  The Transiting Exoplanet Survey Satellite (TESS) has an exceptionally large
plate scale of 21"/px, causing most TESS light curves to record the blended
light of multiple stars. This creates a danger of misattributing variability
observed by TESS to the wrong source, which would invalidate any analysis. We
develop a method that can localize the origin of variability on the sky to
better than one fifth of a pixel. Given measured frequencies of observed
variability (e.g., from periodogram analysis), we show that the corresponding
best-fit sinusoid amplitudes to raw light curves extracted from each pixel are
distributed the same as light from the variable source. The primary assumption
of this method is that other nearby stars are not variable at the same
frequencies. Essentially, we are using the high frequency resolution of TESS to
overcome limitations from its low spatial resolution. We have implemented our
method in an open source Python package, TESS Localize
(github.com/Higgins00/TESS-Localize), that determines the location of a
variable source on the sky given TESS pixel data and a set of observed
frequencies of variability. Our method utilizes the TESS Pixel Response
Function models, and we characterize systematics in the residuals of fitting
these models to data. Given the ubiquity of source blending in TESS light
curves, verifying the source of observed variability should be a standard step
in TESS analyses.
