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
($\alpha_1$; $M_* < 0.5 M_{\odot}$) of the present day stellar mass function
(PDMF) using the pixel space fitting of integrated light spectra. It can be
used to constrain the initial mass function (IMF) of stellar systems with
relaxation timescales exceeding the Hubble time and testing the IMF
universality hypothesis. We provide two versions of the technique: (1) a fully
unconstrained determination of the age, metallicity, and $\alpha_1$ and (2) a
constrained fitting by imposing the externally determined mass-to-light ratio
of the stellar population. We have tested our approach by Monte-Carlo
simulations using mock spectra and conclude that: (a) age, metallicity and
$\alpha_1$ can be precisely determined by applying the unconstrained version of
the 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 the
precision and reduces the degeneracies, however its systematic errors will
cause biased $\alpha_1$ estimates; (c) standard Lick indices cannot constrain
the PDMF because they miss most of the mass function sensitive spectral
features; (d) the $\alpha_1$ determination remains unaffected by the high-mass
IMF shape ($\alpha_3$; $M_* \ge 1 M_{\odot}$) variation for stellar systems
older than 8 Gyr, while the intermediate-mass IMF slope ($\alpha_2$; $0.5 \le
M_* < 1 M_{\odot}$) may introduce biases into the best-fitting $\alpha_1$
values if it is different from the canonical value $\alpha_2 = 2.3$. We
analysed observed intermediate resolution spectra of ultracompact dwarf
galaxies with our technique and demonstrated its applicability to real data.
