PR-drag pile-up scenario: flux level at 2 μm (left) and 10 μm (right) for an A0 star and carbon grains (top); and K0 star and astrosilicate grains (bottom). See Sect. 2.4 and Appendix C for the methodology. The vertical dashed line corresponds to the location of the sublimation radius r_s as a function of grain size, while the full and dashed horizontal lines indicate the β = 0.5 and β = 1 limits, respectively.