A universal initial mass function (IMF) is not intuitive, but so far no convincing evidence for a variable IMF exists. The detection of systematic variations of the IMF with star-forming conditions would be the Rosetta Stone for star formation.



In this contribution an average or Galactic-field IMF is defined, stressing that there is evidence for a change in the power-law index at only two masses: near 0.5 M⊙ and near 0.08 M⊙. Using this supposed universal IMF, the uncertainty inherent in any observational estimate of the IMF is investigated by studying the scatter introduced by Poisson noise and the dynamical evolution of star clusters. It is found that this apparent scatter reproduces quite well the observed scatter in power-law index determinations, thus defining the fundamental limit within which any true variation becomes undetectable. The absence of evidence for a variable IMF means that any true variation of the IMF in well-studied populations must be smaller than this scatter.



Determinations of the power-law indices α are subject to systematic errors arising mostly from unresolved binaries. The systematic bias is quantified here, with the result that the single-star IMFs for young star clusters are systematically steeper by Δα≈0.5 between 0.1 and 1 M⊙ than the Galactic-field IMF, which is populated by, on average, about 5-Gyr-old stars. The MFs in globular clusters appear to be, on average, systematically flatter than the Galactic-field IMF (Piotto & Zoccali; Paresce & De Marchi), and the recent detection of ancient white-dwarf candidates in the Galactic halo and the absence of associated low-mass stars (Ibata et al.; Mendez & Minniti) suggest a radically different IMF for this ancient population. Star formation in higher metallicity environments thus appears to produce relatively more low-mass stars. While still tentative, this is an interesting trend, being consistent with a systematic variation of the IMF as expected from theoretical arguments.

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On the variation of the initial mass function

The Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data provide stringent limits on deviations from the minimal, six-parameter Λ cold dark matter model. We report these limits and use them to constrain the physics of cosmic inflation via Gaussianity, adiabaticity, the power spectrum of primordial fluctuations, gravitational waves, and spatial curvature. We also constrain models of dark energy via its equation of state, parity-violating interaction, and neutrino properties, such as mass and the number of species. We detect no convincing deviations from the minimal model. The six parameters and the corresponding 68% uncertainties, derived from the WMAP data combined with the distance measurements from the Type Ia supernovae (SN) and the Baryon Acoustic Oscillations (BAO) in the distribution of galaxies, are: Ω b h 2 = 0.02267+0.00058 –0.00059, Ω c h 2 = 0.1131 ± 0.0034, ΩΛ = 0.726 ± 0.015, ns = 0.960 ± 0.013, τ = 0.084 ± 0.016, and at k = 0.002 Mpc-1. From these, we derive σ8 = 0.812 ± 0.026, H 0 = 70.5 ± 1.3 km s-1 Mpc–1, Ω b = 0.0456 ± 0.0015, Ω c = 0.228 ± 0.013, Ω m h 2 = 0.1358+0.0037 –0.0036, z reion = 10.9 ± 1.4, and t 0 = 13.72 ± 0.12 Gyr. With the WMAP data combined with BAO and SN, we find the limit on the tensor-to-scalar ratio of r 1 is disfavored even when gravitational waves are included, which constrains the models of inflation that can produce significant gravitational waves, such as chaotic or power-law inflation models, or a blue spectrum, such as hybrid inflation models. We obtain tight, simultaneous limits on the (constant) equation of state of dark energy and the spatial curvature of the universe: –0.14 < 1 + w < 0.12(95%CL) and –0.0179 < Ω k < 0.0081(95%CL). We provide a set of WMAP distance priors, to test a variety of dark energy models with spatial curvature. We test a time-dependent w with a present value constrained as –0.33 < 1 + w 0 < 0.21 (95% CL). Temperature and dark matter fluctuations are found to obey the adiabatic relation to within 8.9% and 2.1% for the axion-type and curvaton-type dark matter, respectively. The power spectra of TB and EB correlations constrain a parity-violating interaction, which rotates the polarization angle and converts E to B. The polarization angle could not be rotated more than –59 < Δα < 24 (95% CL) between the decoupling and the present epoch. We find the limit on the total mass of massive neutrinos of ∑m ν < 0.67 eV(95%CL), which is free from the uncertainty in the normalization of the large-scale structure data. The number of relativistic degrees of freedom (dof), expressed in units of the effective number of neutrino species, is constrained as N eff = 4.4 ± 1.5 (68%), consistent with the standard value of 3.04. Finally, quantitative limits on physically-motivated primordial non-Gaussianity parameters are –9 < f local NL < 111 (95% CL) and –151 < f equil NL < 253 (95% CL) for the local and equilateral models, respectively.

https://iopscience.iop.org/article/10.1088/0067-0049/180/2/330/pdf

Five-year wilkinson microwave anisotropy probe observations: cosmological interpretation

We present cosmological parameter constraints based on the final nine-year WMAP data, in conjunction with a number of additional cosmological data sets. The WMAP data alone, and in combination, continue to be remarkably well fit by a six-parameter CDM model. When WMAP data are combined with measurements of the high-l cosmic microwave background (CMB) anisotropy, the baryon acoustic oscillation (BAO) scale, and the Hubble constant, the matter and energy densities, bh 2 , ch 2 , and , are each determined to a precision of 1.5%. The amplitude of the primordial spectrum is measured to within 3%, and there is now evidence for a tilt in the primordial spectrum at the 5 level, confirming the first detection of tilt based on the five-year WMAP data. At the end of the WMAP mission, the nine-year data decrease the allowable volume of the six-dimensional CDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their CDM parameter fits are consistent. New limits on deviations from the six-parameter model are presented, for example: the fractional contribution of tensor modes is limited to r < 0.13 (95% CL); the spatial curvature parameter is limited to k = 0.0027 +0.0039 0.0038 ; the summed mass of neutrinos is limited to P m < 0.44 eV (95% CL); and the number of relativistic species is found to lie within Ne = 3.84±0.40, when the full data are analyzed. The joint constraint on Ne and the primordial helium abundance, YHe, agrees with the prediction of standard Big Bang nucleosynthesis. We compare recent Planck measurements of the Sunyaev‐Zel’dovich eect with our seven-year measurements, and show their mutual agreement. Our analysis of the polarization pattern around temperature extrema is updated. This confirms a fundamental prediction of the standard cosmological model and provides a striking illustration of acoustic oscillations and adiabatic initial conditions in the early universe. Subject headings: cosmic microwave background, cosmology: observations, early universe, dark matter, space vehicles, space vehicles: instruments, instrumentation: detectors, telescopes

/pdf/nine-year-wilkinson-microwave-anisotropy-probe-wmap-2akqcincu6.pdf

Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results

Protostars and Planets VI

▪ Abstract Stellar clusters are born embedded within giant molecular clouds (GMCs) and during their formation and early evolution are often only visible at infrared wavelengths, being heavily obscured by dust. Over the past 15 years advances in infrared detection capabilities have enabled the first systematic studies of embedded clusters in galactic molecular clouds. In this article we review the current state of empirical knowledge concerning these extremely young protocluster systems. From a survey of the literature we compile the first extensive catalog of galactic embedded clusters. We use the catalog to construct the mass function and estimate the birthrate for embedded clusters within ∼2 kpc of the sun. We find that the embedded cluster birthrate exceeds that of visible open clusters by an order of magnitude or more indicating a high infant mortality rate for protocluster systems. Less than 4–7% of embedded clusters survive emergence from molecular clouds to become bound clusters of Pleiades age. Th...

http://www.ifa.hawaii.edu/%7Ereipurth/reviews/ladalada.pdf

Embedded Clusters in Molecular Clouds

We report the results of the first sensitive L-band survey of the intermediate-age (2.5-30 Myr) clusters NGC 2264, NGC 2362, and NGC 1960. We use JHKL colors to obtain a census of the circumstellar disk fractions in each cluster. We find disk fractions of 52% ± 10%, 12% ± 4%, and 3% ± 3% for the three clusters, respectively. Together with our previously published JHKL investigations of the younger NGC 2024, Trapezium, and IC 348 clusters, we have completed the first systematic and homogeneous survey for circumstellar disks in a sample of young clusters that both span a significant range in age (0.3-30 Myr) and contain statistically significant numbers of stars whose masses span nearly the entire stellar mass spectrum. Analysis of the combined survey indicates that the cluster disk fraction is initially very high (≥80%) and rapidly decreases with increasing cluster age, such that one-half the stars within the clusters lose their disks in 3 Myr. Moreover, these observations yield an overall disk lifetime of ~6 Myr in the surveyed cluster sample. This is the timescale for essentially all the stars in a cluster to lose their disks. This should set a meaningful constraint for the planet-building timescale in stellar clusters. The implications of these results for current theories of planet formation are briefly discussed.

https://iopscience.iop.org/article/10.1086/320685/pdf

Disk Frequencies and Lifetimes in Young Clusters

We reconsider the structure and formation of OB association in view of recent radio and infrared observations of the adjacent molecular clouds. As a result of this reexamination, we propose that OB subgroups are formed in a step-by-step process which involves the propagation of ionization (I) and shock (S) fronts through a molecular cloud complex. OB stars formed at the edge of a molecular cloud drive these I-S fronts into the cloud. A layer of dense neutral material accumulates between the I and S fronts and eventually becomes gravitationally unstable. This process is analyzed in detail. Several arguments concerning the temperature and mass of this layer suggest that a new OB subgroup will form. After approximately one-half million years, these stars will emerge from and disrupt the star-forming layer. A new shock will be driven into the remaining molecular cloud and will initiate another cycle of star formation.Several observed properties of OB associations are shown to follow from a sequential star-forming mechanism. These include the spatial separation and systematic differences in age of OB subgroups in a given association, the regularity of subgroup masses, the alignment of subgroups along the galactic plane, and their physical expansion. Detailed observations of ionizationmore » fronts, masers, IR sources, and molecular clouds are also in agreement with this model. Finally, this mechanism provides a means of dissipating a molecular cloud and exposing less massive stars (e.g., T Tauri stars) which may have formed ahead of the shock as part of the original cloud collapsed and fragmented.« less

Sequential formation of subgroups in OB associations

In this paper, we investigate the level of star formation activity within nearby molecular clouds. We employ a uniform set of infrared extinction maps to provide accurate assessments of cloud mass and structure and compare these with inventories of young stellar objects within the clouds. We present evidence indicating that both the yield and rate of star formation can vary considerably in local clouds, independent of their mass and size. We find that the surface density structure of such clouds appears to be important in controlling both these factors. In particular, we find that the star formation rate (SFR) in molecular clouds is linearly proportional to the cloud mass (M 0.8) above an extinction threshold of A K ≈ 0.8 mag, corresponding to a gas surface density threshold of Σgas ≈ 116 M ☉ pc2. We argue that this surface density threshold corresponds to a gas volume density threshold which we estimate to be n(H2) ≈ 104 cm–3. Specifically, we find SFR (M ☉ yr–1) = 4.6 ± 2.6 × 10–8 M 0.8 (M ☉) for the clouds in our sample. This relation between the rate of star formation and the amount of dense gas in molecular clouds appears to be in excellent agreement with previous observations of both galactic and extragalactic star-forming activity. It is likely the underlying physical relationship or empirical law that most directly connects star formation activity with interstellar gas over many spatial scales within and between individual galaxies. These results suggest that the key to obtaining a predictive understanding of the SFRs in molecular clouds and galaxies is to understand those physical factors which give rise to the dense components of these clouds.

On the Star Formation Rates in Molecular Clouds

An evolutionary sequence, from protostars to pre-main sequence stars, for the classification of young stellar objects is derived by comparing the predictions of the theoretical protostar models of Adams and Shu (AS, 1986) with the morphological classification scheme of Lada and Wilking (1984). It is shown that the AS models adequately explain the emergent spectral energy distributions of unidentified objects with negative spectral indices in the mid-IR and near-IR in both Taurus and Ophiuchus. If the infalling dust envelope is then completely removed, the spectra of the underlying stars and nebular disks used by AS provide a natural explanation for the near-IR and mid-IR excesses and the positive spectral indices of embedded T Tauri stars. It is found that the addition of a simple physical model for residual dust envelopes can reproduce the far-IR excesses found in some of these T Tauri stars.

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Charles J. Lada

Papers

Embedded Clusters in Molecular Clouds

Disk Frequencies and Lifetimes in Young Clusters

Sequential formation of subgroups in OB associations

On the Star Formation Rates in Molecular Clouds

Spectral evolution of young stellar objects