  (Abridged) The rest-frame near-IR spectra of intermediate age (1-2 Gyr)
stellar populations are dominated by carbon based absorption features offering
a wealth of information. Yet, spectral libraries that include the near-IR
wavelength range do not sample a sufficiently broad range of ages and
metallicities to allow for accurate calibration of stellar population models
and thus the interpretation of the observations. In this paper we investigate
the integrated J- and H-band spectra of six intermediate age (1-3 Gyr) and old
(>10 Gyr) globular clusters in the Large Magellanic Cloud, using observations
obtained with the SINFONI IFU at the VLT. H-band C2 and K-band 12CO(2-0)
feature strengths are compared to the models of Maraston (2005). C2 is
reasonably well reproduced by the models at all ages, while 12CO(2-0) shows
good agreement for older (age>2 Gyr) populations, but the younger (1.3 Gyr)
globular clusters do not follow the models. We argue that this is due to the
fact that the empirical calibration of the models relies on only a few Milky
Way carbon star spectra, which show different 12CO(2-0) index strengths than
the LMC stars. The C2 absorption feature strength correlates strongly with age.
It is present essentially only in populations that have 1-2 Gyr old stars,
while its value is consistent with zero for older populations. The distinct
spectral energy distribution observed for the intermediate age globular
clusters in the J- and H-bands agrees well with the model predictions of
Maraston for the contribution from the thermally pulsing asymptotic giant
branch phase (TP-AGB). We show that the H-band C2 absorption feature and the
J-, H-band spectral shape can be used as an age indicator for intermediate age
stellar populations in integrated spectra of star clusters and galaxies.

Cosmology and Nongalactic Astrophysics