Are there any extragalactic high speed dark matter particles in the Solar neighborhood?

We use the APOSTLE suite of cosmological hydrodynamical simulations of the Local Group to examine the high speed tail of the local dark matter velocity distribution in simulated Milky Way analogues. The velocity distribution in the Solar neighborhood is well approximated by a generalized Maxwellian distribution sharply truncated at a well-defined maximum ``escape" speed. The truncated generalized Maxwellian distribution accurately models the local dark matter velocity distribution of all our Milky Way analogues, with no evidence for any separate extragalactic high-speed components. The local maximum speed is well approximated by the terminal velocity expected for particles able to reach the Solar neighborhood in a Hubble time from the farthest confines of the Local Group. This timing constraint means that the local dark matter velocity distribution is unlikely to contain any high-speed particles contributed by the Virgo Supercluster ``envelope", as argued in recent works. Particles in the Solar neighborhood with speeds close to the local maximum speed can reach well outside the virial radius of the Galaxy, and, in that sense, belong to the Local Group envelope posited in earlier work. The local manifestation of such envelope is thus not a distinct high-speed component, but rather simply the high-speed tail of the truncated Maxwellian distribution.