Galactic Stellar and Substellar Initial Mass Function

TL;DR

This work provides a comprehensive synthesis of the Galactic IMF across disks, spheroid, globular clusters, and young populations, showing a robust two-regime shape: a power-law at high masses and a lognormal form at low masses. By combining luminosity functions with mass–luminosity relations, it derives present-day and initial mass distributions for stars and brown dwarfs, including binary-correction effects, and links these to Galactic mass-to-light ratios. It finds that brown dwarfs contribute significantly to the substellar census, while the spheroid and globular clusters favor a higher characteristic mass and a negligible brown dwarf population, implying environmental and metallicity influences. Theoretical interpretation favors turbulence-driven fragmentation as a plausible mechanism for the IMF’s universal shape, with primordial IMFs possibly top-heavy and a declining characteristic mass toward the present epoch, shaping the Galaxy’s light, mass budget, and chemical evolution.

Abstract

We review recent determinations of the present day and initial mass functions in various components of the Galaxy, disk, spheroid, young and globular clusters. As a general feature, the IMF is well described by a power-law form for $m\ga 1 \msol$ and a lognormal form below. The extension of the disk IMF into the brown dwarf (BD) regime is in good agreement with observations and yields a disk BD number-density comparable to the stellar one $\sim 0.1 \pc3$. The IMF of young clusters is found to be consistent with the disk field IMF, providing the same correction for unresolved binaries. The spheroid IMF relies on much less robust grounds. Within all the uncertainties, it is found to be similar to the one derived for globular clusters, and is well represented also by a lognormal form with a characteristic mass slightly larger than for the disk. The IMF characteristic of early star formation remains undetermined, but different observational constraints suggest that it does not extend below $\sim 1 \msol$. These IMFs allow a reasonably robust determination of the Galactic present-day and initial stellar and brown dwarf contents. They also have important galactic implications in yielding more accurate mass-to-light ratio determinations. The M/L ratios obtained with the disk and the spheroid IMF yield values 1.8 and 1.4 smaller than a Salpeter IMF, respectively. This general IMF determination is examined in the context of star formation theory. (shortened)

Figures (22)

• Figure 1: Disk mass function derived from the local V-band LF (circles and solid line) and K-band LF (squares and dash-line). The solid line and the two surrounding dash-lines display the lognormal form given by eq.[\ref{['IMFdisk']}], whereas the dotted line illustrates the 4-segment power-law form of Kroupa (2002). The empty circles and squares for $\log \, m\ge -0.15$ display the MF obtained for $t=10$ Gyr and 1 Gyr, respectively, illustrating the age uncertainty on the MF for $m>0.7\,\hbox{M}_\odot$. The empty triangles and dotted error bars display the MF obtained from the bulge LF (see text).
• Figure 2: Disk mass function derived from the system K-band LF (solid squares and solid line) and the HST corrected MF (triangles and short-dash-line) from Zheng et al. (2001). The solid line and surrounding dotted lines display the lognormal form given by eq.[\ref{['IMFdisk']}] for single objects, as in Figure \ref{['pasp_MF1_col.ps']}, whereas the dash-line illustrates the lognormal form given by eq.[\ref{['IMFsys']}].
• Figure 3: Luminosity functions for the Galactic disk predicted with the IMF (eq.[\ref{['IMFdisk']}]) and a constant SFR. Solid: stars+BDs; long-dash: BDs only ($m\le 0.072\,\hbox{M}_\odot$); long dash-dot: T-dwarfs only (J-H$<$0.5 and H-K$<$0.5); short dash-dot: objects below the D-burning minimum mass ($m\le 0.012\,\hbox{M}_\odot$). The short-dash lines illustrate the range of uncertainty in the IMF (eq.[\ref{['IMFdisk']}]). The dotted line in the middle panel displays the result obtained with a power-law IMF with $x=0$ ($\xi(\log \, m)=constant$) with the same normalisation at 0.1 $\hbox{M}_\odot$ as IMF (eq.[\ref{['IMFdisk']}]). The dotted line in the bottom panel displays the results obtained with the system IMF (eq.[\ref{['IMFsys']}]). The histogram displays the nearby LF (Henry & McCarthy 1990). Empty and filled squares are estimated L-dwarf densities by Gizis et al. (2000) and Kirkpatrick (1999, 2000)+Burgasser (2001), respectively. Triangles are estimated T-dwarf densities from Burgasser (2001).
• Figure 4: Pleiades Mass Function calculated with the Baraffe et al. (1998) and Chabrier et al. (2000) MMRs, from various observations : squares : Hambly et al. (1999); triangles : Dobbie et al. (2002b); circles : Moraux et al. (2003). The short-dash and long-dash lines display the single (eq.[\ref{['IMFdisk']}]) and system (eq.[\ref{['IMFsys']}]) field MFs, respectively, arbitrarily normalized to the present data.
• Figure 5: Mass Function calculated for various young clusters with the Baraffe et al. (1998) and Chabrier et al. (2000) MMRs, from various data. Solid circles: $\sigma$-Or (Béjar et al. 2001); filled squares : $\alpha$-Per (Barrado y Navascues et al. 2002); empty symbols : Pleiades (Hambly et al., 1999, squares; Moraux et al., 2003, circles; Dobbie et al., 2002b, triangles); filled triangles : M35 (Barrado y Navascues et al. 2002). The ages for each cluster are indicated. The dashed line illustrates the field system MF (eq.[\ref{['IMFsys']}]), while the dotted lines display various power-law segments $\xi(m)=dN/d\log m\propto m^{-x}$, as derived by the aforementioned authors, with : $x=-0.2$ ($\sigma$-Or), $x=-0.4$ ($\alpha$-Per), $x=-0.4$ (Pleiades), $x=-0.2$ and -1.9 (M35).