Constrained Transport Algorithms for Numerical Relativity. I. Development of a Finite Difference Scheme

A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and engineering electromagnetics, and has properties of a finite differential calculus on a four-dimensional manifold. It is motivated by the arguments that 1) an evolutionary scheme that naturally satisfies the Bianchi identities will propagate the constraints, and 2) methods in which temporal and spatial derivatives commute will satisfy the Bianchi identities implicitly. The proposed algorithm exactly propagates the constraints in a local Riemann normal coordinate system; {\it i.e.}, all terms in the Bianchi identities (which all vary as $\partial^3 g$) cancel to machine roundoff accuracy at each time step. In a general coordinate basis, these terms, and those that vary as $\partial g\partial^2 g$, also can be made to cancel, but differences of connection terms, proportional to $(\partial g)^3$, will remain, resulting in a net truncation error. Detailed and complex numerical experiments with four-dimensional staggered grids will be needed to completely examine the stability and convergence properties of this method. If such techniques are successful for finite difference implementations of numerical relativity, other implementations, such as finite element (and eventually pseudo-spectral) techniques, might benefit from schemes that use four-dimensional grids and that have temporal and spatial derivatives that commute.Comment: 27 pages, 5 figure

Poynting Flux Dominated Jets in Decreasing Density Atmospheres. I. The Non-relativistic Current-driven Kink Instability and the Formation of "Wiggled" Structures

Non-relativistic three-dimensional magnetohydrodynamical (MHD) simulations of Poynting flux dominated (PFD) jets are presented. Our study focuses on the propagation of strongly magnetized hypersonic, but sub-Alfv\'enic ($C^{2}_{\rm s} \ll V^{2}_{\rm jet} < V^{2}_{\rm A}$) flow and on the subsequent development of a current-driven (CD) kink instability. This instability may be responsible for the ``wiggled'' structures seen in sub-parsec scale (VLBI) jets. In the present paper, we investigate the nonlinear behavior of PFD jets in a variety of external ambient magnetized gas distributions, including those with density, pressure, and temperature gradients. Our numerical results show that the jets can develop CD distortions in the trans-Alfv\'enic flow case, even when the flow itself is still strongly magnetically dominated. An internal non-axisymmetric body mode grows on time scales of order of the Alfv\'en crossing time and distorts the structure and magnetic configuration of the jet. The kink ($m=1$) mode of the CD instability, driven by the radial component of the Lorentz force, grows faster than other higher order modes ($m>1$). In the jet frame the mode grows locally and expands radially at each axial position where the jet is unstable: the instability, therefore, does not propagate as a wave along the jet length. A naturally-occurring, external helically magnetized wind, which is (quasi-) axially current-free, surrounds the well-collimated current-carrying jet and reduces velocity shear between the jet and external medium. This stabilizes the growth of MHD Kelvin-Helmholtz surface modes in the inner jet flow.Comment: 70 pages, 23 figures, 3 tables, Appendix, submitted to Ap

3-D Simulations of MHD Jets - The Stability Problem

Non-relativistic three-dimensional magnetohydrodynamic simulations of Poynting-flux-dominated (PFD) jets are presented. Our study focuses on the propagation of strongly magnetized hypersonic but sub-Alfv\'enic flow ($C_{\rm s}^2 << V_{\rm jet}^2 < V_{\rm A}^2$) and the development of a current-driven (CD) kink instability. This instability may be responsible for the "wiggled" structures seen in VLBI-scale AGN jets. In the present paper we investigate the nonlinear behavior of PFD jets in a variety of external ambient magnetized gas distributions, including those with density, pressure, and temperature gradients. Our numerical results show that PFD jets can develop kink distortions in the trans-Alfv\'enic flow case, even when the flow itself is still strongly magnetically dominated. In the nonlinear development of the instability, a non-axisymmetric mode grows on time scales of order the Alfv\'en crossing time (in the jet frame) and proceeds to disrupt the kinematic and magnetic structure of the jet. Because of a large scale poloidal magnetic field in the ambient medium, the growth of surface modes ({\it i.e.}, MHD Kelvin-Helmholtz instabilities) is suppressed. The CD kink mode ($m = 1$) grows faster than the other higher order modes ($m > 1$), driven in large part by the radial component of the Lorentz force.Comment: 6 pages, 3 figures; to appear in Plasmas in the Laboratory and in the Universe, Como, Italy, 16-19 Sep, 200

Spatially Resolved Chemistry in Nearby Galaxies II. The Nuclear Bar in Maffei 2

We present 2" - 10" imaging of eleven transitions from nine molecular species across the nuclear bar in Maffei 2. The data were obtained with the BIMA and OVRO interferometers. The ten detected transitions are compared with existing CO isotopologues, HCN, CS and millimeter continuum data. Dramatic spatial variations among the mapped species are observed across the nuclear bar. A principle component analysis is performed to characterize correlations between the transitions, star formation and molecular column density. The analysis reveals that HCN, HNC, HCO+ and 3 mm continuum are tightly correlated, indicating a direct connection to massive star formation. We find two main morphologically distinct chemical groups, CH3OH, SiO and HNCO comprising the grain chemistry molecules, versus HCN, HNC, HCO+ and C2H, molecules strong in the presence of star formation. The grain chemistry molecules, HNCO, CH3OH and SiO, trace hydrodynamical bar shocks. The near constancy of the HNCO/CH3OH, SiO/CH3OH and SiO/HNCO ratios argue that shock properties are uniform across the nucleus. HCN/HCO+, HCN/HNC, HCN/CS and HCN/CO ratios are explained primarily by variations in density. High HCO+/N2H+ ratios are correlated with the C2H line, suggesting that this ratio may be a powerful new dense photon-dominated region (PDR) probe in external galaxies. C2H reveals a molecular outflow along the minor axis. The morphology and kinematics of the outflow are consistent with an outflow age of 6-7 Myrs.Comment: 26 pages, 11 figures; Accepted to the Astrophysical Journa

SIMsim: An End-to-End Simulation of The Space Interferometer Mission

We present the basic elements and first results of an end-to-end simulation package whose purpose is to test the validity of the Space Interferometer Mission design. The fundamental simulation time step is one millisecond, with substructure at 1/8 ms, and the total duration of the simulation is five years. The end product of a given "wide-angle" astrometry run is an estimated grid star catalog over the entire sky with an accuracy of about 4 micro-arcseconds. SIMsim is divided into five separate modules that communicate via data pipes. The first generates the 'truth' data on the spacecraft structure and laser metrology. The second module generates uncorrupted fringes for the three SIM interferometers, based on the current spacecraft orientation, target stars' positions, etc. The third module reads out the CCD white light fringe data at specified times, corrupting that and the metrology data with appropriate errors. The data stream out of this module represents the basic data stream on the simulated spacecraft. The fourth module performs fringe-fitting tasks on this data, recovering the total path delay, and the fifth and final module inverts the entire metrology/delay dataset to ultimately determine the instantaneous path delay on a fiducial baseline fixed in space. (Pathlength feed forward is used every few milliseconds to re-position the interferometer to keep the fringes in the delay window.) The average of all such delays over an integration time (typically 30 s) is reported as one of several hundred thousand measured stellar delays over the five-year period, which are then inverted to produce the simulated catalog. Future plans include taking into account more sources of error from the SIM error budget and including narrow angle observations in the observing plan.Comment: 12 pages, 10 figures; in SPIE conference, Interferometry in Space, Waikoloa, HI, 26-28 August, 200