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PDS 70 hosts two massive, still-accreting planets and the inclined orientation of its protoplanetary disk presents a unique opportunity to directly probe the vertical gas structure of a planet-hosting disk. Here, we use high-spatial-resolution (${\approx}$0."1;10 au) observations in a set of CO isotopologue lines and HCO$^+$ J=4-3 to map the full 2D $(r,z)$ disk structure from the disk atmosphere, as traced by $^{12}$CO, to closer to the midplane, as probed by less abundant isotopologues and HCO$^+$. In the PDS 70 disk, $^{12}$CO traces a height of $z/r\approx0.3$, $^{13}$CO is found at $z/r\approx0.1$, and C$^{18}$O originates at, or near, the midplane. The HCO$^+$ surface arises from $z/r\approx0.2$ and is one of the few non-CO emission surfaces constrained with high fidelity in disks to date. In the $^{12}$CO J=3-2 line, we resolve a vertical dip and steep rise in height at the cavity wall, making PDS 70 the first transition disk where this effect is directly seen in line emitting heights. In the outer disk, the CO emission heights of PDS 70 appear typical for its stellar mass and disk size and are not substantially altered by the two inner embedded planets. By combining CO isotopologue and HCO$^+$ lines, we derive the 2D gas temperature structure and estimate a midplane CO snowline of ${\approx}$56-85 au. This implies that both PDS 70b and 70c are located interior to the CO snowline and are likely accreting gas with a high C/O ratio of ${\approx}$1.0, which provides context for future planetary atmospheric measurements from, e.g., JWST, and for properly modeling their formation histories., Comment: 24 pages, 14 figures, accepted for publication in ApJ

The discovery of planets in binaries is one the most interesting outcomes of planetary research. With the growing number of discoveries has also grown the interest on describing their formation, long-term evolution and potential habitability. In this work we revisit the dynamics of planets in S-type binary systems. For that purpose we develop explicit formulas for the secularized octupolar Hamiltonian, coupled with general relativistic corrections and non-conservative interactions. We implemented those formulas in an open-source package \texttt{SecDev3B}, that can be used to reproduce our results or test improved versions of the models. In order to test it, we study the long-term dynamical evolution of S-type binary planets during the pre-main-sequence phase of stellar evolution. During that phase, stellar radius significantly changes in timescales similar to secular timescales. We hypothesize that when close-encounters between the planet and its host star happens (e.g. via Lidov-Kozai effect), particularities in the secular formalism plus changes in stellar radius may alter significantly the dynamical evolution. We study the well-known binary planet HD 80606b and found that an octupolar expansion of the conservative Hamiltonian is required to properly predict its dynamical evolution. We also apply the dynamical model, enriched with results coming from stellar evolutionary models, to demonstrate that in S-type systems around low-mass stars, with relative high inclinations ($\itot\ge 60^\circ$), moderate eccentricities ($0.2\le e\le 0.4$) and planets located around 1 AU, the evolution of stellar radius during the first few hundreds of Myr, alters significantly the timescales of dynamical evolution., Comment: 20 pages, 7 figures, Submitted to MNRAS