Planetesimal Dynamics in Inclined Binary Systems: The Role of Gas-Disk Gravity

We investigate the effects of gas-disk gravity on the planetesimal dynamics in inclined binary systems, where the circumprimary disk plane is tilted by a significant angle ($i_B$) with respect to the binary disk plane. Our focus is on the Lidov-Kozai mechanism and the evolution of planetesimal eccentricity and inclination. Using both analytical and numerical methods, we find that, on one hand, the disk gravity generally narrows down the Kozai-on region, i.e., the Lidov-Kozai effect can be suppressed in certain parts of (or even the whole of) the disk, depending on various parameters. In the Kozai-off region, planetesimals would move on orbits close to the mid-plane of gas-disk, with the relative angle ($i^{'}$) following a small amplitude periodical oscillation. On the other hand, when we include the effects of disk gravity, we find that the Lidov-Kozai effect can operate even at arbitrarily low inclinations ($i_B$), although lower $i_B$ leads to a smaller Kozai-on region. Furthermore, in the Kozai-on region, most planetesimals' eccentricities can be excited to extremely high values ($\sim 1$), and such extreme high eccentricities usually accompany orbital flipping, i.e., planetesimal orbit flips back and forth between anterograde and retrograde. Once a planetesimal reaches very high orbital eccentricity, gas drag damping will shrink the planetesimal orbit, forming a "hot planetesimal" on a near circular orbit very close to the primary star. Such a mechanism, if replacing the planetesimals and gas drag damping with Jupiters and tidal damping respectively, may lead to frequent production of hot-Jupiters.