We present the results of a statistical study of the star formation rates (SFR) derived from the Galaxy Evolution Explorer (GALEX) observations in the ultraviolet continuum and in the Hα emission line for a sample of about 800 luminous compact galaxies (LCGs). Galaxies in this sample have a compact structure and include one or several regions of active star formation. Global galaxy characteristics (metallicity, luminosity, stellar mass) are intermediate between ones of the nearby blue compact dwarf (BCD) galaxies and Lyman-break galaxies (LBGs) at high redshifts z > 2 -3. SFRs were corrected for interstellar extinction which was derived from the optical Sloan Digital Sky Survey (SDSS) spectra. We find that SFRs derived from the galaxy luminosities in the far ultraviolet (FUV) and near ultraviolet (NUV) ranges vary in a wide range from 0.18 M ⊙ yr −1 to 113 M ⊙ yr −1 with median values of 3.8 M ⊙ yr −1 and 5.2 M ⊙ yr −1 , respectively. Simple regression relations are found for luminosities L(Hα) and L(UV) as functions of the mass of the young stellar population, the starburst age, and the galaxy metallicity. We consider the evolution of L(Hα), L(FUV) and L(NUV) with a starburst age and introduce new characteristics of star formation, namely the initial Hα, FUV and NUV luminosities at zero starburst age.

We propose a technique for estimation of the mass m of the young stellar population and the starburst age T in luminous compact galaxies (LCGs). For this purpose we use LCG Hα emission line luminosities from the Sloan Digital Sky Survey (SDSS) spectra and Galaxy Evolution Explorer (GALEX) FUV and NUV continuum luminosities. The method is intended for quick estimation of m and T in large galaxy samples and does not require spectral energy distribution (SED) fitting. Estimated m and T for the sample of about 550 LCGs are compared with the same values derived from the SED fitting in the wavelength range λλ 3800 -9200Å. We obtain the average differences in log m and T of 0.27 and 0.87 Myr, respectively. This technique could be used for selection of galaxies with desired ranges of m and T or for reducing a range of parameter variations in SED fitting.

We study Hα, far-and near-ultraviolet luminosity functions (LF) of the sample of 795 luminous compact star-forming galaxies with z < 0.65. The parameters of optimal functions for LFs are obtained using the maximum likelihood method and the accuracy of fitting is estimated with the χ 2 method. We find that these LFs cannot be reproduced by the Schechter function because of an excess of very luminous galaxies. On the other hand, the Saunders function, the log-normal distribution and some new related functions are good approximations of LFs. The fact that LFs are not reproduced by the Schechter function can be explained by the propagating star formation. This may result in an excess of luminous starbursts with the mass of a young stellar population above 2 × 10 8 M ⊙ as compared to the LF of the quiescent galaxies. The most luminous compact galaxies are characterised by Hα luminosities of ≥ 5 × 10 42 erg s −1 and star formation rates of ≥ 40 M ⊙ yr −1 .

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