Precession and polar alignment of accretion discs in triple (or multiple) stellar systems

We investigate the mechanism of polar alignment for accretion discs in hierarchical systems (HSs) with more than two stars. In eccentric binary systems, low mass discs that are sufficiently tilted to the binary orbit align in a polar configuration with respect to the binary plane by aligning their angular momentum to the binary eccentricity vector. In HSs, secular evolution of the orbital parameters makes the eccentricity vector of the system precess with time. This precession undermines the stability of the polar orbit for accretion discs hosted in HSs. We analytically show that the binary criteria for polar alignment derived in the literature are necessary but not sufficient conditions for polar alignment in HSs. Then, we derive an analytical criterion for polar alignment in HSs. In general, we find that discs orbiting the innermost level of a HS can go polar. Conversely, radially extended discs orbiting the outer levels of a HS cannot polarly align and evolve as orbiting around a circular binary. We confirm our findings through detailed numerical simulations. Also, our results are compatible with the observed distribution of disc-orbit mutual inclination. Finally, we compare the observed distribution of disc inclinations in the binary and in the HS populations. Binaries host mainly coplanar discs, while HSs show a wide range of disc inclinations. We suggest that the wider range of inclinations in HSs results from the secular oscillation of their orbital parameters (such as Kozai-Lidov oscillations), rather than from a different initial condition or evolution between HSs and binaries.