Gemini-GRACES high-quality spectra of Kepler evolved stars with transiting planets. I. Detailed characterization of multi-planet systems Kepler-278 and Kepler-391

(abridged) Kepler-278 and Kepler-391 are two of the three evolved stars known to date on the RGB to host multiple short-period transiting planets. Moreover, these planets are among the smallest discovered around RGB stars. Here we present a detailed stellar and planetary characterization of these remarkable systems. Based on high-quality spectra from Gemini-GRACES for Kepler-278 and Kepler-391, we obtained refined stellar parameters and precise chemical abundances for 25 elements. Also, combining our new stellar parameters with a photodynamical analysis of the Kepler light curves, we determined accurate planetary properties of both systems. The precise spectroscopic parameters of Kepler-278 and Kepler-391, along with their high $^{12}\mathrm{C}/^{13}\mathrm{C}$ ratios, show that both stars are just starting their ascent on the RGB. The planets Kepler-278b, Kepler-278c, and Kepler-391c are warm sub-Neptunes, whilst Kepler-391b is a hot sub-Neptune that falls in the hot super-Earth desert and, therefore, it might be undergoing photoevaporation of its outer envelope. The high-precision obtained in the transit times allowed us not only to confirm Kepler-278c's TTV signal, but also to find evidence of a previously undetected TTV signal for the inner planet Kepler-278b. From the presence of gravitational interaction between these bodies we constrain, for the first time, the mass of Kepler-278b ($M_{\mathrm{p}}$ = 56 $\substack{+37\\-13}$ $M_{\mathrm{\oplus}}$) and Kepler-278c ($M_{\mathrm{p}}$ = 35 $\substack{+9.9\\ -21} $ $M_{\mathrm{\oplus}}$). Finally, our photodynamical analysis also shows that the orbits of both planets around Kepler-278 are highly eccentric ($e \sim$ 0.7) and, surprisingly, coplanar. Further observations of this system are needed to confirm the eccentricity values presented here.