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CCD $B-$ and $I-$band surface photometry is presented for a sample of 51 dwarf and low surface brightness galaxies. The main selection criterion was their extremely narrow HI linewidths ($\Delta{V}_{20}<100~{\rm km~s}^{-1}$), chosen in order to examine the Tully--Fisher (TF) relation between linewidth and absolute magnitude at the low--luminosity end. In this regime, a substantial fraction of the linewidth is attributable to turbulent rather than rotational motion. Therefore, it is not surprising that the original TF relation, an expression of the scaling relation between mass (from the linewidth due to rotation) and luminosity, does not hold in this regime.
If we assume the linewidth is due to both turbulent and rotational motion, we obtain a mass for the dwarfs which does correlate with luminosity. However, the relation is distinct from the TF relation for spirals, and indicates the presence of an increasing amount of dark matter at low luminosities. We find that the locus of dwarf galaxies in the mass/luminosity plane is well fit by the theoretical prediction of Dekel \& Silk [1986, ApJ, 303, 39], $M/L\propto{L}^{-0.37}$, where $M/L$ decreases with increasing $L$, while the spirals follow a relation in which $M/L$ increases with increasing $L$ ($M/L\propto{L}^{0.2}$), which corresponds to the observed slope ($\sim{7}$) of the TF relation for spirals. For dwarfs fainter than $L_B/L_{\odot} \sim{10^7}$, the observed $M/L$ is $\sim{20}$, while it drops to unity for $L_B/L_{\odot} \sim{10^{9.5}}$.
The Dekel--Silk relation arises in low mass systems with massive dark halos which undergo extensive mass loss due to supernova--driven winds. The halo allows the galaxy to remain bound even as most of the gas is removed, drastically reducing the rate of star formation. The trend towards higher $M/L$ at lower $L$ is the result of the lower escape velocity of the less massive systems, allowing the gas to be removed more efficiently.
The same relation has previously been seen to hold for dwarf Spheroidal galaxies, providing further evidence for a common evolutionary history of these two types of dwarf systems, radically different from ``normal'' early-- and late--type galaxies.
