Cosmic-neighbor-associated distances to VHE and candidate VHE BL Lacs via SDSS photometric redshifts

BL Lac objects have distances that are difficult to estimate because their optical spectra rarely show identifiable emission or absorption lines. We present a method to constrain BL Lac distances by associating them with their cosmic neighborhoods (local overdensities in the cosmic web) identified in optical fields. Distances to galaxies in these neighborhoods are estimated using the Sloan Digital Sky Survey (SDSS) photometric redshifts. Using cosmic-neighborhood associations previously established from multi-object spectroscopy and BL Lacs with spectroscopically measured redshifts as control samples, we find that the redshifts of the associated neighborhoods can be recovered with an accuracy of $\mathrm{\Delta }z\sim 0.02-0.04$. When multiple candidate neighborhoods are present in the field, we rank the candidate associations using a central-location criterion. In 50% of cases, the BL Lac is associated with the correct neighborhood. We provide distance estimates for BL Lac objects without secure redshift measurements, focusing on sources detected at very high energies (VHE; $E>100$,GeV) and on candidate VHE emitters. Combining intervening absorption systems, host-galaxy imaging, $\gamma$-ray constraints, and our SDSS group-association method, we propose likely redshifts for TXS 0141$+$268 ($z\sim 0.93-0.95$), PKS 0735$+$178 ($z=0.64$), 3FHL J0905.5$+$1357 ($z=0.644$), B2 0912$+$29 ($z=0.53$), 3FHL J1120.8$+$4212 ($z=0.363$), BZB J1243$+$3627 ($z=0.485$), 3FHL J1253.1$+$5300 ($z=0.664$), and RX J2156.0$+$1818 ($z=0.635$). Finally, we discuss how forthcoming narrow-band photometric-redshift surveys can improve blazar distance estimates via group-association techniques.