Constraining the orientation of the spin axes of extrasolar minor bodies 1I/2017 U1 (`Oumuamua) and 2I/Borisov

Context. The orientation of the spin axis of a comet is defined by the values of its equatorial obliquity and its cometocentric longitude of the Sun. These parameters can be computed from the components of the nongravitational force caused by outgassing, if the cometary activity is well characterized. The trajectories of known interstellar bodies passing through the Solar System show nongravitational accelerations. Aims. The spin-axis orientation of 1I/2017 U1 (`Oumuamua) remains to be determined; for 2I/Borisov, the already released results are mutually exclusive. Here, we investigate the orientation of the spin axes of `Oumuamua and 2I/Borisov using public orbit determinations that consider outgassing. Methods. We applied a Monte Carlo simulation using the covariance matrix method together with Monte Carlo random search techniques to compute the distributions of equatorial obliquities and cometocentric longitudes of the Sun at perihelion of `Oumuamua and 2I/Borisov from the values of the nongravitational parameters. Results. We find that the equatorial obliquity of `Oumuamua could be about 93 deg, if it has a very prolate (fusiform) shape, or close to 16 deg, if it is very oblate (disk-like). Different orbit determinations of 2I/Borisov gave obliquity values of 59 deg and 90 deg. The distributions of cometocentric longitudes were in general multimodal. Conclusions. The most probable spin-axis direction of `Oumuamua in equatorial coordinates is (280 degrees, +46 degrees) if very prolate or (312 deg, -50 deg) if very oblate. For the orbit determinations of 2I/Borisov used here, we find most probable poles pointing near (275 deg, +65 deg) and (231 deg, +30 deg), respectively. Although our analysis favors an oblate shape for 2I/Borisov, a prolate one cannot be ruled out.