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Register a new userVariations in Integrated Galactic Initial Mass Functions due to Sampling Method and Cluster Mass Function
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[abridged] Stars are thought to be formed predominantly in clusters. The clusters are formed following a cluster initial mass function (CMF) similar to the stellar initial mass function (IMF). Both the IMF and the CMF favour low-mass objects. The numerous low-mass clusters will lack high mass stars. If the integrated galactic initial mass function originates from stars formed in clusters, the IGIMF could be steeper than the IMF. We investigate how well constrained this steepening is and how it depends on the choice of sampling method and CMF. We compare analytic sampling to several implementations of random sampling of the IMF, and different CMFs. We implement different IGIMFs into GALEV to obtain colours and metallicities for galaxies. Choosing different ways of sampling the IMF results in different IGIMFs. Depending on the lower cluster mass limit and the slope of the cluster mass function, the steepening varies between very strong and negligible. We find the size of the effect is continuous as a function of the power-law slope of the CMF, if the CMF extends to masses smaller than the maximum stellarmass. The number of O-stars detected by GAIA might help in judging on the importance of the IGIMF effect. The impact of different IGIMFs on integrated galaxy photometry is small, within the intrinsic scatter of observed galaxies. Observations of gas fractions and metallicities could rule out at least the most extreme sampling methods. As we still do not understand the details of star formation, one sampling method cannot be favoured over another. Also, the CMF at very low cluster masses is not well constrained observationally. These uncertainties need to be taken into account when using an IGIMF, with severe implications for galaxy evolution models and interpretations of galaxy observations.
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Few topics in astronomy initiate such vigorous discussion as whether or not the initial mass function (IMF) of stars is universal, or instead sensitive to the initial conditions of star formation. The distinction is of critical importance: the IMF influences most of the observable properties of stellar populations and galaxies, and detecting variations in the IMF could provide deep insights into the process by which stars form. In this review, we take a critical look at the case for IMF variations, with a view towards whether other explanations are sufficient given the evidence. Studies of the field, local young clusters and associations, and old globular clusters suggest that the vast majority were drawn from a universal IMF: a power-law of Salpeter index ($Gamma=1.35$) above a few solar masses, and a log normal or shallower power-law ($Gamma sim 0-0.25$) between a few tenths and a few solar masses (ignoring the effects of unresolved binaries). The shape and universality of the IMF at the stellar-substellar boundary is still under investigation and uncertainties remain large, but most observations are consistent with a IMF that declines ($Gamma < -0.5$) well below the hydrogen burning limit. Observations of resolved stellar populations and the integrated properties of most galaxies are also consistent with a universal IMF, suggesting no gross variations in the IMF over much of cosmic time. There are indications of non-standard IMFs in specific local and extragalactic environments, which clearly warrant further study. Nonetheless, there is no clear evidence that the IMF varies strongly and systematically as a function of initial conditions after the first few generations of stars.
We have undertaken the largest systematic study of the high-mass stellar initial mass function (IMF) to date using the optical color-magnitude diagrams (CMDs) of 85 resolved, young (4 Myr < t < 25 Myr), intermediate mass star clusters (10^3-10^4 Msun), observed as part of the Panchromatic Hubble Andromeda Treasury (PHAT) program. We fit each clusters CMD to measure its mass function (MF) slope for stars >2 Msun. For the ensemble of clusters, the distribution of stellar MF slopes is best described by $Gamma=+1.45^{+0.03}_{-0.06}$ with a very small intrinsic scatter. The data also imply no significant dependencies of the MF slope on cluster age, mass, and size, providing direct observational evidence that the measured MF represents the IMF. This analysis implies that the high-mass IMF slope in M31 clusters is universal with a slope ($Gamma=+1.45^{+0.03}_{-0.06}$) that is steeper than the canonical Kroupa (+1.30) and Salpeter (+1.35) values. Using our inference model on select Milky Way (MW) and LMC high-mass IMF studies from the literature, we find $Gamma_{rm MW} sim+1.15pm0.1$ and $Gamma_{rm LMC} sim+1.3pm0.1$, both with intrinsic scatter of ~0.3-0.4 dex. Thus, while the high-mass IMF in the Local Group may be universal, systematics in literature IMF studies preclude any definitive conclusions; homogenous investigations of the high-mass IMF in the local universe are needed to overcome this limitation. Consequently, the present study represents the most robust measurement of the high-mass IMF slope to date. We have grafted the M31 high-mass IMF slope onto widely used sub-solar mass Kroupa and Chabrier IMFs and show that commonly used UV- and Halpha-based star formation rates should be increased by a factor of ~1.3-1.5 and the number of stars with masses >8 Msun are ~25% fewer than expected for a Salpeter/Kroupa IMF. [abridged]
We discuss the possibility that gravitational focusing, is responsible for the power-law mass function of star clusters $N(log M) propto M^{-1}$. This power law can be produced asymptotically when the mass accretion rate of an object depends upon the mass of the accreting body as $dot{M} propto M^2$. While Bondi-Hoyle-Littleton accretion formally produces this dependence on mass in a uniform medium, realistic environments are much more complicated. However, numerical simulations in SPH allowing for sink formation yield such an asymptotic power-law mass function. We perform pure N-body simulations to isolate the effects of gravity from those of gas physics and to show that clusters naturally result with the power-law mass distribution. We also consider the physical conditions necessary to produce clusters on appropriate timescales. Our results help support the idea that gravitationally-dominated accretion is the most likely mechanism for producing the cluster mass function.
We present a method for investigating variations in the upper end of the stellar Initial Mass Function (IMF) by probing the production rate of ionizing photons in unresolved, compact star clusters with ages <~10 Myr and with different masses. We test this method by performing a pilot study on the young cluster population in the nearby galaxy NGC5194 (M51a), for which multi-wavelength observations from the Hubble Space Telescope are available. Our results indicate that the proposed method can probe the upper end of the IMF in galaxies located out to at least ~10 Mpc, i.e., a factor ~200 further away than possible by counting individual stars in young compact clusters. Our results for NGC5194 show no obvious dependence of the upper mass end of the IMF on the mass of the star cluster down to ~1000 M_sun, although more extensive analyses involving lower mass clusters and other galaxies are needed to confirm this conclusion.
Star formation rates (SFR) larger than 1000 Msun/ yr are observed in extreme star bursts. This leads to the formation of star clusters with masses > 10^6 Msun in which crowding of the pre-stellar cores may lead to a change of the stellar initial mass function (IMF). Indeed, the large mass-to-light ratios of ultra-compact dwarf galaxies and recent results on globular clusters suggest the IMF to become top-heavy with increasing star-forming density. We explore the implications of top-heavy IMFs in these very massive and compact systems for the integrated galactic initial mass function (IGIMF), which is the galaxy-wide IMF, in dependence of the star-formation rate of galaxies. The resulting IGIMFs can have slopes, alpha_3, for stars more massive than about 1 Msun between 1.5 and the Salpeter slope of 2.3 for an embedded cluster mass function (ECMF) slope (beta) of 2.0, but only if the ECMF has no low-mass clusters in galaxies with major starbursts. Alternatively, beta would have to decrease with increasing SFR >10 Msun/ yr such that galaxies with major starbursts have a top-heavy ECMF. The resulting IGIMFs are within the range of observationally deduced IMF variations with redshift.
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