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Star forming dwarf galaxies (SFDGs) are characterized by low mass, low chemical abundances, high gas and dark matter (DM) content. They constitute one of the most common types of galaxies in the local universe (e.g., de Lapparent 2003) and increase in importance with redshift. SFDGs reside in low density environments, mostly with lack of massive neighbors (Weisz et al. 2011, Weisz et al. 2011). In this review, with focus on starburst dwarfs, we will consider a range of morphological types - Sm/Im, dI, gas rich low surface brightness galaxies (LSBGs) and blue compact galaxies (BCGs).

More than 70% of all galaxies in the local universe are SFDGs (Karachentsev et al. 2004). Most of these live a quiet family life and consume their gas at a slow pace (e.g. Lee et al. 2009). This leads to a modest chemical enrichment, in the low mass end probably further diluted by selective metal ejection by stellar winds or infall of fresh gas. Occasionally SFDGs go wild and enter a starburst phase but in most cases eventually return to the quiescent phase without changing their properties radically. Most of the basic characteristics of SFDGs have been summarized in the review paper by Gallagher III and Hunter (1984).

There is no commonly accepted definition of a dwarf galaxy. In the traditional sense (Hodge 1971), a dwarf refers to a galaxy of low luminosity and small size and low surface brightness. Sometimes only one of these criteria is used (e.g. Hunter and Gallagher 1986, Tammann 1980, Pildis et al. 1997). Normally a magnitude limit of MB ~ -16 is applied and this is useful under normal conditions. But gas rich galaxies can change the luminosity and surface brightness drastically if they enter into a starburst phase violating both the luminosity and the surface brightness criteria. A mass constraint combined with a relative gas mass fraction is probably the most relevant (but hard to apply) way of characterizing a SFDG.

As is evident from studies of the local sample of SFDGs (e.g. Grebel 1997, Skillman et al. 2003, Tolstoy et al. 2009, Weisz et al. 2011), the details of the star formation history (SFH) of SFDGs can be very different from individual to individual. Over long time scales it is controlled by feedback processes (Meurer et al. 1995) and environmental influences. Starburst galaxies are rare and, in the present epoch, do not significantly influence the evolution of star forming dwarfs as a type (Gallagher III et al. 1984, Brinchmann et al. 2004, Lee et al. 2009). On the individual level however, starbursts may significantly alter the conditions momentarily although it seems unlikely that a major fraction of the gas can be permanently expelled as a consequence of the supernovae winds and thus transform a gas rich galaxy to a gas poor. An increase in the star formation rate (SFR) with a factor of 2-3 may be sustained over long time periods while it is unclear if an extraordinary increase in SFR can survive over a time long enough to consume a significant fraction of the gas before it is quenched by feedback effects. The major difference between the bursting state and the normal one seems rather to be the mode of star formation, the tendency for stars to form in super star clusters (SSCs) (e.g. Meurer et al. 1995, Adamo et al.2010) and possibly switch to a flatter IMF (Scalo 1990, Harayama et al. 2008, Weidner et al. 2011).

Why is it interesting to study SFDGs? In many respects these galaxies resemble our notions of the fundamental building blocks of galaxies in the early universe. Very likely, the first dwarf population was the main driver of the cosmic reionization. Searches for Lyman continuum leakage from local SFDGs are therefore important to better constrain the intergalactic ionization field in the early days.

Simulations of structure formation show that dwarfs merge into more massive units. Locally, we can directly study this process and its effect on the star formation, morphology and gas content. We can learn about star formation processes, shocks and chemical pollution. The lack of shear and the slow rotation of low mass SFDGs open for direct studies of the star formation processes and its evolution over long time scales. The rich variation in star formation histories (SFHs) and the frequent occurrence of SFDGs in the local universe give us a wealth of information in great detail. The low dust content make them transparent and relatively easy to study. Finally, dwarfs help us to understand the nature of dark matter (DM). It is still a puzzle why dwarfs have such a surprisingly low baryon/DM ratio with respect to the cosmic value (McGaugh et al. 2010).

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