Annihilation signatures of hidden sector dark matter within early-forming microhalos

If the dark matter is part of a hidden sector with only very feeble couplings to the Standard Model, the lightest particle in the hidden sector will generically be long lived and could come to dominate the energy density of the Universe prior to the onset of nucleosynthesis. During this early matter-dominated era, density perturbations will grow more quickly than otherwise predicted, leading to a large abundance of sub-Earth-mass dark matter microhalos. Since the dark matter does not couple directly to the Standard Model, the minimum halo mass is much smaller than expected for weakly interacting dark matter, and the smallest halos could form during the radiation-dominated era. In this paper, we calculate the evolution of density perturbations within the context of such hidden sector models and use a series of $N$-body simulations to determine the outcome of nonlinear collapse during radiation domination. The resulting microhalos are extremely dense, which leads to very high rates of dark matter annihilation and to large indirect detection signals that resemble those ordinarily predicted for decaying dark matter. We find that the Fermi Collaboration’s measurement of the high-latitude gamma-ray background rules out a wide range of parameter space within this class of models. The scenarios that are most difficult to constrain are those that feature a very long early matter-dominated era; if microhalos form prior to the decay of the unstable hidden sector matter, the destruction of these microhalos effectively heats the dark matter, suppressing the later formation of microhalos.

Figure 1

The evolution of the fractional density perturbations in dark matter for a mode with $k=1.5\times {10}^7{\mathrm{pc}}^{-1}$ that enters the horizon prior to an EMDE with $T_{\mathrm{RH}}=16\mathrm{GeV}$ and $T_{\mathrm{dom}}=233\mathrm{GeV}$. Upon entering the horizon ($k=aH$), ${\delta }_X$ grows logarithmically with the scale factor, $a$. It transitions to linear growth during the EMDE and then returns to logarithmic growth after reheating. This mode goes nonlinear during the radiation-dominated era, and the top (green) curve shows its evolution according to spherical collapse theory. The bottom (blue) curve shows the continued linear-theory evolution; $\delta$ resumes linear growth when the Universe becomes matter dominated (MD).

Figure 2

The evolution of an overdense region that collapses during radiation domination. The solid lines show the spherically averaged matter density profile at four different redshifts. The minimum radius of the profile at each redshift corresponds to a sphere that contains 100 particles. The dotted lines show the density of the radiation at these same redshifts. The spherical-collapse model predicts that this overdense region should collapse at $z_c=3.9\times {10}^7$, but the matter density grows slowly until the matter density within the smoothing scale ($R_f={10}^{-8}{h}^{-1}\mathrm{kpc}$) exceeds the radiation density, which occurs at $z_{\mathrm{rc}}=4.2\times {10}^5$. At that point, the central density increases dramatically, forming a bound object with a central density that exceeds the background matter density by over 4 orders of magnitude.

Figure 3

The annihilation boost factor, $B_0$, as a function of the ratio of the temperatures at the beginning of the EMDE, $T_{\mathrm{dom}}$, and at the time of reheating, $T_{\mathrm{RH}}$, for ${\alpha }_X=0.01$ (dashed curves) and ${\alpha }_X=0.1$ (solid). For each curve, we adopt ${\xi }_{\inf }=1$, $m_X/m_{Z^{\prime }}=20$ and we select $\epsilon$ and $m_X$ such that ${\mathrm{\Omega }}_X{h}^2\simeq 0.11$. The resulting values of $\epsilon$ and $m_X$ are shown in Fig. 5. The gray and blue curves represent the results that are found following our optimistic and conservative procedures, respectively. In scenarios with a very long EMDE, gravitational heating significantly disrupts the microhalo population, reducing the boost factors to values near that predicted for a standard thermal history, $B_0\sim {10}^6$.

Figure 4

The dark matter’s effective lifetime as a function of mass, for the same parameters as adopted in Fig. 3. Again, the gray and blue curves represent the results found following our optimistic and conservative procedures, respectively, with ${\alpha }_X=0.01$ (dashed curves) and ${\alpha }_X=0.1$ (solid). Results are shown only for $T_{\mathrm{dom}}/T_{\mathrm{RH}}\gtrsim 1.1$, and thus these curves do not extend to arbitrarily low masses. The black curves represent the lower limits on ${\tau }_{\mathrm{eff}}$ in this model, as derived from Fermi’s measurement of the high-latitude gamma-ray background [35, 36]. These constraints rule out scenarios with an EMDE for dark matter masses lighter than $m_X\lesssim 6–7\mathrm{TeV}$ for ${\alpha }_X=0.01$ and lighter than $\sim 60–70\mathrm{TeV}$ for ${\alpha }_X=0.1$. For higher masses, gravitational heating significantly disrupts the microhalo population, reducing the boost factors to acceptable levels.

Figure 5

Some of the features and constraints found across the parameter space of the vector portal dark matter model, for the case of ${\xi }_{\inf }=1$ and $m_X/m_{Z^{\prime }}=20$. The dashed curves represent the regions of this plane that yield a relic abundance equal to the measured dark matter density, ${\mathrm{\Omega }}_X{h}^2\simeq 0.11$, for choices of ${\alpha }_X=0.01$ and ${\alpha }_X=0.1$. In the blue region, the hidden sector never dominates the energy density of the early universe, and the red region is excluded by the measured light element abundances and other cosmological considerations. Throughout the gray region, the EMDE leads to the formation and survival of a large population of microhalos, resulting in large boost factors (following our conservative procedure) that are currently ruled out by Fermi’s measurement of the high-latitude gamma-ray background. In the lower right portions of this figure, gravitational heating leads to the suppression of this microhalo population, reducing the boost factors and resulting in gamma-ray emission at acceptable levels. Note that in the lowest portions of the region labeled “No Early Matter-Dominated Era” the energy density of the $Z^{\prime }$ population is still sizable, leading to non-negligible contributions to the annihilation boost factor.

Figure 6

The contribution to the isotropic gamma-ray background from dark matter annihilations in the hidden sector model discussed in the text (with $m_X/m_{Z^{\prime }}=20$). In each frame, the contributions from the Galactic halo are shown as dotted and dotted-dashed lines, representing the emission from direct production and from inverse Compton scattering, respectively. The dashed lines represent the cosmological contribution, including electromagnetic cascades. The solid lines denote the sum of these components. In each frame, the normalization (and corresponding dark matter annihilation rate) has been set to the maximum value allowed by the data (at the 95% confidence level). The gray region shows this maximal dark matter contribution combined with the astrophysical spectrum predicted by a multi-wavelength analysis; see Ref. [36] for details.

Figure 7

Lower limits on the dark matter’s effective lifetime (95% confidence level) as a function of mass. Here we have adopted $m_X/m_{Z^{\prime }}=20$. The solid curves treat the systematic errors (shown as a blue band around the error bars in Fig. 6) as entirely independent and uncorrelated. At the other extreme, the dashed curve has been derived assuming that the systematic errors are fully correlated, moving upward or downward together in unison. These curves are the same as those shown with the same line types in Fig. 4. For details, see Ref. [36].

Figure 8

The threshold for linear collapse, ${\delta }_c$, as a function of the collapse scale factor, $a_c$, for three values of the reheat temperature, $T_{\mathrm{RH}}$. The light, solid lines represent ${\delta }_c$ computed using the spherical collapse model as described in Sec. 4, while the dark, dotted lines employ the fitting formula presented in this Appendix. The arrows mark the values of $a_{\mathrm{RH}}$ as defined in Eq. (b1).