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We numerically explore on galaxy scales the Dipolar dark matter (DM) modelbased on the concept of gravitational polarization. This DM model has beenproposed as a natural way to reproduce observed tight galactic scalingrelations such as the baryonic Tully-Fisher relation and the RadialAcceleration Relation. We present a customized version of the \texttt{RAMSES}code including for the first time the dynamics of this Dipolar DM in $N$-bodysimulations. As a first application of this code, we check that we recover anequilibrium configuration that had been found analytically, where a low densityDipolar DM halo is at rest with respect to its central galaxy, recovering theaforementioned scaling relations. A characteristic signature of thisequilibrium model is that it harbours a dynamical instability with acharacteristic time depending on the Dipolar DM halo density, which we recovernumerically. This represents a first step towards more involved simulationsneeded to test this framework, ranging from galaxy interactions to structureformation.

Dipolar dark matter simulations on galaxy scales with the RAMSES code