Enhanced Axion-wind near Earth's Surface

Several detection strategies for wave-like dark matter make use of gradients in the dark matter field, e.g. searches for spin-dependent derivative interactions in CASPEr-wind or experiments looking for oscillating forces. These gradients are usually suppressed by the local dark matter velocity $\sim 10^{-3}$. In this note we investigate how these gradients are modified in the presence of additional quadratic interactions of the dark matter field with ordinary matter. In this case the dark matter density and field are modified in the vicinity of Earth, affecting the detection sensitivity due to the change in the local field value at the Earth's surface but also due to the gradient of the field profile itself. We also use this opportunity to present results on the expected field profiles in presence of a non-vanishing relative velocity of the dark matter with respect to Earth. We also comment how this ameliorates the divergences that appear for certain attractive coupling values.