Particle loads for cosmological simulations with equal-mass dark matter and baryonic particles

Traditional cosmological hydrodynamical simulations usually assume equal-numbered but unequal-mass dark matter and baryonic particles, which can lead to spurious collisional heating due to energy equipartition. To avoid such a numerical heating effect, a simulation setup with equal-mass dark matter and baryonic particles, which corresponds to a particle number ratio of $N_{\rm DM}:N_{\rm gas} = Ω_{\rm cdm} / Ω_{\rm b}$, is preferred. However, previous studies have typically used grid-based particle loads to prepare such initial conditions, which can only reach specific values for $N_{\rm DM}:N_{\rm gas}$ due to symmetry requirements. In this study, we propose a method based on the glass approach that can generate two-component particle loads with more general $N_{\rm DM}:N_{\rm gas}$ ratios. The method simultaneously relaxes two Poisson particle distributions by introducing an additional repulsive force between particles of the same component. We show that the final particle load closely follows the expected minimal power spectrum, $P(k) \propto k^{4}$, exhibits good homogeneity and isotropy properties, and remains sufficiently stable under gravitational interactions. Both the dark matter and gas components individually also exhibit uniform and isotropic distributions. We apply our method to two-component cosmological simulations and demonstrate that an equal-mass particle setup effectively mitigates the spurious collisional heating that arises in unequal-mass simulations. Our method can be extended to generate multi-component uniform and isotropic distributions. Our code based on Gadget-2 is available at https://github.com/liaoshong/gadget-2glass .

💡 Research Summary

This paper addresses a critical numerical artifact in cosmological hydrodynamical simulations known as “spurious collisional heating” and presents a novel method for generating initial conditions that effectively eliminates it.

The standard approach for simulating both dark matter (DM) and baryonic gas has been to use an equal number of particles for each component but assign them different masses according to the cosmological density parameters (Ω_cdm and Ω_b). This unequal-mass setup, however, leads to an unphysical transfer of kinetic energy from the more massive DM particles to the lighter gas particles due to energy equipartition, artificially heating the gas and affecting galaxy properties like disk thickness and dark matter substructure. The solution is to use equal-mass particles for both components, which necessitates a particle number ratio of N_DM : N_gas = Ω_cdm / Ω_b (approximately 5.35:1 for Planck cosmology). Existing methods to create such initial conditions, primarily grid-based templates, are limited to specific, symmetric ratios (e.g., 7:1, 4:1) and cannot achieve the precise, general ratios required by different cosmologies.

To overcome this limitation, the authors propose a new method based on the “glass” technique for generating uniform and isotropic particle distributions. The core innovation is the simultaneous relaxation of two separate Poisson distributions (one for DM, one for gas) under a modified anti-gravity force. For each particle, the total force is composed of the standard anti-gravitational force from all particles in the combined system, plus an additional repulsive force scaled by a factor C, which acts only from particles of the same component. This extra term, with C_gas = (N_tot/N_gas)^(2/3) and C_DM = (N_tot/N_DM)^(2/3), encourages particles of the same type to avoid each other while the entire system evolves toward a uniform glass-like state. A final short relaxation phase with the additional force turned off ensures good global force balance.

The properties of the resulting two-component particle loads are thoroughly analyzed. The total matter power spectrum follows the expected minimal “glass” spectrum, P(k) ∝ k^4, up to the Nyquist frequency. Both the DM and gas components individually exhibit good uniformity and isotropy. Quantitative comparisons show that this simultaneous relaxation method better preserves the uniformity of each individual component compared to an older method of simply combining two independently generated glasses.

The practical efficacy of the method is demonstrated through cosmological simulations. Simulations initialized with these equal-mass particle loads show a dramatic suppression of the spurious collisional heating effect that is clearly present in simulations using the traditional unequal-mass setup. This confirms that the method successfully achieves its primary goal of removing this numerical artifact.

In summary, this work provides a flexible and robust method for creating multi-component initial conditions with arbitrary particle number ratios, directly tailored to cosmological parameters. By enabling equal-mass particle simulations, it enhances the accuracy of numerical studies of galaxy formation and cosmic structure. The authors have implemented this method in a publicly available code based on Gadget-2, facilitating its adoption by the wider astrophysics community. The approach is also noted to be extensible for generating loads with more than two components.