We present a new technique for the determination of the low-mass slope (α1; M*⊙) of the present-day stellar mass function (PDMF) using the pixel-space fitting of integrated light spectra. The technique can be used to constrain the initial mass function (IMF) of stellar systems with relaxation time-scales exceeding the Hubble time and to test the IMF universality hypothesis. We provide two versions of the technique: (i) a fully unconstrained determination of the age, metallicity and α1; and (ii) a constrained fitting by imposing the externally determined mass-to-light ratio of the stellar population. We tested our approach with Monte Carlo simulations using mock spectra and conclude that: (i) age, metallicity and α1 can be precisely determined by applying the unconstrained version of the code to high signal-to-noise ratio data sets (S/N = 100, R = 7000 yields Δα1 ≈ 0.1); (ii) the M/L constraint significantly improves the precision and reduces the degeneracies; however, its systematic errors cause biased α1 estimates; (iii) standard Lick indices cannot constrain the PDMF because they miss most of the mass function-sensitive spectral features; (iv) the α1 determination remains unaffected by the high-mass IMF shape (α3; M* ≥ 1 M⊙) variation for stellar systems older than 8 Gyr, while the intermediate-mass IMF slope (α2; 0.5 ≤ M*⊙) may introduce biases into the best-fitting α1 values if it is different from the canonical value α2 = 2.3. We analysed observed intermediate-resolution spectra of ultracompact dwarf galaxies with our technique and demonstrated its applicability to real data.
