Grain alignment and disruption by radiative torques in dense molecular
  clouds and implication for polarization holes
  Dust polarization induced by aligned grains is widely used to study magnetic
fields in various environments, including star-forming regions. However, the
question of to what optical depth grain alignment still exists in a dense
molecular cloud (MC) is unclear. In this paper, we aim to achieve analytical
formulae for the minimum size of aligned grains ($a_{\rm align}$) and
rotational disruption ($a_{\rm disr}$) by RAdiative Torques (RATs) as a
function of the local physical parameters within dense MCs. We first find the
analytical approximations for the radiation strength and the mean wavelength of
the attenuated radiation field in a dense MC without and with embedded stars
and then derive analytical formulae for $a_{\rm align}$ and $a_{\rm disr}$ as
functions of the visual extinction $A_{V}$ and the gas density. We find that
within a starless core of density $n_{\rm H}\sim 10^{5}\rm cm^{-3}$, grains of
size $a<0.25\mu m$ can be aligned up to $A_{V}\sim 5$ by RATs, whereas
micron-sized grains can still be aligned at $A_{V}\sim 50$. The increase in the
alignment size with $A_{V}$ can explain the presence of polarization holes
observed toward starless cores. For MCs with an embedded protostar, we find
that the efficiency of both alignment and rotational disruption increases
toward the protostar due to the increasing radiation strength. Such a
disruption effect results in the decrease of the polarization degree with
$A_{V}$ or emission intensity, which reproduces the popular polarization holes
observed toward the location of protostars. Finally, we derive the formula for
the maximum $A_{V}$ where grain alignment still exists in a starless core and
discuss its potential for constraining grain growth.
