Probing the temperature structure of the inner region of a protoplanetary disk

Context. Disk temperature structure is crucial for the formation of planets. Midplane heating induced by disk accretion plays a key role in determining the disk temperature, particularly at the inner disk midplane where planets are formed. However, the efficiency of accretion heating has been not well constrained by observations. Aims. Our aim is to observationally constrain the physical properties of the inner region of the CW Tau disk, where the midplane heating potentially takes place. Methods. We constructed two-dimensional physical models of the CW Tau disk that take the midplane heating into account. We compared the models with the ALMA dust continuum observations at Bands 4, 6, 7, and 8, with an angular resolution of 0″. 1. The observed brightness temperatures are almost wavelength-independent at ≲10 au. Results. We find that if the maximum dust size is amax ≲100 µm, the brightness temperatures predicted by the model exceed the observed values, regardless of the efficiency of accretion heating. The low observed brightness temperatures can be explained if millimeter scattering reduces the intensity. If the disk is passive, amax needs to be either ~150 µm or more than a few cm. The accretion heating significantly increases the brightness temperature, particularly when amax ≲ 300 µm; thus, the value of amax must be either ~300 µm or over a few cm. The midplane temperature is expected to be ~1.5–3 times higher than the observed brightness temperatures, depending on the models. The dust settling effectively increases the temperature of the dust responsible for the millimeter emission in the active disk, which leads to the model with 300 µm-sized dust overpredicting the brightness temperatures when strong turbulence is absent. Porous dust (porosity of 0.9) makes the accretion heating more efficient, so that some sort of reduction in accretion heating is required. Conclusions. The brightness temperature is not a simple function of the dust temperature because of the effect of scattering and midplane heating – even when the disk is optically thick. The current data of the CW Tau disk are not sufficient to allow us to discriminate between the passive and active disk models. Future observations at longer wavelengths and higher angular resolution will help to constrain the heating mechanisms of the inner regions of protoplanetary disks