On the Meaning and Inapplicability of the Zeldovich Relations of Magnetohydrodynamics

Considering a plasma with an initially weak large scale field subject to nonhelical turbulent stirring, Zeldovich (1957), for two-dimensions, followed by others for three dimensions, and Zeldovich et al. (1983) have presented formulae of the form $=f(R_M){Bbar}^2$. Such ``Zeldovich relations'' have sometimes been interpreted to provide steady-state relations between the energy associated with the fluctuating magnetic field and that associated with a large scale or mean field multiplied by a function $f$ that depends on spatial dimension and a magnetic Reynolds number $R_M$. Here we dissect the origin of these relations and pinpoint pitfalls that show why they are inapplicable to realistic, dynamical MHD turbulence and that they disagree with many numerical simulations. For 2-D, we show that when the total magnetic field is determined by a vector potential, the standard Zeldovich relation applies only transiently, characterizing a maximum possible value that the field energy can reach before necessarily decaying. in relation to a seed value $Bbar$. In 3-D, we show that the standard Zeldovich relations are derived by balancing subdominant terms. In contrast, balancing the dominant terms shows that the fluctuating field can grow to a value independent of $R_M$ and the initially imposed $Bbar$, as seen in numerical simulations. We also emphasize that these Zeldovich relations of nonhelical turbulence imply nothing about the amount mean field growth in a helical dynamo. In short, by re-analyzing the origin of the Zeldovich relations, we highlight that they are inapplicable to realistic steady-states of large $R_M$ MHD turbulence.Comment: 7 pages, accepted to Astronomische Nachrichte

Dynamical magnetic relaxation: A nonlinear magnetically driven dynamo

A non-linear, time-dependent, magnetically driven dynamo theory which shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for large scale magnetic helicity, small scale magnetic helicity, velocity, and the electromotive force are solved. The magnetic helicity on small scales relaxes to drive significant large scale helical field growth on dynamical (Alfv\'en crossing) time scales, independent of the magnitude of finite microphysical transport coefficients, after which the growing kinetic helicity slows the growth to a viscously limited pace. This magnetically driven dynamo complements the nonlinear kinetic helicity driven dynamo; for the latter, the growing magnetic helicity fluctuations suppress, rather than drive, large scale magnetic helicity growth. A unified set of equations accommodates both types of dynamos.Comment: 13 pages, in press, Physics of Plasma

Comets, carbonaceous chondrites, and interstellar clouds: Condensation of carbon

Comets, carbonaceous chondrites, and interstellar clouds are discussed in relation to information on interstellar dust. The formation and presence of carbon in stars, comets, and meteorites is investigated. The existence of graphite in the interstellar medium, though it is predicted from thermodynamic calculations, is questioned and the form of carbon contained in comets is considered

The bispectrum of redshifted 21-cm fluctuations from the dark ages

Brightness-temperature fluctuations in the redshifted 21-cm background from the cosmic dark ages are generated by irregularities in the gas-density distribution and can then be used to determine the statistical properties of density fluctuations in the early Universe. We first derive the most general expansion of brightness-temperature fluctuations up to second order in terms of all the possible sources of spatial fluctuations. We then focus on the three-point statistics and compute the angular bispectrum of brightness-temperature fluctuations generated prior to the epoch of hydrogen reionization. For simplicity, we neglect redshift-space distortions. We find that low-frequency radio experiments with arcmin angular resolution can easily detect non-Gaussianity produced by non-linear gravity with high signal-to-noise ratio. The bispectrum thus provides a unique test of the gravitational instability scenario for structure formation, and can be used to measure the cosmological parameters. Detecting the signature of primordial non-Gaussianity produced during or right after an inflationary period is more challenging but still possible. An ideal experiment limited by cosmic variance only and with an angular resolution of a few arcsec has the potential to detect primordial non-Gaussianity with a non-linearity parameter of f_NL ~ 1. Additional sources of error as weak lensing and an imperfect foreground subtraction could severely hamper the detection of primordial non-Gaussianity which will benefit from the use of optimal estimators combined with tomographic techniques.Comment: 15 pages, 4 figures, revised version accepted for publication in ApJ (contains an improved discussion of gas temperature fluctuations

Relativistic Precessing Jets and Cosmological Gamma Ray Bursts

We discuss the possibility that gamma-ray bursts may result from cosmological relativistic blob emitting neutron star jets that precess past the line of sight. Beaming reduces the energy requirements, so that the jet emission can last longer than the observed burst duration. One precession mode maintains a short duration time scale, while a second keeps the beam from returning to the line of sight, consistent with the paucity of repeaters. The long life of these objects reduces the number required for production as compared to short lived jets. Blobs can account for the time structure of the bursts. Here we focus largely on kinematic and time scale considerations of beaming, precession, and blobs--issues which are reasonably independent of the acceleration and jet collimation mechanisms. We do suggest that large amplitude electro-magnetic waves could be a source of blob acceleration.Comment: 15 pages, plain TeX, accepted to ApJ