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We present a new technique for the determination of the low-mass slope($\alpha_1$; $M_* < 0.5 M_{\odot}$) of the present day stellar mass function(PDMF) using the pixel space fitting of integrated light spectra. It can beused to constrain the initial mass function (IMF) of stellar systems withrelaxation timescales exceeding the Hubble time and testing the IMFuniversality hypothesis. We provide two versions of the technique: (1) a fullyunconstrained determination of the age, metallicity, and $\alpha_1$ and (2) aconstrained fitting by imposing the externally determined mass-to-light ratioof the stellar population. We have tested our approach by Monte-Carlosimulations using mock spectra and conclude that: (a) age, metallicity and$\alpha_1$ can be precisely determined by applying the unconstrained version ofthe code to high signal-to-noise datasets (S/N=100, R=7000 yield $\Delta\alpha_1 \approx 0.1$); (b) the $M/L$ constraint significantly improves theprecision and reduces the degeneracies, however its systematic errors willcause biased $\alpha_1$ estimates; (c) standard Lick indices cannot constrainthe PDMF because they miss most of the mass function sensitive spectralfeatures; (d) the $\alpha_1$ determination remains unaffected by the high-massIMF shape ($\alpha_3$; $M_* \ge 1 M_{\odot}$) variation for stellar systemsolder than 8 Gyr, while the intermediate-mass IMF slope ($\alpha_2$; $0.5 \leM_* < 1 M_{\odot}$) may introduce biases into the best-fitting $\alpha_1$values if it is different from the canonical value $\alpha_2 = 2.3$. Weanalysed observed intermediate resolution spectra of ultracompact dwarfgalaxies with our technique and demonstrated its applicability to real data.

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