Model Achieves Radius Valley Reproduction and 0.2 Stability for Kepler Exoplanets

Scientists are tackling the enduring puzzle of why exoplanet sizes fall into distinct categories, revealing a ‘radius valley’ separating rocky super-Earths from gaseous sub-Neptunes, and a tendency for planets within the same system to be similarly sized. Matthias Y. He from NASA Ames Research Center and Penn State University, alongside Eric B. Ford from Penn State University, and colleagues, present a novel model combining planetary dynamics with atmospheric loss to explain these observed patterns. Their research, building on the SysSim forward models, is the first multi-planet simulation successfully reproducing both the radius valley and the striking similarity in planet sizes within individual systems. This breakthrough suggests that initial planet mass clustering, followed by atmospheric stripping via photoevaporation, powerfully shapes the exoplanet population , and importantly, indicates a potentially lower occurrence rate of Venus and Earth-like planets than previously thought.

Exoplanet Sizes Explained by Hybrid Model

Scientists have unveiled a new model explaining the distribution of exoplanet sizes observed by the Kepler space telescope, successfully reproducing two key patterns: the radius valley separating super-Earths and sub-Neptunes, and a preference for planets within the same system to have similar sizes. This breakthrough stems from a “hybrid” approach combining a clustered multi-planet model, based on the stability of orbital architectures determined by angular momentum deficit, with a joint mass-radius-period model accounting for atmospheric loss via photoevaporation. The research team, led by Matthias He and Eric Ford, demonstrated that models generating the most pronounced radius valleys require an initial population of planets peaking at approximately 2.1 Earth radii, subsequently sculpted by photoevaporation into the observed bimodal distribution of final planet radii. Experiments show the hybrid model necessitates strongly clustered initial planet masses to accurately match observed size similarity metrics, suggesting that the preference for intra-system radius similarity originates from a clustering of masses during the planets’ primordial formation.
Notably, the model also naturally replicates the observed radius cliff, a steep drop-off in planet occurrence beyond 2.5 Earth radii, further validating its predictive power. This work represents the latest iteration of the SysSim forward models, and crucially, is the first multi-planet model capable of simultaneously reproducing both the radius valley and the intra-system size similarity patterns detected by Kepler. The study establishes that the occurrence of Venus and Earth-like planets is reduced by a factor of 2-4 in the hybrid models compared to previous clustered models that didn’t account for envelope mass loss, providing insights into the prevalence of potentially habitable worlds. This innovative hybrid model provides a robust framework for understanding the processes that shape exoplanet populations, and opens avenues for future research into the interplay between atmospheric evolution and orbital dynamics. The findings suggest that initial conditions and subsequent atmospheric stripping play crucial roles in determining the final distribution of planet sizes, and that clustering of initial planet masses is a key factor in explaining the observed patterns of intra-system size similarity. Ultimately, this research contributes to a more complete picture of how planetary systems form and evolve, and informs the search for potentially habitable planets beyond our solar system.

SysSim forward modelling of Kepler exoplanet systems

Scientists developed a novel hybrid model to explain the distribution of exoplanet sizes observed by the Kepler space telescope, addressing both the radius valley separating super-Earths and sub-Neptunes and the tendency for planets within the same system to have similar sizes. This work pioneers a forward modelling approach, SysSim, which generates synthetic planetary systems and compares them to the observed Kepler data using approximate Bayesian computation (ABC). The study meticulously simulates the entire Kepler detection pipeline, from generating physical planetary systems to mimicking the observed transit signals and measurement uncertainties, enabling a robust comparison between model predictions and real observations. The SysSim framework operates by first defining a model for the underlying distribution of exoplanetary systems, drawing planetary systems and assigning them to stars, then simulating the Kepler detection process to create an “observed catalog” of planets.

Researchers then compare this simulated catalog to the actual Kepler planet catalog using statistical metrics, quantified by a “distance function”, to assess the goodness of fit for the model’s parameters. This iterative process, involving generating numerous synthetic systems and refining the model parameters, allows for a comprehensive exploration of the exoplanet population and the constraints on planetary system architectures. The team employed a differential evolution algorithm to optimise the distance function, generating a large sample of “training points” for subsequent analysis. To. The inference stage involves drawing parameter sets from a prior distribution, evaluating the distance function using the emulator, and accepting those falling below a predefined distance threshold, effectively mapping out the most probable regions of parameter space.

Previous SysSim models established a “clustered” approach, where planets are drawn from a Poisson point process, with the number of planets per cluster determined by zero-truncated Poisson distributions with rate parameters λc and λp. This latest installment of SysSim introduces a hybrid model combining these clustered architectures with a joint mass-radius-period model incorporating photoevaporation-driven envelope mass loss, as described by Neil & Rogers 2020. The team found that models producing the deepest radius valleys require a primordial population of planets with initial radii peaking at 1.8 R⊕, subsequently sculpted by photoevaporation into a bimodal distribution of final planet radii. Crucially, the hybrid model necessitates strongly clustered initial planet masses to accurately reproduce the observed patterns of intra-system size similarity, suggesting that the preference for similar-sized planets within a system originates from clustering in the primordial mass distribution. The study reveals that the occurrence of Venus and Earth-like planets decreases by a factor of 4 in the hybrid models compared to previous clustered models lacking envelope mass-loss considerations.

Photoevaporation and Angular Momentum Shape Exoplanet Populations significantly

Scientists have unveiled a new model for exoplanet populations observed by the Kepler space telescope, successfully reproducing both the radius valley, a gap separating super-Earths and sub-Neptunes, and the preference for similar sizes among planets within the same system. This “hybrid” model combines a clustered multi-planet framework, governed by angular momentum deficit stability, with a joint mass-radius-period model driven by photoevaporation, a process where planetary atmospheres are eroded by stellar radiation. Experiments revealed that models generating the most pronounced radius valleys originate from a primordial planet population peaking at a radius of 1.8 R⊕, subsequently shaped by photoevaporation into a bimodal distribution of final planet radii. The team measured strongly clustered initial planet masses as a requirement for accurately matching observed size similarity metrics, demonstrating that the preference for intra-system radius similarity stems from clustering in the primordial mass distribution.

Results demonstrate that this hybrid model naturally reproduces the observed radius cliff, a steep drop-off in planet occurrence beyond 4 R⊕, a significant achievement in exoplanet modelling. Tests prove that the SysSim forward models, now at their latest iteration, are the first multi-planet model capable of simultaneously reproducing both the radius valley and intra-system size similarity patterns, marking a substantial step forward in our understanding of planetary system architecture. Researchers computed occurrence rates and fractions of stars with planets for various planet types, discovering that the occurrence of Venus and Earth-like planets decreases by a factor of four in the hybrid models compared to earlier clustered models lacking envelope mass-loss calculations. Data shows that the model generates synthetic planetary systems by drawing from a defined population model, simulating Kepler’s detection pipeline, and comparing the simulated results to the actual Kepler planet catalog using approximate Bayesian computation.

The procedure involves generating a “physical catalog” of planets assigned to stars, then an “observed catalog” simulating Kepler’s detection efficiency, and finally comparing the simulated catalog to the Kepler data using statistical metrics to quantify model goodness-of-fit. Scientists recorded that previous SysSim models incorporated features like clustered planets drawn from Poisson point processes, a dependence of planet occurrence on host star spectral type, and a procedure enforcing AMD-stability criteria for multi-planet systems. The new model builds upon these foundations, offering a more comprehensive and accurate representation of observed exoplanet populations and paving the way for future investigations into planetary system formation and evolution. This breakthrough delivers a powerful tool for interpreting current and future exoplanet observations, potentially revealing insights into the prevalence of habitable worlds beyond our solar system.

Photoevaporation explains exoplanet radius valley formation

Scientists have developed a new hybrid model to explain observed patterns in exoplanet populations, specifically the radius valley separating super-Earths and sub-Neptunes, and the tendency for planets within the same system to have similar sizes. This model combines a clustered multi-planet framework, based on angular momentum deficit stability, with a joint mass-radius-period model driven by photoevaporation, a process where planetary atmospheres are eroded by stellar radiation. The research demonstrates that a primordial population of planets with initial radii peaking at a certain value, when subjected to photoevaporation, can produce the observed bimodal distribution of final planet radii and the steep drop-off in planet radii beyond a specific point. The hybrid model successfully reproduces both the radius valley and the intra-system size similarity observed in Kepler data, representing the first multi-planet model to achieve this simultaneously.

Crucially, the model suggests that the preference for similar-sized planets within a system originates from clustering in the initial distribution of planet masses. However, the authors acknowledge limitations, noting that the occurrence of Venus and Earth-like planets is reduced by a factor of four compared to previous clustered models lacking envelope mass-loss considerations. Future research should focus on refining the model parameters and exploring the impact of different initial conditions to better constrain the occurrence rates of potentially habitable planets and further investigate the processes shaping exoplanetary systems.