Present-day Stellar Mass Function Research Articles

The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

We calculate the stellar integrated galactic initial mass function (IGIMF) in the presence of cluster-to-cluster variations of the IMF. Variations of the IMF for a population of coeval clusters that populate the initial cluster mass function (ICLMF) are taken into account in the form of Gaussian distribution functions of the IMF parameters. For the tapered power-law function used in this work, these are the slope at the high-mass end, Γ, the slope at the low-mass end, γ, and the characteristic mass Mch. The level of variations is modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for the population of young clusters in the present-day Milky Way, which are σΓ = 0.6, σγ = 0.25, and σMch = 0.27 M⊙. We find that increasing the levels of dispersion for γ and Γ tends to moderately flatten the IGIMF at the low and high-mass end, respectively. The characteristic mass of the IGIMF is, however, strongly impacted by variations in Mch. Increasing the value of σMch shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can provide a simple explanation for the bottom-heavy stellar mass function that is inferred for early-type galaxies since these are likely the result of a merger of disk galaxies where the physical conditions of the star-forming gas may vary significantly both in time and space in the merging system. The effect of IMF variations on the IGIMF is compared to the effects of other processes and sources of systematic variations such as those due to variations in the shape of ICLMF, the gas-phase metallicity, and the galactic star formation rate (SFR) which can potentially affect the maximum mass of stellar clusters in a galaxy and set the mean value of the characteristic mass in clusters. For the various dependencies we have explored, we found that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. For the regimes at low metallicity where the IGIMF resembles a single power law, an increased level of IMF variations renders the IGIMF steeper and more bottom heavy, especially at low SFRs. On the other hand, variations in the IMF in the high mass regime can be easily dominated by variations in the slope of the ICLMF. We compare our results of the metallicity and SFR-dependent IGIMF to a sample of Milky Way ultra-faint dwarf (UFD) satellite galaxies that have available metallicity measurements. The present-day stellar mass function of these galaxies is a good analog to the IGIMF at the time their overall population of stars formed. We show that the slope of the stellar mass function of the UFD galaxies measured for stars in the mass range [0.4, 0.8] M⊙ can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. Our results suggest that the inclusion of IMF variations in models of galaxy formation and evolution is of vital importance in order to improve our understanding of star formation and star formation feedback effects on galactic scales.

Erratum: “A High-resolution Multiband Survey of Westerlund 2 with the Hubble Space Telescope. III. The Present-day Stellar Mass Function” (2017, AJ, 153, 122)*

Erratum: “A High-resolution Multiband Survey of Westerlund 2 with the Hubble Space Telescope. III. The Present-day Stellar Mass Function” (2017, AJ, 153, 122)*

Was the Milky Way a chain galaxy? Using the IGIMF theory to constrain the thin-disc star formation history and mass

The observed present-day stellar mass function (PDMF) of the solar neighborhood is a mixture of stellar populations born in star-forming events that occurred over the life-time of the thin disk of the Galaxy. Assuming stars form in embedded clusters which have stellar initial mass functions (IMFs) which depend on the metallicity and density of the star-forming gas clumps, the integrated galaxy-wide IMF (IGIMF) can be calculated. The shape of the IGIMF thus depends on the SFR and metallicity. Here, the shape of the PDMF for stars more massive than $1\,M_\odot$ in combination with the mass density in low-mass stars is used to constrain the current star-formation rate (SFR), the star formation history (SFH) and the current stellar plus remnant mass ($M_*$) in the Galactic thin disk. This yields the current SFR, $\dot{M}_*= 4.1^{+3.1}_{-2.8}~M_\odot$yr$^{-1}$, a declining SFH and $M_*=2.1^{+3.0}_{-1.5}\times 10^{11}M_\odot$, respectively, with a V-band stellar mass-to-light ratio of $M_*/L_V=2.79^{+0.48}_{-0.38}$.These values are consistent with independent measurements. We also quantify the surface density of black holes and neutron stars in the Galactic thin disk. The invariant canonical IMF can reproduce the PDMF of the Galaxy as well as the IGIMF, but in the universal IMF framework it is not possible to constrain any of the above Galactic properties. Assuming the IGMF theory is the correct framework and in combination with the vertical velocity dispersion data of stars, it follows that the Milky Way would have appeared as a chain galaxy at high redshift.

A High-resolution Multiband Survey of Westerlund 2 with the Hubble Space Telescope. III. The Present-day Stellar Mass Function

Abstract We present a detailed analysis of the spatial distribution of the stellar population and the present-day mass function (PDMF) of the Westerlund 2 (Wd2) region using the data from our high-resolution multiband survey with the Hubble Space Telescope. We used state-of-the-art artificial star tests to determine spatially resolved completeness maps for each of the broadband filters. We reach a level of completeness of 50% down to mag ( ) and mag ( ) in the optical and mag and mag (both ) in the infrared throughout the field of view. We had previously reported that the core of Wd2 consists of two clumps: namely the main cluster and the northern clump. From the spatial distribution of the completeness-corrected population, we find that their stellar surface densities are and , respectively, down to mag. We find that the PDMF of Wd2 has a slope of , which translates to a total stellar cluster mass of . The spatial analysis of the PDMF reveals that the cluster population is mass-segregated and most likely primordial. In addition, we report the detection of a stellar population of spatially uniformly distributed low-mass ( ) stars, extending into the gas ridges of the surrounding gas and dust cloud, as well as a confined region of reddened stars, likely caused by a foreground CO cloud. We find hints that a cloud–cloud collision might be the origin of the formation of Wd2.

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.

Evidence for top-heavy stellar initial mass functions with increasing density and decreasing metallicity

Residual-gas expulsion after cluster formation has recently been shown to leave an imprint in the low-mass present-day stellar mass function (PDMF) which allowed the estimation of birth conditions of some Galactic globular clusters (GCs) such as mass, radius and star formation efficiency. We show that in order to explain their characteristics (masses, radii, metallicity, PDMF) their stellar initial mass function (IMF) must have been top-heavy. It is found that the IMF is required to become more top-heavy the lower the cluster metallicity and the larger the pre-GC cloud-core density are. The deduced trends are in qualitative agreement with theoretical expectation. The results are consistent with estimates of the shape of the high-mass end of the IMF in the Arches cluster, Westerlund 1, R136 and NGC 3603, as well as with the IMF independently constrained for ultra-compact dwarf galaxies (UCDs). The latter suggests that GCs and UCDs might have formed along the same channel or that UCDs formed via mergers of GCs. A fundamental plane is found which describes the variation of the IMF with density and metallicity of the pre-GC cloud-cores simultaneously. The implications for the evolution of galaxies and chemical enrichment over cosmological times are expected to be major.

How do galaxies acquire their mass?

We introduce a toy model that describes (in a single equation) the mass in stars as a function of halo mass and redshift. Our model includes the suppression of gas accretion from gravitational shock heating and AGN jets mainly for M_halo > M_shock ~ 10^12 M_Sun and from a too hot IGM onto haloes with v_circ < 40 km/s, as well as stellar feedback that drives gas out of haloes mainly with v_circ < 120 km/s. We run our model on the merger trees of the haloes and subhaloes of a high-resolution dark matter cosmological simulation. The galaxy mass is taken as the maximum between the mass given by the model and the sum of the masses of its progenitors (reduced by tidal stripping). Designed to reproduce the present-day stellar mass function of galaxies, our model matches fairly well the evolution of the cosmic stellar density. It leads to the same z=0 relation between central galaxy stellar and halo mass as the one found by abundance matching and also as that previously measured at high mass on SDSS centrals. Our model also predicts a bimodal distribution (centrals and satellites) of stellar masses for given halo mass, in good agreement with SDSS observations. The relative importance of mergers depends much more on stellar than halo mass. Galaxies with m_stars > 10^11 M_Sun/h acquire most of their mass through mergers (mostly major and gas-poor), as expected from our model's shutdown of gas accretion at high M_halo. However, mergers are rare for m_stars < 10^11 M_Sun/h (greater than our mass resolution), a consequence of the curvature of the stellar vs. halo mass relation. So gas accretion must be the dominant growth mechanism for intermediate and low mass galaxies, e.g. dwarf ellipticals in clusters, except that gas-rich galaxy mergers account for the bulk of the growth of ellipticals with m_stars ~ 10^10.5 M_Sun/h, which we predict must be the typical mass of ULIRGs.

Effects of the integrated galactic IMF on the chemical evolution of the solar neighbourhood

The initial mass function determines the fraction of stars of different intial mass born per stellar generation. In this paper, we test the effects of the integrated galactic initial mass function (IGIMF) on the chemical evolution of the solar neighbourhood. The IGIMF (Weidner & Kroupa 2005) is computed from the combination of the stellar intial mass function (IMF), i.e. the mass function of single star clusters, and the embedded cluster mass function, i.e. a power law with index beta. By taking into account also the fact that the maximum achievable stellar mass is a function of the total mass of the cluster, the IGIMF becomes a time-varying IMF which depends on the star formation rate. We applied this formalism to a chemical evolution model for the solar neighbourhood and compared the results obtained by assuming three possible values for beta with the results obtained by means of a standard, well-tested, constant IMF. In general, a lower absolute value of beta implies a flatter IGIMF, hence a larger number of massive stars and larger metal ejection rates. This translates into higher type Ia and II supernova rates, higher mass ejection rates from massive stars and a larger amount of gas available for star formation, coupled with lower present-day stellar mass densities. (abridged) We also discuss the importance of the present day stellar mass function (PDMF) in providing a way to disentangle among various assumptions for beta. Our results indicate that the model adopting the IGIMF computed with beta ~2 should be considered the best since it allows us to reproduce the observed PDMF and to account for most of the chemical evolution constraints considered in this work.

A robust statistical estimation of the basic parameters of single stellar populations - I. Method

The colour-magnitude diagrams of resolved single stellar populations, such as open and globular clusters, have provided the best natural laboratories to test stellar evolution theory. Whilst a variety of techniques have been used to infer the basic properties of these simple populations, systematic uncertainties arise from the purely geometrical degeneracy produced by the similar shape of isochrones of different ages and metallicities. Here we present an objective and robust statistical technique which lifts this degeneracy to a great extent through the use of a key observable: the number of stars along the isochrone. Through extensive Monte Carlo simulations we show that, for instance, we can infer the four main parameters (age, metallicity, distance and reddening) in an objective way, along with robust confidence intervals and their full covariance matrix. We show that systematic uncertainties due to field contamination, unresolved binaries, initial or present-day stellar mass function are either negligible or well under control. This technique provides, for the first time, a proper way to infer with unprecedented accuracy the fundamental properties of simple stellar populations, in an easy-to-implement algorithm.

Testing the Relation between the Local and Cosmic Star Formation Histories

Recently, there has been great progress toward observationally determining the mean star formation history of the universe. When accurately known, the cosmic star formation rate could provide much information about Galactic evolution, if the Milky Way's star formation rate is representative of the average cosmic star formation history. A simple hypothesis is that our local star formation rate is proportional to the cosmic mean. In addition, to specify a star formation history, one must also adopt an initial mass function (IMF); typically it is assumed that the IMF is a smooth function, which is constant in time. We show how to test directly the compatibility of all these assumptions by making use of the local (solar neighborhood) star formation record encoded in the present-day stellar mass function. Present data suggest that at least one of the following is false: (1) the local IMF is constant in time; (2) the local IMF is a smooth (unimodal) function; and/or (3) star formation in the Galactic disk was representative of the cosmic mean. We briefly discuss how to determine which of these assumptions fail and also improvements in observations, which will sharpen this test.