# Dynamical Response of Dark Matter to Galaxy Evolution Affects Direct-Detection Experiments

## Global View

The simulations are drawn from Petersen et al. (2016). An initially exponential stellar disk is embedded in an initially axisymmetric NFW dark matter halo. After the bar forms and significant secular evolution takes place, the halo has a significant non-axisymmetric wake.

The halo wake (($m$>0)+($m$=0;$n$>=0), filled color) with the bar position and length indicated as the thick black line. The wake lags behind the bar (rotating clockwise) at $R>0.5R_d$, but is generally aligned with the bar within 0.5$R_d$, where we observe significant trapping (see this work).

## Results

At the solar circle, significant deformation from a spherical distribution is observed, corresponding to a significant increase in detectability simply from the density enhancement. The velocity structure further increases the detectability of dark matter.

In-plane relative DM density as a function of bar radius and bar angle for the fdNFW model. Left panel: the simulation at $T=4$ Gyr versus the pristine NFW model. Right panel: the simulation at $T=4$ Gyr versus an adiabatically contracted model. The best choice solar position is marked with an ‘x’. The possible solar locations consistent with astronomical uncertainties are denoted by the hatched region. Both panels show similar features, including a quadrupole disturbance owing to the bar that appears as a density enhancement trailing the bar. The patchiness in the relative density determinations owe to the self-consistent evolution.

Speed distribution at the solar position in three different halo models. The hatched region around the fdNFW line indicates the extent of the possible solar locations in the simulation. The pNFW model is plotted as a dot-dashed line. The SHM is plotted as a dashed line. Inset: zoom-in on the peak of the speed distribution, with the extent of the solar position uncertainty indicated as a shaded band. Thin lines represent individual realizations of the region of interest used to calculate the solar position speed distribution. $|v|=220$ km s$^{-1}$, the peak of the SHM, is marked as a vertical dashed line. Note that peaks for individual realizations range between 230 and 280 km s$^{-1}$.

Radial ($v_r$) versus tangential ($v_\theta$) velocities in galactocentric coordinates at the solar position for the fdNFW model. To illustrate the deviation from an isotropic distribution, we plot circles with $|v|$= 50; 100; 200 km s$^{-1}$. The velocity of the Sun in $v_r-v_\theta$ space is marked with a white ’x’.

## Analysis

The standard halo model (SHM) produces qualitatively different results from the self-consistent NFW model. The dependence of the detection rate on vmin is qualitatively different--which results in significantly different detection rate (and therefore DM particle mass) estimates.

Upper panel: dR=d(vmin) as a function of vmin for various halo models. Line styles are the same as in Figure 5. The shaded region around the fiducial NFW model (black line) represents the total positional uncertainty effects on both density and the velocity distribution. Middle panel: detectability relative to the standard halo model, (dR=d(vmin)model􀀀dR=d(vmin)SHM)=(dR=d(vmin)SHM). The shaded region again reflects the total uncertainty from both density and velocity distributions. Bottom panel: detectability relative to the pristine NFW model, (dR=d(vmin)mode􀀀 dR=d(vmin)pNFW)=(dR=d(vmin)pNFW). The shaded region is the same as in the middle and upper panels. The vertical lines indicate the reported sensitivity limits for several direct detection experiments at m=5 GeV. The experiments are labeled above the figure, with the target nuclei listed in parentheses. Experiments are discussed further in Section IV B. Each experiment also has a horizontal line spanning m=10 GeV (left) to m=5 GeV (right, connecting to the vertical line) to demonstrate how the vmin threshold would change as a function of WIMP mass.

Upper panel: Annual modulation fraction, (Rmax􀀀 Rmin)=(Rmax+Rmin), as a function of vmin. The models are shown following the same convention as in Figures 5 and 6. Middle panel: relative enhancement factor for the fiducial dynamical NFW model and the adiabatically contracted NFW model, compared to the SHM. Bottom panel: relative enhancement factor for the fiducial model and the adiabatically contracted model, compared to the pristine NFW profile.

## Conclusions

The major results of the paper are as follows:

1. The density of the DM halo at the solar position strongly depends on the Earth’s location relative to the stellar bar. Smaller angles relative to the bar as well as a smaller ratio of Rsun=Rbar can increase the density relative to a spherical distribution by a factor of 2.

2. The DM velocity profile is reshaped by the stellar+ shadow bar. The characteristic quadrupole wake in the DM that forms as a response to the stellar bar lags the bar in velocity and, therefore, enhances the detectability of DM when compared to the SHM by a factor of 1.5 at vmin=300 km s-11 and up to a factor of 40 at vmin=650 km s-1 for a cored NFW halo model.

3. Due to the dependence of the detectability relative to the SHM with vmin, experiments need to move beyond the SHM to compare with other experiments that have different energy thresholds. Specifically, the results based on a number of recent astrophysical models together suggest the importance of the MW evolutionary history to modeling DM detection rates.

4. Similarly, annual modulation in the DM signal will have different detectabilities compared to the SHM as a function of vmin. The stellar+shadow bar, when compared to the adiabatic contraction model, reduces the annual modulation signal for experiments sensitive to high energy thresholds and boosts the annual modulation signal for experiments sensitive to low energy thresholds.

5. When compared to the SHM, we expect an enhancement in detectability and annual modulation. We use an adiabatic contraction model that fixes the gravitational potential of the disk to calibrate the importance of dynamical evolution to the DM detection predictions. When we compare our full model to this adiabatically contracted model, we expect an enhancement in detectability, but a decrease in the annual modulation signal. This illustrates the influence of dynamical evolution.