Star formation in SFDGs is strongly self regulated. In its simple form it can be quantified as a function of gas temperature and density where the density dependence roughly can be described as a quadratic Schmidt-type law (Schmidt 1959, Larson 1969). As massive stars are formed, the gas is heated and ionized, striving to quench further star formation. But there is also a positive feedback from star formation that seems to stimulate cloud formation, as demonstrated in the correlation between stellar surface density and the presence of young stars (Hunter et al. 1998). Chemodynamical modelling demonstrate that these feedback effects on the order of a few Myr, establishes an equilibrium that stabilizes the star formation (Koeppen et al. 1995). Because of the density dependence, low mass SFDGs consume their gas very slowly, on a time scale larger than a Hubble time (Hunter and Gallagher 1985, Hunter and Elmegreen 2004). occasionally, e.g. when galaxies collide and merge, bursts of star formation may occur. All these basic properties of SFDGs were discussed amost 40 years ago by Searle et al. (1973). Some of the most metal poor galaxies resemble young systems and for a period of time the possibility that these galaxies could be genuinely young was discussed. After a while it became evident that almost all young galaxy candidates hosted a regular component with colours similar to an old stellar population (e.g., Hunter and Gallagher 1985). It is now generally believed that, with few exceptions, the minimum age of the oldest population in the SFDGs is at least 1-2 Gyr. Whether this is true or not for the most widely discussed young galaxy candidate I Zw 18, is still a matter of debate (Östlin 2000, Izotov and Thuan 2004, Tosi et al. 2007) whereas a second young candidate, SBS 0335-052, is still lacking any evidence for the presence of old stars.
While the fundamental principles of local star formation processes can be fairly well understood, the parameters determining the global star formation processes partly have to be determined empirically. We know that small, gas rich SFDGs have consumed less than ~ 5% of their present gas mass in star formation (Schombert et al. 2001). The relative amount of stars increases with luminosity. We can think of three basic scenarios to explain this. Either the star formation efficiency increases with mass so that most of the stars in massive galaxies were formed at high redshifts while the low mass galaxies have had more or less a constant SFR. This is the closed-box scenario. In the other two scenarios the box is open. We can assume that the star formation efficiencies (SFEs) have been comparable but low mass galaxies have to a larger extent renewed their gas supply through a continuous infall of fresh gas. In the third alternative SFEs are similar but we now assume that the massive galaxies have expelled their gas. Finally we have to be open for the possibility both the SFE and the mass in-and outflows are dependent on both the galaxy mass and metallicity. We can hope to distinguish between the alternatives through observations of the chemical abundances and in observations of the environments around the galaxies.
The SFR in low mass galaxies have been determined using different methods: the UV flux, the 7.7µ PAH flux, the FIR dust emission, the radio continuum or the H luminosity (Kennicutt Jr. 1998, Sargsyan and Weedman 2009). While most methods give information about the present SFR, radio continuum fluxes also give a direct measurement of the SFR during the latest 108 years (Condon et al. 2002). The most common method however is to use the H luminosity, after correction for dust extinction. This works quite well in most SFDGs. At higher masses, and in particular in starbursts (Heckman et al. 1998), a substantial fraction of the ionizing radiation is absorbed by dust and extinction corrections are not adequate. Therefore the SFR determined from H has to be supplemented by the amount derived from the far infrared. In low mass galaxies with low SFRs or in LSB galaxies, where the star forming regions are sparsely distributed, we notice a significant difference between the SFR determined from H as that derived from the UV flux (but see Lee et al. 2009, Lee et al. 2010). These observations and recent analyses of GALEX data (Lee et al. 2011) indicate that stochastic effects due to low SFR per area have more impact on H than on the UV fluxes, representing a broader range in stellar mass. UV fluxes therefore may be more useful to measure SFR in the low mass - low surface luminosity end.
Using H, Kennicutt Jr. (1989) studied star formation in disk galaxies and found that the SFRs declined dramatically at a H I surface density of 3-4 M / pc2. He derived a value for this critical column density from the Toomre criterion. In a later investigation Kennicutt Jr. (1998) derived a relation between SFR and gas over a wide mass range, incorporating dwarfs as well as massive starburst galaxies. He found that the SFR follows the relation nowadays called the Kennicutt-Schmidt law, i.e. SFR g1.4, where g is the gas surface mass density. As a first approximation one may interpret this relation if the SFR is a product between the surface mass density and the collapse time of a supermassive molecular cloud. But Kennicutt also found that the SFR correlated with the rotation period of the disk so there must also be some dynamics involved. How valid are these relations for the SFDGs? In a study of star formation in dI galaxies, Hunter et al. (1998) found that gas was a factor of ~ 2 lower than the critical density in disk galaxies. In the FIGGS survery, the low mass end of SFDGs is mapped in H I (Roychowdhury et al. 2009). Some of the galaxies investigated, as well as other dIs, have surface densities below the critical limit. The FIGGS survey contains galaxies with surface densities constantly below the Kennicutt threshold. The median H I mass of 2.8 × 107 M and a median blue magnitude MB = -13.2. These galaxies do have lower SFR than the Kennicutt-Schmidt law predicts but star formation is not completely halted. They should be quite relevant as templates for the first generation galaxies in the early universe.
Star formation cannot occur without formation of molecular clouds. All massive molecular clouds collapse and form stars. This is evident from the nearly linear relation between SFR and mass of molecular clouds (Leroy et al. 2005). Leroy et al. calculated the ratio between molecular gas mass and K luminosity, B luminosity, FIR luminosity and dynamical mass. Somewhat surprisingly these ratios were not found to vary significantly along the Hubble sequence. The dwarf galaxies in this respect are just scaled down versions of larger galaxies. The molecular mass is proportional to the stellar mass. The Mmol / Mmol+HI ratio however, increases with mass. Thus, the more massive galaxies are more efficient in forming molecular clouds, probably as an effect of increasing pressure with gas mass. The resulting increased density in the gas governs the formation of molecules. The scatter in the SFR-Mmol relation however increases with decreasing mass and as mentioned above the H2 content of low mass SFDGs is still an open issue.
In previous sections we discussed the star formation activity in different SFDG types based on the B luminosity. A more accurate information be be obtained from H. Hunter and Elmegreen (2004) investigated over 100 SFDGs and compared the SFR between galaxies of types classified as Im, BCDs, Sm and Sab-Sd galaxies. A prominent difference between BCDs and the other types is the high concentration of star formation towards the centre in BCGs and that there is a much stronger gradient in the ratio between the H and V luminosities. This indicates that gas recently migrated from the outer regions to the inner within one gigayear. As a consequence, the gas surface densities have increased. Consequently, applying the Kennicutt-Schmidt law, the star formation rate per gas mass has increased and the surface brightness is higher. The star formation efficiency, however, does not seem to be significantly higher in BCDs compared to the other types.
In the 11HUGS survey, ~300 SFDGs within the 11 Mpc distance are imaged in H and UV. An important result is that most of the stars formed in these galaxies are formed in a quiescent mode. Only about 1/4 are formed in bursts and only a few % of the galaxies are now in a bursting mode (in their study a burst was defined as a galaxy having an equivalent width in H, EW(H) > 100Å). This result is in agreement with the star formation properties of galaxies in the SDSS where it is argued that 20% of the star formation occurs in bursts (Brinchmann et al. 2004).
This modest, well regulated SF activity is confirmed also in more detailed studies of galaxies the backyard universe. Recently a study of colour-magnitude diagrams of 60 local dwarf galaxies from the ANGST project was presented (Weisz et al. 2011). Almost 80% of these are SFDGs. The galaxies range in MB from -8.23 to -17.77 and in distance from 1.3 to 4.6 Mpc. It was found that on average, the typical dwarf galaxy formed 50% of its stellar mass by z ~ 2 and 60% by z ~ 1. Much of the differences between the different morphological types (including dSph) occur during the latest 1 Gyr and is strongly environmentally dependent. Stellar feedback seems to have less importance for the transition between the different types. Instead, a mechanism of the type 'tidal stirring' (Mayer et al. 2001, Mayer et al. 2001, Mayer et al. 2006) seems to be more attractive. A simple description of the SF history, as e.g an exponentially decaying SF, appears to be inconsistent with the observations. A more complex SF history is needed.