(a) The CPD temperature required to explain the observed ¹³CO emission, as a function of the CPD diameter. The upper horizontal axis shows the planet mass corresponding to the CPD diameter assuming that the CPD radius is 1/3 of the Hill radius: ﹩{R}_{\mathrm{CPD}}={(1/3){R}_{\mathrm{Hill}}=(1/3)({M}_{p}/3{M}_{* })}^{1/3}﹩. The dashed horizontal line shows AS 209's circumstellar disk temperature at 206 au, 22 K (Law et al. 2021b). The gray-shaded region shows the planet mass constrained by the width of the ¹²CO gap, 0.42–4.2 M _Jup, adopting a range of disk viscosities α = 10⁻⁴–10⁻² (see Section 4.1). (b) A lower limit to the CPD gas mass inferred from the ¹³CO emission (blue) and an upper limit to the CPD gas mass inferred from the null detection of C¹⁸O (red). The dashed curves show M _CPD = 1.0, 0.3, 0.1, and 0.03 M _p (from left to right). (c) The CPD dust mass inferred from the nondetection of the continuum emission. The solid curve assumes a maximum grain size of 1 mm, while the dashed curve assumes a maximum grain size of 1 μm. (d) The CPD dust-to-gas mass ratio obtained from the inferred CPD gas and dust masses. In this figure, the black solid/dashed curves show lower (temperature in panel (a)) or upper (dust mass in panel (c)) limits, while the gray hatched regions present the allowed region in the parameter space bounded by limits from the ¹³CO (blue) and C¹⁸O (red) data.