1. Background and Purpose of Research

 The dependency of the structure of the three-dimensional gray atmosphere on the solar constant and the runaway greenhouse states. The dependency of the structure of the three-dimensional gray atmosphere on the solar constant and the runaway greenhouse states. 1.b. Previous Studies on the Runaway Greenhouse State

a. Background of Research

In one-dimensional (1D) atmospheric models, it is known that there is a critical value of incident solar radiation flux over which no atmosphere-ocean coexisting equilibrium state can exist. When the critical value is exceeded, the temperature of the atmosphere will continue to rise, leading to a state known as a "runaway greenhouse state". As will be explained below, the emergence of a runaway greenhouse state is believed to be a crucial event in the formation and evolution of a terrestrial planets.

During the formation stage of terrestrial planets, volatile components such as water vapor are present in the atmosphere due to degassing caused by violent planetesimal impact (Abe and Matsui, 1985, etc.). Abe and Matsui (1988) resolved the structure of the Earth's primitive atmosphere using a 1D radiative convective equilibrium model to estimate the energy influx into the atmosphere resulting from solar radiation and planetesimal impact. Their results showed that in situations where the energy flux from planetesimal accumulation exceed 300 W/m2, oceans cannot exist and all planetary water will exist as vapor in the atmosphere. This state corresponds to the runaway greenhouse state. Based on these results, it has been theorized that the Earth's primitive atmosphere and oceans were formed through the following process: The overabundance of water vapor in the atmosphere increases its optical depth, causing the surface temperature to increase to approximately 1500 K. At such high temperatures, the surface rocks become molten and form a magma ocean. The dissolution of water vapor from the atmosphere into the magma ocean then acts as a regulating mechanism that limits the water vapor in the atmosphere to a near constant value of 1021 Kg, which is nearly equal to the Earth's present ocean mass. Then, as the energy flux from planetesimal accumulation decreases, the water vapor condenses and forms the oceans.

1.a. Background of Research The dependency of the structure of the three-dimensional gray atmosphere on the solar constant and the runaway greenhouse states. The dependency of the structure of the three-dimensional gray atmosphere on the solar constant and the runaway greenhouse states. 1.b. Previous Studies on the Runaway Greenhouse State