We compare the H \beta line strengths of 1.90 < z < 2.35 star-forming galaxies observed with the near-IR grism of the Hubble Space Telescope with ground-based measurements of Ly \alpha from the HETDEX Pilot Survey and narrow-band imaging .
By examining the line ratios of 73 galaxies , we show that most star-forming systems at this epoch have a Ly \alpha escape fraction below \sim 6 \% .
We confirm this result by using stellar reddening to estimate the effective logarithmic extinction of the H \beta emission line ( c _ { { H } \beta } = 0.5 ) and measuring both the H \beta and Ly \alpha luminosity functions in a \sim 100 , 000 Mpc ^ { 3 } volume of space .
We show that in our redshift window , the volumetric Ly \alpha escape fraction is at most 4.4 ^ { +2.1 } _ { -1.2 } \% , with an additional systematic \sim 25 \% uncertainty associated with our estimate of extinction .
Finally , we demonstrate that the bulk of the epoch ’ s star-forming galaxies have Ly \alpha emission line optical depths that are significantly greater than that for the underlying UV continuum .
In our predominantly [ O III ] \lambda 5007 -selected sample of galaxies , resonant scattering must be important for the escape of Ly \alpha photons .