Spirals, shadows & precession in HD 100453 -- I. The orbit of the binary

In recent years, several protoplanetary discs have been observed to exhibit spirals, both in scattered light and (sub)millimetre continuum data. The HD 100453 binary star system hosts such a disc around its primary. Previous work has argued that the spirals were caused by the gravitational interaction of the secondary, which was assumed to be on a circular orbit, coplanar with the disc (meaning here the large outer disc, as opposed to the very small inner disc). However, recent observations of the CO gas emission were found incompatible with this assumption. In this paper, we run SPH simulations of the gas and dust disc for seven orbital configurations taken from astrometric fits and compute synthetic observations from their results. Comparing to high-resolution ALMA $^{12}$CO data, we find that the best agreement is obtained for an orbit with eccentricity $e=0.32$ and semi-major axis $a=207$ au, inclined by $61^\circ$ relative to the disc plane. The large misalignment between the disc and orbit planes is compatible with the tidal evolution of a circumprimary disc in an eccentric, unequal-mass binary star.