Comparison between models L_inlow (yellow line) and L_outlow (red line). The reference model (ref, blue line) corresponds to a Z = 1 Z_⊙ star with Ṁ_start = 1 × 10⁻⁸ M_⊙ yr⁻¹. The stellar luminosity is artificially reduced by 25% in the inner 1 AU (L_inlow) and outside 1 AU (L_outlow). Panel a shows the evolution of the accretion rate. The dotted black line shows the termination criterion used in our simulations of Ṁ = 10⁻¹¹ M_⊙ yr⁻¹. Panel b shows the temperature structure of the initial disk model. For model L_inlow the inner disk region is cooler compared to the reference model, and for model L_outlow the outer disk region is cooler. The dotted black line shows the ambient temperature of 20 K.