The 200-300 GHz Survey for 18 Class II Disks in the Ophiuchus Star-Forming Complex

We measured the 198-310 GHz flux densities of 18 Class II protoplanetary disks in the Ophiuchus star-forming complex using the Submillimeter Array (SMA). The $\sim$200-300 GHz spectral indices (${\alpha }_{200-300}$) of these disks are $2.3_{-0.5}^{+0.2}$. In this observed frequency range, emission properties of the Ophiuchus disks are very similar to the 48 spatially compact Class II disks in the Taurus-Auriga region observed in a previous SMA survey. Combining the Ophiuchus and Taurus-Auriga samples, the Pearson correlation coefficient between ${\alpha }_{200-300}$ and the flux density at 250 GHz ($F_{250\mathrm{G}\mathrm{H}\mathrm{z}}$) is 0.27 ($p=0.02$). We do not find a convincing correlation between ${\alpha }_{200-300}$ and the $R_{95\mathrm{\%}}$ radius of the disks. Our interpretation for the ${\alpha }_{200-300}$ values being close to 2 in the spatially compact disks is that at $\gtrsim 200$ GHz frequencies, the continuum emission in these disks is dominated by optically thick dust thermal emission, independent of $F_{250\mathrm{G}\mathrm{H}\mathrm{z}}$ and $R_{95\mathrm{\%}}$. As a result, the (sub)millimeter luminosity and the apparent disk size are positively correlated, which has been found in numerous resolved emission surveys of Class II disks. In young clusters with ages of $\sim$1-2 Myr, Class II disks with smaller radii or lower (sub)millimeter luminosities are not necessarily those in which the dust mass budget has been consumed or dispersed.