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

Abstract

We present a new technique for the determination of the low-mass slope ($α_1$; $M_* < 0.5 M_{\odot}$) 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 $α_1$ 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 $α_1$ can be precisely determined by applying the unconstrained version of the code to high signal-to-noise datasets (S/N=100, R=7000 yield $Δα_1 \approx 0.1$); (b) the $M/L$ constraint significantly improves the precision and reduces the degeneracies, however its systematic errors will cause biased $α_1$ estimates; (c) standard Lick indices cannot constrain the PDMF because they miss most of the mass function sensitive spectral features; (d) the $α_1$ determination remains unaffected by the high-mass IMF shape ($α_3$; $M_* \ge 1 M_{\odot}$) variation for stellar systems older than 8 Gyr, while the intermediate-mass IMF slope ($α_2$; $0.5 \le M_* < 1 M_{\odot}$) may introduce biases into the best-fitting $α_1$ values if it is different from the canonical value $α_2 = 2.3$. We analysed observed intermediate resolution spectra of ultracompact dwarf galaxies with our technique and demonstrated its applicability to real data.