  One of the main science motivations for the ESA PLAnetary Transit and
Oscillations (PLATO) mission is to measure exoplanet transit radii with 3%
precision. In addition to flares and starspots, stellar oscillations and
granulation will enforce fundamental noise floors for transiting exoplanet
radius measurements. We simulate light curves of Earth-sized exoplanets
transiting continuum intensity images of the Sun taken by the HMI instrument
aboard SDO to investigate the uncertainties introduced on the exoplanet radius
measurements by stellar granulation and oscillations. After modeling the solar
variability with a Gaussian process, we find that the amplitude of solar
oscillations and granulation is of order 100 ppm -- similar to the depth of an
Earth transit -- and introduces a fractional uncertainty on the depth of
transit of 0.73% assuming four transits are observed over the mission duration.
However, when we translate the depth measurement into a radius measurement of
the planet, we find a much larger radius uncertainty of 3.6%. This is due to a
degeneracy between the transit radius ratio, the limb-darkening, and the impact
parameter caused by the inability to constrain the transit impact parameter in
the presence of stellar variability. We find that surface brightness
inhomogeneity due to photospheric granulation contributes a lower limit of only
2 ppm to the photometry in-transit. The radius uncertainty due to granulation
and oscillations, combined with the degeneracy with the transit impact
parameter, accounts for a significant fraction of the error budget of the PLATO
mission, before detector or observational noise is introduced to the light
curve. If it is possible to constrain the impact parameter or to obtain
follow-up observations at longer wavelengths where limb-darkening is less
significant, this may enable higher precision radius measurements.
