We present a numerical model for the globular cluster luminosity function (GCLF) which characterizes globular cluster systems (GCSs) around galaxies. This model is based on the idea that globular clusters formed in the cores of self-gravitating, magnetized, supergiant molecular clouds (SGMCs). A distribution of core masses is built up through a series of collisions within a parent SGMC. Massive cores are assumed to be destroyed (at a mass-dependent rate) by the act of star formation, allowing for the establishment of a Unique, steady state mass spectrum. The model, which allows only for coalescent collisions between cores, fits observed GCS mass spectra very well above the GCLF peak mass m_* approx= 1.6 x 10~5 solar mass, which is remarkably constant from galaxy to galaxy. We suggest that it represents the critical mass above which the cores of SGMCs become susceptible to internal disruption. Our fits to the mass spectra of the Milky Way, M31, and M87 GCSs predict that, in a given SGMC, the lifetimes of such cores should decrease at higher masses. The crucial factor in determining the shape of the GCLF is the ratio β of characteristic core disruption and collision timescales. It is shown that β does not differ between SGMCs in a single protogalaxy; this accounts for observations that GCLFs are independent of galactocentric radius. However, β does differ, and the overall shape of the GCLF along with it, between GCSs. Finally, our model suggests an "inside-out" sequence of GCS formation.
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机译：我们为球状星团发光度函数（GCLF）提供了一个数值模型，该模型描述了围绕星系的球状星团系统（GCSs）。该模型基于这样的思想，即球状团簇在自重，磁化，超巨型分子云（SGMC）的核心中形成。核心质量的分布是通过父SGMC中的一系列碰撞建立的。假定大质量核由于恒星形成而被破坏（以质量相关的速率），从而建立了唯一的稳态质谱。该模型仅允许岩心之间发生聚结碰撞，该模型很好地拟合了观测到的GCS质谱，其远高于GCLF峰值质量m_ *约= 1.6 x 10〜5太阳质量，该质量在银河系与银河系之间非常恒定。我们建议它代表了临界质量，在此临界质量以上，SGMC的核心变得容易受到内部破坏。我们对银河系，M31和M87 GCS的质谱拟合表明，在给定的SGMC中，此类核的寿命在较高质量下会降低。确定GCLF形状的关键因素是特征堆芯破裂和碰撞时间尺度的比值β。结果表明，在单个原星系中，SGMC之间的β值没有差异。这说明了观察到的GCLF与半中心半径无关。但是，在GCS之间，β确实不同，GCLF的整体形状也不同。最后，我们的模型提出了GCS形成的“由内而外”的顺序。
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