Stellar winds on the main-sequence

Aims. We develop a method for estimating the properties of stellar winds for low-mass main-sequence stars between masses of 0.4 M⊙ and 1.1 M⊙ at a range of distances from the star. Methods. We use 1D thermal pressure driven hydrodynamic wind models run using the Versatile Advection Code. Using in situ measurements of the solar wind, we produce models for the slow and fast components of the solar wind. We consider two radically different methods for scaling the base temperature of the wind to other stars: in Model A, we assume that wind temperatures are fundamentally linked to coronal temperatures, and in Model B, we assume that the sound speed at the base of the wind is a fixed fraction of the escape velocity. In Paper II of this series, we use observationally constrained rotational evolution models to derive wind mass loss rates. Results. Our model for the solar wind provides an excellent description of the real solar wind far from the solar surface, but is unrealistic within the solar corona. We run a grid of 1200 wind models to derive relations for the wind properties as a function of stellar mass, radius, and wind temperature. Using these results, we explore how wind properties depend on stellar mass and rotation. Conclusions. Based on our two assumptions about the scaling of the wind temperature, we argue that there is still significant uncertainty in how these properties should be determined. Resolution of this uncertainty will probably require both the application of solar wind physics to other stars and detailed observational constraints on the properties of stellar winds. In the final section of this paper, we give step by step instructions for how to apply our results to calculate the stellar wind conditions far from the stellar surface