- 1Department of Physics, Massachusetts Institute of Technology, Cambridge, United States of America
- 2Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, United States of America
- 3School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom
Introduction. Lava planets have been a focus of astronomical exploration due to their detectability [1, 2]. To reach rock-melting temperatures, they usually have extremely close-in orbits; the resultant tidal locking forms a permanent dayside and nightside. Most research on lava world emission spectroscopy, except [3, 4], treats the entire planet as one vertical column and predicts secondary eclipse depths (SEDs) [5, 6]. However, future observations may provide phase curve constraints reflecting the 2D distribution of radiative flux from lava planets (controlled by both radiation and dynamics). Historically, two scenarios have been considered: one with a thick atmosphere which mostly homogenizes the Day-Night Temperature Contrast (DNTC) [7], the other with a thin DNTC-preserving atmosphere likely composed of rock vapor [8]. As shown by [3, 4, 9, 10, 11], in a thin atmosphere, the extreme DNTC drives a supersonic flow with a significant Surface-Atmosphere Temperature Contrast (SATC). In this work, we calculate radiative flux profiles and corresponding phase curves for lava planets with thin SiO atmospheres and highlight observable features.
Methods. We begin by simulating the SiO atmospheric flow using Kang's [9] implementation of the Ingersoll model with condensation [12, 13]. For simplicity, we assume Earth density; we choose planetary masses of 0.25, 0.5, 1.0, and 2.0 Me and substellar temperatures (SST) of 2500, 2625, 2750, 2875, and 3000 K. The host star is set to a 4440 K, 0.701 Rsun, 0.7 Msun K-dwarf. Figure 1 shows typical output from this model.
Figure 1. 1.0 Me, 2750 K SST temperature/pressure. (a): adiabatic, (b): isothermal. The surface is irradiated beyond 90° due to the planet’s proximity to its host star [14]; the kinks in the atmospheric temperature curve are physical and explained in [9].
At many colatitudes, a huge SATC is present, implying potential spectral features. To see these features, we run a correlated-k calculation with petitRADTRANS [15, 16] at each colatitude using 200 layers, no scattering, and H/He broadening. Previous simulations have suggested the possibility for an ultraviolet absorption–induced thermal inversion [5], but adiabatic cooling associated with dynamics may disrupt this inversion. For simplicity, we assume isothermal and adiabatic temperature structures to capture limits of the radiative heating/cooling effects explored by [4]. Finally, we pass the resulting spectral radiances through SPIDERMAN [17] with a circular, 90°-inclination orbit to generate SEDs/phase curves.
Results. Figure 2 plots SEDs at various wavelengths; note the 7500–12500 nm SiO band’s placement within the nominal 5000–10000 nm range of JWST’s MIRI Low-Resolution Spectrometer (LRS) [18].
Figure 2. 1.0 Me, 3000 K SST SEDs (in ppm of host star flux). (a): adiabatic, (b): isothermal. Depths plotted for surface emission (dotted gray) and surface+atmosphere absorption/emission (solid black). 8000 nm (approx. SiO band peak) and MIRI’s LRS range are indicated.
We see that for adiabatic atmospheres, the spectral flux density is halved within this band; isothermal atmospheres produce a smaller reduction.
Figure 3 shows 2D spectral radiance profiles and phase curves. While the isothermal phase curve largely resembles that of blackbody emission, the adiabatic phase curve exhibits a unique double-peak structure deviating by O(10) ppm from this shape—small, but significant. This structure stems from the suppression of outgoing radiation near the substellar point by optically thick upper-atmosphere SiO, which makes the flux distribution resemble a “donut.” This feature was not seen by [4] due to their use of a single-layer emission spectroscopy approximation.
Figure 3. 1.0 Me, 3000 K SST phase curves. (a): adiabatic, (b): isothermal. Dotted line: phase curve of surface blackbody radiation without absorption. Solid line: true phase curve. Dashed line: SED–normalized blackbody phase curve (for comparison). Visualizations of surface (top row) and true (bottom row) spectral radiances are shown.
Figure 4. 8000 nm SiO absorption, measured by SED reduction (top panels; [i] – [ii] in Fig. 3) and the maximum deviation of the phase curve from a scaled blackbody phase curve (bottom panels; [iii] – [iv] in Fig. 3). (a)/(c): adiabatic, (b)/(d): isothermal. Black circles denote simulated cases.
The prominence of the 8000 nm SiO band peak at secondary eclipse is shown in Figure 4. As expected, the dip in SED increases with planetary mass (larger emitting area) and SST. JWST recently found the nearby lava world GJ 367 b to have an SED of 79 ± 4 ppm [19], proving that resolution of O(10) ppm exoplanet emissions is possible. Referring to Figure 4, this suggests the adiabatic case (~40 ppm) is potentially observable, while placing the isothermal case and “donut” feature (~10 ppm) at the limits of detection.
Conclusion. Although many uncertainties remain regarding lava worlds, the 7500–12500 nm SiO band is ideally placed for JWST MIRI observations. We find the shape of the phase curve may be significantly altered by the “donut” shape radiation profile shown in Fig. 3. This feature may be detectable, enabling additional probing of atmospheric structure for large, hot planets. Aside from detection efforts, future work should aim to simulate the planetwide atmosphere for other volatiles, atmospheric structures, and broadening parameters.
[1] Santerne A. et al., 2018, Nature Astronomy 2 393–400
[2] Wang K. et al., 2024, MNRAS 534 1913–1927
[3] Nguyen T. et al., 2020, MNRAS 499 4605–4612
[4] Nguyen T. et al., 2022, MNRAS 513 6125–6133
[5] Zilinskas M. et al., 2022, A&A 661 A126.
[6] Piette A. et al., 2023, ApJ 954 29
[7] Koll D., 2022, ApJ 924 134
[8] Schaefer L. and Fegley B., 2009, ApJ 703 L113
[9] Kang W. et al., 2021, ApJ 907 67
[10] Castan T. and Menou K., 2011, ApJL 743 L36
[11] Kite E. et al., 2016, ApJ 828 80
[12] Ingersoll A. et al., 1985, Icar 64 375
[13] Ingersoll A., 1989, Icar 81 298
[14] Kopal Z., 1954, MNRAS 114 101
[15] Mollière P. et al., 2019, A&A 627 A67
[16] Yurchenko S. et al., 2021, MNRAS 510, 903–919
[17] Louden T. and Kreidberg L., 2018, MNRAS 477 2613–2627
[18] Kendrew S. et al., 2015, PASP 127 623
[19] Zhang M. et al., 2024, ApJL 961 L44
How to cite: Garza, M., Kang, W., and Piette, A.: Observability of Spectral Features of SiO Lava World Atmospheres: Distribution of Outgoing Radiative Flux and Phase Curves, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–12 Sep 2025, EPSC-DPS2025-1323, https://doi.org/10.5194/epsc-dps2025-1323, 2025.
