Lyman-α at cosmic noon I: Lyα spectral type selection of z ∼ 2 – 3 Lyman break galaxies with broadband imaging

High-redshift Lyman break galaxies (LBGs) are efficiently selected in deep images using as few as three broadband filters, and have been shown to have multiple intrinsic and small- to large-scale environmental properties related to Lyman-α. In this paper we demonstrate a statistical relationship between net Lyman-α equivalent width (net Lyα EW) and the optical broadband photometric properties of LBGs at z ∼ 2. We show that LBGs with the strongest net Lyα EW in absorption (aLBGs) and strongest net Lyα EW in emission (eLBGs) separate into overlapping but discrete distributions in (U_n−R) colour and R-band magnitude space, and use this segregation behaviour to determine photometric selection criteria by which sub-samples with a desired Lyα spectral type can be selected using data from as few as three broadband optical filters. We propose application of our result to current and future large-area and all-sky photometric surveys that will select hundreds of millions of LBGs across many hundreds to thousands of Mpc, and for which spectroscopic follow-up to obtain Lyα spectral information is prohibitive. To this end, we use spectrophotometry of composite spectra derived from a sample of 798 LBGs divided into quartiles on the basis of net Lyα EW to calculate selection criteria for the isolation of Lyα-absorbing and Lyα-emitting populations of z ∼ 3 LBGs using ugri broadband photometric data from the Vera Rubin Observatory Legacy Survey of Space and Time (LSST).