Evolution of Magnetic Fields in Freely Decaying Magnetohydrodynamic Turbulence

We study the evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence. By quasi-linearizing the Navier-Stokes equation, we solve analytically the induction equation in quasi-normal approximation. We find that, if the magnetic field is not helical, the magnetic energy and correlation length evolve in time respectively as E_B \propto t^{-2(1+p)/(3+p)} and \xi_B \propto t^{2/(3+p)}, where p is the index of initial power-law spectrum. In the helical case, the magnetic helicity is an almost conserved quantity and forces the magnetic energy and correlation length to scale as E_B \propto (log t)^{1/3} t^{-2/3} and \xi_B \propto (log t)^{-1/3} t^{2/3}.Comment: 4 pages, 2 figures; accepted for publication in PR

An Inexpensive Liquid Crystal Spectropolarimeter for the Dominion Astrophysical Observatory Plaskett Telescope

A new, inexpensive polarimetric unit has been constructed for the Dominion Astrophysical Observatory (DAO) 1.8-m Plaskett telescope. It is implemented as a plug-in module for the telescope's existing Cassegrain spectrograph, and enables medium resolution (R~10,000) circular spectropolarimetry of point sources. A dual-beam design together with fast switching of the wave plate at rates up to 100Hz, and synchronized with charge shuffling on the CCD, is used to significantly reduce instrumental effects and achieve high-precision spectropolarimetric measurements for a very low cost. The instrument is optimized to work in the wavelength range 4700 - 5300A to simultaneously detect polarization signals in the H beta line as well as nearby metallic lines. In this paper we describe the technical details of the instrument, our observing strategy and data reduction techniques, and present tests of its scientific performance.Comment: 32 pages, 15 figures. Accepted for publication in PAS

A search for strong, ordered magnetic fields in Herbig Ae/Be stars

The origin of magnetic fields in intermediate-mass and high-mass stars is fundamentally a mystery. Clues toward solving this basic astrophysical problem can likely be found at the pre-main sequence (PMS) evolutionary stage. With this work, we perform the largest and most sensitive search for magnetic fields in pre-main sequence Herbig Ae/Be (HAeBe) stars. Sixty-eight observations of 50 HAeBe stars have been obtained in circularly polarised light using the FORS1 spectropolarimeter at the ESO VLT. An analysis of both Balmer and metallic lines reveals the possible presence of weak longitudinal magnetic fields in photospheric lines of two HAeBe stars, HD 101412 and BF Ori. The intensity of the longitudinal fields detected in HD 101412 and BF Ori suggest that they correspond to globally-ordered magnetic fields with surface intensities of order 1 kG. Monte Carlo simulations of the longitudinal field measurements of the undetected stars allow us to place an upper limits of about 300 G on the general presence of aligned magnetic dipole magnetic fields, and of about 500 G on perpendicular dipole fields. We find that the observed bulk incidence of magnetic HAeBe stars in our sample is 8-12%, in good agreement with that of magnetic main sequence stars of similar masses. We also find that the rms longitudinal field intensity of magnetically-detected HAeBe stars is similar to that of Ap stars and consistent with magnetic flux conservation during stellar evolution. These results are all in agreement with the hypothesis that the magnetic fields of main sequence Ap/Bp stars are fossils, which already exist within the stars at the pre-main sequence stage. Finally, we explore the ability of our new magnetic data to constrain magnetospheric accretion in Herbig Ae/Be stars.Comment: Accepted by Monthly Notices of the Royal Astronomical Society, 2007 January 11. Received 2007 January 11; in original form 2006 August 18. The paper contains 18 pages, 11 figures and 2 table

Two new bright Ae stars

Two newly identified Ae stars, nu Cyg and kappa UMa, were discovered in the course of the Magnetic Survey of Bright MS stars (Monin et al. 2002). We pre sent their Halpha profiles along with measurements of their equivalent width and parameters of emission features. Emission in the Halpha line of nu Cyg is variable on a time scale of 3 years. kappa UMa exhibits weak emission which is rather stable. The emission is thought to arise from a circumstellar disk, and we have estimated the size of that disk.Both new emission stars are IRAS sources. Their IR color excesses are consistent with those of classical Ae stars. Thus, nu Cyg and kappa UMa appear not to belong to the class of Herbig Ae/Be stars. We argue that the frequency of Ae stars may be underestimated due to the difficulty of detection of weak emission in some A stars.Comment: 6 pages,3 figures, submitted to A&

Equilibrium solutions of the shallow water equations

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy cascade, and a 2-d turbulent {\it inverse} energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrain the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.Comment: 4 pages, no figures. Submitted to Physical Review Letter

Passive tracer in a flow corresponding to a two dimensional stochastic Navier Stokes equations

In this paper we prove the law of large numbers and central limit theorem for trajectories of a particle carried by a two dimensional Eulerian velocity field. The field is given by a solution of a stochastic Navier--Stokes system with a non-degenerate noise. The spectral gap property, with respect to Wasserstein metric, for such a system has been shown in [9]. In the present paper we show that a similar property holds for the environment process corresponding to the Lagrangian observations of the velocity. In consequence we conclude the law of large numbers and the central limit theorem for the tracer. The proof of the central limit theorem relies on the martingale approximation of the trajectory process

Fractal dimension crossovers in turbulent passive scalar signals

The fractal dimension $\delta_g^{(1)}$ of turbulent passive scalar signals is calculated from the fluid dynamical equation. $\delta_g^{(1)}$ depends on the scale. For small Prandtl (or Schmidt) number $Pr<10^{-2}$ one gets two ranges, $\delta_g^{(1)}=1$ for small scale r and $\delta_g^{(1)}$=5/3 for large r, both as expected. But for large $Pr> 1$ one gets a third, intermediate range in which the signal is extremely wrinkled and has $\delta_g^{(1)}=2$. In that range the passive scalar structure function $D_\theta(r)$ has a plateau. We calculate the $Pr$-dependence of the crossovers. Comparison with a numerical reduced wave vector set calculation gives good agreement with our predictions.Comment: 7 pages, Revtex, 3 figures (postscript file on request

CO Line Emission and Absorption from the HL Tau Disk: Where is all the dust?

We present high-resolution infrared spectra of HL Tau, a heavily embedded young star. The spectra exhibit broad emission lines of hot CO gas as well as narrow absorption lines of cold CO gas. The column density for this cooler material (7.5+/-0.2 x 10^18 cm-2) indicates a large column of absorbing gas along the line of sight. In dense interstellar clouds, this column density of CO gas is associated with Av~52 magnitudes. However, the extinction toward this source (Av~23) suggests that there is less dust along the line of sight than inferred from the CO absorption data. We discuss three possibilities for the apparent paucity of dust along the line of sight through the flared disk: 1) the dust extinction has been underestimated due to differences in circumstellar grain properties, such as grain agglomeration; 2) the effect of scattering has been underestimated and the actual extinction is much higher; or (3) the line of sight through the disk is probing a gas-rich, dust-depleted region, possibly due to the stratification of gas and dust in a pre-planetary disk.Comment: To be published in The Astrophysical Journa

Intermittency in the large N-limit of a spherical shell model for turbulence

A spherical shell model for turbulence, obtained by coupling $N$ replicas of the Gledzer, Okhitani and Yamada shell model, is considered. Conservation of energy and of an helicity-like invariant is imposed in the inviscid limit. In the $N \to \infty$ limit this model is analytically soluble and is remarkably similar to the random coupling model version of shell dynamics. We have studied numerically the convergence of the scaling exponents toward the value predicted by Kolmogorov theory (K41). We have found that the rate of convergence to the K41 solution is linear in 1/N. The restoring of Kolmogorov law has been related to the behaviour of the probability distribution functions of the instantaneous scaling exponent.Comment: 10 pages, Latex, 3 Postscript figures, to be published on Europhys. Let