  In this paper we explore a class of quadratic polynomials having Siegel disks
with unbounded type rotation numbers. We prove that any boundary point of
Siegel disks of these polynomials is a Lebesgue density point of their
filled-in Julia sets, which generalizes the corresponding result of McMullen
for bounded type rotation numbers. As an application, this result can help us
construct more quadratic Julia sets with positive area. Moreover, we also
explore the canonical candidate model for quasiconformal surgery of quadratic
polynomials with Siegel disks. We prove that for any irrational rotation
number, any boundary point of ``Siegel disk'' of the canonical candidate model
is a Lebesgue density point of its ``filled-in Julia set'', in particular the
critical point $1$ is a measurable deep point of the ``filled-in Julia set''.
