  We present the results of the first combined dark matter search targeting the
Galactic Centre using the ANTARES and IceCube neutrino telescopes. For dark
matter particles with masses from 50 to 1000 GeV, the sensitivities on the
self-annihilation cross section set by ANTARES and IceCube are comparable,
making this mass range particularly interesting for a joint analysis. Dark
matter self-annihilation through the $\tau^+\tau^-$, $\mu^+\mu^-$, $b\bar{b}$
and $W^+W^-$ channels is considered for both the Navarro-Frenk-White and
Burkert halo profiles. In the combination of 2,101.6 days of ANTARES data and
1,007 days of IceCube data, no excess over the expected background is observed.
Limits on the thermally-averaged dark matter annihilation cross section
$\langle\sigma_A\upsilon\rangle$ are set. These limits present an improvement
of up to a factor of two in the studied dark matter mass range with respect to
the individual limits published by both collaborations. When considering dark
matter particles with a mass of 200 GeV annihilating through the $\tau^+\tau^-$
channel, the value obtained for the limit is $7.44 \times 10^{-24}
\text{cm}^{3}\text{s}^{-1}$ for the Navarro-Frenk-White halo profile. For the
purpose of this joint analysis, the model parameters and the likelihood are
unified, providing a benchmark for forthcoming dark matter searches performed
by neutrino telescopes.
