First Larson cores for various equations of state. The hydrostatic equilibrium equations are integrated with n₀ = 100 n_ad as boundary condition. We present cases with γ = 5∕3 (blue), γ = 4∕3 (cyan), full eos (red), and isothermal (black). The legends correspond to the labels of the simulations, with solid lines for n_ad = 10¹⁰ cm⁻³ and dashed lines for 10⁹ cm⁻³. We also show the case γ = 7∕5 with n_ad = 2.45 × 10¹⁰ cm⁻³ by Bate et al. (2003, green). The values of n₀ are chosenfor illustrative purpose, and the actual values reached in simulations depend on the resolution (highest density resolved, see Fig. 7). The circle indicates the radius at which the density reaches 10⁷   cm ⁻³, a reference ambient density that truncates the core. As long as the density profile decreases steeply enough, the choice of this truncation density has no strong effect on the resulting mass.