[Paper Review] Radiative shocks in galaxy formation. I: Cooling of a primordial plasma with no sources of heating

M. I. Forcada-Miro, S. D. M. White|ArXiv.org|Dec 16, 1997

Cosmology and Gravitation Theories3 references4 citations

TL;DR

This paper investigates radiative shocks in primordial plasma during galaxy formation using a 1-D Lagrangian code that models both gas and dark matter. It finds that bremsstrahlung cooling dominates in systems with circular velocities >100 km/s, allowing accurate analytic modeling of shocks and cooling waves, while line cooling leads to shock front oscillations that grow over time, limiting analytic predictability.

ABSTRACT

We use a 1-D Lagrangian code which follows both a gaseous and a dark component to study the radiative shocks that appear in the evolution of spherical scale-free perturbations in an Einstein-de Sitter Universe. The detailed behaviour of the shock depends on whether the radiative cooling is dominated by bremsstrahlung or line cooling. Bremsstrahlung is the main energy loss mechanism for systems with circular velocity $V_{c} > 100 km s^{-1}$. In this case, we can reproduce the kinematics of the shock and of the cooling wave to a high degree of accuracy with a simple analytic model. When line cooling dominates, the shock front can be unstable to oscillations. The period and amplitude of the oscillations increase in time as the universe expands. For such systems, our analytic model provides only a rough estimate of the mean evolution. We believe that now we fully understand the effect radiative cooling has in the shocks that appear in spherical models for galaxy formation.

Motivation & Objective

• To understand the role of radiative cooling in shaping shock dynamics during galaxy formation in a primordial plasma.
• To determine how different cooling mechanisms—bremsstrahlung versus line cooling—affect shock structure and stability.
• To assess the validity of analytic models in predicting shock evolution under varying cooling regimes.
• To investigate the impact of cosmic expansion on shock oscillations driven by line cooling.
• To provide a comprehensive framework for interpreting shock behavior in spherical, scale-free perturbations in an Einstein-de Sitter universe.

Proposed method

• Uses a 1-D Lagrangian hydrodynamics code to simulate spherical, scale-free perturbations in an Einstein-de Sitter universe.
• Tracks both gaseous and dark matter components simultaneously to model gravitational collapse and shock formation.
• Incorporates detailed radiative cooling processes, distinguishing between bremsstrahlung and line cooling mechanisms.
• Applies analytic models to compare with numerical results, focusing on shock kinematics and cooling wave propagation.
• Analyzes the temporal evolution of shock oscillations under line cooling dominance, particularly their period and amplitude growth.
• Validates numerical results against analytic approximations to assess accuracy and limitations of simplified models.

Experimental results

Research questions

• RQ1 How does radiative cooling influence the formation and structure of shocks in a primordial plasma during galaxy formation?
• RQ2 Under what conditions does bremsstrahlung dominate over line cooling in shock cooling mechanisms?
• RQ3 To what extent can analytic models accurately reproduce the kinematics of shocks and cooling waves in the presence of bremsstrahlung cooling?
• RQ4 What causes shock front oscillations when line cooling dominates, and how do their properties evolve over time?
• RQ5 How does cosmic expansion affect the growth of oscillations in line-cooling-dominated shocks?

Key findings

• Bremsstrahlung cooling dominates in systems with circular velocities exceeding 100 km/s, enabling high-accuracy reproduction of shock and cooling wave kinematics via analytic models.
• In systems dominated by line cooling, shock fronts become unstable and exhibit growing oscillations in both period and amplitude as the universe expands.
• The amplitude and period of oscillations increase over time due to the expanding background, indicating a time-dependent instability mechanism.
• Analytic models provide only a rough estimate of the mean evolution in line-cooling-dominated systems, due to the complex, oscillatory shock dynamics.
• The study confirms that radiative cooling fundamentally shapes shock behavior in spherical galaxy formation models, with distinct outcomes depending on the dominant cooling process.
• The numerical simulations demonstrate that the transition between cooling regimes (bremsstrahlung vs. line) determines the stability and predictability of shock evolution.