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

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 $\sim 10^{12.5}{h}^{-1}{M}_{\odot }$ to $\sim 10^{15}{h}^{-1}{M}_{\odot }$, 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.

arXiv commentFixed Newtonian force results. Figs. 5, 9 and 10 updated. Matches accepted version

References in corpus (45)

• The Structure of Cold Dark Matter Halos
• Efficient Computation of CMB anisotropies in closed FRW models
• Cosmological Hydrodynamics with Adaptive Mesh Refinement: a new high resolution code called RAMSES
• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• Cosmic Growth History and Expansion History
• Transients from Initial Conditions in Cosmological Simulations
• Relativistic second-order perturbations of the Einstein-de Sitter Universe
• Black hole formation in the Friedmann universe: Formulation and computation in numerical relativity
• Generation of Vorticity and Velocity Dispersion by Orbit Crossing
• Tracing the Dark Matter Sheet in Phase Space
• A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
• General relativity and cosmic structure formation
• Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
• Asymmetric galaxy correlation functions
• The Properties of Cosmic Velocity Fields
• Exploring Vainshtein mechanism on adaptively refined meshes
• Gravitational redshift and other redshift-space distortions of the imaginary part of the power spectrum
• Alignments of Radio Galaxies in Deep Radio Imaging of ELAIS N1
• Computing General Relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach
• Inhomogeneous Cosmology with Numerical Relativity
• Integration of inhomogeneous cosmological spacetimes in the BSSN formalism
• The cosmological background of vector modes
• Imprints of relativistic effects on the asymmetry of the halo cross-correlation function: from linear to non-linear scales
• The DTFE public software: The Delaunay Tessellation Field Estimator code
• Cosmological Dynamics
• The missing link: a nonlinear post-Friedmann framework for small and large scales
• Testing dark matter and geometry sustained circular velocities in the Milky Way with Gaia DR2
• Gravitational redshifts from large-scale structure
• Gravitational lensing in metric theories of gravity
• The Generation of Vorticity in Cosmological N-body Simulations
• Relativistic distortions in the large-scale clustering of SDSS-III BOSS CMASS galaxies
• Weak-lensing observables in relativistic N-body simulations
• GRAMSES: a new route to general relativistic $N$-body simulations in cosmology. Part I. Methodology and code description
• Gravitational lensing by spinning and escaping lenses
• The Limited Accuracy of Linearized Gravity
• The fully non-linear post-Friedmann frame-dragging vector potential: Magnitude and time evolution from N-body simulations
• Weak lensing induced by second-order vector mode
• Vorticity generation in the Universe: A perturbative approach
• f(R) gravity on non-linear scales: The post-Friedmann expansion and the vector potential
• GRAMSES: a new route to general relativistic $N$-body simulations in cosmology. Part II. Initial conditions
• Redshift-space distortions from vector perturbations
• Effective dark matter power spectra in $f(R)$ gravity
• Kinematic effect in gravitational lensing by clusters of galaxies
• Gravitational corrections to light propagation in a perturbed FLRW-universe and corresponding weak lensing spectra
• Redshift-space distortions from vector perturbations II: Anisotropic signal

Cited by in corpus (9)

• A tale of analogies: gravitomagnetic effects, rotating sources, observers and all that
• Cosmology using numerical relativity
• Looking for a twist: probing the cosmological gravitomagnetic effect via weak lensing-kSZ cross correlations
• Measuring cosmic filament spin with the kinetic Sunyaev-Zel'dovich effect
• Structure formation and quasi-spherical collapse from initial curvature perturbations with numerical relativity simulations
• EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes
• GrGadget: an N-body TreePM relativistic code for cosmological simulations
• Measuring the gravitomagnetic distortion from rotating halos I: methods
• The frame-dragging vector potential on galaxy scales from Dark-Matter-only Newtonian $N$-body simulations