XENON1T solar axion and the Higgs boson emerging from the dark

In a recent letter we proposed a new non-thermal mechanism of Dark Matter production based on vacuum misalignment, where both the Higgs boson and a very light pseudo-scalar $\eta$ emerge from the Dark sector. In this letter, we identify the parameter space in a composite scenario where the light pseudo-scalar can be produced in the sun and explain the XENON1T excess in electron recoil data. The model's Dark Matter candidate has a mass around $50$ TeV and out of range for Direct Detection. Testable predictions include Gravitational waves at frequencies in the Hz range from a cosmological phase transition, an exotic decay $Z \to \gamma + \mbox{inv.}$ with rates $4 \div 16 \cdot 10^{-12}$ testable at a future Tera-Z collider, and an enhancement by $17\div 40$ % of the branching ratio $K_L \to \pi^0 + \mbox{inv.}$, not enough to explain the KOTO anomaly. All these predictions may be confirmed by future experiments.