The GRAVITY Young Stellar Object survey. VII. The inner dusty disks of T Tauri stars

These protoplanetary disks in T Tauri stars play a central role in star and planet formation. We spatially resolve at sub-au scales the innermost regions of a sample of T Tauri's disks to better understand their morphology and composition. We extended our homogeneous data set of 27 Herbig stars and collected near-IR K-band observations of 17 T Tauri stars, spanning effective temperatures and luminosities in the ranges of ~4000-6000 K and ~0.4-10 Lsun. We focus on the continuum emission and develop semi-physical geometrical models to fit the interferometric data and search for trends between the properties of the disk and the central star. The best-fit models of the disk's inner rim correspond to wide rings. We extend the Radius-luminosity relation toward the smallest luminosities (0.4-10 Lsun) and find the R~L^(1/2) trend is no longer valid, since the K-band sizes measured with GRAVITY are larger than the predicted sizes from sublimation radius computation. No clear correlation between the K-band half-flux radius and the mass accretion rate is seen. Having magnetic truncation radii in agreement with the K-band GRAVITY sizes would require magnetic fields as strong as a few kG, which should have been detected, suggesting that accretion is not the main process governing the location of the half-flux radius of the inner dusty disk. Our measurements agree with models that take into account the scattered light. The N-to-K band size ratio may be a proxy for disentangling disks with silicate features in emission from disks with weak and/or in absorption silicate features. When comparing inclinations and PA of the inner disks to those of the outer disks (ALMA) in nine objects of our sample, we detect misalignments for four objects.