Aims.We constrain the past star formation histories of a sample of 25 distant ($\bar{z}\sim 0.7$) luminous infrared galaxies (LIRGs) detected with the mid infrared cameras ISOCAM and MIPS onboard the ISO and Spitzer satellites. Methods.We used high-resolution VLT-FORS2 spectroscopy in addition to a comprehensive library of 200 000 model optical spectra to derive Bayesian likelihood estimates of the star formation histories of these galaxies, based on analysis of Balmer absorption lines and the 4000 Å break. Results. The locus of distant LIRGs in the diagram defined by H$\delta_{\rm A}$ and D4000 is roughly comparable to that of local LIRGs observed with IRAS, suggesting that no trend toward an evolution is detected between the local and distant LIRGs. We obtain similar results when using either the H8 or the H$\delta_{\rm A}$ Balmer absorption-line indices in combination with D4000.
By computing a birthrate parameter ($b={\it SFR}/\langle {\it SFR}\rangle$) of $4\pm1$, we confirme that the distant LIRGs are currently experiencing a major phase of star formation. The most likely duration of the bursts is 0.10$^{+0.16}_{-0.06}$ Gyr, during which the LIRGs produce ~5–10% of their current stellar mass. No evidence was found for successive starbursts on the scale of a few times 107 yr, such as those predicted by some numerical simulations of major mergers. However, the high number density of those galaxies suggests that they could have experienced between two and four LIRG phases until the present epoch. This scenario is not consistent with the formation of the $z\sim0.7$ LIRGs through the continuous star formation characterizing isolated spiral galaxies as has been independently argued based on their morphology. Instead, minor mergers, tidal interactions, or gas accretion remain plausible triggering mechanisms for more than half of the distant LIRGs that do not harbor the morphology of major mergers.