Transitional disks are protoplanetary disks around young stars, with inner
holes or gaps which are surrounded by optically thick outer, and often inner,
disks. Here we present observations of 62 new transitional disks in the Orion A
star-forming region. These were identified using the \textit{Spitzer Space
Telescope}'s Infrared Spectrograph and followed up with determinations of
stellar and accretion parameters using the Infrared Telescope Facility's SpeX.
We combine these new observations with our previous results on transitional
disks in Taurus, Chamaeleon I, Ophiuchus and Perseus, and with archival X-ray
observations. This produces a sample of 105 transitional disks of "cluster" age
3 Myr or less, by far the largest hitherto assembled. We use this sample to
search for trends between the radial structure in the disks and many other
system properties, in order to place constraints on the possible origins of
transitional disks. We see a clear progression of host star accretion rate and
the different disk morphologies. We confirm that transitional disks with
complete central clearings have median accretion rates an order of magnitude
smaller than radially continuous disks of the same population. Pre-transitional
disks --- those objects with gaps that separate inner and outer disks --- have
median accretion rates intermediate between the two. Our results from the
search for statistically significant trends, especially related to M˙,
strongly support that in both cases the gaps are far more likely to be due to
the gravitational influence of Jovian planets or brown dwarfs orbiting within
the gaps, than to any of the photoevaporative, turbulent or grain-growth
processes that can lead to disk dissipation. We also find that the fraction of
Class II YSOs which are transitional disks is large, 0.1-0.2, especially in the
youngest associations.Comment: 96 pages, 25 figures, resubmitted to Ap
