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It is known that the millimeter dust thermal emission of protoplanetary disksis affected by scattering, such that for optically thick disks the emissiondecreases with respect to the pure absorption case and the spectral indices canreach values below 2. The latter can also be obtained with temperaturegradients. Using simple analytical models of radiative transfer in thin slabs,we quantify the effect of scattering, vertical temperature gradients, and dustsettling on the emission and spectral indices of geometrically thin face-onaccretion disks around young stars. We find that in vertically isothermal diskswith large albedo ($\omega_{\nu} \gtrsim 0.6$), the emergent intensity canincrease at optical depths between $10^{-2}$ and $10^{-1}$. We show that dustsettling has important effects on the spectral indices in the optically thickregime, since the disk emission mainly traces small dust grains in the upperlayers of the disk. The $\lambda = 870 \ \mu$m emission of these small grainscan hide large grains at the disk mid plane when the dust surface density islarger than $\sim$ 3.21 g cm$^{-2}$. Finally, because of the change of theshape of the spectral energy distribution, optically thick disks at 1.3 mm andgrains with sizes between 300 $\mu$m $< a_{\rm max} <$ 1 mm have a 7 mm flux$\sim 60$\% higher than the extrapolation from higher millimeter frequencies,assumed when scattering is neglected. This effect could provide an explanationto the excess emission at $\lambda = 7$ mm reported in several disks.

Effects of scattering, temperature gradients, and settling on the derived dust properties of observed protoplanetary disks