Self-interacting asymmetric dark matter coupled to a light massive dark photon

Abstract

Dark matter (DM) with sizeable self-interactions mediated by a light species offers a compelling explanation of the observed galactic substructure; furthermore, the direct coupling between DM and a light particle contributes to the DM annihilation in the early universe. If the DM abundance is due to a dark particle-antiparticle asymmetry, the DM annihilation cross-section can be arbitrarily large, and the coupling of DM to the light species can be significant. We consider the case of asymmetric DM interacting via a light (but not necessarily massless) Abelian gauge vector boson, a dark photon. In the massless dark photon limit, gauge invariance mandates that DM be multicomponent, consisting of positive and negative dark ions of different species which partially bind in neutral dark atoms. We argue that a similar conclusion holds for light dark photons; in particular, we establish that the multi-component and atomic character of DM persists in much of the parameter space where the dark photon is sufficiently light to mediate sizeable DM self-interactions. We discuss the cosmological sequence of events in this scenario, including the dark asymmetry generation, the freeze-out of annihilations, the dark recombination and the phase transition which gives mass to the dark photon. We estimate the effect of self-interactions in DM haloes, taking into account this cosmological history. We place constraints based on the observed ellipticity of large haloes, and identify the regimes where DM self-scattering can affect the dynamics of smaller haloes, bringing theory in better agreement with observations. Moreover, we estimate the cosmological abundance of dark photons in various regimes, and derive pertinent bounds.

Figures (13)

• Figure 1: To the right of the solid lines, the condition \ref{['eq:MDasym']} is satisfied: an asymmetry is generated both in $p_{_D}$ and $e_{_D}$. We have set $q_\phi = 1$. Left: We fix the fine structure constant to $\alpha_{_D} = \alpha_{_{D, \rm min}}(m_{\bf p})$ (lower solid blue line) and $\alpha_{_D} = 10 \, \alpha_{_{D, \rm min}}(m_{\bf p})$ (upper solid blue line), where $\alpha_{_{D, \rm min}}(m_{\bf p})$ is the minimum value which allows sufficient annihilation of the thermal population of dark protons in the early universe [c.f. Eq. \ref{['eq:alpha ann']}, where we set the dark-to-ordinary temperature ratio at the time of freeze-out to $\xi_{\rm ann} = 0.5$]. Obviously, larger values of $\alpha_{_D}$ imply that more parameter space is encompassed in the multi-component DM realisation. To the right of the yellow dashed line, the $p_{_D} - p_{_D}$ collisions manifest as long-range in haloes with rotational velocity $\bar{v} \gtrsim 10 \: {\rm km/ s}$ [c.f. Eq. \ref{['eq:long-range']}]. Right: We consider $p_{_D}^+ - p_{_D}^+$ collisions in DM haloes, according to what described in Sec. \ref{['sec:self-inter']}. For the blue (lower) line, we pick the minimum value of $\alpha_{_D}(m_{\bf p}, M_{_D})$ for which, under the assumption of single-component DM, there can be a significant effect on the dynamics of small haloes. In particular, we fix the momentum-transfer cross-section to $\sigma_{\bf pp} / m_{\bf p} = 0.5 \: {\rm cm^2/ g}$ at $\bar{v} = 10 \: {\rm km/ s}$. This ensures that the ellipticity of larger haloes is retained, since $\sigma_{\bf pp}/m_{\bf p}$ decreases with $\bar{v}$. (Note though, that the value of $\alpha_{_D}$ specified in this way may be smaller than $\alpha_{_{D, \rm min}}$.) For the green (upper) line, we pick $\alpha_{_D}$ by setting $\sigma_{\bf pp} / m_{\bf p} = 1 \: {\rm cm^2/ g}$ at $\bar{v} = 220 \: {\rm km/s}$. This yields the maximum value of $\alpha_{_D}(m_{\bf p}, M_{_D})$ that is currently considered compatible with the observed ellipticity of haloes. For this choice of $\alpha_{_D}$, to the left of the green dot-dashed line, $\alpha_{_D} < \alpha_{_{D,\rm min}}$ and the scenario does not appear viable. That is to say, if for the $m_{\bf p}, \, M_{_D}$ values to the left of the green dot-dashed line, we set $\alpha_{_D} \gtrsim \alpha_{_{D, \rm min}}$, then the $p_{_D}^+ - p_{_D}^+$ interaction in haloes is too strong. However, when the formation of dark atoms in the early universe is taken into account, the DM self-scattering is suppressed, $\alpha_{_D}$ can be larger while respecting the ellipticity bound, and this part of the $m_{\bf p} - M_{_D}$ plane can produce viable scenarios, as we show in Sec. \ref{['sec:self-inter']}. In the grey-shaded regions, the perturbativity limit is exceeded, $\alpha_{_D} > 4\pi$, for the two choices of $\alpha_{_D}$ (lower and upper region respectively).
• Figure 2: Bounds on the dark-to-ordinary temperature ratio, $\xi = T_{_{\rm D}} / T_{_{\rm V}}$, vs the dark photon mass $M_{_D}$, assuming $\epsilon\to 0$. In the blue-shaded region on the top left, the extra radiation due to relativistic dark photons exceeds the BBN limit. This bound applies to $\xi_{_{\rm BBN}}$ (i.e. evaluated at the time of BBN). In the red-shaded regions on the right, the relic abundance of the dark photons may alter the time of matter-radiation equality or dominate the DM density. Each region corresponds to the value of $q_\phi^2 \alpha_{_D}$ shown on the plot. These bounds apply to $\xi_{\gamma_{_D}}$ (i.e. evaluated at the time of the dark photon chemical decoupling). We have assumed that $m_\phi \approx v_{_D}$. To the right of the grey dashed line, the cosmological abundance of the dark photons may decay into SM charged fermions if the dark force mixes kinetically with hypercharge. If the decay is sufficiently fast, the bounds on $\xi$ may be relaxed or eliminated.
• Figure 3: In the red-shaded region, DM self-interaction rate violates the condition \ref{['eq:MW cond']}; this region is disfavoured by ellipticity of Milky-Way-size and larger haloes. In the region enclosed by the blue solid line, the DM self-scattering satisfies the condition \ref{['eq:DW cond']} and can affect the dynamics of dwarf-galaxy-size haloes. In the cross-hatched region, the DM annihilation in the early universe is insufficient, under minimal assumptions; this bound can be relaxed if more annihilation channels exist. In the grey-shaded region, the consistency condition of Eq. \ref{['eq:muD upper']} is not satisfied; this region does not correspond to any meaningful parameter space. The dashed grey lines denote fixed values of the residual ionisation fraction $x_{_D}$. For each of the plots in this set, the binding energy $\Delta$, the dark photon mass $M_{_{D}}$ and the dark-to-ordinary temperature ratio at the time of dark recombination $\xi_{_{\rm DR}}$ are fixed to the values mentioned in the plot labels. For the annihilation bound, we take $\xi_{\rm ann} = \xi_{_{\rm DR}}$. In this set of plots, the atom-atom scattering was estimated according to Ref. Cline:2013pca (c.f. Eq. (\ref{['eq:CL sigma HH']})) and atom-ion collisions were ignored.
• Figure 4: Same as Fig. \ref{['fig:CL_alphaVmH']}, but with the atom-atom and atom-ion scattering estimated according to Ref. CyrRacine:2012fz (c.f. Eqs. \ref{['eq:Gamma HH']} - \ref{['eq:Gamma He']}). To facilitate the visual identification of the method used, in this and subsequent sets of plots using the approach of Ref. CyrRacine:2012fz, red shading has been switched to pink.
• Figure 5: Same as in Fig. \ref{['fig:CL_alphaVmH']}, for fixed values of $\alpha_{_D}$, $M_{_D}$ and $\xi_{_{\rm DR}}$. We have used the approach of Ref. Cline:2013pca for atom-atom scattering.