Lyman-alpha at Cosmic Noon I: Ly-alpha 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-alpha. In this paper we demonstrate a statistical relationship between net Lyman-alpha equivalent width (net Lya EW) and the optical broadband photometric properties of LBGs at z~2. We show that LBGs with the strongest net Lya EW in absorption (aLBGs) and strongest net Lya 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 criteria by which sub-samples with a desired Lya 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 Lya 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 Lya EW to calculate criteria for the selection of Lya absorbing and Lya emitting populations of z~3 LBGs using $ugri$ broadband photometric data from the Vera Rubin Observatory Legacy Survey of Space and Time (LSST).