The quark surface of a strange star has a very low emissivity for X-ray photons . I find that a small amount of normal matter at the quark surface with temperature in the range 10 ^ { 7 } \raisebox { -1.72 pt } { $ \stackrel { < } { \scriptstyle \sim } $ } T _ { { } _ { S } } % \ll mc ^ { 2 } / k \simeq 6 \times 10 ^ { 9 } K is enough to produce X-rays with high luminosity , L _ { X } \simeq 10 ^ { 32 } -10 ^ { 34 } ( \Delta M / 10 ^ { -22 } M _ { \odot } ) ^ { 2 } erg s ^ { -1 } . For the total atmosphere mass \Delta M \sim ( 10 ^ { -20 } -10 ^ { -19 } ) M _ { \odot } , this luminosity may be as high as the Eddington limit . The mean energy of X-ray photons which are radiated from such a low-mass atmosphere of a strange star is \sim 10 ^ { 2 } ( T _ { { } _ { S } } / 10 ^ { 8 } { K } ) ^ { 0.45 } \simeq 30 - 300 times larger than the mean energy of X-ray photons which are radiated from the surface of both a neutron star and a strange star with a massive normal-matter envelope , \Delta M \sim 10 ^ { -5 } M _ { \odot } , for a fixed temperature at the stellar core . This raises the possibility that some black hole candidates with hard X-ray spectra are , in fact , such strange stars with a low-mass atmosphere . The X-ray emission from single strange stars is estimated . \keywords stars : atmospheres - X-rays : stars - radiation mechanisms : thermal