  From an assumed signal in a Dark Matter (DM) direct detection experiment a
lower bound on the product of the DM--nucleon scattering cross section and the
local DM density is derived, which is independent of the local DM velocity
distribution. This can be combined with astrophysical determinations of the
local DM density. Within a given particle physics model the bound also allows a
robust comparison of a direct detection signal with limits from the LHC.
Furthermore, the bound can be used to formulate a condition which has to be
fulfilled if the particle responsible for the direct detection signal is a
thermal relic, regardless of whether it constitutes all DM or only part of it.
We illustrate the arguments by adopting a simplified DM model with a Z'
mediator and assuming a signal in a future xenon direct detection experiment.
