We present observations with the Cosmic Origins Spectrograph onboard the Hubble Space Telescope of eight compact star-forming galaxies at redshifts z=0.02811-0.06540, with low oxygen abundances 12+log(O/H)=7.43-7.82 and extremely high emission-line flux ratios O32=[OIII]5007/[OII]3727~22-39, aiming to study the properties of Ly-alpha emission in such conditions. We find a diversity in Ly-alpha properties. In five galaxies Ly-alpha emission line is strong, with equivalent width (EW) in the range 45-190A. In the remaining galaxies, weak Ly-alpha emission with EW(Ly-alpha)~2-7A is superposed on a broad Ly-alpha absorption line, indicating a high neutral hydrogen column density N(HI)~(1-3)x10^21 cm^-2. We examine the relation between the Ly-alpha escape fraction fesc(Ly-alpha) and the Lyman continuum escape fraction fesc(LyC), using direct measures of the latter in eleven low-redshift LyC leakers, to verify whether fesc(Ly-alpha) can be an indirect measure of escaping LyC radiation. The usefulness of O32, of the Ly-alpha equivalent width EW(Ly-alpha) and of the Ly-alpha peak separation Vsep as indirect indicators of Ly-alpha leakage is also discussed. It is shown that there is no correlation between O32 and fesc(Ly-alpha). We find an increase of fesc(Ly-alpha) with increasing EW(Ly-alpha) for EW(Ly-alpha)<100A, but for higher EW(Ly-alpha)>150A the fesc(Ly-alpha) is nearly constant attaining the value of ~0.25. We find an anticorrelation between fesc(Ly-alpha) and Vsep, though not as tight as the one found earlier between fesc(LyC) and Vsep. This finding makes Vsep a promising indirect indicator of both the Ly-alpha and ionizing radiation leakage.
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