Early Planet Formation in Embedded Disks (eDisk) XIV: Flared Dust Distribution and Viscous Accretion Heating of the Disk around R CrA IRS 7B-a

We performed radiative transfer calculations and observing simulations to reproduce the 1.3-mm dust-continuum and C$^{18}$O (2-1) images in the Class I protostar R CrA IRS7B-a, observed with the ALMA Large Program ``Early Planet Formation in Embedded Disks (eDisk)". We found that the dust disk model passively heated by the central protostar cannot reproduce the observed peak brightness temperature of the 1.3-mm continuum emission ($\sim$195 K), regardless of the assumptions about the dust opacity. Our calculation suggests that viscous accretion heating in the disk is required to reproduce the observed high brightness temperature. The observed intensity profile of the 1.3-mm dust-continuum emission along the disk minor axis is skewed toward the disk far side. Our modeling reveals that such an asymmetric intensity distribution requires flaring of the dust along the disk's vertical direction with the scale-height following $h/r \sim r^{0.3}$ as function of radius. These results are in sharp contrast to those of Class II disks, which show geometrically flat dust distributions and lower dust temperatures. From our modeling of the C$^{18}$O (2-1) emission, the outermost radius of the gas disk is estimated to be $\sim$80 au, larger than that of the dust disk ($\sim$62 au), to reproduce the observed distribution of the C$^{18}$O (2-1) emission in IRS 7B-a. Our modeling unveils a hot and thick dust disk plus a larger gas disk around one of the eDisk targets, which could be applicable to other protostellar sources in contrast to more evolved sources.