height is much larger than the characteristic thickness of neutron star atomsphere ($\sim  0.01
- 1$ cm, see, e.g. [@zps96]). This is an essential feature. It is known that a completely bare strange star has very low emissivity in X-rays[@afo86]. We emphasize here that [*the existence of the massive atmosphere described above makes a strange star to radiate thermal emission in a similar way as does a neutron star*]{} (except the polar caps, see below). Another comment is that the “atmosphere” discussed here is conceptually different from the atmosphere of a neutron star, which is defined by the equilibrium of the gravitational energy and the thermal kinetic energy of the particles. Neutron star atmospheres are naturally formed even without accretion. The strange star “atmospheres” discussed in this paper, however, are formed due to the materials’ fallback, and hence, are not subject to the definition above.

Shortly after a bare strange star is born, it is believed that a typical pulsar magnetosphere with Goldreich-Julian[@gj69] density will be formed slightly above the bare quark surface (typical height $z_{\rm c}\sim 10^{-8}$cm, see Sect.3.1), mainly due to the pair multiplication via $\gamma-B$, $\gamma-\gamma$[@xq98], or $\gamma-E$[@usov98] processes. When such a magnetosphere is formed, a space-charge-limited 