A new technique for the determination of the initial mass function in unresolved stellar populations

We present a new technique for the determination of the low-mass slope (alpha(1); M-* < 0.5 M-circle dot) 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 alpha(1); 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 alpha(1) 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 delta alpha(1) approximate to 0.1); (ii) the M/L constraint significantly improves the precision and reduces the degeneracies; however, its systematic errors cause biased alpha(1) estimates; (iii) standard Lick indices cannot constrain the PDMF because they miss most of the mass function-sensitive spectral features; (iv) the alpha(1) determination remains unaffected by the high-mass IMF shape (alpha(3); M-* >= 1 M-circle dot) variation for stellar systems older than 8 Gyr, while the intermediate-mass IMF slope (alpha(2); 0.5 < M-* < 1 M-circle dot) may introduce biases into the best-fitting alpha(1) values if it is different from the canonical value alpha(2) = 2.3. We analysed observed intermediate-resolution spectra of ultracompact dwarf galaxies with our technique and demonstrated its applicability to real data.