of the solar neighbourhood relation to low metallicities. Such clusters may fit in situ into the same Galactic closed-box model as many disk stars. Timescales for halo and disk GC formation are computed based on this assumption. However, a single closed box cannot account for a second branch in the GC age-metallicity data. This problem is addressed by assuming that some GCs did not form in situ within the closed box of the Galaxy, but rather were formed within separate parent objects whose chemical evolution was characterised by longer star formation timescales than the Milky Way box. These parent objects were eventually acquired by the Milky Way. Estimates are made of the initial mass and star formation timescale of those objects that contributed GCs to the accreted component of the Milky Way.
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Notes
This estimate of the GC formation rate would be a lower limit if the original Galactic GC system has been significantly reduced in number by disruptive processes, such as stellar dynamical evaporation and tidal shocking, as predicted by theoretical models such as those of Aguilar et al. (1988), Chernoff and Weinberg (1990), Gnedin and Ostriker (1997), Murali and Weinberg (1997), Vesperini (1998), Gnedin et al. (1999), Takahashi and Portegies Zwart (2000), Fall and Zhang (2001), Vesperini and Zepf (2003), McLaughlin and Fall (2008), Prieto and Gnedin (2008), Whitehead et al. (2013), and Webb et al. (2017).
This conclusion does depend upon whether the oldest GC ages in Leaman et al. (2013) also match the oldest Population II (and III) stars in the Galaxy. If the oldest field stars predated the first GCs by 0.5 Gyr then the solid curve in Fig. 1 for a Galactic age of 13.5 Gyr would be applicable, and it could be concluded that the majority, if not all, of the GCs with \(\mathrm{[Fe/H]} < -1.6\) are lower branch objects.
The disk models of Bekki (2014) for systems with baryonic masses of \(6.6 \times 10^{9}\) \(M_{\odot }\) or less (halo masses of \(10^{11}\) \(M_{\odot }\) or less) are mostly characterised by a fraction of gas in molecular hydrogen that does not exceed 0.3, and is typically less than 0.1 for baryonic disk masses of \(6.6 \times 10^{8}\) \(M_{\odot }\) or less.
We thank Andreas Burkert for suggesting this point to the author.
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Smith, G.H. The Milky Way globular cluster system within the context of a closed box. Astrophys Space Sci 365, 193 (2020). https://doi.org/10.1007/s10509-020-03897-0
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DOI: https://doi.org/10.1007/s10509-020-03897-0