Exoplanets and Stellar Physics

Abstract:

Close-in giant exoplanets with temperatures greater than 2,000 K ('ultra-hot Jupiters') have been the subject of extensive efforts to determine their atmospheric properties using thermal emission measurements from the Hubble Space Telescope (HST) and Spitzer Space Telescope^1-3. However, previous studies have yielded inconsistent results because the small sizes of the spectral features and the limited information content of the data resulted in high sensitivity to the varying assumptions made in the treatment of instrument systematics and the atmospheric retrieval analysis^3-12. Here we present a dayside thermal emission spectrum of the ultra-hot Jupiter WASP-18b obtained with the NIRISS¹³ instrument on the JWST. The data span 0.85 to 2.85 μm in wavelength at an average resolving power of 400 and exhibit minimal systematics. The spectrum shows three water emission features (at >6σ confidence) and evidence for optical opacity, possibly attributable to H^-, TiO and VO (combined significance of 3.8σ). Models that fit the data require a thermal inversion, molecular dissociation as predicted by chemical equilibrium, a solar heavy-element abundance ('metallicity', [Formula: see text] times solar) and a carbon-to-oxygen (C/O) ratio less than unity. The data also yield a dayside brightness temperature map, which shows a peak in temperature near the substellar point that decreases steeply and symmetrically with longitude towards the terminators.

Abstract:

This paper examines the energetics of a convective flow subject to an oscillation with a period $t_{\rm osc}$ much smaller than the convective time-scale $t_{\rm conv}$, allowing for compressibility and uniform rotation. We show that the energy of the oscillation is exchanged with the kinetic energy of the convective flow at a rate $D_R$ that couples the Reynolds stress of the oscillation with the convective velocity gradient. For the equilibrium tide and inertial waves, this is the only energy exchange term, whereas for p modes there are also exchanges with the potential and internal energy of the convective flow. Locally, $\left| D_R \right| \sim u^{\prime 2} / t_{\rm conv}$, where $u^{\prime}$ is the oscillating velocity. If $t_{\rm conv} \ll t_{\rm osc}$ and assuming mixing length theory, $\left| D_R \right|$ is $\left( \lambda_{\rm conv} / \lambda_{\rm osc} \right)^2$ smaller, where $\lambda_{\rm conv}$ and $\lambda_{\rm osc}$ are the characteristic scales of convection and the oscillation. Assuming local dissipation, we show that the equilibrium tide lags behind the tidal potential by a phase $\delta(r) \sim r \omega_{\rm osc} / \left( g(r) t_{\rm conv}(r) \right)$, where g is the gravitational acceleration. The equilibrium tide can be described locally as a harmonic oscillator with natural frequency $\left( g/r \right)^{1/2}$ and subject to a damping force $-u^{\prime}/t_{\rm conv}$. Although $\delta(r)$ varies by orders of magnitude through the flow, it is possible to define an average phase shift $\overline{\delta }$ which is in good agreement with observations for Jupiter and some of the moons of Saturn. Finally, $1 / \overline{\delta }$ is shown to be equal to the standard tidal dissipation factor.