  The high-energy radiation fields of T Tauri stars (TTS) should affect the
surrounding circumstellar disk, having implications for disk transport and
heating. Yet, observational evidence of the effect of high-energy fields on
disks is scarce. Here we investigate the connection between X-ray emission and
the innermost gas disk by leveraging the variability of TTS. We obtained
multiple epochs of coordinated data (taken either simultaneously or within a
few hours) of accreting TTS with the Hubble Space Telescope, the Neil Gehrels
Swift Observatory, and the Chandra X-ray Observatory. We measured the
far-ultraviolet (FUV) H2 bump feature at 1600 A, which traces gas <1 AU from
the star; the near-ultraviolet (NUV) emission, from which we extract the
accretion luminosity; and also the X-ray luminosity. We do not find a
correlation between the FUV H2 bump and X-ray luminosity. Therefore, an
observable tracer of the effect of X-ray ionization in the innermost disk
remains elusive. We report a correlation between the FUV H2 bump and accretion
luminosity, linking this feature to the disk surface density. We also see a
correlation between the X-ray luminosity and the accretion column density,
implying that flaring activity may influence accretion. These results stress
the importance of coordinated multiwavelength work to understand TTS.
