  We present the first dynamical mass measurements for Lyman alpha galaxies at
high redshift, based on velocity dispersion measurements from rest-frame
optical emission lines and size measurements from HST imaging, for a sample of
nine galaxies drawn from four surveys. These measurements enable us to study
the nature of Lyman alpha galaxies in the context of galaxy scaling relations.
The resulting dynamical masses range from 1e9 to 1e10 solar masses. We also fit
stellar population models to our sample, and use them to plot the Lyman alpha
sample on a stellar mass vs. line width relation. Overall, the Lyman alpha
galaxies follow well the scaling relation established by observing star forming
galaxies at lower redshift (and without regard for Lyman alpha emission),
though in 1/3 of the Lyman alpha galaxies, lower-mass fits are also acceptable.
In all cases, the dynamical masses agree with established stellarmass-linewidth
relation. Using the dynamical masses as an upper limit on gas mass, we show
that Lyman alpha galaxies resemble starbursts (rather than "normal" galaxies)
in the relation between gas mass surface density and star formation activity,
in spite of relatively modest star formation rates. Finally, we examine the
mass densities of these galaxies, and show that their future evolution likely
requires dissipational ("wet") merging. In short, we find that Lyman alpha
galaxies are low mass cousins of larger starbursts.
