  The nature of pulsar is still unknown because of non-perturbative effects of
the fundamental strong interaction, and different models of pulsar inner
structures are then suggested, either conventional neutron stars or quark
stars. Additionally, a state of quark-cluster matter is conjectured for cold
matter at supranuclear density, as a result pulsars could thus be quark-cluster
stars. Besides understanding different manifestations, the most important issue
is to find an effective way to observationally differentiate those models.
X-ray polarimetry would play an important role here. In this letter, we focus
on the thermal X-ray polarization of quark/quark-cluster stars. While the
thermal X-ray linear polarization percentage is typically higher than ~10% in
normal neutron star models, the percentage of quark/quark-cluster stars is
almost zero. It could then be an effective method to identify
quark/quark-cluster stars by soft X-ray polarimetry. We are therefore expecting
to detect thermal X-ray polarization in the coming decades.
