  We use data from the Transiting Exoplanet Survey Satellite (TESS) to search
for, and set limits on, optical to near-infrared photometric variability of the
well-vetted, candidate James Webb Space Telescope (JWST) spectrophotometric
standards. Our search of 37 of these candidate standards has revealed
measurable periodic variability in 15 stars. The majority of those show
variability that is less than half a percent; however, four stars are observed
to vary photometrically, from minimum to maximum flux, by more than 1% (the G
dwarf HD 38949 and three fainter A dwarfs). Variability of this size would
likely impact the error budget in the spectrophotometric calibration of the
science instruments aboard JWST. For the 22 candidate standards with no
detected variability, we report upper limits on the observed changes in flux.
Despite some systematic noise, all stars brighter than 12 magnitude in the TESS
band show a 3 sigma upper limit on the total change in brightness of less than
half a percent on time scales between an hour and multiple weeks, empirically
establishing their suitability as spectrophotometric standards. We further
discuss the value and limits of high-cadence, high-precision photometric
monitoring with TESS as a tool to vet the suitability of stars to act as
spectrophotometric standards.
