The first neutron star-neutron star (NS-NS) merger was discovered on August
17, 2017 through gravitational waves (GW170817) and followed with
electromagnetic observations. This merger was detected in an old elliptical
galaxy with no recent star formation. We perform a suite of numerical
calculations to understand the formation mechanism of this merger. We probe
three leading formation mechanisms of double compact objects: classical
isolated binary star evolution, dynamical evolution in globular clusters and
nuclear cluster formation to test whether they are likely to produce NS-NS
mergers in old host galaxies. Our simulations with optimistic assumptions show
current NS-NS merger rates at the level of 10^-2 yr^-1 from binary stars, 5 x
10^-5 yr^-1 from globular clusters and 10^-5 yr^-1 from nuclear clusters for
all local elliptical galaxies (within 100 Mpc^3). These models are thus in
tension with the detection of GW170817 with an observed rate 1.5 yr^-1 (per 100
Mpc^3; LIGO/Virgo estimate). Our results imply that either (i) the detection of
GW170817 by LIGO/Virgo at their current sensitivity in an elliptical galaxy is
a statistical coincidence; or that (ii) physics in at least one of our three
models is incomplete in the context of the evolution of stars that can form
NS-NS mergers; or that (iii) another very efficient (unknown) formation channel
with a long delay time between star formation and merger is at play.Comment: A&A: accepte