The Cosmological Simulation Code OpenGadget3 -- Implementation of Self-Interacting Dark Matter

Abstract

Dark matter (DM) could be subject to non-gravitational self-interactions which is relevant to resolve potential problems of cold DM on small scales. Their impact on astrophysical objects such as galaxies and galaxy clusters allows for constraining the strength of this scattering and eventually further properties of the cross-section. To model self-interacting dark matter (SIDM), N-body simulations are a crucial tool widely employed by the SIDM community. In this paper, we describe the SIDM implementation in the cosmological hydrodynamical N-body code OpenGadget3 and release it to the public. It is capable of simulating elastic scattering for various differential cross-sections, including strongly anisotropic cross-sections. Beyond single-species models, the code also allows simulating a two-species model with cross-species interactions. In addition to describing the numerical schemes for modelling various flavours of SIDM, we discuss the technical challenges of implementing them. Moreover, we demonstrate through several test problems that OpenGadget3 can accurately simulate DM self-interactions. Furthermore, we assess the performance of the code and provide scaling tests. Lastly, we highlight remaining challenges in the context of SIDM and describe directions for improving the current state of the art.

Figures (16)

• Figure 1: Illustration of the numerical representation and the scattering process for the SIDM scheme. The black circles denote numerical particles, with the black dots inside illustrating that they consist of numerous physical DM particles. The numerical particles evolve from the pre-scattered state (left) to the post-scattered state (right) by changing the direction of their momentum vectors in their centre-of-mass frame.
• Figure 1: An illustration of the computed table using the ZSlice method. Shown is the computed Rutherford scattering angle with $w=200\,\mathrm{km} \, \mathrm{s}^{-1}$ and $N_x=N_h=100$. The connected points show the flow of equal scattering angle $\theta_\mathrm{cms}$. To keep the figure readable, only every tenth point has been drawn. One of the quadrilaterals encountered in interpolation is highlighted in red.
• Figure 2: Illustration of the drag force. A phase-space patch of physical DM particles (dark grey) moves through a DM background density. Due to small-angle scatterings, its velocity changes. Each scattering event gives rise to a parallel and perpendicular velocity change compared to the initial direction of motion. Over many scattering events, the parallel velocity changes sum up ($\delta v_\parallel$) and give rise to a drag force ($F_\mathrm{drag}$). The corresponding perpendicular velocity changes are expected to average out ($\delta v_\perp$), i.e. the direction of motion does not change. However, the second moment of the perpendicular velocity component increases over time ($\langle \delta v_\perp^2 \rangle > 0$), i.e. the perpendicular velocity dispersion of the phase-space patch increases.
• Figure 2: Example of the ZSlice interpolation scheme. One quadrilateral is highlighted in red. The interpolation for the velocity from it is indicated by the blue points. They are used for the final interpolation along the blue line to obtain the scattering angle. The resulting point is indicated by the black point.
• Figure 3: Viscosity cross-section as a function of velocity for different models. We illustrate the velocity dependence of different models implemented in OpenGadget3. These are a velocity-independent cross-section (black), the velocity-dependent model according to Eq. \ref{['eq:veldep']} (light green), a model with a simple parametrisation for a resonant feature as given by Eq. \ref{['eq:resonant']} (blue), Møller scattering as expressed by Eq. \ref{['eq:moeller_dcs']} (orange), and Rutherford scattering following Eq. \ref{['eq:rutherford_dcs']} (dark green). The cross-section normalisation parameter is set to $\sigma_{0,\mathrm{V}} = 10 \, \mathrm{cm}^2 \, \mathrm{g}^{-1}$ and for the velocity-dependent cross-section, $w = 10 \, \mathrm{km} \, \mathrm{s}^{-1}$.