A Study of the Luminosity and Mass Functions of the Young IC 348 Cluster Using FLAMINGOS Wide-Field Near-Infrared Images

Three-component models of the initial mass function (IMF) are made to consider possible origins for the observed relative variations in the numbers of brown dwarfs, solar-to-intermediate-mass stars and high-mass stars. The differences between the IMFs observed for clusters, field and remote field are also discussed. Three distinct physical processes that should dominate the three stellar mass regimes are noted. The characteristic mass for most star formation is identified with the thermal Jeans mass in the molecular cloud core, and this presumably leads to the middle mass range by the usual collapse and accretion processes. Pre-stellar condensations (PSCs) observed in millimetre-wave continuum studies presumably form at this mass. Significantly smaller self-gravitating masses require much larger pressures and may arise following dynamical processes inside these PSCs, including disc formation, tight-cluster ejection, and photoevaporation as studied elsewhere, but also gravitational collapse of shocked gas in colliding PSCs. Significantly larger stellar masses form in relatively low abundance by normal cloud processes, possibly leading to steep IMFs in low-pressure field regions, but this mass range can be significantly extended in high-pressure cloud cores by gravitationally focused gas accretion on to PSCs and by the coalescence of PSCs. These models suggest that the observed variations in brown dwarf, solar-to-intermediate-mass and high-mass populations are the result of dynamical effects that depend on environmental density and velocity dispersion. They accommodate observations ranging from shallow IMFs in cluster cores to Salpeter IMFs in average clusters and whole galaxies to steep and even steeper IMFs in field and remote field regions. They also suggest how the top-heavy IMFs in some starburst clusters may originate and they explain bottom-heavy IMFs in low surface brightness galaxies.

We use the results of a new, multi-epoch, multi-wavelength, near-infrared census of the Trapezium Cluster in Orion to construct and to analyze the structure of its infrared (K band) luminosity function. Specifically, we employ an improved set of model luminosity functions to derive this cluster's underlying Initial Mass Function (IMF) across the entire range of mass from OB stars to sub-stellar objects down to near the deuterium burning limit. We derive an IMF for the Trapezium Cluster that rises with decreasing mass, having a Salpeter-like IMF slope until near ~0.6 M_sun where the IMF flattens and forms a broad peak extending to the hydrogen burning limit, below which the IMF declines into the sub-stellar regime. Independent of the details, we find that sub-stellar objects account for no more than ~22% of the total number of likely cluster members. Further, the sub-stellar Trapezium IMF breaks from a steady power-law decline and forms a significant secondary peak at the lowest masses (10-20 times the mass of Jupiter). This secondary peak may contain as many as \~30% of the sub-stellar objects in the cluster. Below this sub-stellar IMF peak, our KLF modeling requires a subsequent sharp decline toward the planetary mass regime. Lastly, we investigate the robustness of pre-main sequence luminosity evolution as predicted by current evolutionary models, and we discuss possible origins for the IMF of brown dwarfs.

ABSTRACTWe review recent determinations of the present‐day mass function (PDMF) and initial mass function (IMF) in various components of the Galaxy—disk, spheroid, young, and globular clusters—and in conditions characteristic of early star formation. As a general feature, the IMF is found to depend weakly on the environment and to be well described by a power‐law form for m≳1 M⊙ and a lognormal form below, except possibly for early star formation conditions. The disk IMF for single objects has a characteristic mass around mc ∼ 0.08 M⊙ and a variance in logarithmic mass σ ∼ 0.7, whereas the IMF for multiple systems has mc ∼ 0.2 M⊙ and σ ∼ 0.6. The extension of the single MF into the brown dwarf regime is in good agreement with present estimates of L‐ and T‐dwarf densities and yields a disk brown dwarf number density comparable to the stellar one, nBD ∼ n* ∼ 0.1 pc−3. The IMF of young clusters is found to be consistent with the disk field IMF, providing the same correction for unresolved binaries, confirming the fact that young star clusters and disk field stars represent the same stellar population. Dynamical effects, yielding depletion of the lowest mass objects, are found to become consequential for ages ≳130 Myr. The spheroid IMF relies on much less robust grounds. The large metallicity spread in the local subdwarf photometric sample, in particular, remains puzzling. Recent observations suggest that there is a continuous kinematic shear between the thick‐disk population, present in local samples, and the genuine spheroid one. This enables us to derive only an upper limit for the spheroid mass density and IMF. Within all the uncertainties, the latter 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, mc ∼ 0.2–0.3 M⊙, excluding a significant population of brown dwarfs in globular clusters and in the spheroid. The IMF characteristic of early star formation at large redshift remains undetermined, but different observational constraints suggest that it does not extend below ∼1 M⊙. These results suggest a characteristic mass for star formation that decreases with time, from conditions prevailing at large redshift to conditions characteristic of the spheroid (or thick disk) to present‐day conditions. These conclusions, however, remain speculative, given the large uncertainties in the spheroid and early star IMF determinations.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 beyond the Milky Way in yielding more accurate mass‐to‐light ratio determinations. The mass‐to‐light ratios obtained with the disk and the spheroid IMF yield values 1.8–1.4 times smaller than for a Salpeter IMF, respectively, in agreement with various recent dynamical determinations. This general IMF determination is examined in the context of star formation theory. None of the theories based on a Jeans‐type mechanism, where fragmentation is due only to gravity, can fulfill all the observational constraints on star formation and predict a large number of substellar objects. On the other hand, recent numerical simulations of compressible turbulence, in particular in super‐Alfvénic conditions, seem to reproduce both qualitatively and quantitatively the stellar and substellar IMF and thus provide an appealing theoretical foundation. In this picture, star formation is induced by the dissipation of large‐scale turbulence to smaller scales through radiative MHD shocks, producing filamentary structures. These shocks produce local nonequilibrium structures with large density contrasts, which collapse eventually in gravitationally bound objects under the combined influence of turbulence and gravity. The concept of a single Jeans mass is replaced by a distribution of local Jeans masses, representative of the lognormal probability density function of the turbulent gas. Objects below the mean thermal Jeans mass still have a possibility to collapse, although with a decreasing probability.

We report the results of deep infrared observations of brown dwarf candidates in the Trapezium Cluster in Orion. Analysis of the JHK color-color diagram indicates that a large fraction (~65% ± 15%) of the observed sources exhibit infrared-excess emission. This suggests the extreme youth of these objects and, in turn, provides strong independent confirmation of the existence of a large population of substellar objects in the cluster. Moreover, this suggests that the majority of these substellar objects are presently surrounded by circumstellar disks similar to the situation for the stellar population of the cluster. This evidence for a high initial disk frequency (>50%) around cluster members of all masses, combined with the smooth continuity of the cluster's initial mass function across the hydrogen-burning limit, suggests that a single physical mechanism is likely responsible for producing the entire cluster mass spectrum down to near the deuterium-burning limit. The results may also indicate that even substellar objects are capable of forming with systems of planetary companions.

We present the results of numerical experiments designed to evaluate the usefulness of near-infrared (NIR) luminosity functions for constraining the initial mass function (IMF) of young stellar populations. We test the sensitivity of the NIR K-band luminosity function (KLF) of a young stellar cluster to varia- tions in the underlying IMF, star-forming history, and premain-sequence mass-to-luminosity relations. Using Monte Carlo techniques, we create a suite of model luminosity functions systematically varying each of these basic underlying relations. From this numerical modeling, we —nd that the luminosity func- tion of a young stellar population is considerably more sensitive to variations in the underlying initial mass function than to either variations in the star-forming history or assumed premain-sequence (PMS) mass-to-luminosity relation. Variations in a clusters star-forming history are also found to produce sig- ni—cant changes in the KLF. In particular, we —nd that the KLFs of young clusters evolve in a system- atic manner with increasing mean age. Our experiments indicate that variations in the PMS mass-to-luminosity relation, resulting from diUerences in adopted PMS tracks, produce only small eUects on the form of the model luminosity functions and that these eUects are mostly likely not detectable observationally. To illustrate the potential eUectiveness of using the KLF of a young cluster to constrain its IMF, we model the observed KLF of the nearby Trapezium cluster. With knowledge of the star- forming history of this cluster obtained from optical spectroscopic studies, we derive the simplest under- lying IMF whose model luminosity function matches the observations. Our derived mass function for the Trapezium spans 2 orders of magnitude in stellar mass and has a peak near the (5 ( M _ ( 0.02) hydrogen-burning limit. Below the hydrogen-burning limit, the mass function steadily decreases with decreasing mass throughout the brown dwarf regime. Comparison of our IMF with that derived by optical and spectroscopic methods for the entire Orion Nebula Cluster suggests that modeling the KLF is indeed a useful tool for constraining the mass function in young stellar clusters particularly at and below the hydrogen-burning limit. Subject headings: infrared: starsopen clusters and associations: generalstars: interiors ¨ stars: low-mass, brown dwarfsstars: luminosity function, mass function ¨ stars: pre-main sequence

We review the success of current simulations in reproducing the observed initial mass function (IMF) in clusters and show that whereas the two main types of simulation invoke the same physics to explain the point at which the IMF flattens from a Salpeter slope, they reproduce the Salpeter tail itself by quite different means. We highlight the fact that a proper modelling of the thermal properties of star-forming gas is probably crucial in explaining why the IMF is apparently quite insensitive to cloud parameters. We also explore how the mass of a cluster’s most massive star depends on cluster mass and how this issue impacts the relationship between the IMF in individual clusters and the integrated galactic IMF. We emphasise the importance of a careful statistical treatment of data in this area.

We study the initial mass function (IMF) of NGC 3603, one of the most massive galactic star-forming regions, to answer a fundamental question in current astrophysics - is the IMF universal, or does it vary? Using our very deep high angular resolution images obtained with the NAOS-CONICA adaptive optics system at the VLT/ESO, we have successfully revealed the low-mass stellar population in the cluster core down to about 0.4 Msun (50 % completeness limit). Based on the JHKsL' color-magnitude and color-color diagrams, we first derive an average age 0.7 Myr for the pre-main sequence stars, and an upper limit of ~2.5 Myr for the main sequence stars. We find an average foreground extinction of Av = 4.5 +- 0.5 mag, with a radial increase of Delta_Av ~ 2.0 mag towards larger radii (r < 50''). From the infrared excess emission identified in the Ks - L' vs J - H color-color diagram, we measure a disk fraction of ~25 % for stars with M > 0.9 Msun in the cluster center (r < 10''). Applying a field star rejection and correcting for incompleteness, we derive the Ks-band luminosity function (LF) for stars simultaneously detected in the JHKs-bands. The LF follows a power-law with an index of alpha ~ 0.27, and shows no turnover or truncation within the detection limit. The IMF for stars within r < 110'' is reasonably fitted by a single power-law with index Gamma ~ -0.74 in the mass range of $0.4 - 20 Msun. This is substantially flatter than the Salpeter-like IMF (Gamma = -1.35). The IMF power-law index decreases from Gamma ~ -0.31 at r < 5'' to Gamma ~ -0.86 at 30'' < r < 110''. This radial steepening of the IMF mainly occurs in the inner r < 30'' field, indicating mass segregation at the very center of the starburst cluster. Analyzing the radial mass density profile, we derive a cluster core radius of ~4''.8 (~0.14 pc), and a lower limit of ~110'' (~3.2 pc) for the cluster size. We also derive an upper limit of r ~ 1260'' (~37 pc) for the cluster size adopting an estimate of the tidal radius of the cluster. Based on the de-projected stellar density distribution, we estimate the total mass and the half-mass radius of NGC 3603 to be about 1.0 - 1.6 x 10^4 Msun and 25'' - 50'' (~0.7 - 1.5 pc), respectively. The derived core radius is > 6 x 10^4 Msun pc^-3. The estimate of the half-mass relaxation time for stars with a typical mass of 1 Msun is 10 - 40 Myr, suggesting that the intermediate- and low-mass stars have not yet been affected significantly by the dynamical relaxation in the cluster. The relaxation time for the high-mass stars is expected to be much smaller, and is comparable to the age of the cluster. We can thus not conclude if the mass segregation of the high-mass stars is primordial or caused by dynamical evolution. Our observation covers at least ~67 % of intermediate- and low-mass stars in NGC 3603, and the stars residing outside the observed field can merely steepen the IMF by Delta_Gamma 30'', we are confident that our IMF adequately describes the whole NGC 3603 starburst cluster. We also thoroughly analyze the systematic uncertainties in our IMF determination. We conclude that the power-law index of NGC 3603 including the systematic uncertainties is Gamma = -0.74^{+0.62}_{-0.47}. Our result thus supports the hypothesis of a top-heavy IMF in starbursts, especially in combination with other studies of similar clusters such as the Arches cluster and the Galactic Center cluster.

The initial and present-day mass functions (ICMF and PDMF, respectively) of the Galactic globular clusters (GCs) are constructed based on their observed luminosities, the stellar evolution and dynamical mass-loss processes, and the mass-to-light ratio (MLR). Under these conditions, a Schechter-like ICMF is evolved for approximately a Hubble time and converted into the luminosity function (LF), which requires finding the values of 5 free parameters: the mean GC age (\tA), the dissolution timescale of a $10^5 \ms$ cluster ($\tau_5$), the exponential truncation mass (\mc) and 2 MLR parametrising constants. This is achieved by minimising the residuals between the evolved and observed LFs, with the minimum residuals and realistic parameters obtained with MLRs that increase with luminosity (or mass). The optimum PMDFs indicate a total stellar mass of $\sim4\times10^7$ \ms\ still bound to GCs, representing $\sim15%$ of the mass in clusters at the beginning of the gas-free evolution. The corresponding ICMFs resemble the scale-free MFs of young clusters and molecular clouds observed in the local Universe, while the PDMFs follow closely a lognormal distribution with a turnover at $\mto\sim7\times10^4$\,\ms. For most of the GC mass range, we find an MLR lower than usually adopted, which explains the somewhat low \mto. Our results confirm that the MLR increases with cluster mass (or luminosity), and suggest that GCs and young clusters share a common origin in terms of physical processes related to formation.

Observed variations in the slope of the stellar initial mass function (IMF) are shown to be consistent with a previously introduced model in which the protostellar gas is randomly sampled from clouds with a self-similar hierarchical structure. Root mean square variations in the IMF slope around the Salpeter value are ±0.4 when only 100 stars are observed, and ±0.1 when 1000 stars are observed. Similar variations should be present in other stochastic models as well. The hierarchical sampling model reproduces the tendency for massive stars to form closer to the center of a cloud at a time somewhat later than the formation time of the lower mass stars. The systematic variation in birth position results from the tendency for the trunk and larger branches of the hierarchical tree of cloud structure to lie closer to the cloud center, while the variations in birth order result from the relative infrequency of stars with larger masses. The hierarchical cloud sampling model has now reproduced most of the reliably observed features of the cluster IMF. The power-law part of the IMF comes from cloud hierarchical structure that is sampled during various star formation processes with a relative rate proportional to the square root of the local density. These processes include turbulence compression, magnetic diffusion, gravitational collapse, and clump or wavepacket coalescence, all of which have about this rate dependence. The low-mass flattening comes from the inability of gas to form stars below the thermal Jeans mass at typical temperatures and pressures. The thermal Jeans mass is the only relevant scale in the problem. Considerations of heating and cooling processes indicate why the thermal Jeans mass should be nearly constant in normal environments and why this mass might increase in starburst regions. In particular, the relative abundance of high-mass stars should increase where the average density of the interstellar medium is very large; accompanying this increase should be an increase in the average total efficiency of star formation. Alternative models in which the rate of star formation is independent of density and the local efficiency decreases systematically with increasing stellar mass can also reproduce the IMF, but this is an adjustable result and not a fundamental property of hierarchical cloud structure, as is the preferred model. The steep IMF in the extreme field is not explained by the model, but other origins are suggested, including one in which massive stars in low-pressure environments halt star formation in their clouds. In this case, the slope of the extreme field IMF is independent of the slope of each component cluster IMF and is given by (γ-1)/α for a cloud mass function slope, -γ~-2, and a power-law relation, ML∝Mαc, between the largest star in a low-pressure cloud, ML, and the cloud mass, Mc. A value of α~1/4 is required to explain the extreme field IMF as a superposition of individual cluster IMFs; cloud destruction by ionizing has this property. We note that the similarity between cluster IMFs and the average IMF from global studies of galaxies implies that most stars form in clusters and that massive stars do not generally halt star formation in the same cloud.

The stellar initial mass functions (IMFs) for the Galactic bulge, the Milky Way, other galaxies, clusters of galaxies, and the integrated stars in the universe are composites from countless individual IMFs in star clusters and associations where stars form. These galaxy-scale IMFs, reviewed in detail here, are not steeper than the cluster IMFs except in rare cases. This is true even though low-mass clusters generally outnumber high-mass clusters and the average maximum stellar mass in a cluster scales with the cluster mass. The implication is that the mass distribution function for clusters and associations is a power law with a slope of -2 or shallower. Steeper slopes, even by a few tenths, upset the observed equality between large- and small-scale IMFs. Such a cluster function is expected from the hierarchical nature of star formation, which also provides independent evidence for the IMF equality when it is applied on subcluster scales. We explain these results with analytical expressions and Monte Carlo simulations. Star clusters appear to be the relaxed inner parts of a widespread hierarchy of star formation and cloud structure. They are defined by their own dynamics rather than by preexisting cloud boundaries.

[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.

A coalescence model using the observed properties of pre-stellar condensations (PSCs) shows how an initially steep initial mass function (IMF) that might be characteristic of primordial cloud fragmentation can change into a Salpeter IMF or shallower IMF in a cluster of normal density after one dynamical time, even if the PSCs are collapsing on their own dynamical time. The model suggests that top-heavy IMFs in some starburst clusters originate with PSC coalescence.

The empirical binary properties of brown dwarfs (BDs) differ from those of normalstars suggesting BDs form a separate population. Recent work by Thies and Krouparevealed a discontinuity of the initial mass function (IMF) in the very-low-mass starregime under the assumption of a low multiplicity of BDs of about 15 per cent. How-ever, previous observations had suggested that the multiplicity of BDs may be sig-nificantly higher, up to 45 per cent. This contribution investigates the implication ofa high BD multiplicity on the appearance of the IMF for the Orion Nebula Cluster,Taurus-Auriga, IC 348 and the Pleiades. We show that the discontinuity remains pro-nounced even if the observed MF appears to be continuous, even for a BD binaryfraction as high as 60%. We find no evidence for a variation of the BD IMF withstar-forming conditions. The BD IMF has a power-law index α BD ≈ +0.3 and about2 BDs form per 10 low-mass stars assuming equal-mass pairing of BDs.Key words: binaries: general — open clusters and associations: general — stars:low-mass, brown dwarfs — stars: luminosity function, mass function

view Abstract Citations (140) References (120) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Main-Sequence Luminosity and Initial Mass Functions of Six Magellanic Cloud Star Clusters Ranging in Age from 10 Megayears to 2.5 Gigayears Mateo, Mario Abstract Deep CCD B and V frames of six star clusters in the Magellanic Clouds (MCs) have been analyzed in order to determine the main-sequence mass functions for the stars in these systems. The clusters span a range in age from 10 Myr to 2.5 Gyr and a range in metallicity from about solar to 1/20th solar. The procedures used to determine the cluster luminosity functions are described in detail. In particular, the counting incompleteness depends sensitively on position on the CCD frame and magnitude, and the appropriate corrections have been empirically determined and applied to convert the observed star counts to "true" luminosity functions (LFs). These LFs were converted to mass functions (MFs) via mass-absolute magnitude relations based on theoretical isochrones that were "fitted" to the cluster color-magnitude diagrams. Both the "classical" models of VandenBerg, Becker, and Brunish and Truran and the "overshoot" models of Bertelli et al. were used in this analysis. Arguments are presented that the observed MFs of the program clusters are very similar to their initial mass function (IMFs). The shapes of IMFs of the six clusters are indistinguishable in the range 0.9-10.5 M_sun_, and there is no reason to reject the hypothesis that the IMFs of the six clusters were drawn from a single power-law IMF with a slope x = 2.52 +/- 0.16, where IMF is proportional to M^-(1+x)^ and M is the stellar mass. This result does not depend significantly on the adopted MC distance scale, or whether "classical" or "overshoot" stellar evolutionary models are used in the analysis. There is some indication that the high-mass end (i.e., log M >~ 0.45) of the average IMF of the six clusters is slightly shallower than the low-mass end. Comparisons with previous work on the MFs of Galactic open clusters shows rough agreement, although the MC cluster MFs do not show the large scatter observed in open clusters. The average IMF of the program clusters is remarkably similar to the solar neighborhood IMF determined by Scalo, and the MC cluster IMF slope is similar to some recent findings for high-mass stars in the LMC. A comparison of the present results with the elegant bimodal IMF model of Larson shows poor agreement. Publication: The Astrophysical Journal Pub Date: August 1988 DOI: 10.1086/166552 Bibcode: 1988ApJ...331..261M Keywords: Globular Clusters; Magellanic Clouds; Main Sequence Stars; Stellar Evolution; Stellar Luminosity; Color-Magnitude Diagram; Metallicity; Stellar Mass; Astrophysics; CLUSTERS: GLOBULAR; CLUSTERS: OPEN; GALAXIES: MAGELLANIC CLOUDS; LUMINOSITY FUNCTION; STARS: EVOLUTION; STARS: STELLAR STATISTICS full text sources ADS | data products SIMBAD (6)

We have developed a technique of IR spectral classification in which we use K-band spectra (R ~ 1000) to derive the spectral types and continuum veilings of young, late-type stars (~1 Myr, >G0). We show close agreement between the spectral types derived in this manner and those obtained optically. We complement previous optical spectroscopy with IR spectra of the most heavily embedded members of the young, embedded cluster L1495E. We critically analyze the translation between observable (spectral type, photometry) and theoretical (Teff, Lbol) parameters and use these data to construct an H-R diagram. We find that the evolutionary tracks of D'Antona & Mazzitelli imply a coeval population of ≤1 Myr and a plausible initial mass function (IMF). However, these models may underestimate the masses of objects near and below the hydrogen burning limit. The models of Swenson produce implausibly old ages and the models of Baraffe et al. yield somewhat old ages and an implausible IMF. We use infrared imaging to show that the spectroscopic sample for this cluster may be seriously incomplete below ~0.15 M☉. After applying a completeness correction to the IMF derived with the tracks of D'Antona & Mazzitelli, we find no evidence for a turnover at low masses; the IMF appears roughly flat in logarithmic mass units. Compared to the results of photometric studies of ρ Oph and NGC 2024, the IMF appears roughly invariant among star-forming environments representing a 2 order of magnitude range in the density of young stars. However, the detailed behavior of the IMF from low stellar masses into the substellar regime will remain uncertain until (1) better evolutionary tracks are available and (2) the sources in the photometric completeness correction can be spectroscopically confirmed as low-mass cluster members.