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The expected episodic or intermittent star formation histories (SFHs) of gasrich dwarf irregular galaxies (dIrrs) are the longstanding puzzles tounderstand their whole evolutional history. Solving this puzzle, we shouldgrasp what physical mechanism causes the quiescent phase of star formationunder the very gas rich condition after the first starburst phase. We considerthat this quiescent phase is kept by lack of H2, which can be important coolantto generate the next generation of stars in the low-metal environment likedIrrs. Furthermore, in dIrrs, H2 formation through gas-phase reactions maydominate the one on dust-grain surfaces because their interstellar medium (ISM)are very plentiful and the typical dust-to-gas ratio of dIrrs (D_dIrrs = 1.31 x10^-2 D_MW, where D_MW is its value for the local ISM) is on the same orderwith a critical value D_cr ~ 10^-2 D_MW. We show that the lack of H2 is mainlyled by H- destruction when gas-phase H2 formation dominates since H- isimportant intermediary of gas-phase H2 formation. H- is destroyed by theradiation from all stars born in the previous starburst phase because H-destroying infrared photon can penetrate the whole ISM of dIrrs. Consideringthe physical process which timescale is the longest as main process inregulating global star formation, we can show this lack of H2 leads thequiescent phase of star formation. Hence, we can say that the stellar radiationwhich destroys H- and leads low H2 abundance should be properly treated instudying SFHs of dIrrs.Comment: 4 pages, 4 figures, accepted for publication in the Astronomy &  Astrophysics Letter

The self regulating star formation of gas rich dwarf galaxies in quiescent phase