The young HD 73583 (TOI-560) planetary system: Two 10-M$_\oplus$ mini-Neptunes transiting a 500-Myr-old, bright, and active K dwarf

We present the discovery and characterisation of two transiting planets observed by \textit{TESS} in the light curves of the young and bright (V=9.67) star HD73583 (TOI-560). We perform an intensive spectroscopic and photometric space- and ground-based follow-up in order to confirm and characterise the system. We found that HD73583 is a young ($\sim 500$~Myr) active star with a rotational period of $12.08 \pm 0.11 $\,d, and a mass and radius of $ 0.73 \pm 0.02 M_\odot$ and $0.65 \pm 0.02 R_\odot$, respectively. HD73583 b ($P_b=6.3980420 _{ - 0.0000062 }^{+0.0000067}$ d) has a mass and radius of $10.2 _{-3.1}^{+3.4} M_\oplus$ and$2.79 \pm 0.10 R_\oplus$, respectively, that gives a density of $2.58 _{-0.81}^{ 0.95} {\rm g\,cm^{-3}}$. HD73583 c ($P_c= 18.87974 _{-0.00074 }^{+0.00086}$) has a mass and radius of $9.7_{-1.7} ^ {+1.8} M_\oplus$ and $2.39_{-0.09}^{+0.10} R_\oplus$, respectively, this translates to a density of $3.88 _{-0.80}^{+0.91} {\rm g\,cm^{-3}}$. Both planets are consistent with worlds made of a solid core surrounded by a volatile envelope. Because of their youth and host star brightness, they both are excellent candidates to perform transmission spectroscopy studies. We expect ongoing atmospheric mass-loss for both planets caused by stellar irradiation. We estimate that the detection of evaporating signatures on H and He would be challenging, but doable with present and future instruments.