Indirect dark matter (DM) detection typically involves the observation of standard model (SM) particles emerging from DM annihilation/decay inside regions of high dark matter concentration. We consider an annihilation scenario in which this reaction has to be initiated by one of the DMs involved being boosted while the other is an ambient non-relativistic particle. This trigger DM must be created, for example, in a previous annihilation or decay of a heavier component of DM. Remarkably, boosted DM annihilating into gamma-rays at a specific point in a galaxy could actually have traveled from its source at another point in the same galaxy or even from another galaxy. Such a non-local behavior leads to a non-trivial dependence of the resulting photon signal on the galactic halo parameters, such as DM density and core size, encoded in the so-called astrophysical $J$-factor. These non-local $J$-factors are strikingly different than the usual scenario. A distinctive aspect of this model is that the signal from dwarf galaxies relative to the Milky Way tends to be suppressed from the typical value to various degrees depending on their characteristics. This feature can thus potentially alleviate the mild tension between the DM annihilation explanation of the observed excess of $sim$ GeV photons from the Milky Ways galactic center vs. the apparent non-observation of the corresponding signal from dwarf galaxies.
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