  The James Webb Space Telescope will provide observational capabilities that
far exceed those of current ground- or space-based instrumentation. In
particular, the NIRSpec instrument will take highly sensitive spectroscopic
data for hundreds of objects simultaneously from 0.6-5.3 microns. Current
photometric observations suggest a large and increasing number of faint (M_UV >
-16) galaxies at high-redshift, with increasing evidence that galaxies at these
redshifts have optical emission lines with extremely high equivalent widths. A
simple model of their emission line fluxes and number density evolution with
redshift is used to predict the number of galaxies that NIRSpec will
serendipitously observe during normal observations with the microshutter array.
At exposure times of ~20 hours in the low-resolution prism mode, the model
predicts that, on average, every open 1x3 'microslit' will contain an
un-targeted galaxy with a detectable [O III] and/or H$\alpha$ emission line;
while most of these detections are predicted to be of [O III], H $\alpha$
detections alone would still number 0.56 per open 'microslit' for this exposure
time. Many of these objects are spectroscopically detectable even when they are
fainter than current photometric limits and/or their flux centroids lie outside
of the open microshutter area. The predicted number counts for such galaxies
match z ~ 2 observations of [O III] emitters from slitless grism spectroscopic
surveys, as well as theoretical predictions based on sophisticated modeling of
galaxy spectral energy distributions. These serendipitous detections could
provide the largest numbers of z > 6 spectroscopic confirmations in the deepest
NIRSpec surveys.
