Generation of highly inclined protoplanetary discs through single stellar flybys

We study the three-dimensional evolution of a viscous protoplanetary disc which is perturbed by a passing star on a parabolic orbit. The aim is to test whether a single stellar flyby is capable to excite significant disc inclinations which would favour the formation of so-called misaligned planets. We use smoothed particle hydrodynamics to study inclination, disc mass and angular momentum changes of the disc for passing stars with different masses. We explore different orbital configurations for the perturber's orbit to find the parameter spaces which allow significant disc inclination generation. Prograde inclined parabolic orbits are most destructive leading to significant disc mass and angular momentum loss. In the remaining disc, the final disc inclination is only below $20^\circ$. This is due to the removal of disc particles which have experienced the strongest perturbing effects. Retrograde inclined parabolic orbits are less destructive and can generate disc inclinations up to $60^\circ$. The final disc orientation is determined by the precession of the disc angular momentum vector about the perturber's orbital angular momentum vector and by disc orbital inclination changes. We propose a sequence of stellar flybys for the generation of misalignment angles above $60^\circ$. The results taken together show that stellar flybys are promising and realistic for the explanation of misaligned Hot Jupiters with misalignment angles up to 60\degr.Comment: 15 pages, 15 figures, accepted for publication in MNRA

From rr-Spin Intersection Numbers to Hodge Integrals

Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of $r$-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by boson-fermion correspondence, and link it with a Hurwitz partition function and a Hodge partition by operators in a $\widehat{GL}(\infty)$ group. Then, from a $W_{1+\infty}$ constraint of the partition function of $r$-spin intersection numbers, we get a $W_{1+\infty}$ constraint for the Hodge partition function. The $W_{1+\infty}$ constraint completely determines the Schur polynomials expansion of the Hodge partition function.Comment: 51 pages, 1 figur