The Initial Mass Function of Low-Mass Stars and Brown Dwarfs in Young Clusters

By K. Luhman, G. Rieke, E. Young, A. Cotera, H. Chen, M. Rieke, G. Schneider, Rodger I. Thompson CfA, S. Obs.. 2000

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We have obtained images of the Trapezium Cluster (140′′ × 140′′; 0.3 pc × 0.3 pc) with the Hubble Space Telescope Near-Infrared Camera and Multi-Object Spectrometer (NICMOS). Combining these data with new ground-based K-band spectra (R = 800) and existing spectral types and photometry, we have constructed an H-R diagram and used it and other arguments to infer masses and ages. To allow comparison with the results of our previous studies of IC 348 and ρ Oph, we first use the models of D'Antona & Mazzitelli. With these models, the distributions of ages of comparable samples of stars in the Trapezium, ρ Oph, and IC 348 indicate median ages of ~0.4 Myr for the first two regions and ~1-2 Myr for the latter. The low-mass initial mass functions (IMFs) in these sites of clustered star formation are similar over a wide range of stellar densities (ρ Oph, n = 0.2-1 × 103 pc-3; IC 348, n = 1 × 103 pc-3; Trapezium, n = 1-5 × 104 pc-3) and other environmental conditions (e.g., presence or absence of OB stars). With current data, we cannot rule out modest variations in the substellar mass functions among these clusters. We then make the best estimate of the true form of the IMF in the Trapezium by using the evolutionary models of Baraffe et al. and an empirically adjusted temperature scale and compare this mass function to recent results for the Pleiades and the field. All of these data are consistent with an IMF that is flat or rises slowly from the substellar regime to about 0.6 M☉ and then rolls over into a power law that continues from about 1 M☉ to higher masses with a slope similar to or somewhat larger than the Salpeter value of 1.35. For the Trapezium, this behavior holds from our completeness limit of ~0.02 M☉ and probably, after a modest completeness correction, even from 0.01-0.02 M☉. These data include ~50 likely brown dwarfs. We test the predictions of theories of the IMF against (1) the shape of the IMF, which is not log-normal, in clusters and the field, (2) the similarity of the IMFs among young clusters, (3) the lowest mass observed for brown dwarfs, and (4) the suggested connection between the stellar IMF and the mass function of prestellar clumps. In particular, most models do not predict the formation of the moderately large numbers of isolated objects down to 0.01 M☉ that we find in the Trapezium.

Subfields: Astronomy and Astrophysics

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THE FIRST HUNDRED BROWN DWARFS DISCOVERED BY THE WIDE-FIELD INFRARED SURVEY EXPLORER (WISE) (2011, result): “This result is in accordance with findings in young star formation regions (e.g., Luhman et al. 2000, Muench et al. 2002, Lucas et al. 2006, Luhman 2007), but the derived masses for those objects should be considered cautiously, as discussed in Baraffe et al. (2003), because models with ages of ∼1…”
THE SPITZER SPACE TELESCOPE SURVEY OF THE ORION A AND B MOLECULAR CLOUDS. I. A CENSUS OF DUSTY YOUNG STELLAR OBJECTS AND A STUDY OF THEIR MID-INFRARED VARIABILITY (2012, background): “This cluster has emerged as an important laboratory for understanding the initial mass function (Hillenbrand 1997; Luhman et al. 2000; Muench et al. 2002), the evolution of disks around young stars (Hillenbrand et al. 1998; Lada et al. 2000, 2004), and the structure and kinematics of young clusters…”
The Spectroscopically Determined Substellar Mass Function of the Orion Nebula Cluster (2004, methodology): “Because J magnitudes are not available for all program stars, for consistency we used (H −K) colors and K magnitudes from HC00 to determine extinction values and estimate bolometric corrections.”
Galactic Stellar and Substellar Initial Mass Function (2003, background): “Finally, as pointed out by Luhman et al. (2000), what is really observed in star forming clusters is not the IMF but the creation function (see §1.2.2).”
Evidence for a T Tauri Phase in Young Brown Dwarfs (2003, background): “For now, we assume an age of ∼ 1–2 Myr for IC 348 (Luhman et al. 2000) and ∼ 3 Myr for Taurus (White & Ghez 2001).”
The initial conditions of star formation in the Ophiuchus main cloud: Kinematics of the protocluster condensations , (2007, background): “This break is reminiscent of the flattening observed in the IMF of field stars below 0.5 M⊙ (e.g. Kroupa 2001; Chabrier 2003), also present in the mass function of L1688 pre-main sequence objects (Luhman et al. 2000; Bontemps et al. 2001).”
Toward Spectral Classification of L and T Dwarfs: Infrared and Optical Spectroscopy and Analysis (2001, background): “Young brown dwarfs have been discovered in large numbers in star-forming regions (see, e.g., Hambly et al. 1999 ; PinÐeld et al. 2000 ; Luhman et al. 2000 ; Lucas & Roche 2000).”
Chandra Orion Ultradeep Project: Observations and Source Lists (2004, background): “…other wide-field ONC catalogs and high spatial resolution studies of the inner core region as necessary (McCaughrean & Stauffer 1994; Hillenbrand 1997; Petr et al. 1998; Simon, Close, & Beck 1999; Lucas & Roche – 19 – 2000; Luhman et al. 2000; Muench et al. 2002; Schertl et al. 2003, and 2MASS).”
The Spectra of T Dwarfs. I. Near-Infrared Data and Spectral Classification (2001, result): “Our T dwarf space density estimate applied to the mass function simulations of Reid et al. (1999) predicts a substellar mass function that goes as dN dM ∝ M−1, consistent with results from various cluster surveys (Luhman et al. 2000).”
Embedded Clusters in Molecular Clouds (2003, methodology): “Using independent observations and different methodology to extract IMFs from the observations, Luhman et al. (2000) derived IMFs for the Trapezium, IC 348, and Ophiuchi clusters and also found good agreement in the shapes of the IMFs of these clusters above the HBL.”
The stellar and sub-stellar IMF of simple and composite populations (2011, methodology): “This is also supported by an impressive observational study (Luhman et al. 2000; Luhman 2004) of many closeby star-forming regions using one consistent methodology to avoid author– author variations.”
The formation of free-floating brown dwarves and planetary-mass objects by photo-erosion of prestellar cores (2004, background): “Now they are routinely observed (e.g. McCaughrean et al. 1995; Luhman et al. 1998; Wilking et al. 1999; Luhman & Rieke 1999; Lucas & Roche 2000; Martín et al. 2000; Luhman et al. 2000; Béjar et al. 2001; Martín et al. 2001; Wilking et al. 2002; McCaughrean et al. 2002).”
The Palomar/MSU Nearby Star Spectroscopic Survey. IV. The Luminosity Function in the Solar Neighborhood and M Dwarf Kinematics (2002, background): “Ignoring those stars in the present 5 We note that Luhman et al. (2000), using a different set of evolutionary tracks, find that the mass function of the Orion Nebula cluster is consistent with a power law, 1, to 0.04M . analysis may affect the derived (U, V, W ) distributions at low velocities,…”
The Substellar Mass Function in σ Orionis (2001, background): “8 below the starÈsubstellar mass borderline have been obtained recently for other young clusters (Luhman et al. 2000 ; Lucas & Roche 2000 ; Hillenbrand & Carpenter 2000 ; Najita et al. 2000 ; et al. 2000 ;Mart• n Moraux et al. 2001), showing that the formation of brown dwarfs is a quite common…”
Inverse dynamical population synthesis: Constraining the initial conditions of young stellar clusters by studying their binary populations (2012, result): “Brown dwarfs have since been detected in the centre of the cluster (Hillenbrand & Carpenter 2000; Luhman et al. 2000; Lucas et al. 2001; Muench et al. 2002), so that the mean mass may decreases to 0.5M⊙ (Scally et al. 2005), in good agreement with the canonical IMF.”
The Orion Nebula and Its Associated Population (2001, methodology): “Both Hillenbrand & Carpenter (2000) and Luhman et al. (2000) find an IMF in agreement with the commonly adopted values, although Hillenbrand & Carpenter find evidence for an excess of more massive stars in the central core of the ONC.”
Brown dwarfs in the Pleiades cluster: Clues to the substellar mass function , (2002, background): “…above 1.5 M , ξ(log M) ∝ M−1.7 in logarithmic mass units (or dN/dM ∝ M−2.7 in linear mass units), and peaks at M 0.25 M before decreasing at lower mass. Luhman et al. (2000) found that ρ Ophiuchus, IC 348 and the Trapezium mass functions ξ(log M) also exhibit a maximum around 0.25 M and are…”