Vector modes in $\Lambda$CDM: the gravitomagnetic potential in dark matter haloes from relativistic $N$-body simulations

TL;DR

This study uses relativistic N-body simulations to analyze the gravitomagnetic potential in dark matter haloes within the b1CDM model, revealing its weak influence on structure formation and potential observational effects.

Contribution

It provides the first detailed analysis of gravitomagnetic vector potential in dark matter haloes using relativistic simulations, highlighting its correlation with halo mass and negligible impact on structure formation.

Findings

Gravitomagnetic potential correlates with halo mass, peaking in the inner regions.

The ratio of gravitomagnetic to scalar potential remains below 1% and decreases with redshift.

Gravitomagnetic acceleration peaks at rom the core, but force ratio is around 10^{-5}.

Abstract

We investigate the transverse modes of the gravitational and velocity fields in $\Lambda$CDM, based on a high-resolution simulation performed using the adaptive-mesh refinement general-relativistic $N$-body code GRAMSES. We study the generation of vorticity in the dark matter velocity field at low redshift, providing fits to the shape and evolution of its power spectrum over a range of scales. By analysing the gravitomagnetic vector potential, which is absent in Newtonian simulations, in dark matter haloes with masses ranging from $\sim10^{12.5}~h^{-1}{M}_{\odot}$ to $\sim10^{15}~h^{-1}{M}_{\odot}$, we find that its magnitude correlates with the halo mass, peaking in the inner regions. Nevertheless, on average, its ratio against the scalar gravitational potential remains fairly constant, below percent level, decreasing roughly linearly with redshift and showing a weak dependence on halo mass. Furthermore, we show that the gravitomagnetic acceleration in haloes peaks towards the core and reaches almost $10^{-10}$ $h$ cm/s$^2$ in the most massive halo of the simulation. However, regardless of the halo mass, the ratio between the magnitudes of the gravitomagnetic force and the standard gravitational force is typically at around the $10^{-5}$ level inside the haloes, again without significant radius dependence. This result confirms that the gravitomagnetic effects have a negligible impact on structure formation, even for the most massive structures, although its behaviour in low density regions remains to be explored. Likewise, the impact on observations remains to be understood in the future.