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At least 505 records · Page 28

California-Kepler Survey. IX. Revisiting the Minimum-mass Extrasolar Nebula with Precise Stellar Parameters

We investigate a possible correlation between the solid surface density Σ of the minimum-mass extrasolar nebula (MMEN) and the host star mass M {sub ⋆} and metallicity [Fe/H]. Leveraging on the precise host star properties from the California-Kepler Survey (CKS), we found that Σ=50{sub −20}{sup +33} g cm{sup −2} (a/1 au){sup −1.75±0.07} (M {sub ⋆}/M {sub ⊙}){sup 1.04±0.22} 10{sup 0.22±0.05[Fe/H]} for Kepler-like systems (1–4R {sub ⊕}; a < 1 au). The strong M {sub ⋆} dependence is reminiscent of previous dust continuum results that the solid disk mass scales with M {sub ⋆}. The weaker [Fe/H] dependence shows that sub-Neptune planets, unlike giant planets, form readily in lower metallicity environment. The innermost region (a < 0.1 au) of an MMEN maintains a smooth profile despite a steep decline of planet occurrence rate: a result that favors the truncation of disks by corotating magnetospheres with a range of rotation periods, rather than the sublimation of dust. The Σ of Kepler multitransiting systems shows a much stronger correlation with M {sub ⋆} and [Fe/H] than singles. This suggests that the dynamically hot evolution that produced single systems also partially removed the memory of formation in disks. Radial-velocity planets yielded a MMEN very similar to CKS planets; transit-timing-variation planets’ postulated convergent migration history is supported by their poorly constrained MMEN. We found that lower mass stars have a higher efficiency of forming/retaining planets: for Sun-like stars, about 20% of the solid mass within ∼1 au are converted/preserved as sub-Neptunes, compared to 70% for late-K to early-M stars. This may be due to the lower binary fraction, lower giant-planet occurrence, or the longer disk lifetime of lower mass stars.

79 ASTRONOMY AND ASTROPHYSICS↗

Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models

We present a generic flux limiter to account for mass limitations from an arbitrary number of substrates in a biogeochemical reaction network. The flux limiter is based on the observation that substrate (e.g., nitrogen, phosphorus) limitation in biogeochemical models can be represented as to ensure mass conservative and non-negative numerical solutions to the governing ordinary differential equations. Application of the flux limiter includes two steps: (1) formulation of the biogeochemical processes with a matrix of stoichiometric coefficients and (2) application of Liebig's law of the minimum using the dynamic stoichiometric relationship of the reactants. This approach contrasts with the ad hoc down-regulation approaches that are implemented in many existing models (such as CLM4.5 and the ACME (Accelerated Climate Modeling for Energy) Land Model (ALM)) of carbon and nutrient interactions, which are error prone when adding new processes, even for experienced modelers. Through an example implementation with a CENTURY-like decomposition model that includes carbon, nitrogen, and phosphorus, we show that our approach (1) produced almost identical results to that from the ad hoc down-regulation approaches under non-limiting nutrient conditions, (2) properly resolved the negative solutions under substrate-limited conditions where the simple clipping approach failed, (3) successfully avoided the potential conceptual ambiguities that are implied by those ad hoc down-regulation approaches. We expect our approach will make future biogeochemical models easier to improve and more robust.

58 GEOSCIENCES↗

Minimum energy efficiency standards for appliances: Old and new economic rationales

In this study, we revisit Hausman and Joskow (1982)'s economic rationales for appliance minimum energy efficiency standards. In addition to the four market failures they argued could justify appliance standards--energy prices below marginal social cost, consumers underestimating energy prices, consumer discount rates above social discount rates, or principal agent problems--we discuss two additional market failures that are relevant and potentially economically important in this context: market power and innovation market failures. We highlight puzzles uncovered by recent empirical results, and suggest directions future research should take to better understand the normative implications of appliance standards.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗