  Transmission spectroscopy is currently the technique best suited to study a
wide range of planetary atmospheres, leveraging the filtering of a star's light
by a planet's atmosphere rather than its own emission. However, as both a
planet and its star contribute to the information encoded in a transmission
spectrum, an accurate accounting of the stellar contribution is pivotal to
enabling robust atmospheric studies. As current stellar models lack the
required fidelity for such accounting, we investigate here the capability of
time-resolved spectroscopy to yield high-fidelity, empirical constraints on the
emission spectra of stellar surface heterogeneities (i.e., spots and faculae).
Using TRAPPIST-1 as a test case, we simulate time-resolved JWST/NIRISS spectra
and demonstrate that with a blind approach incorporating no physical priors, it
is possible to constrain the photospheric spectrum to less than 0.5% and the
spectra of stellar heterogeneities to within 10%, a precision that enables
photon-limited (rather than model-limited) science. Now confident that
time-resolved spectroscopy can propel the field in an era of robust
high-precision transmission spectroscopy, we introduce a list of areas for
future exploration to harness its full potential, including wavelength
dependency of limb darkening and hybrid priors from stellar models as a means
to further break the degeneracy between the position, size, and spectra of
heterogeneities.
