Stellar population studies provide unique clues to constrain galaxy formation models. So far, detailed studies based on absorption line strengths have mainly focused on the optical spectral range although many diagnostic features are present in other spectral windows. In particular, the near-infrared (NIR) can provide a wealth of information about stars, such as evolved giants, that have less evident optical signatures. Due to significant advances in NIR instrumentation and extension of spectral libraries and stellar population synthesis (SPS) models to this domain, it is now possible to perform in-depth studies of spectral features in the NIR to a high level of precision. In the present work, taking advantage of state-of-the-art SPS models covering the NIR spectral range, we introduce a new set of NIR indices constructed to be maximally sensitive to the main stellar population parameters, namely age, metallicity and initial mass function (IMF). We fully characterize the new indices against these parameters as well as their sensitivity to individual elemental abundance variations, velocity dispersion broadening, wavelength shifts, signal-to-noise ratio and flux calibration. We also present, for the first time, a method to ensure that the analysis of spectral indices is not affected by sky contamination, which is a major challenge when dealing with NIR spectroscopy. Moreover, we discuss two main applications: (i) the ability of some NIR spectral indices to constrain the shape of the low-mass IMF and (ii) current issues in the analysis of NIR spectral indices for future developments of SPS modelling.
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