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.

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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.

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

We present the results of N2H + (1-0) observations of 35 dense molecular cloud cores from the northern and southern hemispheres where massive stars and star clusters are formed. Line emission has been detected in 33 sources, for 28 sources detailed maps have been obtained. Peak N2H + column densities lie in the range: 3:6 10 12 1:5 10 14 cm 2 . Intensity ratios of (01-12) to (23-12) hyperfine components are slightly higher than the LTE value. The optical depth of (23-12) component toward peak intensity positions of 10 sources is0:2 1. In many cases the cores have elongated or more complex structures with several emission peaks. In total, 47 clumps have been revealed in 26 sources. Their sizes lie in the range 0.3-2.1 pc, the range of virial masses is30 3000 M. Mean N2H + abundance for 36 clumps is 5 10 10 . Integrated intensity maps with axial ratios<2 have been fitted with a power-law radial distribution r p convolved with the telescope beam. Mean power-law index for 25 clumps is close to 1.3. For reduced maps where positions of low intensity are rejected mean power-law index is close to unity corresponding to ther 2 density profile provided N 2H + excitation conditions do not vary inside these regions. In those cases where we have relatively extensive and high quality maps, line widths of the cores either decrease or stay constant with distance from the center, implying an enhanced dynamical activity in the center. There is a correlation between total velocity gradient direction and elongation angle of the cores. However, the ratio of rotational to gravitational energy is too low (4 10 4 - 7:1 10 2 ) for rotation to play a significant role in the dynamics of the cores. A correlation between mean line widths and sizes

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N 2 H + (1-0) survey of massive molecular cloud cores

We have conducted a survey of HCN and HNC (two rotational transitions each) in our standard sample of 11 cirrus cores and 27 Clemens-Barvainis translucent cores whose structures and chemistry have been studied earlier in this series. Both species are seen in all 38 objects. HCNH+ has been searched in three objects. These results are modeled in terms of our previous hydrostatic equilibrium and n ~ r-α structures together with other chemical and physical properties derived earlier. A detailed program has been written to handle the complex radiative transfer of the hyperfine splitting (hfs) of HCN. It is shown that serious errors are made in deriving HCN abundances by methods that ignore the hfs. Both HCN and HNC abundances are high, typically 1(-8) in most sources. The chemically important ratio HCN/HNC is found to be ~2.5 if these species are spatially centrally peaked and ~6 if not. Both species abundances increase monotonically with increasing extinction in the 1.2-2.7 mag range (edge to center), thus displaying the same characteristic transition between diffuse and dense cloud chemistry as do most other species we have studied. HCN/HNC decreases with increasing extinction to a value of 1.3 at Av0 ~ 10, approaching the expected value of 1.0 for dense clouds. Two types of ion-molecule chemistry models have been carried out: a full model using the Standard Model rate file and comprising 409 species (by Lee and Herbst), and a simplified model comprising 21 nitrogen-bearing species for conditions relevant to translucent clouds. Good agreement between observations and chemistry models is achieved throughout the translucent extinction range. Important conclusions are that (1) neutral-neutral reactions such as N + CH2 dominate the chemistry of HCN; (2) low ion-polar reaction rates are strongly favored over high ones; (3) the reaction C+ + NH3 → H2NC+ → HNC is unimportant, thus largely uncoupling the CN and NH chemistries; (4) the ratio HCN/HNC is not a particularly important diagnostic of the CN chemistry; (5) model NH3 abundances are at least a factor 100 lower than observed in translucent clouds, even if the reaction N+H+3→NH+2 is permitted at Langevin rate.

http://iopscience.iop.org/article/10.1086/304228/pdf

The Physics and Chemistry of Small Translucent Molecular Clouds. VIII. HCN and HNC

We present the results of N2H+(1-0) observations of 35 dense molecular cloud cores from the northern and southern hemispheres where massive stars and star clusters are formed Line emission has been detected in 33 sources, for 28 sources detailed maps have been obtained The optical depth of (23-12) component toward peak intensity positions of 10 sources is ~ 02-1 In total, 47 clumps have been revealed in 26 sources Integrated intensity maps with aspect ratios < 2 have been fitted with a power-law radial distribution $r^{-p}$ convolved with the telescope beam Mean power-law index is close to unity corresponding to the $\sim r^{-2}$ density profile provided N2H+ excitation conditions do not vary inside these regions Line widths of the cores either decrease or stay constant with distance from the center The ratio of rotational to gravitational energy is too low for rotation to play a significant role in the dynamics of the cores A correlation between mean line widths and sizes of clumps has been found

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N2H+(1-0) survey of massive molecular cloud cores

We present a multiwavelength study of W40 star-forming region using IR observations in UKIRT JHK bands, Spitzer IRAC bands & Herschel PACS bands; 2.12 micron H2 narrow-band imaging; & radio observations from GMRT (610 & 1280 MHz), in a FoV of ~34'x40'. Spitzer observations along with NIR observations are used to identify 1162 Class II/III & 40 Class I sources in the FoV. The NN stellar surface density analysis shows that majority of these YSOs constitute the embedded cluster centered on the source IRS1A South. Some YSOs, predominantly younger population, are distributed along & trace the filamentary structures at lower stellar surface density. The cluster radius is obtained as 0.44pc - matching well with the extent of radio emission - with a peak density of 650pc^-2. The JHK data is used to map the extinction which is subsequently used to compute the cloud mass. It has resulted in 126 Msun & 71 Msun for the central cluster & the northern IRS5 region, respectively. H2 narrow-band imaging displays significant emission, which prominently resembles fluorescent emission arising at the borders of dense regions. Radio analysis shows this region as having blister morphology, with the radio peak coinciding with a protostellar source. Free-free emission SED analysis is used to obtain physical parameters of the overall region & the IRS5 sub-region. This multiwavelength scenario is suggestive of star formation having resulted from merging of multiple filaments to form a hub. Star formation seems to have taken place in two successive epochs, with the first epoch traced by the central cluster & the high-mass star(s) - followed by a second epoch which is spreading into the filaments as uncovered by the Class I sources & even younger protostellar sources along the filaments. The IRS5 HII region displays indications of swept-up material which has possibly led to the formation of protostars.

W40 region in the Gould Belt : An embedded cluster and H II region at the junction of filaments

Radial density profiles for the sample of dense cores associated with high-mass star-forming regions from southern hemisphere have been derived using the data of observations in continuum at 250 GHz. Radial density profiles for the inner regions of 16 cores (at distances ≲0.2−0.8 pc from the center) are close on average to the ρ ∝ r
 −α dependence, where α = 1.6 ± 0.3. In the outer regions density drops steeper. An analysis with various hydrostatic models showed that the modified Bonnor-Ebertmodel, which describes turbulent sphere confined by external pressure, is preferable compared with the logotrope and polytrope models practically in all cases. With a help of the Bonnor-Ebert model, estimates of central density in a core, non-thermal velocity dispersion and core size are obtained. The comparison of central densities with the densities derived earlier from the CS modeling reveals differences in several cases. The reasons of such differences are probably connected with the presence of density inhomogenities on the scales smaller than the telescope beam. In most cases non-thermal velocity dispersions are in agreement with the values obtained from molecular line observations.

L. E. Pirogov

Papers

N 2 H + (1-0) survey of massive molecular cloud cores

The Physics and Chemistry of Small Translucent Molecular Clouds. VIII. HCN and HNC

N2H+(1-0) survey of massive molecular cloud cores

W40 region in the Gould Belt : An embedded cluster and H II region at the junction of filaments

Density profiles in molecular cloud cores associated with high-mass star-forming regions