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Sub-Neptune type exoplanets are abundant in our galaxy yet have no solar system analogs. They exist in a broad range of stellar forcing and rotational regimes that are distinctly different from solar system planets and more commonly studied hot Jupiters. Here we present simulations that explore global atmospheric circulation of sub-Neptunes generated with a two-dimensional shallow-water model, SWAMPE. We explore the circulation regimes of synchronously rotating sub-Neptunes with a focus on the interaction of planetary rotation rate and radiative timescale in a variety of stellar insolations. In highly irradiated, short-timescale regimes, our models exhibit high day-night geopotential contrasts. As the timescales become longer, the geopotential contrasts and longitudinal variability decrease, while temporal variability increases. The transition from day-to-night flow to jet-dominated flow is primarily driven by the radiative timescale. Strong- and medium-forcing regimes exhibit transitions between day-to-night flow and jet-dominated flow at similar points in the parameter space. Weak-forcing regime differs due to comparatively stronger rotational effects. Planetary rotation period dominates in determining equator-to-pole geopotential contrast. Our simulations exhibit higher time variability when either radiative timescale or rotation period is long., Comment: Accepted for publication in PSJ on 5/12/2023. 25 pages, 1 table, 11 figures

In this study, we compare two analytic energy balance models with explicit dependence on obliquity to study the likelihood of different stable ice configurations. We compare the results of models with different methods of heat transport and different insolation distributions. We show that stable partial ice cover is possible for any obliquity, provided the insolation distribution is sufficiently accurate. Additionally, we quantify the severity of the transition to the Snowball state as different model parameters are varied. In accordance with an earlier study, transitions to the Snowball state are more severe for higher values of the albedo contrast and energy transport across latitudes in both model; however, we find that the Snowball transition is not equally likely across both models. This work is general enough to apply to any rapidly rotating planet and could be used to study the likelihood of Snowball transitions on planets within the habitable region of other stars., Comment: 14 pages, 6 figures. Accepted for publication in Planetary Science Journal

We derive the Legendre series expansion for the insolation distribution on rapidly rotating planets as a function of sine of the latitude and the planet's obliquity. We give an explicit formula for the coefficients of this series as it depends on the obliquity and approximate the convergence rate. We determine the optimal truncation of the series for use in climate models and compare this approximation to other approximations in the literature., Comment: 29 pages, 8 figures

In this paper, we use a sixth order Legendre series expansion to approximate the mean annual insolation by latitude of a planet with obliquity angle $\beta$, leading to faster computations with little loss in the accuracy of results. We discuss differences between our method and selected computational results for insolation found in the literature., Comment: 5 pages, 2 figures