Self-similar collapse of isothermal spheres and star formation.
TL;DR: In this paper, the problem of the gravitational collapse of isothermal spheres by applying the similarity method to the gas-dynamic flow is considered, and two types of similarity solutions are obtained: one is the prototype for starting states which correspond to unstable hydrostatic equilibrium; the other, for states where the mass of the cloud slightly exceeds the maximum limit allowable for hydrostatic equilibria.
Abstract: We consider the problem of the gravitational collapse of isothermal spheres by applying the similarity method to the gas-dynamic flow. We argue that a previous solution obtained by Larson and Penston to describe the stages prior to core formation is physically artificial; however, we find that the flow following core formation does exhibit self-similar properties.The latter similarity solution shows that the inflow in the dense central regions proceeds virtually at free-fall before the material is arrested by a strong radiating shock upon impact with the surface of the core. Two types of similarity solutions are obtained: one is the prototype for starting states which correspond to unstable hydrostatic equilibrium; the other, for states where the mass of the cloud slightly exceeds the maximum limit allowable for hydrostatic equilibrium. In both cases, an r/sup -2/ law holds for the density distribution in the static or nearly static outer envelope, and an r/sup -3///sup 2/ law holds for the freely falling inner envelope. Rapid infall is initiated at the head of the expansion wave associated with the dropping of the central regions from beneath the envelope. A numerical example is presented which is shown to be in good agreement with the envelopemore » dynamics obtained in previous studies of star formation using hydrodynamic codes.« less
Citations
More filters
TL;DR: In this paper, an overall theoretical framework and the observations that motivate it are outlined, outlining the key dynamical processes involved in star formation, including turbulence, magnetic fields, and self-gravity.
Abstract: 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.
2,522 citations
Cites background from "Self-similar collapse of isothermal..."
...In the opposite case, considered by Shu (1977), one assumes that the evolution to the r−2 density profile is quasi-static (most likely due to the effects of magnetic fields—see below), so that the infall velocities are negligible at the moment of protostar formation....
[...]
TL;DR: In this article, the authors combined information drawn from studies of individual clouds into a combined and updated statistical analysis of star-formation rates and efficiencies, numbers and lifetimes for spectral energy distribution (SED) classes, and clustering properties.
Abstract: The c2d Spitzer Legacy project obtained images and photometry with both IRAC and MIPS instruments for five large, nearby molecular clouds. Three of the clouds were also mapped in dust continuum emission at 1.1 mm, and optical spectroscopy has been obtained for some clouds. This paper combines information drawn from studies of individual clouds into a combined and updated statistical analysis of star-formation rates and efficiencies, numbers and lifetimes for spectral energy distribution (SED) classes, and clustering properties. Current star-formation efficiencies range from 3% to 6%; if star formation continues at current rates for 10 Myr, efficiencies could reach 15-30%. Star-formation rates and rates per unit area vary from cloud to cloud; taken together, the five clouds are producing about 260 M ☉ of stars per Myr. The star-formation surface density is more than an order of magnitude larger than would be predicted from the Kennicutt relation used in extragalactic studies, reflecting the fact that those relations apply to larger scales, where more diffuse matter is included in the gas surface density. Measured against the dense gas probed by the maps of dust continuum emission, the efficiencies are much higher, with stellar masses similar to masses of dense gas, and the current stock of dense cores would be exhausted in 1.8 Myr on average. Nonetheless, star formation is still slow compared to that expected in a free-fall time, even in the dense cores. The derived lifetime for the Class I phase is 0.54 Myr, considerably longer than some estimates. Similarly, the lifetime for the Class 0 SED class, 0.16 Myr, with the notable exception of the Ophiuchus cloud, is longer than early estimates. If photometry is corrected for estimated extinction before calculating class indicators, the lifetimes drop to 0.44 Myr for Class I and to 0.10 for Class 0. These lifetimes assume a continuous flow through the Class II phase and should be considered median lifetimes or half-lives. Star formation is highly concentrated to regions of high extinction, and the youngest objects are very strongly associated with dense cores. The great majority (90%) of young stars lie within loose clusters with at least 35 members and a stellar density of 1 M ☉ pc–3. Accretion at the sound speed from an isothermal sphere over the lifetime derived for the Class I phase could build a star of about 0.25 M ☉, given an efficiency of 0.3. Building larger mass stars by using higher mass accretion rates could be problematic, as our data confirm and aggravate the "luminosity problem" for protostars. At a given T bol, the values for L bol are mostly less than predicted by standard infall models and scatter over several orders of magnitude. These results strongly suggest that accretion is time variable, with prolonged periods of very low accretion. Based on a very simple model and this sample of sources, half the mass of a star would be accreted during only 7% of the Class I lifetime, as represented by the eight most luminous objects.
1,752 citations
Cites background or methods from "Self-similar collapse of isothermal..."
...Considering a Shu model (Shu 1977), the wave of infall propagates outward at the sound speed until it reaches the outer bound of the region that will collapse....
[...]
...Models with mean accretion rates onto the star faster than the Shu (1977) rate are not supported by these observations....
[...]
...For the inside-out collapse model (Shu 1977), the mass infall rate is given by Ṁ = m0a 3/G, (10) with m0 = 0.975 and a is the sound speed....
[...]
...In fact, the luminosities seen in Class 0 sources are mostly similar to or less than predictions (Young & Evans 2005) of the evolution in Lbol-Tbol space based on simple inside-out collapse models (Shu 1977), with constant accretion rates and unit efficiency....
[...]
...Young & Evans (2005) did that for the standard Shu model (Shu 1977), assuming unit efficiency and spherical radiative transfer....
[...]
TL;DR: A review of the successes and problems of both the classical dynamical theory and the standard theory of magnetostatic support, from both observational and theoretical perspectives, is given in this paper.
Abstract: Understanding the formation of stars in galaxies is central to much of modern astrophysics. However, a quantitative prediction of the star formation rate and the initial distribution of stellar masses remains elusive. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift (known as ambipolar diffusion in astrophysics). Recently, however, both observational and numerical work has begun to suggest that supersonic turbulent flows rather than static magnetic fields control star formation. To some extent, this represents a return to ideas popular before the importance of magnetic fields to the interstellar gas was fully appreciated. This review gives a historical overview of the successes and problems of both the classical dynamical theory and the standard theory of magnetostatic support, from both observational and theoretical perspectives. The outline of a new theory relying on control by driven supersonic turbulence is then presented. Numerical models demonstrate that, although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic-scale star formation. It suggests that individual star-forming cores are likely not quasistatic objects, but dynamically collapsing. Accretion onto these objects varies depending on the properties of the surrounding turbulent flow; numerical models agree with observations showing decreasing rates. The initial mass distribution of stars may also be determined by the turbulent flow. Molecular clouds appear to be transient objects forming and dissolving in the larger-scale turbulent flow, or else quickly collapsing into regions of violent star formation. Global star formation in galaxies appears to be controlled by the same balance between gravity and turbulence as small-scale star formation, although modulated by cooling and differential rotation. The dominant driving mechanism in star-forming regions of galaxies appears to be supernovae, while elsewhere coupling of rotation to the gas through magnetic fields or gravity may be important.
1,630 citations
Cites background or methods from "Self-similar collapse of isothermal..."
...As an immediate consequence of the assumed singular 1/r2 initial density profile, the Shu (1977) model predicts constant protostellar accretion rates Ṁ⋆ = 0.975c 3 s/G, with sound speed cs and gravitational constant G....
[...]
...One application of this result is that for isopedic disks the derived mass accretion rate is just a scaled version of the original Shu (1977) rate, i.e. Ṁ ≈ (1 + H0) c3s/G, with the dimensionless parameter H0 depending on the effective mass-to-flux ratio....
[...]
...The standard solution was derived by Shu (1977) considering the evolution of initially singular isothermal spheres as they leave equilibrium....
[...]
...In particular Shu (1977) proposed the self-similar collapse of initially quasi-static singular isothermal spheres as the most likely description of the star formation process....
[...]
...The basis of the Shu (1977) model is the singular isothermal sphere, i.e. the theory assumes radial density profiles ρ ∝ 1/r2 at all radii r as starting conditions of protostellar collapse....
[...]
TL;DR: In this paper, the authors discuss both the observation and chemistry of complex molecules in assorted interstellar regions in the Milky Way and discuss both their spectra and chemistry, and conclude that complex molecules are excellent probes of the physical conditions and history of the sources where they reside.
Abstract: Of the over 150 different molecular species detected in the interstellar and circumstellar media, approximately 50 contain 6 or more atoms. These molecules, labeled complex by astronomers if not by chemists, all contain the element carbon and so can be called organic. In the interstellar medium, complex molecules are detected in the denser sources only. Although, with one exception, complex molecules have only been detected in the gas phase, there is strong evidence that they can be formed in ice mantles on interstellar grains. The nature of the gaseous complex species depends dramatically on the source where they are found: in cold, dense regions they tend to be unsaturated (hydrogen-poor) and exotic, whereas in young stellar objects, they tend to be quite saturated (hydrogen-rich) and terrestrial in nature. Based on both their spectra and chemistry, complex molecules are excellent probes of the physical conditions and history of the sources where they reside. Because they are detected in young stellar objects, complex molecules are expected to be common ingredients for new planetary systems. In this review, we discuss both the observation and chemistry of complex molecules in assorted interstellar regions in the Milky Way.
1,470 citations
Goddard Space Flight Center1, Université de Montréal2, Space Science Institute3, Herzberg Institute of Astrophysics4, European Space Agency5, École Polytechnique Fédérale de Lausanne6, Space Telescope Science Institute7, University of Arizona8, University of Exeter9, Max Planck Society10, NASA Headquarters11, Arizona State University12, UK Astronomy Technology Centre13
TL;DR: The James Webb Space Telescope (JWST) as discussed by the authors is a large (6.6 m), cold (<50 K), infrared-optimized space observatory that will be launched early in the next decade into orbit around the second Earth-Sun Lagrange point.
Abstract: The James Webb Space Telescope (JWST) is a large (6.6 m), cold (<50 K), infrared (IR)-optimized space observatory that will be launched early in the next decade into orbit around the second Earth–Sun Lagrange point. The observatory will have four instruments: a near-IR camera, a near-IR multiobject spectrograph, and a tunable filter imager will cover the wavelength range, 0.6 < ; < 5.0 μ m, while the mid-IR instrument will do both imaging and spectroscopy from 5.0 < ; < 29 μ m. The JWST science goals are divided into four themes. The key objective of The End of the Dark Ages: First Light and Reionization theme is to identify the first luminous sources to form and to determine the ionization history of the early universe. The key objective of The Assembly of Galaxies theme is to determine how galaxies and the dark matter, gas, stars, metals, morphological structures, and active nuclei within them evolved from the epoch of reionization to the present day. The key objective of The Birth of Stars and Protoplanetary Systems theme is to unravel the birth and early evolution of stars, from infall on to dust-enshrouded protostars to the genesis of planetary systems. The key objective of the Planetary Systems and the Origins of Life theme is to determine the physical and chemical properties of planetary systems including our own, and investigate the potential for the origins of life in those systems. Within these themes and objectives, we have derived representative astronomical observations. To enable these observations, JWST consists of a telescope, an instrument package, a spacecraft, and a sunshield. The telescope consists of 18 beryllium segments, some of which are deployed. The segments will be brought into optical alignment on-orbit through a process of periodic wavefront sensing and control. The instrument package contains the four science instruments and a fine guidance sensor. The spacecraft provides pointing, orbit maintenance, and communications. The sunshield provides passive thermal control. The JWST operations plan is based on that used for previous space observatories, and the majority of JWST observing time will be allocated to the international astronomical community through annual peer-reviewed proposal opportunities.
1,372 citations