The large scale structure of the universe.

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

Radiation, winds, and jets from the active nucleus of a massive galaxy can interact with its interstellar medium, and this can lead to ejection or heating of the gas. This terminates star formation in the galaxy and stifles accretion onto the black hole. Such active galactic nuclei (AGN) feedback can account for the observed proportionality between the central black hole and the host galaxy mass. Direct observational evidence for the radiative or quasar mode of feedback, which occurs when AGN are very luminous, has been difficult to obtain but is accumulating from a few exceptional objects. Feedback from the kinetic or radio mode, which uses the mechanical energy of radio-emitting jets often seen when AGN are operating at a lower level, is common in massive elliptical galaxies. This mode is well observed directly through X-ray observations of the central galaxies of cool core clusters in the form of bubbles in the hot surrounding medium. The energy flow, which is roughly continuous, heats the hot intraclu...

Observational Evidence of Active Galactic Nuclei Feedback

We provide scaling relations and fitting formulae for adiabatic cold dark matter cosmologies that account for all baryon effects in the matter transfer function to better than 10% in the large-scale structure regime. They are based upon a physically well-motivated separation of the effects of acoustic oscillations, Compton drag, velocity overshoot, baryon infall, adiabatic damping, Silk damping, and cold dark matter growth suppression. We also find a simpler, more accurate, and better motivated form for the zero-baryon transfer function than previous works. These descriptions are employed to quantify the amplitude and location of baryonic features in linear theory. While baryonic oscillations are prominent if the baryon fraction Ωb/Ω0 Ω0h2 + 0.2, the main effect in more conventional cosmologies is a sharp suppression in the transfer function below the sound horizon. We provide a simple but accurate description of this effect and stress that it is not well approximated by a change in the shape parameter Γ.

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Baryonic features in the matter transfer function

Halo Models of Large Scale Structure

We examine the effect of weak, small-scale magnetic field structure on the rate of reconnection in a strongly magnetized plasma. This affects the rate of reconnection by reducing the transverse scale for reconnection flows and by allowing many independent flux reconnection events to occur simultaneously. Allowing only for the first effect and using Goldreich & Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we find a lower limit for the reconnection speed ~VA-3/16L3/4, where VA is the Alfven speed, L is the Lundquist number, and is the large-scale magnetic Mach number of the turbulence. We derive an upper limit of ~VA2 by invoking both effects. We argue that generic reconnection in turbulent plasmas will normally occur at close to this upper limit. The fraction of magnetic energy that goes directly into electron heating scales as -2/5L8/5, and the thickness of the current sheet scales as -3/5L-2/5. A significant fraction of the magnetic energy goes into high-frequency Alfven waves. The angle between adjacent field lines on the same side of the reconnection layer is ~-1/5L6/5 on the scale of the current sheet thickness. We claim that the qualitative sense of these conclusions, that reconnection is fast even though current sheets are narrow, is almost independent of the local physics of reconnection and the nature of the turbulent cascade. As the consequence of this the Galactic and solar dynamos are generically fast, i.e., do not depend on the plasma resistivity.

https://iopscience.iop.org/article/10.1086/307233/pdf

Reconnection in a weakly stochastic field

We perform direct three-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2π threaded by strong uniform magnetic fields. We use a pseudospectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along local magnetic field lines. The results are consistent with the scaling law ∥ ~ recently proposed by Goldreich & Sridhar. Here ∥ (and ⊥) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations that may be a sign of limitations to the model or our inability to fully resolve the inertial range of turbulence in our simulations.

The Anisotropy of Magnetohydrodynamic Alfvénic Turbulence

We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size $2\pi$ threaded by strong uniform magnetic fields. We use a pseudo-spectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale-{\it independent}. We discuss why this is {\it not} the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along {\it local} magnetic field lines. The results are consistent with the scaling law $\tilde{k}_{\parallel} \sim \tilde{k}_{\perp}^{2/3}$ proposed by Goldreich and Sridhar (1995, 1997). Here $\tilde{k}_{\|}$ (and $\tilde{k}_{\perp}$) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations which may be a sign of limitations to the model, or our inability to fully resolve the inertial range of turbulence in our simulations.

The Anisotropy of MHD Alfv\'{e}nic Turbulence

We analyze three-dimensional numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic field. We sum over nonlinear interactions within Fourier wave bands and find that the timescale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions, we show that the turbulent motions in the plane perpendicular to the local mean magnetic field are similar to ordinary hydrodynamic turbulence, while motions parallel to the field are consistent with a scaling correction that arises from the eddy anisotropy. We present the structure tensor describing velocity statistics of Alfvenic and pseudo-Alfvenic turbulence. Finally, we confirm that an imbalance of energy moving up and down magnetic field lines leads to a slow decay of turbulent motions, and speculate that this imbalance is common in the interstellar medium, where injection of energy is intermittent both in time and space.

https://iopscience.iop.org/article/10.1086/324186/pdf

Simulations of Magnetohydrodynamic Turbulence in a Strongly Magnetized Medium

We analyze 3D numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic field. We sum over nonlinear interactions within Fourier wavebands and find that the time scale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions we show that the turbulent motions in the plane perpendicular to the local mean magnetic field are similar to ordinary hydrodynamic turbulence while motions parallel to the field are consistent with a scaling correction which arises from the eddy anisotropy. We present the structure tensor describing velocity statistics of Alfvenic and pseudo-Alfvenic turbulence. Finally, we confirm that an imbalance of energy moving up and down magnetic field lines leads to a slow decay of turbulent motions and speculate that this imbalance is common in the interstellar medium where injection of energy is intermittent both in time and space.

Ethan T. Vishniac

Papers

Reconnection in a weakly stochastic field

The Anisotropy of Magnetohydrodynamic Alfvénic Turbulence

The Anisotropy of MHD Alfv\'{e}nic Turbulence

Simulations of Magnetohydrodynamic Turbulence in a Strongly Magnetized Medium

Simulations of MHD Turbulence in a Strongly Magnetized Medium