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 (${\alpha }_1$; $M_{\ast }<0.5M_{\odot }$) 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 (${\alpha }_3$; $M_{\ast }\ge 1M_{\odot }$) variation for stellar systems older than 8 Gyr, while the intermediate-mass IMF slope (${\alpha }_2$; $0.5\le M_{\ast }<1M_{\odot }$) 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.

Accepted to MNRAS, 7 pages, 4 figures

References in corpus (11)

• Evidence for top-heavy stellar initial mass functions with increasing density and decreasing metallicity
• The Nature of UCDs: Internal Dynamics from an Expanded Sample and Homogeneous Database
• Evolution of dwarf early-type galaxies I. Spatially resolved stellar populations and internal kinematics of Virgo cluster dE/dS0 galaxies
• Why haven't loose globular clusters collapsed yet?
• Halo globular clusters observed with AAOmega: dark matter content, metallicity and tidal heating
• Kinematics and stellar populations of the dwarf elliptical galaxy IC 3653
• A comprehensive Nbody study of mass segregation in star clusters: Energy equipartition and escape
• The influence of gas expulsion and initial mass-segregation on the stellar mass-function of globular star clusters
• The chemical composition of Ultracompact Dwarf Galaxies in the Virgo and Fornax Clusters
• Searches for Ultra-Compact Dwarf Galaxies in Galaxy Groups
• Stellar Population Constraints on the Dark Matter Content and Origin of Ultra-Compact Dwarf Galaxies

Cited by in corpus (5)

• The Dawes Review 8: Measuring the Stellar Initial Mass Function
• Radial Trends in IMF-Sensitive Absorption Features in Two Early-Type Galaxies: Evidence for Abundance-Driven Gradients
• Isolated compact elliptical galaxies: Stellar systems that ran away
• Measuring the stellar population parameters of the early-type galaxy NGC 3923 -- The challenging measurement of the initial mass function
• Explaining the stellar initial mass function with the theory of spatial networks