Major Features of the Distribution of Exoplanets of Sun-like Stars, Highlighted by the Peak-Gap-Peak Feature

Abstract
Planets of sun-like stars display an unexpected richness of features in the distribution of planet semi-major axes (“a”). These features provide essential new observational insight of how planet formation and evolution actually occurs. These features show too strong of associations with physical characteristics to have occurred by chance. This follows publication of statistical demonstrations showing that the peak-gap-peak feature has too many objects outside the gap for this feature to have been produced by a random distribution. These features are a major part of the distribution of planets distances from their stars. Such significant features will inevitably have a major impact on the understanging of the formation and evolution of planets.

Introduction

Proto-planetary disks are often thought to form separate inner and outer disks separated by a gap, but seeing this structure is not expected due to being erased by subsequent planet migration. Such a “peak-gap-peak” structure indeed appears to be present in the distribution of semi-major axes a of planets of metal-rich single stars of low enough mass to have convective zones. Just as would be expected from the inner and outer disk picture, the boundary of the gap with the outer peak is the sharpest boundary. We now find that the a of this boundary exhibits a dependence on the square root of the stellar mass, consistent with the distance corresponding to what could have been the same equilibrium temperature T_eq at a time when the luminosity of the protostar was proportional to its mass. We also explore how there may be inner pileups bounding the gap that correspond with being in resonance with the sharp outer peak.

Findings

We highlight the Peak-Gap-Peak (PGP) feature as the empty region in the center of Fig. 1 that slants upwards:

Figure 1: Gap-peak boundary shifts to more distant semi-major axes with increasing stellar mass, consistent with constant T_eq.

Planets of metal-rich ([Fe/H] ≥ 0) single "convective" (mass less than 1.29 M_sun) stars (rSC stars) comprise almost 40% of planets found by radial velocity (RV). Among this population, the broad pileup of planets starting at a less than 1 AU going outward has a deep gap that separates the broad pileup into two pileups.

The most striking boundary is where the gap of no planets suddenly gives rise to a sharp peak, with the highest density of planets per log semi-major axis “a” being found right next to the gap. The distance of this boundary from the star of 1.9 AU for solar-mass stars shows a dependence on the square root of the stellar mass.

Figure 2: Counts of planets at the same T_eq, separating planets of rSC stars (red unfilled) from all others (green filled).

Inwards of this peak is a deep gap extending down to below 1.5 AU, where there are a few objects with periods corresponding to a 3:2 period resonance with the peak. Further inwards, the density of planets becomes higher below 1.2 AU, where periods correspond to a 1:2 resonance with the outer peak. It is remarkable that this PGP feature extends in stellar mass only up to where stars only have very small or no convective zone. This is also at or near the stellar mass at which the occurrence distribution of planets with “a” less than 1 AU drops very low. This suggests that planets of stars on different sides of this boundary in stellar mass have undergone different formation or evolution histories. We will present this feature as part of some general patterns of the parameters of planets, including how among planets of single stars with M_star < 1.29 M_sun, there is a correlation of eccentricity with stellar metallicity at shorter periods. The eccentricity of planets of metal-poor stars versus of metal-rich stars appears to be influenced by the changing relative density of planets in the PGP.

Discussion

That planets are preferentially found at radii corresponding to what could have been the same equilibrium temperature suggests that planet formation follows common patterns. The observed presence of these features goes against the current consensus which is that random migration would erase pileups from formation, but these features are easily reproduced in the public catalog exoplanet.org. For these features to survive places limits on how much migration occurs in the regions displaying the PGP feature.

Conclusion

The presence of features that survive planet evolution challenges the prevailing view that too much random migration erases any signs of structure arising from formation.

Video 1: Public talk on PGP feature from 2017.

References

Taylor, Stuart F., Astron. Nachr , 340, 723 (2019), ADS

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