Semi-analytic calculations for extended mid-infrared emission associated with FU Ori-type objects

Aims. Near-infrared imaging polarimetry at high-angular resolutions has revealed an intriguing distribution of circumstellar dust toward FU Ori-type objects (FUors). These dust grains are probably associated with either an accretion disk or an infalling envelope. Follow-up observations in the mid-infrared would lead us to a better understanding of the hierarchy of the mass accretion processes onto FUors (that is envelope and disk accretion), which hold keys for understanding the mechanism of their accretion outbursts and the growth of low-mass young stellar objects (YSOs) in general. Methods. We developed a semi-analytic method to estimate the mid-infrared intensity distributions using the observed polarized intensity (PI) distributions in the H band (lambda = 1.65 mu m). This new method allows us to estimate the intensity levels with an order-of-magnitude accuracy, assuming that the emission is a combination of scattered and thermal emission from circumstellar dust grains illuminated and heated by a central source, but the radiation heating through the inner edge of the dust disk is negligible due to the obscuration by an optically thick compact disk. We have derived intensity distributions for two FUors, FU Ori and V1735 Cyg, at three wavelengths (lambda = 3.5, 4.8, and 12 mu m) for various cases, with a star or a flat compact self-luminous disk as an illuminating source; an optically thick disk or an optically thin envelope for circumstellar dust grains; and three different dust models. The calculations were carried out for typical aspect ratios of the disk surface and the envelope z/r of similar to 0.1, similar to 0.2, and similar to 0.4. Results. We have been able to obtain self-consistent results for many cases and regions, in particular when the viewing angle of the disk or envelope is zero (face-on). Our calculations suggest that the mid-infrared extended emission at the above wavelengths is dominated by the single scattering process. The contribution of thermal emission is negligible unless we add an additional heating mechanism such as adiabatic heating in spiral structures and/or fragments. The uncertain nature of the central illuminating source, the distribution of circumstellar dust grains and the optical properties of dust grains yield uncertainties in the intensity levels on orders of magnitude, for example, 20-800, for the aspect ratio of the disk or the envelope of similar to 0.2 and lambda = 3-13 mu m. Conclusions. The new method we have developed is useful for estimating the detectability of the extended mid-infrared emission. Observations with the forthcoming extremely large telescopes, with a telescope diameter of 24-39 m, would yield a breakthrough for the above research topic at angular resolutions comparable to the existing near-infrared observations. The new semi-analytic method is complementary to full radiative transfer simulations, which offer more accurate calculations but only with specific dynamical models and significant computational time.