Revisiting the dynamical masses of the transiting planets in the young AU Mic system: Potential AU\,Mic b inflation at sim 20 Myr

Understanding planet formation is important in the context of the origin of planetary systems in general and of the Solar System in particular, as well as to predict the likelihood of finding Jupiter, Neptune, and Earth analogues around other stars. We aim to precisely determine the radii and dynamical masses of transiting planets orbiting the young M star AU\,Mic using public photometric and spectroscopic datasets. We performed a joint fit analysis of the TESS and CHEOPS light curves and more than 400 high-resolution spectra collected with several telescopes and instruments. We characterise the stellar activity and physical properties (radius, mass, density) of the transiting planets in the young AU\,Mic system through joint transit and radial velocity fits with Gaussian processes. We determine a radius of $R_ p b $=\,4.79\,pm \,0.29 R$_ a mass of p b $=\,9.0\,pm \,2.7 M$_ and a bulk density of $ p b $\,=\,0.49\,pm \,0.16 $ for the innermost transiting planet AU\,Mic\,b. For the second known transiting planet, AU\,Mic\,c, we infer a radius of p c $=\,2.79\,pm \,0.18 R$_ a mass of p c $=\,14.5\,pm \,3.4 M$_ and a bulk density of $ p c $\,=\,3.90\,pm \,1.17 $. According to theoretical models, AU\,Mic\,b may harbour an $ envelope larger than 5 by mass, with a fraction of rock and a fraction of water. AU\,Mic\,c could be made of rock and/or water and may have an $ atmosphere comprising at most 5 of its mass. AU\,Mic\,b has retained most of its atmosphere but might lose it over tens of millions of years due to the strong stellar radiation, while AU\,Mic\,c likely suffers much less photo-evaporation because it lies at a larger separation from its host. Using all the datasets in hand, we determine a 3sigma upper mass limit of p d i oplus $ for the AU\,Mic 'd' TTV-candidate. In addition, we do not confirm the recently proposed existence of the planet candidate AU\,Mic\,'e' with an orbital period of 33.4 days. We investigated the level of the radial velocity variations and show that it is lower at longer wavelength with smaller changes from one observational campaign to another.