We review current understanding of star formation, outlining an overall theoretical framework and the observations that motivate it. A conception of star formation has emerged in which turbulence plays a dual role, both creating overdensities to initiate gravitational contraction or collapse, and countering the effects of gravity in these overdense regions. The key dynamical processes involved in star formation—turbulence, magnetic fields, and self-gravity— are highly nonlinear and multidimensional. Physical arguments are used to identify and explain the features and scalings involved in star formation, and results from numerical simulations are used to quantify these effects. We divide star formation into large-scale and small-scale regimes and review each in turn. Large scales range from galaxies to giant molecular clouds (GMCs) and their substructures. Important problems include how GMCs form and evolve, what determines the star formation rate (SFR), and what determines the initial mass function (IMF). Small scales range from dense cores to the protostellar systems they beget. We discuss formation of both low- and high-mass stars, including ongoing accretion. The development of winds and outflows is increasingly well understood, as are the mechanisms governing angular momentum transport in disks. Although outstanding questions remain, the framework is now in place to build a comprehensive theory of star formation that will be tested by the next generation of telescopes.

/pdf/theory-of-star-formation-sol2jzngnw.pdf

Theory of Star Formation

The universality of interstellar turbulence is examined from observed structure functions of 27 giant molecular clouds and Monte Carlo modeling. We show that the structure functions, ?v = vol?, derived from wide-field imaging of 12CO J=1-0 emission from individual clouds are described by a narrow range in the scaling exponent, ?, and the scaling coefficient, vo. The similarity of turbulent structure functions emphasizes the universality of turbulence in the molecular interstellar medium and accounts for the cloud-to-cloud size/line width relationship initially identified by Larson. The degree of turbulence universality is quantified by Monte Carlo simulations that reproduce the mean squared velocity residuals of the observed cloud-to-cloud relationship. Upper limits to the variation of the scaling amplitudes and exponents for molecular clouds are ~10%-20%. The measured invariance of turbulence for molecular clouds with vastly different sizes, environments, and star formation activity suggests a common formation mechanism such as converging turbulent flows within the diffuse interstellar medium and a limited contribution of energy from sources within the cloud with respect to large-scale driving mechanisms.

https://iopscience.iop.org/article/10.1086/425978/pdf

The Universality of Turbulence in Galactic Molecular Clouds

We present results of an extensive mapping survey of N2H+(1-0) in about 60 low mass cloud cores already mapped in the NH3(1,1) inversion transition line. The survey has been carried out at the FCRAO antenna with an angular resolution about 1.5 times finer than the previous ammonia observations. Cores with stars typically have map sizes about a factor of two smaller for N2H+ than for NH3, indicating the presence of denser and more centrally concentrated gas compared to starless cores. Significant correlations are found between NH3 and N2H+ column densities and excitation temperatures in starless cores, but not in cores with stars, suggesting a different chemical evolution of the two species. Velocity gradients range between 0.5 and 6 km/s/pc, similar to what has been found with NH3 data. ``Local'' velocity gradients show significant variation in both magnitude and direction, suggesting the presence of complexmotions not interpretable as simple solid body rotation. Integrated intensity profiles of starless cores present a ``central flattening'' and are consistent with a spherically symmetric density law n ~ r^{-1.2} for r < ~0.03 pc and n ~ r^{-2} at larger r. Cores with stars are better modelled with single density power laws with n ~ r^{-2}. Line widths change across the core but we did not find a general trend. The deviation in line width correlates with the mean line width, suggesting that the line of sight contains ~ 10 coherence lengths. The corresponding value of the coherence length, ~ 0.01 pc, is similar to the expected cutoff wavelength for MHD waves. This similarity may account for the increased ``coherence'' of line widths on small scales. Despite of the finer angular resolution, the majority of N2H+ and NH3 maps show a similar ``simple'' structure, with single peaks and no elongation.

Dense Cores in Dark Clouds. XIV. N2H+(1-0) maps of dense cloud cores

The optically thin critical densities and the effective excitation densities to produce a 1 K km/s (or 0.818 Jy km/s ) spectral line are tabulated for 12 commonly observed dense gas molecular tracers. The dependence of the critical density and effective excitation density on physical assumptions (i.e., gas kinetic temperature and molecular column density) is analyzed. Critical densities for commonly observed dense gas transitions in molecular clouds (i.e., HCN 1–0, HCO+ 1–0, N2H+ 1–0) are typically 1-2 orders of magnitude larger than effective excitation densities because the standard definitions of critical density do not account for radiative trapping and 1 K km/s lines are typically produced when radiative rates out of the upper energy level of the transition are faster than collisional depopulation. The use of effective excitation density has a distinct advantage over the use of critical density in characterizing the differences in density traced by species such as NH3, HCO+, N2H+, and HCN, as well as their isotopologues; but, the effective excitation density has the disadvantage that it is undefined for transitions when Eu/kTk, for low molecular column densities, and for heavy molecules with complex spectra (i.e., CH3CHO).

https://iopscience.iop.org/article/10.1086/680342/pdf

The Critical Density and the Effective Excitation Density of Commonly Observed Molecular Dense Gas Tracers

We present and discuss the results of the Herschel Gould Belt survey (HGBS) observations in an ~11 deg2 area of the Aquila molecular cloud complex at d ~ 260 pc, imaged with the SPIRE and PACS photometric cameras in parallel mode from 70 μm to 500 μm. Using the multi-scale, multi-wavelength source extraction algorithm getsources, we identify a complete sample of starless dense cores and embedded (Class 0-I) protostars in this region, and analyze their global properties and spatial distributions. We find a total of 651 starless cores, ~60% ± 10% of which are gravitationally bound prestellar cores, and they will likely form stars inthe future. We also detect 58 protostellar cores. The core mass function (CMF) derived for the large population of prestellar cores is very similar in shape to the stellar initial mass function (IMF), confirming earlier findings on a much stronger statistical basis and supporting the view that there is a close physical link between the stellar IMF and the prestellar CMF. The global shift in mass scale observed between the CMF and the IMF is consistent with a typical star formation efficiency of ~40% at the level of an individual core. By comparing the numbers of starless cores in various density bins to the number of young stellar objects (YSOs), we estimate that the lifetime of prestellar cores is ~1 Myr, which is typically ~4 times longer than the core free-fall time, and that it decreases with average core density. We find a strong correlation between the spatial distribution of prestellar cores and the densest filaments observed in the Aquila complex. About 90% of the Herschel-identified prestellar cores are located above a background column density corresponding to AV ~ 7, and ~75% of them lie within filamentary structures with supercritical masses per unit length ≳16 M⊙/pc. These findings support a picture wherein the cores making up the peak of the CMF (and probably responsible for the base of the IMF) result primarily from the gravitational fragmentation of marginally supercritical filaments. Given that filaments appear to dominate the mass budget of dense gas at AV> 7, our findings also suggest that the physics of prestellar core formation within filaments is responsible for a characteristic “efficiency” for the star formation process in dense gas.

/pdf/a-census-of-dense-cores-in-the-aquila-cloud-complex-spire-4dv0mrkdgf.pdf

A census of dense cores in the Aquila cloud complex: SPIRE/PACS observations from the Herschel Gould Belt survey

We obtained continuum maps at a wavelength of 350 μm for eight gas–dust clouds from the southern hemisphere using the APEX-12m telescope. The clouds are related to the regions of the formation of high-mass stars and star clusters and have dense cores. The core sizes estimated at half the maximum intensity at a wavelength of 350 μm are 0.1–0.2 pc. The core masses and gas mean densities lie in the ranges 20–1000 Mʘ and (0.3–7.3)·106 cm−3, respectively. A comparison of the obtained data at a wavelength of 350 μm with observation data of the same objects at a wavelength of 1.2 mm was carried out. From the intensity ratios at two wavelengths reduced to one angular resolution, the spatial distributions of the average dust temperature on the line of sight are calculated. Dust temperature maps in most objects correlate with intensity distributions at a wavelength of 350 μm. A decrease in the dust temperature with distance from the center is detected in most cores. The obtained dust temperature profiles in most cases turned out to be close to linear ones. Using a simple spherically symmetric model of a dust cloud, it is shown that temperature profiles close to the observed ones can be obtained under the assumption of the presence of an internal source by varying the density profile parameters and specifying a powerlaw index β of the dust emissivity dependence on frequency as a constant. It is shown that the dust temperature estimates strongly depend on the chosen value of β. It is considered how possible variations of β in the cloud can affect the results obtained. 

L. E. Pirogov

Papers

Dust Temperature Profiles in Dense Cores Related to the High-Mass Star-Forming Regions

Molecular multi-line and dust continuum studies of high mass star forming regions