HD 164604 c: A Second Giant Planet on a 15 Yr Orbit and Constraints on the Planet–Planet Mutual Inclination*

Abstract We report the discovery of a new massive giant planet, HD 164604 c ( a c = 5.55 6 − 0.10 + 0.093 au, e c = 0.19 6 − 0.078 + 0.078 , and m c = 9 . 5 − 1.25 + 1.2 , or 7 . 6 − 1.0 + 1.0 M Jup ), orbiting a K3.5 dwarf, The result is based on the combined analysis of high-precision radial velocity data and astrometry from Hipparcos and the second and third data releases of Gaia. We refine the orbital parameters of the inner planet HD 164604 b to a b = 1.36 2 − 0.012 + 0.012 au, e b = 0.47 9 − 0.021 + 0.027 , and m b = 13 . 2 − 1.5 + 1.8 M Jup (or