On the interplay between flaring and shadowing in disks around Herbig Ae/Be stars

Context. Based on their spectral energy distribution, Herbig stars have been categorized into two observational groups, reflecting their overall disk structure: group I members have disks with a high degree of flaring as opposed to their group II counterparts. Literature results show that the structure of the disk is a strong function of the disk mass in mu m-sized dust grains. Aims. We investigate the 5-35 mu m Spitzer IRS spectra of a sample of 13 group I sources and 20 group II sources. We focus on the continuum emission to study the underlying disk geometry. Methods. We have determined the [30/13.5] and [13.5/7] continuum flux ratios. The 7-mu m flux excess with respect to the stellar photosphere is measured, as a marker for the strength of the near-IR emission produced by the hot inner disk. We have compared our data to the spectra produced by self-consistent passive-disk models, for which the same quantities were derived. Results. We confirm the results by Meijer et al. (2008, A&A, 492, 451) that the differences in continuum emission between group I and II sources can largely be explained by a difference in amount of small dust grains. However, we report a strong correlation between the [30/13.5] and [13.5/7] flux ratios for Meeus group II sources. Moreover, the [30/13.5] flux ratio decreases with increasing 7-mu m excess for all targets in the sample. To explain these correlations with the models, we need to introduce an artificial scaling factor for the inner disk height. In roughly 50% of the Herbig Ae/Be stars in our sample, the inner disk must be inflated by a factor 2 to 3 beyond what hydrostatic calculations predict. Conclusions. The total disk mass in small dust grains determines the degree of flaring. We conclude, however, that for any given disk mass in small dust grains, the shadowing of the outer (tens of AU) disk is determined by the scale height of the inner disk (similar to 1 AU). The inner disk partially obscures the outer disk, reducing the disk surface temperature. Here, for the first time, we prove these effects observationally.