Doppler effect on indirect detection of dark matter using dark matter only simulations

Indirect detection of dark matter is a major avenue for discovery. However, baryonic backgrounds are diverse enough to mimic many possible signatures of dark matter. In this work, we study the newly proposed technique of dark matter velocity spectroscopy [E. G. Speckhard, K. C. Y. Ng, J. F. Beacom, and R. Laha, Phys. Rev. Lett. 116, 031301 (2016)]. The nonrotating dark matter halo and the Solar motion produce a distinct longitudinal dependence of the signal which is opposite in direction to that produced by baryons. Using collisionless dark matter only simulations of Milky Way like halos, we show that this new signature is robust and holds great promise. We develop mock observations by a high energy resolution x-ray spectrometer on a sounding rocket, the Micro-X experiment, to our test case, the 3.5 keV line. We show that by using six different pointings, Micro-X can exclude a constant line energy over various longitudes at $\ge 3\sigma$. The halo triaxiality is an important effect, and it will typically reduce the significance of this signal. We emphasize that this new smoking gun in motion signature of dark matter is general and is applicable to any dark matter candidate which produces a sharp photon feature in annihilation or decay.

Figure 1

The projected column density of Halo 374 [35], the most spherical halo in the suite of simulations used here. The color scale is given in units of the surface brightness observed at the distance of the Sun, 8 kpc from the halo center. The diagram illustrates the basic principle of velocity spectroscopy: X-ray photons due to sterile neutrino dark matter decay are collected from within the field of view (shaded triangle) at the Sun’s position. The net blue- or redshift of observed photons is determined by the line of sight relative to the Sun’s velocity. In this simple model, the energy shift $\delta E/E=(v_{\odot }/c)\sin \ell \cos b$ (see Sec. 2a).

Figure 2

We plot the decay line spectrum $d\mathcal{F}/dE$ as a function of fractional shift in the energy $\delta E/E$ for six different pointings $\ell$, with $b=25°$. This compares the empirical histograms (solid) computed from the N-body simulation against the analytic Gaussian model (dashed) computed from an NFW profile with an analytic velocity dispersion model. The Gaussian line profile agrees closely with the empirical spectrum. The data for all six pointings are normalized relative to one another, and the x-axis is multiplied by 1000 for clarity.

Figure 3

An example of a synthetic Micro-X observation. The histogram gives the observed photons in 1 eV bins. This is roughly the energy resolution of Micro-X, though we emphasize that this is only to guide the eye; the likelihood analysis itself is unbinned. The dashed black curves show the model fit, with the horizontal error bars giving the position of the line centroid and $1\sigma$ uncertainty. This uncertainty is computed via the extended likelihood analysis described by Ref. [95]. The vertical red dashed lines give the line energy as predicted by the analytic model.

Figure 4

Velocity spectroscopy on the Milky Way analogue Halo 374. This shows the position of the observed line centroid due to sterile neutrino decay as a function of Galactic longitude $\ell$, with latitude $b=25°$. Here we compare results as computed from the $N$-body simulation (see Sec. 3b) for the instrumental parameters of Micro-X with our analytic model (Sec. 2) as well as a simple sinusoidal model, showing excellent agreement between the three. Note that the error bars represent ${\sigma }_{\mathrm{cent}}$, the $1\sigma$ uncertainty in the energy of the line centroid. This uncertainty is dominated by the Poisson statistics; we see that for hypothetical exposures with 10x and 100x the photon counts, the error bars shrink considerably. This also illustrates that the analytic NFW model (Sec. 2b), the small-FOV sinusoidal model, and the $N$-body data are indistinguishable until a 100x exposure is considered. For the purposes of this plot and the sky maps (Figs. 7 and 8), we estimate ${\sigma }_{\mathrm{cent}}=({\sigma }_E^2+{\sigma }_{\text{instr}}^2{)}^{1/2}C(N_b/N_s)N_s^{-1/2}$, where $C(R)=\sqrt{1+4R}$ is a factor given by the optimal Cramer-Rao bound.

Figure 5

PDFs of the detection significance for Doppler shifting of the dark matter decay line, given in units of $\sigma$. Vertical dashed lines and shaded regions give the 95% confidence interval. We see that for the fiducial Micro-X parameters (red), 95% of observations allow us to exclude $\delta E/E=0$ globally by $3\sigma$ or greater. If we model a hypothetical observing mission with 10x the exposure time (gray), we find that the detection significance increases drastically, giving an $8.8\sigma$ detection in 95% of observations. These PDFs were sampled from $10^5$ synthetic Micro-X observations. Observations were randomly distributed between all haloes in the simulation suite, with the relative orientation of the Sun to the halo randomized as well.

Figure 6

The contribution of subhaloes to the total observed DM decay flux. The bars give the fraction of all Micro-X pointings containing a subhalo that contributes more than some fraction of the total flux, i.e., we find that at $\ell =\pm 105°$, about 10% of pointings contain a subhalo bright enough to contribute over 1% of the total flux for that pointing. The number of pointings dominated by (10% or 50% of total flux) a single subhalo is low, at the $\sim 1\%$ level. This plot is symmetric in $\ell$, so only half of the pointings are plotted here.

Figure 7

Sky maps illustrating the principle of velocity spectroscopy for our Micro-X observation on Halo 374. Top: The flux map. Middle: The dipole pattern in the line energy induced by our motion relative to the Milky Way halo. Bottom: The significance of the detection of Doppler shifting of a dark matter decay line, indicating the exclusion of $\delta E/E=0$ by a Micro-X observation. The maps shown are actually the convolution of the sky brightness with the 20°-radius field of view. Therefore, the observed flux, Doppler shift, and significance are given by the color at the small X’s. Black circles indicate the FoV of Micro-X on the sky for the six pointings considered here.

Figure 8

An asymmetric Milky Way halo (Halo 800 with $b/a=0.60$ and $c/a=0.42$) can skew the significance of the observed signal to the east or west. Each field of view (black circles in the sky map where $b=25°$) corresponds to a data point in the right-hand plot. The gray shaded region indicates the $1\sigma$ uncertainties for the analytic model derived from a spherical NFW profile fit to this halo.