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

TL;DR

This work addresses spurious collisional heating in cosmological simulations by introducing a two-component glass-based particle-load method that supports arbitrary $N_{ m DM}:N_{ m gas}$ ratios and equal-mass dark matter and baryonic particles. The method simultaneously relaxes two Poisson distributions under total anti-gravity plus intra-component repulsion, with intra-component forces scaled by $C_{ m gas}$ and $C_{ m DM}$ and final off-switch steps, producing $P(k) \\propto k^{4}$ and highly uniform, isotropic loads. When applied to Planck-like cosmologies, equal-mass initializations mitigate the small-scale power transfer seen in unequal-mass runs, aligning results with high-resolution benchmarks in both pure gravity and non-radiative hydrodynamics. The approach, implemented in Gadget-2 and extensible to multi-component systems, provides a practical, flexible tool for accurate initial conditions across diverse cosmologies.

Abstract

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 .

Figures (11)

• Figure 1: Visualization of a two-component glass-based particle load consisting of $24^3$ gas particles and $73945$$(\approx 42^3)$ dark matter particles (i.e., $N_{\rm DM}:N_{\rm gas} = 5.35:1$). From left to right, the panels show the gas (blue), dark matter (orange), and total particles within a slice of thickness $L_{\rm box}/24$, projected onto the $xy$-plane. The particle distributions visually demonstrate that both individual components and the entire particle set exhibit glass-like characteristics, i.e., overall uniformity and isotropy.
• Figure 2: Power spectra of a two-component glass-based particle loads with $N_{\rm gas} = 64^3$ and $N_{\rm DM} = 1402203 \approx 112^3$ (i.e., $N_{\rm DM}:N_{\rm gas} = 5.35:1$). The blue, orange, and purple curves show the power spectra of the gas particles, and the dark matter particles, and the entire set respectively. The horizontal dashed lines show the Poisson noise power spectra. The dotted lines represent the power-law power spectra; the upper dotted line is for $P(k) \propto k^{2.5}$, and the lower one is for the minimal power spectrum, $P(k) \propto k^4$. The vertical line segments at the bottom mark the particle Nyquist frequencies ($k_{\rm Ny}$) for different particle sets. Overall, all power spectra approximately follow the minimal power spectrum at scales below $k_{\rm Ny}$ and gradually become dominated by Poisson noise at $k \gtrsim k_{\rm Ny}$, demonstrating glass-like properties.
• Figure 3: Homogeneity properties. The upper panel shows the PDFs of the Voronoi cell volume associated with each particle. As before, gas particles, dark matter particles, and the entire particle set are represented in blue, orange, and purple, respectively. The Voronoi cell volumes are normalized to the mean particle volume for each particle set, i.e., $\bar{V} = L_{\rm box}^3 / N_{i}$ with $i =$ gas, DM, or total. For comparison, the results from a single-component glass load and a Poisson particle distribution, both generated with the same total number of particles $N_{\rm DM} + N_{\rm gas}$, are shown in cyan and gray, respectively. The lower panel displays similar PDFs but for the distance to the nearest neighbor. Here, the distances are normalized to the mean inter-particle separation, i.e., $\bar{d} = L_{\rm box} / N_{i}^{1/3}$. From this figure, particles in all three sets occupy space evenly, with their nearest-neighbor distances close to the mean inter-particle separation, indicating that the distributions are relatively uniform.
• Figure 4: Isotropy properties. To quantify the isotropy of particle loads, we determine the vector pointing from each particle to its nearest neighbor and compute the polar angle $\theta$ and the azimuthal angle $\phi$ (with respect to the Cartesian coordinate axes of the periodic box). The upper panel shows the PDFs of $\cos \theta$ for gas particles (blue), dark matter particles (orange), and the entire particle set (purple). Similarly, the lower panel displays that PDFs of the azimuthal angle $\phi$. Both the distributions of $\cos \theta$ and $\phi$ are uniform, indicating that there is no preferred direction in the particle distributions.
• Figure 5: Property of force balance. The entire particle load is evolved under gravitational interactions from $a_0 = 0.001$ to $a = 1$ within the SCDM cosmology. The top panel shows that fraction of particles in the identified FOF groups as a function of the expansion factor ($a / a_0$), whereas the bottom panel plots the number of particles for the largest FOF group in different snapshots. The purple curves represent the two-component particle loads with $N_{\rm DM} : N_{\rm gas} = 5.35:1$. For comparison, the traditional single-component glass load with identical total number of particles is plotted with cyan dotted lines. The two-component particle load exhibits behavior similar to that of the traditional single-component glass load and is fairly stable to prevent artificial structures from forming due to noise.