Density limits in stellarators are caused mainly by enhanced impurityradiation leading to a collapse of the temperature on the time scale of theenergy confinement time rather than on a fast MHD time scale, which ischaracteristic for a loss of equilibrium. A simple model can be establishedwhich computes the temperature in the plasma with a fixed heating profile anda temperature-dependent radiation profile. If the temperature-dependentradiation function has one or several extrema, multiple solutions of thetransport equation exist. Radiative collapse occurs when the high-temperaturebranch merges with an unstable temperature branch. The bifurcation point is afunction of the heating power and the plasma density. Thus a density limit canbe defined by the existence of the upper bifurcation point, where the stablehigh-temperature branch ceases to exist. It is shown that bifurcation andsudden temperature collapse does not occur below a power threshold. Anomalousthermal conductivity and the details of the impurity radiation, which in thepresent model is assumed to be in corona equilibrium, determine the scaling ofthe density limit. Some numerical examples are given, one with radiationcentred in the plasma core and the other one with boundary radiation. Thescaling of the density limit is dependent on the localization of theradiation. A model of the anomalous transport is developed, which leads toGyro-Bohm scaling of the confinement time. The density limit based on thistransport model is compared with experimental findings in Wendelstein 7-AS andWendelstein 7-A.