We present optical spectroscopy of two samples of GALEX grism selected Ly \alpha emitters ( LAEs ) : one at z = 0.195 - 0.44 and the other at z = 0.65 - 1.25 .
We have also observed a comparison sample of galaxies in the same redshift intervals with the same UV magnitude distributions but with no detected Ly \alpha .
We use the optical spectroscopy to eliminate active galactic nuclei ( AGNs ) and to obtain the optical emission-line properties of the samples .
We compare the luminosities of the LAEs in the two redshift intervals and show that there is dramatic evolution in the maximum Ly \alpha luminosity over z = 0 - 1 .
Focusing on the z = 0.195 - 0.44 samples alone , we show that there are tightly defined relations between all of the galaxy parameters and the rest-frame equivalent width ( EW ) of H \alpha .
The higher EW ( H \alpha ) sources all have lower metallicities , bluer colors , smaller sizes , and less extinction , consistent with their being in the early stages of the galaxy formation process .
We find that 75 \pm 12 \% of the LAEs have EW ( H \alpha ) > 100 Å , and , conversely , that 31 \pm 13 \% of galaxies with EW ( H \alpha ) > 100 Å are LAEs .
We correct the broadband magnitudes for the emission-line contributions and use spectral synthesis fits to estimate the ages of the galaxies .
We find a median age of 1.1 \times 10 ^ { 8 } yr for the LAE sample and 1.4 \times 10 ^ { 9 } yr for the UV-continuum sample without detected Ly \alpha .
The median metallicity of the LAE sample is 12 + \log ( O/H ) =8.24 , or about 0.4 dex lower than the UV-continuum sample .