Probing the 2D temperature structure of protoplanetary disks with
  Herschel observations of high-J CO lines
  The gas temperature structure of protoplanetary disks is a key ingredient for
interpreting various disk observations and for quantifying the subsequent
evolution of these systems. The comparison of low- and mid-$J$ CO rotational
lines is a powerful tool to assess the temperature gradient in the warm
molecular layer of disks. Spectrally resolved high-$J$ ($J_{\rm u} > 14$) CO
lines probe intermediate distances and heights from the star that are not
sampled by (sub-)millimeter CO spectroscopy. This paper presents new {\it
Herschel}/HIFI and archival PACS observations of $^{12}$CO, $^{13}$CO and \cii
\ emission in 4 Herbig AeBe (HD 100546, HD 97048, IRS 48, HD 163296) and 3 T
Tauri (AS 205, S CrA, TW Hya) disks. In the case of the T Tauri systems AS 205
and S CrA, the CO emission has a single-peaked profile, likely due to a slow
wind. For all other systems, the {\it Herschel} CO spectra are consistent with
pure disk emission and the spectrally-resolved lines (HIFI) and the CO
rotational ladder (PACS) are analyzed simultaneously assuming power-law
temperature and column density profiles, using the velocity profile to locate
the emission in the disk. The temperature profile varies substantially from
disk to disk. In particular, $T_{\rm gas}$ in the disk surface layers can
differ by up to an order of magnitude among the 4 Herbig AeBe systems with HD
100546 being the hottest and HD 163296 the coldest disk of the sample. Clear
evidence of a warm disk layer where $T_{\rm gas} > T_{\rm dust}$ is found in
all the Herbig Ae disks. The observed CO fluxes and line profiles are compared
to predictions of physical-chemical models. The primary parameters affecting
the disk temperature structure are the flaring angle, the gas-to-dust mass
ratio the scale height and the dust settling.
