New FUSE far-UV spectroscopy of the nearby metal-deficient (Zsun/8) cometary Blue Compact Dwarf (BCD) galaxy Markarian (Mrk) 59 is discussed. The data are used to investigate element abundances in its interstellar medium. The H I absorption lines are characterized by narrow cores which are interstellar in origin and by broad wings which are stellar in origin. The mean interstellar H I column density is ~ 7x10E20 cm-2 in Mrk 59. No H2 lines are seen and N(H2) is < 10E15 cm-2 at the 10 sigma level. The lack of diffuse H2 is due to the combined effect of a strong UV radiation field which destroys the H2 molecules and a low metallicity which leads to a scarcity of dust grains necessary for H2 formation. P-Cygni profiles of the S VI 933.4, 944.5 A and O VI 1031.9, 1037.6 A lines are seen, indicating the presence of very hot O stars and a stellar wind terminal velocity of ~ 1000 km/s. By fitting the line profiles with multiple components having each a velocity dispersion b = 7 km/s and spanning a radial velocity range of 100 km/s, some of which can be saturated, we derive heavy element abundances in the neutral gas. We find log N(O I)/N(H I) = -5.0+/-0.3 or [O I/H I] = -1.5 for the neutral gas, about a factor of 10 below the oxygen abundance of the supergiant H II region, implying self-enrichment of the latter.
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