Robust Limits from Upcoming Neutrino Telescopes and Implications on
  Minimal Dark Matter Models
  Experimental developments in neutrino telescopes are drastically improving
their ability to constrain the annihilation cross-section of dark matter. In
this paper, we employ an angular power spectrum analysis method to probe the
galactic and extra-galactic dark matter signals with neutrino telescopes. We
first derive projections for a next generation of neutrino telescope that is
inspired by KM3NeT. We emphasise that such analysis is much less sensitive to
the choice of dark matter density profile. Remarkably, the projected
sensitivity is improved by more than an order of magnitude with respect to the
existing limits obtained by assuming the Burkert dark matter density profile
describing the galactic halo. Second, we analyse minimal extensions to the
Standard Model that will be maximally probed by the next generation of neutrino
telescopes. As benchmark scenarios, we consider Dirac dark matter in $s$- and
$t$-channel models with vector and scalar mediators. We follow a global
approach by examining all relevant complementary experimental constraints. We
find that neutrino telescopes will be able to competitively probe significant
portions of parameter space. Interestingly, the anomaly-free $L_{\mu}-L_{\tau}$
model can potentially be explored in regions where the relic abundance is
achieved through freeze-out mechanism.
