Chris Ormel's research page

Kepler-221 is a star with four planets orbiting it. Among these planets, three of them -- b, c, and e -- are in resonance, meaning that their orbits follow a unique rhythm. Mathematically, their period ratios follow integers, similar to how dancers following the same beat. But for Kepler-221 there’s a great mystery: the fourth planet, d, does not fit into this rhythm; it breaks the chain of resonance orbits.

To understand how this unusual arrangement came to be, we have investigated a novel idea about the system’s history. We believe that Kepler-221 originally harbored five planets, all linked through a chain of mean motion resonance. But as the system evolved, the resonances broke and two of the planets collided and merged into what is now planet d. This collision disrupted the original pattern for a while, but over time, the three planets not involved in the collision settled back into their original resonant orbits with the help of dissipative interactions with the host star.

We used N-body simulations to test this model and successfully reproduce the present-day orbital configuration of the system. Our results show that certain factors were especially important. For instance, planet d played a role in helping the other planets settle back into their rhythmic orbits. Additionally, the masses of the planets had to fall within specific ranges to allow this stable pattern to form and persist over time.

This model -- where a brief phase of orbital instability results in the permanent breaking of some but not all resonances -- not only explains the strange orbital setup of Kepler-221 but can also help us to understand other star systems with similar patterns, like Kepler-402 and K2-138. By piecing together the story of these distant worlds, we get a clearer picture of how planetary systems form and evolve over billions of years.

The solar system does not end at the Neptune's orbit (30 au). Beyond the 8th planet, a vast number of bodies and their number continuous to grow due to ever more sensitive surveys. How did these bodies end up in these regions. The most widely accepted model suggest that an outward-migrating Neptune---possibly triggered by a dynamical instability, such as the infamous Nice model---destabilized bodies residing in an ancient, primordial belt. While most of these bodies either collided with the giant planets or were ejected from the Solar System, some were scattered to orbits beyond Neptune, forming distinct populations now classified as "plutino's", "scattered disk", and "hot classicals". The only exception are the cold classicals. The dynamical properties of these bodies indicate an uneventful past---they have formed in situ and remained undisturbed.

Further insight comes from the size distribution of trans-Neptunian objects (TNOs). Interestingly, the cold TNOs exhibit a size distribution strikingly similar to that of dynamically hot TNOs. This suggests that all TNOs originally formed with a tapered-exponential size distribution---which is, b.t.w., also consistent with studies simulating planetesimal formation---and that additional processes influenced the high-mass end of the distribution. This aligns naturally with the pebble accretion mechanism, which requires an initiation mass. In this process, only sufficiently large bodies can efficiently accrete pebbles, whereas smaller objects experience little to no growth.

Using a streamlined numerical model that facilitates a MCMC analysis, we have explored the conditions necessary to reproduce the present-day size distribution of dynamically hot TNOs. Our results indicate a correlation between the velocity field---either turbulent or laminar---and the aerodynamic size of particles, τ_s. This finding is expected, as the combination of these two parameters defines the mass threshold at which pebble accretion takes off. A key implication is that we cannot distinguish between large pebbles approaching the bodies at low velocity and smaller pebbles approach the bodies at low Δv, except that growth in the former scenario is much faster. However, if we take a leap of faith and conjecture that the solar system primordial belt resembled conditions similar to pebble rings seen in ALMA, the additional constraints can break the degeneracies (see figure). Then, the pebbles' aerodynamic size -- a hugely important quantity in planet formation studies -- can be determined to be about 0.01.

Clouds are ubiquitous in planets' atmospheres. On Earth, cloud particles consist of water ice. But for hot-Jupiters the temperature are so high that silicates and iron start to evaporate in the deep atmosphere, while they condense out at higher altitudes. Hence, we expect clouds to be made from these condensates. Clouds affect the light transmitted through the atmosphere, smearing out the molecular lines and displaying their own, unique absorption features. The increasingly precise atmospheric spectra data from facilities like JWST calls for a cloud model that contains many physical and chemical principles. But this comes often at the expense of making the runtime of such model very long. Often, millions of excutions must be run in order to retrieve the atmospheric properties. What is needed is a balanced approached that is both computationally efficient as well as physically realistic.

Accordingly, we have developed ExoLyn: a 1D multispecies cloud model tailored towards retrieval of atmospheric spectra. ExoLyn includes nucleation, condensation and sublimation reactions--to be specified by the user--and transport processes in a generic framework, meaning that it can equally well be applied to hot-Jupiters as to sub-Neptunes. ExoLyn can compute the composition of cloud particles at each depth, and resolve the layered cloud structure. For hot Jupiters, we find that silicate-dominant clouds lie on top of an iron-dominated layer. On sub-Neptune planets, NaCl and KCl clouds form, and can reproduce a flat near-infrared transmission spectrum, as observed on GJ1214 b. The characteristics of the clouds generated by ExoLyn agree with more complex models, but it takes only 2 seconds to compute the cloud structure.

ExoLyn is open-sourced on Github: https://github.com/helonghuangastro/exolyn. ExoLyn opens the possibility to jointly model the gas and solid components on the exoplanet atmosphere, empowering more reliable retrieval of cloud composition in exoplanet atmospheres.

Protoplanetary disks are the cradles of planet formation. They often display intriguing features like bright rings and dark gaps in both continuum (dust) and line emission maps. Traditionally, it is thought that a planet's composition is inherited directly from the disk. Planets do affect the disk, however, e.g., by opening gaps and changing the rotation profile -- effects that are in principle observable. In this study, we propose that accreting giant planets offer another indirect signature: they alter the disk's local chemical inventory.

Recently, our team developed a novel module to the Athena++ hydrodynamical code, which allowed us to follow phase change processes, e.g., ice sublimation. Through these simulations, we demonstrated that an accreting planet located beyond the methane snowline has the ability to heat the surrounding gas, leading to the sublimation of carbon-rich ices from pebbles. This mechanism locally enhances the disk’s gas-phase carbon-to-oxygen (C/O) ratio, providing a potential explanation for the observed line-emission rings detected in many sources by the Atacama Large Millimeter/submillimeter Array (ALMA). Specifically, our findings offer a compelling explanation for MWC 480, a protoplanetary disk where previous observations have identified molecular line-emission rings within a continuum gap (see figure). Our work has shown that this co-incidence can be naturally explained if a planet is present in the D76 gap (which is still to be confirmed).

The research unveils how the planet accretion influences the local disk chemistry, creating detectable chemical footprints in the form of molecular emissions. As such, the study sheds new light on the intricate relationship between these disks and the planets they give birth to. It also showcases how the interplay between state-of-the-art numerical tools and cutting-edge observations efforts contribute to advance the field of planet formation.

It has been a long-standing mystery where the water, key to life on Earth, came from. A variety of scenarios have been put forward, including the possibility that it was delivered to Earth by comets or asteroids, outgassed by volcanic activity, or produced by oxidizing reactions during the magma ocean stage. Yet, at a mass fraction of 0.1%, Earth remains overall a dry planet. On the other hand, the dominant type of exoplanets, super-Earths and sub-Neptunes, reveal a wide distribution of water inventories. Their water contents is likely determined during the planet formation process, when a protoplanet was accreting pebbles from the gaseous disk and formed its first atmosphere. But what regulates volatile delivery to protoplanets in this phase?

Pebbles containing water ice accreted by protoplanets are thought to be the main source of water. However, during accretion, the planetary atmosphere could become hot enough for the ice to sublimate and avoid direct accretion of water. The water ends up in the proto-atmosphere. But it may not remain there as (for low-mass planets) these atmosphere interact vigorously with the natal disk, a process known as recycling. The vapor may hence flow back to the disk (after freezing out as ice grains) limiting the water inventory of atmosphere and planet. However, the recycling hypothesis, has never been tested for high molecular weight vapors with hydrodynamical simulations.

To incorporate these features, we have designed a new phase change module on top of the recently-developed multi-dust fluid approach (Huang & Bai 2022) for the popular hydrodynamic code Athena++. In our new module, the movement of gas, pebbles, and vapor, are followed, while accounting for sublimation of ices in a self-consistent way. We find that the extent and the amount of vapor a planet is able to hold on to is determined by the relative size of the sublimation front and the atmosphere. When the sublimation front lies deep inside the atmosphere, vapor tends to be locked deep in the atmosphere and keeps accumulating through a positive feedback mechanism. This situation is illustrated in the video: the accumulation of vapor enlarges the atmosphere, rendering it impossible for the water vapor to escape. These planets become wet. On the other hand, when the sublimation front exceeds the (bound) atmosphere, the ice component of incoming pebbles can be fully recycled and the vapor content reaches a low, steady value. Low disk temperature, small planet mass and high volatile pebble fluxes render the planet atmosphere vapor-rich. The phase change module we have developed can also be employed to study the chemical composition of the gas in the vicinity of accreting planets and around disk snowlines.

Over 5000 exoplanets have been discovered to date, with most of them being transiting planets detected by space missions such as Kepler, TESS, and ground-based observations. With such a large observed population, statistical analyses are possible. It is especially intriguing to do this for multi-planet systems harboring planets in orbital resonance. These systems provide indirect evidence of planet migration during their formation stages in gas-rich disks.

One prediction for a planet pair in a stable resonance is that the inner planet's orbital ellipse is misaligned with the outer one. Unfortunately, the transit method is usually not capable of observing the longitude of periapsis of the planet orbits, which makes direct identification of resonances impossible. Here, we have developed a statistical method to calculate the fraction of resonant planet pairs in the observed population, which does not rely on the exact orbital architectures.

This method uses two distributions of period ratios: a uniform distribution for non-resonant pairs and a log-normal distribution for resonant pairs. Applying a Monte Carlo Markov Chain technique, it is found that approximately 15% of planet pairs are in resonance, and the majority of resonant planets migrated over significant distances in their proto-disks. Furthermore, an upper limit on the surface density of the gas was derived, because two-planet resonance would break when the surrounding gas disk would become too dense. By refining the two-planet resonance trapping criterion, the upper limit of the gas surface density was found to be consistent with that of the Minimum Mass solar nebula.

In the future, this method may also be applied to extract the tidal interaction with the host stars, planetesimal scattering, and stellar encounter history of the observed planet population. With an increasing number of exoplanet detections foreseen in the coming decades, these findings will bring us a step closer to understanding planet formation physics.

Pebbles -- the aerodynamically active particles in protoplanetary disks -- are essential in driving planet growth. This is mainly because they drift efficiently in the disk, such that the planet growth is not limited by the local solid budget. When a pebble drifts across the planet orbit, gas drag dissipates its energy, resulting in their capture by the planet. The Stokes number (St) describes a pebble's aerodynamical size. Larger pebbles or a lower gas density both increase the Stokes number. This work focuses on the accretion of those pebbles more loosely coupled to gas: St>1 but where drift is still significant. In contrast to the St<1 pebbles, the regime of large pebble accretion has not been investigated thoroughly before.

We performed numerical simulations to integrate the large pebble's orbit in a 2D, global reference frame. The planet moves in fixed Keplerian orbits and the pebble undergoes both gas drag and gravity from the star and the planet. We varied the pebble's Stokes number in different simulations. It is found that for St>1 pebbles, they are more likely to directly hit the finite surface of the planet, rather than settling down the planet's gravitational well, due to the combination of gravity and drag. We found that pebbles of Stokes number 70<St<400 are most favorable to be accreted, with the accretion efficiency approaching 100%. That is, almost every pebble in this size range that drifts past the planet will be swallowed by the planet. For higher Stokes numbers, the drift of pebble is so slow that it will be captured outside of the planet's orbit in a mean motion resonance. However, we found that the collision velocity among these pebbles are so high that they are likely to fragment to smaller sizes, which are highly likely to be accreted.

The St>1 pebbles may be produced when planetesimals collide with each other, or when the gas density becomes low. The latter scenario could be achieved in the debris disk phase. We proposed a debris disk model where the primordial H/He gas is blown away by fast photoevaporation and the diluted CO gas is replenished by the outgassing from solids. We followed the drift and accretion of ~10μm-sized dusts particles, which could be produced during collision of larger particles. In such low density debris disk, the 30μm dust will become St>1 pebbles and be accreted at high efficiency. We find up to ~0.3 Earth mass of these pebbles will be accreted by an Earth-mass planet, mostly in the debris disk phase as St>1 pebbles. In conclusion, planets could still accrete solid material in the late phase of disk evolution, mainly by small-sized but aerodynamically big pebbles. This late accretion could contribute several percentage of the planet mass and shape the chemical composition of these planets atmospheres.

Protoplanetary disks, the cradle of baby planets, contain a large amount of building blocks for planet formation -- (sub)millimeter-size solid particles --pebbles. Yet, how, when, and where planets start to form is an outstanding question. In the past decade, through the Atacama Large Millimeter/submillimeter Array (ALMA) in Chile, it was revealed that a large number of protoplanetary disks are ringed. Rather than smoothly distributed over the disk, pebbles tend to be concentrated in one or more annular ring structures.

Based on the latest insights in planetesimal formation, pebble accretion and using the REBOUND N-body framework, we have calculated the potential for these rings to spawn planets. It turns out that conditions for pebble accretion are ideal in these rings, offering an opening for planet formation at large distances. A baby planet formed in the ring quickly grows off the pebbles in the mother ring. Depending on the nature of the ring, two distinct outcomes are possible. If the baby planet stays trapped in (or close to) the ring, it will grow fat and destroy the mother ring. On the other hand, if the planet can migrate inwards, it leaves room for one of its smaller siblings to grow. As a result, a chain of planets can form inside the disk. This is the situation depicted in the space-time figure above, where multiple planets, depicted by black lines, leave the ring.

Our results may offer new insights on the relationship between planets and these ALMA rings. It is widely believed that these rings are a consequence of dynamical sculpting by a planet interior to it -- that is, the planet must arrive first. Our work shows, however, that multiple planets can form from these rings, in a timely manner and without necessarily destroying the rings. In this view, ringed disk are the cradle of present-day planetary systems containing massive planets.

ALMA -- the world-leading interferometry facility operating at mm-wavelengths -- is sensitive to emission from the cold, dense midplane regions of planet-forming disks. Most straightforward is to look at the dust continuum emission, but it can also probe line emission, originating from rotational transitions in molecules. Earlier, DSHARP has reported that many disks exhibit annular substructure, i.e., "rings" or "gaps". Now, MAPS repeats this exercise (for five disks) with a variety of lines from molecules such CO, HCN, C2H and their isotopes. Annular ring-like features are again plentiful. But the question arises: is there a correlation between the continuum and line emission and what does such a (non-)correlation mean?

On first sight, the answer seems yes, as substantial overlap is present. In the figure, the fraction of overlap between a given line feature (gap or emission ring) and its equivalent in the dust is denoted by a circle. For example, for GM Aur >60% of gap features in the lines are coincident with a DSHARP emission ring (this rises to 80% when limiting the analysis to features within 150 au). However, these associations could also be simply due to chance. By placing the lines at arbitrary locations (following a radial distribution consistent with the observations), we see that the ensuing random distribution -- the colored violin plots -- match the observations. A universal statistical correlation cannot be substantiated. But there are also exceptions. In MWC 480 it is clear that rings in molecular lines correlate with gaps in the continuum.

The implication of a clear (non-)correlation are potentially significant. For example, it has been proposed that planets are responsible for carving out gaps in the gas, also leading to pressure maxima where dust particles would naturally gather. Could a non-correlation therefor imply that many DSHARP rings are not associated with planets after all? Perhaps. But the statistical approach in which all lines are treated equally (e.g., there is no distinction between a line from the nitrile group and CO) may ultimately be limited. To address formidable questions, requires more detailed physical and chemical modelling and more data. Game on!

The red dwarf star TRAPPIST-1 is home to the largest number (which is seven) of Earth-sized planets ever found in a single planet system. Three of these planets may be suitable to harbor liquid water or even life and will be prime targets for the recently-launched JWST spacecraft. Different from the terrestrial planets in our solar system, scientists have determined that it is likely that the TRAPPIST-1 planets formed early in their gas-rich protoplanet disk. Planets will then migrate inwards because of planet-disk gravitational interaction until they reach the inner edge of the gaseous disk.

But why do planets not crash into each other? Mean motion resonances can trap planets during their convergent migration at locations where the orbital periods follow a ratio of integer numbers. Examples in the solar system are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa, and Io, and the 2:3 resonance between Pluto and Neptune. These are examples of first order resonances. However, in the TRAPPIST-1 system, the inner two planets are captured in weaker, higher order resonances than the outer planets. There must therefore be special mechanisms that operated in this system. Indeed, the peculiar dynamical configuration has puzzled many scientists since its discovery and attempts to solve it have typically focused only on a piece of the puzzle. In a recent study, accepted for publication in the MNRAS, Huang and Ormel have studied the problem from a planet formation perspective.

They propose a model in which planets form at the H₂O snowline, then migrate towards the disk’s inner edge. The innermost two planets b and c enter a gas-free disk cavity early after their formation (See figure, panel a). Then, the outer planets migrate inward to join the resonance chain. Meanwhile, the spacing between planets b and c and the outer planets expand, because planet c still experiences a slight inward push from the disk (panel b). During its migration away from the disk edge, planet c can be trapped in three-body resonances at several locations, but this depends on the arrival time of the outer planets. When the outer planets arrive late, planet c will avoid the first locations and can then be trapped in the three body resonance corresponding to the location where it is presently observed (Φ₄;panel c). Hence, the dynamical configuration of the seven billion-year-old TRAPPIST-1 planets was already set in the first million years after their formation.

A protoplanetary disk consist of rotating dense gas and dust which continues to feed onto the newly formed star. Starting from the iconic HL tau image, the Atacama Large Millimeter/submillimeter Array (ALMA) in the Atacama Desert of Northern Chile has observed many protoplanetary disks at (sub)millimeter wavelengths. It has revealed that a large fraction of disks harbor annular dust structures, e.g., “rings”, typically seen at distances of tens of au. This reflects a concentration of pebble-sized particles, ~100um--mm in size with a total mass of at least ~10 Earth masses per ring. As of today, it is unclear how these rings come about, how (long) they survive, and what role they play for the formation of planets. Pressure maximum in the gas disk is a popular explanation for these rings, because particles get trapped in these locations. However, it is unclear what the nature of these pressure bumps is and whether they will survive for disk lifetimes (~Myr). Even though many previous study invoke that these pressure bumps are carved by planets, direct observational detection of these planets is often lacking. And it also brings up a chicken or egg question: are planets carving the rings or are these rings somehow assisting planet formation?

In this paper, we present an alternative explanation for the origin of these dust substructures, involving only dust-gas aerodynamics in a standard smooth gas disk devoid of local pressure maxima. We develop the Clumpy Ring Model (CRM), in which we postulate that ALMA rings are a manifestation of a dense, clumpy midplane which is actively forming planetesimals. The clumpy medium itself hardly experiences radial drift, because its mass is dominated by pebble-sized particles, but clumps lose mass by disintegration, vertical transport and planetesimal formation. Therefore, for its long-term survival clumps must be continuously fed by an influx of pebbles from the outer disk regions. To quantitatively compare our results to the observations, we write down the 1D transport equations and numerically solve for the density distribution with time.

The CRM well explains not only the location and separation of the rings, but also their intensity and relative contrasts. Because the rings of the CRM produce large quantities of planetesimals, they are natural sites for the formation of planets. These massive planetesimal belts can also explain the huge mass budget inferred for some debris disk. Future research about how these clumpy rings help with planet formation and the link between protoplanetary disk and debris disks are ongoing.

Following our previous research efforts, we have conducted numerical calculations about the thermal evolution of the envelope of pebble-accreting protoplanets. These protoplanets emerge early, when the protoplanetary gas disk is still present. Due to the accretion of solids, their envelope becomes hot, sublimating the infalling pebbles and transforming mm-sized solid particles (“pebbles”) into a metal vapor (e.g, SiO2). This transformation greatly affects the thermodynamical evolution of the protoplanet. For example, planets end up with a small "core" but may still undergo runaway gas accretion due to the high molecular weight and small pressure scale height of the atmosphere.

Using a novel numerical scheme we can now simulate the thermal evolution of the envelope for the entire period during the growth of the planet by pebble accretion: from their humble beginnings as rocks to the point where they enter runaway gas accretion. In the animation you see how the profiles of total density (solid black), vapor density (after sublimation from pebbles; dashed black) and temperature (red). Initially, most pebbles end up in the core, but after it reaches slightly above 2 Earth masses pebbles completely evaporate. Thereafter, the vapor mass (M_Z,env) of the envelope rapidly increases. But the contribution of H+He gas, accreted from the gas disk surrounding the planet, also increases rapidly (M_xy). If the gas disk by this time (~5 Myr) has not dispersed, the planet can accrete much greater amounts of H+He gas and will turn into a Jupiter planet (not simulated).

What we end up with is an envelope characterized by a composition gradient. At late times it can clearly be seen that the ratio ρ/ρ_Z is decreasing within the envelope (the space between the two black lines is increasing throughout). Interestingly, this feature is in striking resemblance to the inference of a so-called "dilute core" for Jupiter by the JUNO mission. Jupiter’s metallicity gradually increases throughout its deep interior, instead of a sudden increase due to a solid core. In future work we will further investigate the connection between the formation scenario (e.g., pebble accretion) and the inferred internal structure of the solar system’s giant planets.