Probing the temperature structure of optically thick discs using polarized emission of aligned grains

Polarized continuum emission from aligned grains in discs around young stellar objects can be used to probe the magnetic field, radiation anisotropy, or drift between dust and gas, depending on whether the non-spherical grains are aligned magnetically, radiatively, or mechanically. We show that it can also be used to probe another key disc property – the temperature gradient – along sightlines that are optically thick, independent of the grain alignment mechanism. We first illustrate the technique analytically using a simple 1D slab model, which yields an approximate formula that relates the polarization fraction to the temperature gradient with respect to the optical depth τ at the τ = 1 surface. The formula is then validated using models of stellar irradiated discs with and without accretion heating. The promises and challenges of the technique are illustrated with a number of Class 0 and I discs with ALMA dust polarization data, including NGC 1333 IRAS4A1, IRAS 16293B, BHB 07-11, L1527, HH 212, and HH 111. We find, in particular, that the sightlines passing through the near-side of a highly inclined disc trace different temperature gradient directions than those through the far-side, which can lead to a polarization orientation on the near-side that is orthogonal to that on the far-side, and that the HH 111 disc may be such a case. Our technique for probing the disc temperature gradient through dust polarization can complement other methods, particularly those using molecular lines.