Matej Malik

On the gap-opening criterion of migrating planets in protoplanetary disks

We perform two-dimensional hydrodynamical simulations to quantitatively explore the torque balance criterion for gap-opening (as formulated by Crida et al. 2006) in a variety of disks when considering a migrating planet. We find that even when the criterion is satisfied, there are instances when planets still do not open gaps. We stress that gap-opening is not only dependent on whether a planet has the ability to open a gap, but whether it can do so quickly enough. This can be expressed as an additional condition on the gap-opening timescale versus the crossing time, i.e. the time it takes the planet to cross the region which it is carving out. While this point has been briefly made in the previous literature, our results quantify it for a range of protoplanetary disk properties and planetary masses, demonstrating how crucial it is for gap-opening. This additional condition has important implications for the survival of planets formed by core accretion in low mass disks as well as giant planets or brown dwarfs formed by gravitational instability in massive disks. It is particularly important for planets with intermediate masses susceptible to Type III-like migration. For some observed transition disks or disks with gaps, we expect that estimates on the potential planet masses based on the torque balance gap-opening criterion alone may not be sufficient. With consideration of this additional timescale criterion theoretical studies may find a reduced planet survivability or that planets may migrate further inwards before opening a gap.

HELIOS–RETRIEVAL: An Open-source, Nested Sampling Atmospheric Retrieval Code; Application to the HR 8799 Exoplanets and Inferred Constraints for Planet Formation

We present an open-source retrieval code named HELIOS-Retrieval (hereafter HELIOS-R), designed to obtain chemical abundances and temperature-pressure profiles from inverting the measured spectra of exoplanetary atmospheres. In the current implementation, we use an exact solution of the radiative transfer equation, in the pure absorption limit, in our forward model, which allows us to analytically integrate over all of the outgoing rays (instead of performing Gaussian quadrature). Two chemistry models are considered: unconstrained chemistry (where the mixing ratios are treated as free parameters) and equilibrium chemistry (enforced via analytical formulae, where only the elemental abundances are free parameters). The nested sampling algorithm allows us to formally implement Occams Razor based on a comparison of the Bayesian evidence between models. We perform a retrieval analysis on the measured spectra of the HR 8799b, c, d and e directly imaged exoplanets. Chemical equilibrium is disfavored by the Bayesian evidence for HR 8799b, c and d. We find supersolar C/O, C/H and O/H values for the outer HR 8799b and c exoplanets, while the inner HR 8799d and e exoplanets have substellar C/O, substellar C/H and superstellar O/H values. If these retrieved properties are representative of the bulk compositions of the exoplanets, then they are inconsistent with formation via gravitational instability (without late-time accretion) and consistent with a core accretion scenario in which late-time accretion of ices occurred differently for the inner and outer exoplanets. For HR 8799e, we find that spectroscopy in the K band is crucial for constraining C/O and C/H. HELIOS-R is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).

Debris discs around M stars: non-existence versus non-detection

Motivated by the reported dearth of debris discs around M stars, we use survival models to study the occurrence of planetesimal discs around them. These survival models describe a planetesimal disc with a small number of parameters, determine if it may survive a series of dynamical processes and compute the associated infrared excess. For the Wide-field Infrared Survey Explorer (WISE) satellite, we demonstrate that the dearth of debris discs around M stars may be attributed to the small semimajor axes generally probed if either: (1) the dust grains behave like blackbodies emitting at a peak wavelength coincident with the observed one; (2) or the grains are hotter than predicted by their blackbody temperatures and emit at peak wavelengths that are shorter than the observed one. At these small distances from the M star, planetesimals are unlikely to survive or persist for time-scales of 300 Myr or longer if the disc is too massive. Conversely, our survival models allow for the existence of a large population of low-mass debris discs that are too faint to be detected with current instruments. We gain further confidence in our interpretation by demonstrating the ability to compute infrared excesses for Sun-like stars that are broadly consistent with reported values in the literature. However, our interpretation becomes less clear and large infrared excesses are allowed if only one of these scenarios holds: (3) the dust grains are hotter than blackbody and predominantly emit at the observed wavelength; (4) or are blackbody in nature and emit at peak wavelengths longer than the observed one. Both scenarios imply that the parent planetesimals reside at larger distances from the star than inferred if the dust grains behaved like blackbodies. In all scenarios, we show that the infrared excesses detected at 22 μm (via WISE) and 70 μm (via Spitzer) from AU Mic are easily reconciled with its young age (12 Myr). Conversely, the existence of the old debris disc (2–8 Gyr) from GJ 581 is due to the large semimajor axes probed by the Herschel PACS instrument. We elucidate the conditions under which stellar wind drag may be neglected when considering dust populations around M stars. The WISE satellite should be capable of detecting debris discs around young M stars with ages ∼10 Myr.

Retrieval Analysis of the Emission Spectrum of WASP-12b: Sensitivity of Outcomes to Prior Assumptions and Implications for Formation History

We analyze the emission spectrum of the hot Jupiter WASP-12b using our HELIOS-R retrieval code and HELIOS-K opacity calculator. When interpreting Hubble and Spitzer data, the retrieval outcomes are found to be prior-dominated. When the prior distributions of the molecular abundances are assumed to be log-uniform, the volume mixing ratio of HCN is found to be implausibly high. A VULCAN chemical kinetics model of WASP-12b suggests that chemical equilibrium is a reasonable assumption even when atmospheric mixing is implausibly rigorous. Guided by (exo)planet formation theory, we set Gaussian priors on the elemental abundances of carbon, oxygen, and nitrogen with the Gaussian peaks being centered on the measured C/H, O/H, and N/H values of the star. By enforcing chemical equilibrium, we find substellar O/H and stellar to slightly superstellar C/H for the dayside atmosphere of WASP-12b. The superstellar carbon-to-oxygen ratio is just above unity, regardless of whether clouds are included in the retrieval analysis, consistent with Madhusudhan et al. Furthermore, whether a temperature inversion exists in the atmosphere depends on one’s assumption for the Gaussian width of the priors. Our retrieved posterior distributions are consistent with the formation of WASP-12b in a solar-composition protoplanetary disk, beyond the water iceline, via gravitational instability or pebble accretion (without core erosion) and migration inward to its present orbital location via a disk-free mechanism, and are inconsistent with both in situ formation and core accretion with disk migration, as predicted by Madhusudhan et al. We predict that the interpretation of James Webb Space Telescope WASP-12b data will not be prior-dominated.

Combining low- to high-resolution transit spectroscopy of HD 189733b: Linking the troposphere and the thermosphere of a hot gas giant

Space-borne low- to medium-resolution (ℛ ~ 10²–10³) and ground-based high-resolution spectrographs (ℛ ~ 10⁵) are commonly used to obtain optical and near infrared transmission spectra of exoplanetary atmospheres. In this wavelength range, space-borne observations detect the broadest spectral features (alkali doublets, molecular bands, scattering, etc.), while high-resolution, ground-based observations probe the sharpest features (cores of the alkali lines, molecular lines). The two techniques differ by several aspects. (1) The line spread function of ground-based observations is ~10³ times narrower than for space-borne observations; (2) Space-borne transmission spectra probe up to the base of thermosphere (P ≳ 10⁻⁶ bar), while ground-based observations can reach lower pressures (down to ~10⁻¹¹ bar) thanks to their high resolution; (3) Space-borne observations directly yield the transit depth of the planet, while ground-based observations can only measure differences in the apparent size of the planet at different wavelengths. These differences make it challenging to combine both techniques. Here, we develop a robust method to compare theoretical models with observations at different resolutions. We introduce πη, a line-by-line 1D radiative transfer code to compute theoretical transmission spectra over a broad wavelength range at very high resolution (ℛ ~ 10⁶, or Δλ ~ 0.01 A). An hybrid forward modeling/retrieval optimization scheme is devised to deal with the large computational resources required by modeling a broad wavelength range ~0.3–2 μm at high resolution. We apply our technique to HD 189733b. In this planet, HST observations reveal a flattened spectrum due to scattering by aerosols, while high-resolution ground-based HARPS observations reveal sharp features corresponding to the cores of sodium lines. We reconcile these apparent contrasting results by building models that reproduce simultaneously both data sets, from the troposphere to the thermosphere. We confirm: (1) the presence of scattering by tropospheric aerosols; (2) that the sodium core feature is of thermospheric origin. When we take into account the presence of aerosols, the large contrast of the core of the sodium lines measured by HARPS indicates a temperature of up to ~10 000K in the thermosphere, higher than what reported in the literature. We also show that the precise value of the thermospheric temperature is degenerate with the relative optical depth of sodium, controlled by its abundance, and of the aerosol deck.

The Peculiar Atmospheric Chemistry of KELT-9b

The atmospheric temperatures of the ultra-hot Jupiter KELT-9b straddle the transition between gas giants and stars, and therefore between two traditionally distinct regimes of atmospheric chemistry. Previous theoretical studies assume the atmosphere of KELT-9b to be in chemical equilibrium. Despite the high ultraviolet flux from KELT-9, we show using photochemical kinetic calculations that the observable atmosphere of KELT-9b is predicted to be close to chemical equilibrium, which greatly simplifies any theoretical interpretation of its spectra. It also makes the atmosphere of KELT-9b, which is expected to be cloud-free, a tightly constrained chemical system that lends itself to a clean set of theoretical predictions. Due to the lower pressures probed in transmission (compared to emission) spectroscopy, we predict the abundance of water to vary by several orders of magnitude across the atmospheric limb depending on temperature, which makes water a sensitive thermometer. Carbon monoxide is predicted to be the dominant molecule under a wide range of scenarios, rendering it a robust diagnostic of the metallicity when analyzed in tandem with water. All of the other usual suspects (acetylene, ammonia, carbon dioxide, hydrogen cyanide, methane) are predicted to be subdominant at solar metallicity, while atomic oxygen, iron, and magnesium are predicted to have relative abundances as high as 1 part in 10,000. Neutral atomic iron is predicted to be seen through a forest of optical and near-infrared lines, which makes KELT-9b suitable for high-resolution ground-based spectroscopy with HARPS-N or CARMENES. We summarize future observational prospects of characterizing the atmosphere of KELT-9b.

Revisiting the Phase Curves of WASP-43b: Confronting Re-analyzed Spitzer Data with Cloudy Atmospheres

Recently acquired Hubble and Spitzer phase curves of the short-period hot Jupiter WASP-43b make it an ideal target for confronting theory with data. On the observational front, we re-analyze the 3.6 and 4.5 μm Spitzer phase curves and demonstrate that our improved analysis better removes residual red noise due to intra-pixel sensitivity, which leads to greater fluxes emanating from the nightside of WASP-43b, thus reducing the tension between theory and data. On the theoretical front, we construct cloud-free and cloudy atmospheres of WASP-43b using our Global Circulation Model (GCM), THOR, which solves the non-hydrostatic Euler equations (compared to GCMs that typically solve the hydrostatic primitive equations). The cloud-free atmosphere produces a reasonable fit to the dayside emission spectrum. The multi-phase emission spectra constrain the cloud deck to be confined to the nightside and have a finite cloud-top pressure. The multi-wavelength phase curves are naturally consistent with our cloudy atmospheres, except for the 4.5 μm phase curve, which requires the presence of enhanced carbon dioxide in the atmosphere of WASP-43b. Multi-phase emission spectra at higher spectral resolution, as may be obtained using the James Webb Space Telescope, and a reflected-light phase curve at visible wavelengths would further constrain the properties of clouds in WASP-43b.

Analytical Models of Exoplanetary Atmospheres. VI. Full Solutions for Improved Two-stream Radiative Transfer, Including Direct Stellar Beam

Two-stream radiative transfer is used frequently in Earth, planetary, and exoplanetary sciences due to its simplicity and ease of implementation. However, a longstanding limitation of the two-stream approximation is its inaccuracy in the presence of medium-sized or large aerosols. This limitation was lifted by the discovery of the improved two-stream technique, where the accuracy of the scattering greenhouse effect is matched to that of multi-stream calculations by construction. In this study, we derive the full solutions for improved two-stream radiative transfer, following its introduction by Heng & Kitzmann, and include contributions from the direct stellar beam. The generalization of the original two-stream flux solutions comes in the form of a correction factor, traditionally set to unity, which is the ratio of a pair of first Eddington coefficients. We derive an analytical expression for this correction factor and also provide a simple fitting function for its ease of use by other workers. We prove that the direct stellar beam is associated with a second Eddington coefficient that is on the order of unity. Setting this second Eddington coefficient to 2/3 and 1/√3 reproduces the Eddington and quadrature closures, respectively, associated with the direct beam. We use our improved two-stream solutions for the fluxes to derive two-stream source function solutions for both the intensity and fluxes.

Diagnosing aerosols in extrasolar giant planets with cross-correlation function of water bands

Transmission spectroscopy with ground-based, high-resolution instruments provides key insight into the composition of exoplanetary atmospheres. Molecules such as water and carbon monoxide have been unambiguously identified in hot gas giants through cross-correlation techniques. A maximum in the cross-correlation function (CCF) is found when the molecular absorption lines in a binary mask or model template match those contained in the planet. Here, we demonstrate how the CCF method can be used to diagnose broadband spectroscopic features such as scattering by aerosols in high-resolution transit spectra. The idea consists in exploiting the presence of multiple water bands from the optical to the near-infrared. We have produced a set of models of a typical hot Jupiter spanning various conditions of temperature and aerosol coverage. We demonstrate that comparing the CCFs of individual water bands for the models constrains the presence and the properties of the aerosol layers. The contrast difference between the CCFs of two bands can reach ~100 ppm, which could be readily detectable with current or upcoming high-resolution stabilized spectrographs spanning a wide spectral range, such as ESPRESSO, CARMENES, HARPS-N+GIANO, HARPS+NIRPS, SPIRou, or CRIRES+.

Aerosol Constraints on the Atmosphere of the Hot Saturn-mass Planet WASP-49b

The strong, nearly wavelength-independent absorption cross section of aerosols produces featureless exoplanet transmission spectra, limiting our ability to characterize their atmospheres. Here we show that even in the presence of featureless spectra, we can still characterize certain atmospheric properties. Specifically, we constrain the upper and lower pressure boundaries of aerosol layers, and present plausible composition candidates. We study the case of the bloated Saturn-mass planet WASP-49b, where near-infrared observations reveal a flat transmission spectrum between 0.7 and 1.0 {\microns}. First, we use a hydrodynamic upper-atmosphere code to estimate the pressure reached by the ionizing stellar high-energy photons at