[Paper Review] Formation of Proto-Globular Cluster Clouds by Thermal Instability

Hyesung Kang, George Lake+1 more|arXiv (Cornell University)|Oct 25, 2000

Astrophysics and Star Formation Studies1 references3 citations

TL;DR

This paper investigates the formation of proto-globular cluster clouds (PGCCs) via thermal instability in protogalactic halos, using 1D spherical hydrodynamic simulations with self-gravity and radiative cooling down to 10⁴ K. It finds that only marginally nonlinear (δ ≳ 1) perturbations in the 10⁵.⁶–10⁸ M☉ range undergo supersonic collapse with high compression (10².⁵–10⁶), enabling gravitational binding and Jeans masses as low as 10⁵.⁵ M☉, forming dense, core-halo PGCCs.

ABSTRACT

Many models of globular cluster formation assume the presence of cold dense clouds in early universe. Here we re-examine the Fall & Rees (1985) model for formation of proto-globular cluster clouds (PGCCs) via thermal instabilities in a protogalactic halo. We first argue, based on the previous study by others, that under the protogalactic environments only nonlinear density inhomogeneities can condense into PGCCs. We then carry out numerical simulations of the collapse of overdense clouds in one-dimensional spherical geometry, including self-gravity and radiative cooling down to T=10^4 K. Since imprinting of Jeans mass at 10^4 K is essential to this model, here we focus on the cases where external UV background radiation prevents the formation of H2 molecules and so prevent the cloud from cooling below 10^4 K. The quantitative results from these simulations can be summarized as follows: 1) Perturbations smaller than M_min ~ (10^{5.6} M_sun) (n_h/0.05 cm3)^{-2} cool isobarically, while perturbations larger than M_max ~ (10^8 M_sun) (n_h/0.05 cm3)^{-2} cool isochorically. On the other hand, intermediate size perturbations (M_min< M_pgcc < M_max) are compressed supersonically. 2) For supersonically collapsing clouds, the density compression factor after they cool to T_c=10^4 K range 10^{2.5}-10^6. 3) For supersonically collapsing clouds the Jeans mass can be reduced to as small as 10^{5.5} M_sun (n_h/0.05 cm3)^{-1/2} at the maximum compression. 4) The density profile of simulated PGCCs can be approximated by a constant core with a halo of rho ~ r^{-2} rather than a singular isothermal sphere.

Motivation & Objective

• To investigate the formation of proto-globular cluster clouds (PGCCs) via thermal instability in protogalactic halos.
• To determine the mass and size scales of thermally unstable clouds that can collapse into gravitationally bound PGCCs.
• To quantify the compression factors and Jeans masses in supersonically collapsing clouds under realistic cooling conditions.
• To assess the role of geometry and nonlinearity in stabilizing PGCC formation against buoyancy-driven instabilities.

Proposed method

• One-dimensional spherical hydrodynamic simulations with self-gravity and radiative cooling down to 10⁴ K.
• Modeling clouds in a protogalactic halo with an external UV background preventing H₂ cooling below 10⁴ K.
• Using the cooling distance lcool as a key scale to define the range of condensing clouds (0.2lcool ≤ Rc ≤ lcool).
• Calculating compression factors and Jeans masses for isobaric vs. supersonic collapse regimes.
• Analyzing density profiles to determine whether PGCCs resemble singular isothermal spheres or have a constant core with r⁻² halo.
• Comparing results with prior 1D plane-parallel and 2D simulations to validate the spherical model's relevance.

Experimental results

Research questions

• RQ1 Which mass and size scales of density perturbations in protogalactic halos can form gravitationally bound PGCCs via thermal instability?
• RQ2 How do compression factors and Jeans masses differ between isobaric and supersonic collapse in thermally unstable clouds?
• RQ3 What is the role of geometry (spherical vs. plane-parallel) in determining the final density contrast and stability of collapsing clouds?
• RQ4 Can nonlinear (δ ≳ 1) perturbations survive buoyancy-driven instabilities to form stable PGCCs?
• RQ5 How do the simulated PGCC density profiles compare to standard models like singular isothermal spheres?

Key findings

• Perturbations with mass M < M_min ≈ 10⁵.⁶ M☉ (n_h/0.05 cm⁻³)⁻² cool isobarically and remain gravitationally unbound.
• Perturbations with M > M_max ≈ 10⁸ M☉ (n_h/0.05 cm⁻³)⁻² cool isochorically and do not form distinct PGCCs due to lack of thermal instability.
• Intermediate-mass clouds (M_min < M_PGCC < M_max) undergo supersonic collapse with density compression factors of 10².⁵ to 10⁶, exceeding isobaric compression.
• The Jeans mass in supersonically collapsing clouds is reduced to as low as 10⁵.⁵ M☉ (n_h/0.05 cm⁻³)⁻¹/² at maximum compression, enabling gravitational binding.
• Simulated PGCCs exhibit a constant core density profile with an outer halo scaling as ρ ∝ r⁻², deviating from the singular isothermal sphere model.
• Only marginally nonlinear (δ ≳ 1) density inhomogeneities can condense into stable PGCCs, as linear perturbations are disrupted by buoyancy-driven instabilities.