PROBABILISTIC MASS–RADIUS RELATIONSHIP FOR SUB-NEPTUNE-SIZED PLANETS - IOPscience
Dec 14, Neptune is the fourth largest planet in terms of diameter, making it the smallest in physical size of the gas giants. The average distance from the. Jan 26, M-R relation between 'small' planets (Neptune-like) and 'large' planets visual estimates of the M-R and mass-density relations, Weiss et al. Jun 27, Here we present the first probabilistic mass–radius relationship (M–R relation for the sample of RV-measured transiting sub-Neptunes (R pl.
Therefore, a statistical "conversion" is necessary to map observed radii to the masses these studies need.
How Big is Neptune? It’s the Smallest Gas Giant, but It’s Still Huge
To date, several M—R relations have been posed in the exoplanet literature. To solve the practical issue described above, Lissauer et al. All of these results were produced via basic least squares regression, which is commonly used in astronomy to fit lines through points. However, this classic technique does not properly account for several issues that are relevant to the small-planet M—R relation: Thankfully, there are solutions to these problems in both the Bayesian and frequentist statistics literature see Section 1 of Kelly for a concise overview.
We present an example of one of these techniques which can be executed using existing numerical algorithms and code Section 4which is effectively a simplified implementation of the Kelly linear regression scheme. Of particular interest is the intrinsic scatter that has not been previously characterized. Theoretical work on planet compositions suggest this scatter should exist: Furthermore, the diversity of choices for exoplanets' internal structures produces a range of radii at a given mass due only to differences in the layers' compositions e.
These theoretical findings motivate us to move beyond deterministic, one-to-one mappings, which are in a sense "mean" relationships.
This average behavior is insufficient and inappropriate if one's aim is to argue for a particular physical process based on full distributions of parameters versus qualitative comparison to observationsor if the purpose is to rule out parts of parameter space, which requires knowledge of the full mass—radius distribution. However, they stop short of computing a relation which is both continuous and probabilistic which they admit would be idealand do not incorporate measurement error, which is significant for small planets.
With the hierarchical Bayesian modeling HBM that we employ here, we do both.
Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets - CaltechAUTHORS
In the process, we also more fully characterize the uncertainty in the M—R relation based on the current data. The effort to understand this uncertainty is important, as quantifying how well constrained the M—R relation parameters are will be a key metric by which we measure the improvement in our understanding of the M—R distribution, especially as TESS and its follow-up observations produce more individual mass and radius measurements.
In this paper we show how a probabilistic M—R relation can be constructed Section 2 and constrained Section 4 using any subset of planetary masses and radii Section 3. We also highlight the observational evidence for this expected intrinsic scatter and quantify it in a statistically robust way that includes uncertainties on the M—R relation parameters Section 5.
About Related Links 1. Among the mission's many firsts and accomplishments, however, one of the most revolutionary is that for the first time we have a robust determination of the relative abundance of different sizes of planets, stretching from Earth-sized all the way up to the largest hot Jupiters Howard et al.
Such planets are unlike anything found in our own solar system, and fundamental questions about their structure and formation are still not understood. Are these Neptune-like planets that form beyond the snow line and contain large amounts of volatile ices Rogers et al. In an attempt to address these questions, a great deal of effort has been invested in acquiring precise masses for a large number of these transiting planets.
How Big is Neptune?
In recent years this has generated a much fuller understanding of the mass—radius relation, especially for sub-Neptune- and super-Earth-sized planets Weiss et al. In particular, there are now several multiplanet Kepler systems like Kepler with masses determined from transit timing variations TTVs; e.
Although rare, such systems are incredibly valuable because with both a mass and a radius we can estimate a planet's bulk composition using models of interior structure and thermal evolution e. Thus far, efforts have been focused on individually determining compositions for this handful of planets. This paucity stands in stark contrast to the over Kepler candidates with only measured radii.
Unfortunately, the vast majority of these candidates are in dynamically inactive systems without strong TTVs or around distant stars too faint for radial velocity measurements. Moreover, even with precise masses and radii there are inherent degeneracies that limit ones ability to constrain the bulk compositions of super-Earth-sized planets.
To some extent, models of planet collisions can set upper limits on the maximum iron or water mass fractions that are physically achievable Marcus et al. Fortunately, models are still able to set clear and useful constraints on composition. This is what we begin to explore in this paper. Whenever possible it is still preferable to obtain a well-measured mass.
This fact means that instead of only examining the radius distribution of Kepler candidates, we can begin thinking about a composition distribution. MODELS In order to understand how planetary radius relates to planet mass and envelope fraction, it is necessary to fully model how a planet cools and contracts due to thermal evolution.
For this work, we have used the thermal evolution presented in Lopez et al.
Similar models are frequently used to track the evolution of sub-Neptunes and hot Jupiters e. Unlike Lopez et al. In essence, the present-day envelope fraction determines the radius, but that envelope fraction may have been strongly affected by formation and photoevaporation.