Theory of Star Formation

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.Comment: 120 pages, to appear in ARAA. No changes from v1 text; permission statement adde

Fractional Zaslavsky and Henon Discrete Maps

This paper is devoted to the memory of Professor George M. Zaslavsky passed away on November 25, 2008. In the field of discrete maps, George M. Zaslavsky introduced a dissipative standard map which is called now the Zaslavsky map. G. Zaslavsky initialized many fundamental concepts and ideas in the fractional dynamics and kinetics. In this paper, starting from kicked damped equations with derivatives of non-integer orders we derive a fractional generalization of discrete maps. These fractional maps are generalizations of the Zaslavsky map and the Henon map. The main property of the fractional differential equations and the correspondent fractional maps is a long-term memory and dissipation. The memory is realized by the fact that their present state evolution depends on all past states with special forms of weights.Comment: 26 pages, LaTe

Dispersive, superfluid-like shock waves in nonlinear optics

In most classical fluids, shock waves are strongly dissipative, their energy being quickly lost through viscous damping. But in systems such as cold plasmas, superfluids, and Bose-Einstein condensates, where viscosity is negligible or non-existent, a fundamentally different type of shock wave can emerge whose behaviour is dominated by dispersion rather than dissipation. Dispersive shock waves are difficult to study experimentally, and analytical solutions to the equations that govern them have only been found in one dimension (1D). By exploiting a well-known, but little appreciated, correspondence between the behaviour of superfluids and nonlinear optical materials, we demonstrate an all-optical experimental platform for studying the dynamics of dispersive shock waves. This enables us to observe the propagation and nonlinear response of dispersive shock waves, including the interaction of colliding shock waves, in 1D and 2D. Our system offers a versatile and more accessible means for exploring superfluid-like and related dispersive phenomena.Comment: 21 pages, 6 figures Revised abstrac

Electron acceleration by wave turbulence in a magnetized plasma

Astrophysical shocks are commonly revealed by the non-thermal emission of energetic electrons accelerated in situ 1-3 . Strong shocks are expected to accelerate particles to very high energies 4-6 ; however, they require a source of particles with velocities fast enough to permit multiple shock crossings. While the resulting diffusive shock acceleration 4 process can account for observations, the kinetic physics regulating the continuous injection of non-thermal particles is not well understood. Indeed, this injection problem is particularly acute for electrons, which rely on high-frequency plasma fluctuations to raise them above the thermal pool 7,8 . Here we show, using laboratory laser-produced shock experiments, that, in the presence of a strong magnetic field, significant electron pre-heating is achieved. We demonstrate that the key mechanism in producing these energetic electrons is through the generation of lower-hybrid turbulence via shock-reflected ions. Our experimental results are analogous to many astrophysical systems, including the interaction of a comet with the solar wind 9 , a setting where electron acceleration via lower-hybrid waves is possible

Mechanism for spectral break in cosmic ray proton spectrum of supernova remnant W44.

Recent observations of supernova remnant W44 by the Fermi spacecraft observatory support the idea that the bulk of galactic cosmic rays is accelerated in such remnants by a Fermi mechanism, also known as diffusive shock acceleration. However, the W44 expands into weakly ionized dense gas, and so a significant revision of the mechanism is required. Here, we provide the necessary modifications and demonstrate that strong ion-neutral collisions in the remnant surrounding lead to the steepening of the energy spectrum of accelerated particles by exactly one power. The spectral break is caused by Alfven wave evanescence leading to the fractional particle losses. The gamma-ray spectrum generated in collisions of the accelerated protons with the ambient gas is calculated and successfully fitted to the Fermi Observatory data. The parent proton spectrum is best represented by a classical test particle power law ∝E(-2), steepening to E(-3) at E(br)≈7 GeV due to deteriorated particle confinement

Proton-helium spectral anomaly as a signature of cosmic ray accelerator.

The much-anticipated proof of cosmic ray (CR) acceleration in supernova remnants must hinge on the full consistency of acceleration theory with the observations; direct proof is impossible because of CR-orbit scrambling. Recent observations indicate deviations between helium and proton CR rigidity spectra inconsistent with the theory. By considering an initial (injection) phase of the diffusive shock acceleration, where elemental similarity does not apply, we demonstrate that the spectral difference is, in fact, a unique signature of the acceleration mechanism. Collisionless shocks inject more He(2+) when they are stronger and so produce harder He(2+) spectra. The injection bias is due to Alfvén waves driven by the more abundant protons, so the He(2+) ions are harder to trap by these waves. By fitting the p/He ratio to the PAMELA data, we bolster the diffusive shock acceleration case for resolving the century-old mystery of CR origin