  We report an in-depth Angle Resolved Photoemission Spectroscopy (ARPES) study
on $2H$-TaS$_2$, a canonical incommensurate Charge Density Wave (CDW) system.
This study demonstrates that just as in related incommensurate CDW systems,
$2H$-TaSe$_2$ and $2H$-NbSe$_2$, the energy gap ($\Delta_{\text{cdw}}\,$) of
$2H$-TaS$_2$ is localized along the K-centered Fermi surface barrels and is
particle-hole asymmetric. The persistence of $\Delta_{\text{cdw}}\,$ even at
temperatures higher than the CDW transition temperature $\it{T}_{\text{cdw}}\,$
in $2H$-TaS$_2$, reflects the similar pseudogap (PG) behavior observed
previously in $2H$-TaSe$_2$ and $2H$-NbSe$_2$. However, in sharp contrast to
$2H$-NbSe$_2$, where $\Delta_{\text{cdw}}\,$ is non-zero only in the vicinity
of a few "hot spots" on the inner K-centered Fermi surface barrels,
$\Delta_{\text{cdw}}\,$ in $2H$-TaS$_2$ is non-zero along the entirety of both
K-centered Fermi surface barrels. Based on a tight-binding model, we attribute
this dichotomy in the momentum dependence and the Fermi surface specificity of
$\Delta_{\text{cdw}}\,$ between otherwise similar CDW compounds to the
different orbital orientations of their electronic states that are involved in
CDW pairing. Our results suggest that the orbital selectivity plays a critical
role in the description of incommensurate CDW materials.
