Understanding polarized dust emission from $\rho$ Ophiuchi A in light of grain alignment and disruption by radiative torques

The alignment of dust grains with the ambient magnetic field produces polarization of starlight as well as thermal dust emission. Using the archival SOFIA/HAWC+ polarimetric data observed toward $\rho$ Ophiuchus (Oph) A cloud hosted by a B association at 89 $\mu$m and 154 $\mu$m, we find that the fractional polarization of thermal dust emission first increases with the grain temperature and then decreases once the grain temperature exceeds $\simeq$ 32-34 K. The latter trend differs from the prediction of the popular RAdiative Torques (RATs) alignment theory which implies a monotonic increase of the polarization fraction with the grain temperature. We perform numerical modeling of polarized dust emission for the $\rho$ Oph-A cloud and calculate the degree of dust polarization by simultaneously considering the dust grain alignment and rotational disruption by RATs. Our modeling results could successfully reproduce both the rising and declining trends of the observational data. Moreover, we show that the alignment of only silicate grains or a mixture of silicate-carbon grains within a composite structure can reproduce observations, assuming that all dust grains follow a power-law size distribution. Our results suggest grains in molecular clouds to have a composite structure. The grain size distribution has slope $\beta<-3.5$, which is steeper than the standard size distribution for the interstellar medium. This could arise from the disruption effect of large grains that enhances the amount of smaller grains. Combination of SOFIA/HAWC+ data with observations at longer wavelengths at 450 $\mu$m and 850 $\mu$m with the JCMT facility would be useful to test the proposed scenario based on grain alignment and disruption by RATs.