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This paper is the first in a series of publications which investigate the stability properties of the complete set of isothermal protoplanetary equilibrium solutions. To perform a non-linear stability analysis, we introduce a fluid dynamics numerical model. We inspect the entire solution set and find five basic dynamical modes: oscillation, pulsation, transition, ejection and collapse. [ABSTRACT FROM AUTHOR]

Today, many extrasolar planets have been detected. Some of them exhibit properties quite different from the planets in our Solar system and they have eluded attempts to explain their formation. One such case is HD 149026 b. It was discovered by Sato et al. A transit-determined orbital inclination results in a total mass of . The unusually small radius can be explained by a condensible element core with an inferred mass of for the best-fitting theoretical model. In the core accretion model, giant planets are assumed to form around a growing core of condensible materials. With increasing core mass, the amount of gravitationally bound envelope mass increases. This continues up to the so-called critical core mass – the largest core allowing a hydrostatic envelope. For larger cores, the lack of static solutions forces a dynamic evolution of the protoplanet, accreting large amounts of gas or ejecting the envelope in the process. This would prevent the formation of HD 149026 b. By studying all possible hydrostatic equilibria we could show that HD 149026 b can remain hydrostatic up to the inferred heavy core. This is possible if it is formed in situ in a relatively low-pressure nebula. This formation process is confirmed by fluid-dynamic calculations using the environmental conditions as determined by the hydrostatic models. We present a quantitative in situ formation scenario for the massive core planet HD 149026 b. Furthermore, we predict a wide range of possible core masses for close-in planets like HD 149026 b. This is different from migration, where typical critical core masses should be expected. [ABSTRACT FROM AUTHOR]