Dark-matter decays and Milky Way satellite galaxies

We consider constraints on a phenomenological dark-matter model consisting of two nearly degenerate particle species using observed properties of the Milky Way satellite galaxy population. The two parameters of this model, assuming the particle masses are $\gtrsim \mathrm{GeV}$, are $v_{\mathrm{k}}$, the recoil speed of the daughter particle, and $\tau$, the lifetime of the parent particle. The satellite constraint that spans the widest range of $v_{\mathrm{k}}$ is the number of satellites that have a mass within 300 pc ${\mathrm{M}}_{300}>5\times {10}^6{\mathrm{M}}_{\odot }$, although constraints based on ${\mathrm{M}}_{300}$ in the classical dwarfs and the overall velocity function are competitive for $v_{\mathrm{k}}\gtrsim 50\mathrm{km}{\mathrm{s}}^{-1}$. In general, we find that $\tau \lesssim 30\mathrm{Gyr}$ is ruled out for $20\mathrm{km}{\mathrm{s}}^{-1}\lesssim v_{\mathrm{k}}\lesssim 200\mathrm{km}{\mathrm{s}}^{-1}$, although we find that the limits on $\tau$ for fixed $v_{\mathrm{k}}$ can change by a factor of $\sim 3$ depending on the star-formation histories of the satellites. We advocate using the distribution of ${\mathrm{M}}_{300}$ in Milky Way satellites, determined by next-generation all-sky surveys and follow-up spectroscopy, as a probe of dark-matter physics.

Figure 1

Velocity function of subhalos. The thick solid lines with error bars represent the CDM velocity functions from the merger trees for the all nodes (left) and dynamical friction (right) samples. The dotted line with error bars show the velocity function for subhalos with ${\mathrm{M}}_{300}>5\times {10}^6{\mathrm{M}}_{\odot }$. The dotted line connecting data points represents an estimated SDSS sky coverage-corrected velocity function for known Milky Way satellites [53], and the thin lines (upper: Aquarius A [61]; lower: Via Lactea II [53]) represent velocity functions found in high-resolution CDM simulations.

Figure 2

Distribution of the number of subhalos or satellites per halo in the host-halo sample for CDM. The upper panel shows the numbers of subhalos in the all nodes and dynamical friction samples both with and without the ${\mathrm{M}}_{300}>5\times {10}^6{\mathrm{M}}_{\odot }$ cut. The middle panel shows the distribution in the number of subhalos satisfying the star-formation criterion for $z_{\mathrm{re}}=7$ and $z_{\mathrm{re}}=11$, and the bottom panel shows the distribution in the number of satellites satisfying both the ${\mathrm{M}}_{300}$ and star-formation criteria.

Figure 3

Distribution of the number of subhalos or satellites per halo in the host-halo sample. Each plot shows distributions for fixed $v_{\mathrm{k}}$ and $\tau$ (top row: $v_{\mathrm{k}}=30\mathrm{km}{\mathrm{s}}^{-1}$; bottom row: $v_{\mathrm{k}}=200\mathrm{km}{\mathrm{s}}^{-1}$; left column: $\tau =20\mathrm{Gyr}$; right column: $\tau =60\mathrm{Gyr}$). Panels have the same meaning as in Fig. 2.

Figure 4

Dependence of the subhalo/satellite distribution on the inner cutoff for the simulation interpolation table for $v_{\mathrm{k}}=30\mathrm{km}{\mathrm{s}}^{-1}$ and $\tau =20\mathrm{Gyr}$. Left: Inner cutoff well within the numerical relaxation range. Center: Inner cutoff just outside the numerical relaxation range, as determined from simulations in which decay is turned off either at the beginning or later in the simulation. Right: Inner cutoff well outside the numerical relaxation region. Plot structure identical to that in Fig. 3.

Figure 5

Exclusion limits in the $v_{\mathrm{k}}-\tau$ parameter space. In both plots, the region (blue) marked “allowed” indicates the region of parameter space that has not yet been excluded. The light-colored (red) region marked “ruled out” and to the right of the dashed line is the part of parameter space that has been ruled out by observations of the galaxy-cluster mass function and the mass-concentration relation in galaxies, groups, and clusters [28, 29, 30]. The solid lines and the regions to the left of the dashed lines show limits from this work. The lower solid line shows the limit on the parameter space from the all nodes subhalo sample, and anything below the upper solid line is also excluded based on the dynamical friction subhalo sample. The light-colored (red) region corresponds to limits using the sample of all nodes subhalos satisfying the star-formation criterion with redshift $z_{\mathrm{re}}$, while the medium-dark (dark red) region shows the additional excluded region using the dynamical friction satellite sample satisfying the same star-formation criterion. Left panel: $z_{\mathrm{re}}=7$ Right panel: $z_{\mathrm{re}}=11$.

Figure 6

Maximum circular velocity functions for $v_{\mathrm{k}}=100\mathrm{km}{\mathrm{s}}^{-1}$ and $\tau =40\mathrm{Gyr}$, for all nodes subsamples (left) and dynamical friction subsamples (right). The line types indicate different subsamples as indicated in the legend: all subhalos, subhalos satisfying the star-formation criterion with $z_{\mathrm{re}}=7$, and subhalos satisfying the star-formation criterion with $z_{\mathrm{re}}=11$. The thin lines of each type indicate that a cut of ${\mathrm{M}}_{300}>5\times {10}^6{\mathrm{M}}_{\odot }$ has been included, and thick lines show the $v_{\max }$ distribution without a cut on ${\mathrm{M}}_{300}$.

Figure 7

Exclusion limits for the $z_{\mathrm{re}}=11$ satellite populations including the limits from the velocity function. Lines and shading of the plot have the same meaning as in Fig. 5.

Figure 8

${\mathrm{M}}_{300}$ distribution for CDM. Line types have the same meaning as in Fig. 6. Thick lines represent all nodes subsamples, and thin lines represent dynamical friction subsamples.

Figure 9

${\mathrm{M}}_{300}$ distributions for those consistent with limits on the $v_{\mathrm{k}}-\tau$ parameter space using the all nodes subhalo sample (top) and those consistent with the dynamical friction subhalo sample (bottom). The line types have the same meaning as in Fig. 6. The thick lines represent all nodes and thin lines represent dynamical friction subsamples.