Stellar population models based on the SDSS-IV MaStar library of stellar spectra. I. Intermediate-age/old models

We use the first release of the SDSS/MaStar stellar library comprising 8646, high (>50) S/N spectra, to calculate integrated spectra of stellar population models. The model spectra cover the wavelength range 0.36-1.03 micron and share the same spectral resolution (R=1800) and flux calibration as the SDSS-IV/MaNGA galaxy data. The parameter space covered by the stellar spectra collected thus far allows the calculation of models with chemical composition -2 <= [Z/H] <= + 0.35 and ages larger than ~200 Myr. These ranges will be extended as MaStar collects further data. Notably, we are able to include spectra for dwarf Main Sequence (MS) stars close to the core H-burning limit of 0.1 Msun. We are also able to include the contribution of cold and metal-rich giants, which manifest themselves with strong absorption bands between 7000 and 10,000 Angstrom. These features will be important for modelling the spectra of massive galaxies. Other novelties include better coverage of the HR diagram at low-metallicity, where we can calculate models as young as 500 Myr. Additionally, we fully include the Blue Horizontal Branch phase. We present models adopting two sets of stellar parameters (T_{eff}, logg, [Z/H]). In a novel approach, the reliability of stellar parameters is tested 'on the fly' using the stellar population models themselves. We test the age and metallicity scale of the new models with Milky Way and Magellanic Clouds GCs with independently measured age and chemical composition. We find that the new MaStar-based models are able to recover ages and metallicities remarkably well, with systematics as low as a few percent for calibration sets with homogeneously derived ages and metallicities. We also fit a MaNGA galaxy spectrum, finding that the new models gain fitting residuals of the order of a few percent comparable to the state-of-art models, but now over a wider wavelength range.