Debiasing the Minimum-Mass Extrasolar Nebula: On the Diversity of Solid Disk Profiles

Abstract

A foundational idea in the theory of in situ planet formation is the "minimum mass extrasolar nebula" (MMEN), a surface density profile ($\Sigma$) of disk solids that is necessary to form the planets in their present locations. While most previous studies have fit a single power-law to all exoplanets in an observed ensemble, it is unclear whether most exoplanetary systems form from a universal disk template. We use an advanced statistical model for the underlying architectures of multi-planet systems to reconstruct the MMEN. The simulated physical and Kepler-observed catalogs allows us to directly assess the role of detection biases, and in particular the effect of non-transiting or otherwise undetected planets, in altering the inferred MMEN. We find that fitting a power-law of the form $\Sigma = \Sigma_0^* (a/a_0)^\beta$ to each multi-planet system results in a broad distribution of disk profiles; $\Sigma_0^* = 336_{-291}^{+727}$ g/cm$^2$ and $\beta = -1.98_{-1.52}^{+1.55}$ encompass the 16th-84th percentiles of the marginal distributions in an underlying population, where $\Sigma_0^*$ is the normalization at $a_0 = 0.3$ AU. Around half of inner planet-forming disks have minimum solid masses of $\gtrsim 40 M_\oplus$ within 1 AU. While transit observations do not tend to bias the median $\beta$, they can lead to both significantly over- and under-estimated $\Sigma_0^*$ and thus broaden the inferred distribution of disk masses. Nevertheless, detection biases cannot account for the full variance in the observed disk profiles; there is no universal MMEN if all planets formed in situ. The great diversity of solid disk profiles suggests that a substantial fraction ($\gtrsim 23\%$) of planetary systems experienced a history of migration.