MHD modeling of the Heliosphere: a critical evaluation of different models

International audienceThe very complicated problem of the solar wind-interstellar medium interaction requires a very sophisticated numerical approach. To achieve such a goal first we need to understand very deeply the results obtained up-to-now. In this paper we gather the results from four different MHD models of the heliospheric interfaces. The comparison of the results invokes several questions. These questions should be addressed before we proceed with the next steps in the MHD modeling of the heliospheric interfaces. Is a jet created between the termination shock and the heliopause (Opher et al., 2003, 2004)? What is the physical meaning of the V-shape of termination shock and heliopause (Washimi and Tanaka, 2001, 2004)? Whether a similar looking result is either due to bending of the heliospheric current sheet as in the model by Pogorelov (2004), Pogorelov et al. (2004) or due to numerical "reconnection" as in the model by Ratkiewicz et al. (2004, 2005)? The purpose of this paper is to open a wider discussion to try to answer these questions

Long-time behaviour of discretizations of the simple pendulum equation

We compare the performance of several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose for the comparison numerical schemes which preserve the qualitative features of solutions (like periodicity). All these schemes are either symplectic maps or integrable (preserving the energy integral) maps, or both. We describe and explain systematic errors (produced by any method) in numerical computations of the period and the amplitude of oscillations. We propose a new numerical scheme which is a modification of the discrete gradient method. This discretization preserves (almost exactly) the period of small oscillations for any time step.Comment: 41 pages, including 18 figures and 4 table

Magnetic Effects at the Edge of the Solar System: MHD Instabilities, the de Laval nozzle Effect and an Extended Jet

To model the interaction between the solar wind and the interstellar wind, magnetic fields must be included. Recently Opher et al. 2003 found that, by including the solar magnetic field in a 3D high resolution simulation using the University of Michigan BATS-R-US code, a jet-sheet structure forms beyond the solar wind Termination Shock. Here we present an even higher resolution three-dimensional case where the jet extends for $150AU$ beyond the Termination Shock. We discuss the formation of the jet due to a de Laval nozzle effect and it's su bsequent large period oscillation due to magnetohydrodynamic instabilities. To verify the source of the instability, we also perform a simplified two dimensional-geometry magnetohydrodynamic calculation of a plane fluid jet embedded in a neutral sheet with the profiles taken from our 3D simulation. We find remarkable agreement with the full three-dimensional evolution. We compare both simulations and the temporal evolution of the jet showing that the sinuous mode is the dominant mode that develops into a velocity-shear-instability with a growth rate of $5 \times 10^{-9} sec^{-1}=0.027 years^{-1}$. As a result, the outer edge of the heliosphere presents remarkable dynamics, such as turbulent flows caused by the motion of the jet. Further study, e.g., including neutrals and the tilt of the solar rotation from the magnetic axis, is required before we can definitively address how this outer boundary behaves. Already, however, we can say that the magnetic field effects are a major player in this region changing our previous notion of how the solar system ends.Comment: 24 pages, 13 figures, accepted for publication in Astrophysical Journal (2004

Quadrupole collectivity beyond N=28: Intermediate-energy Coulomb excitation of 47,48Ar

We report on the first experimental study of quadrupole collectivity in the very neutron-rich nuclei \nuc{47,48}{Ar} using intermediate-energy Coulomb excitation. These nuclei are located along the path from doubly-magic Ca to collective S and Si isotopes, a critical region of shell evolution and structural change. The deduced $B(E2)$ transition strengths are confronted with large-scale shell-model calculations in the $sdpf$ shell using the state-of-the-art SDPF-U and EPQQM effective interactions. The comparison between experiment and theory indicates that a shell-model description of Ar isotopes around N=28 remains a challenge.Comment: Accepted for publication in Physical Review Letters, typos fixed in resubmission on April 1

Effects of a Local Interstellar Magnetic Field on Voyager 1 and 2 Observations

We show that that an interstellar magnetic field can produce a north/south asymmetry in solar wind termination shock. Using Voyager 1 and 2 measurements, we suggest that the angle $\alpha$ between the interstellar wind velocity and magnetic field is $30^{\circ} < \alpha < 60^{\circ}$. The distortion of the shock is such that termination shock particles could stream outward along the spiral interplanetary magnetic field connecting Voyager 1 to the shock when the spacecraft was within $\sim 2~AU$ of the shock. The shock distortion is larger in the southern hemisphere, and Voyager 2 could be connected to the shock when it is within $\sim 5~AU$ of the shock, but with particles from the shock streaming inward along the field. Tighter constraints on the interstellar magnetic field should be possible when Voyager 2 crosses the shock in the next several years.Comment: 12 pages, 5 figure

Comment on `conservative discretizations of the Kepler motion'

We show that the exact integrator for the classical Kepler motion, recently found by Kozlov ({\it J. Phys. A: Math. Theor.\} {\bf 40} (2007) 4529-4539), can be derived in a simple natural way (using well known exact discretization of the harmonic oscillator). We also turn attention on important earlier references, where the exact discretization of the 4-dimensional isotropic harmonic oscillator has been applied to the perturbed Kepler problem.Comment: 6 page

Observation of mutually enhanced collectivity in self-conjugate 3876^{76}_{38}Sr38_{38}

The lifetimes of the first 2$^{+}$ states in the neutron-deficient $^{76,78}$Sr isotopes were measured using a unique combination of the $\gamma$-ray line-shape method and two-step nucleon exchange reactions at intermediate energies. The transition rates for the 2$^{+}$ states were determined to be $B$(E2;2$^{+}$$\to 0^{+}$) = 2220(270) e$^{2}$fm$^{4}$ for $^{76}$Sr and 1800(250) e$^{2}$fm$^{4}$ for $^{78}$Sr, corresponding to large deformation of $\beta_2$ = 0.45(3) for $^{76}$Sr and 0.40(3) for $^{78}$Sr. The present data provide experimental evidence for mutually enhanced collectivity that occurs at $N$ = $Z$ = 38. The systematic behavior of the excitation energies and $B$(E2) values indicates a signature of shape coexistence in $^{76}$Sr, characterizing $^{76}$Sr as one of most deformed nuclei with an unusually reduced $E$(4$^{+}$)/$E$(2$^{+}$) ratio.Comment: Accepted for publication in Physical Review C Rapid Communicatio

Mirror Energy Differences at Large Isospin Studied through Direct Two-Nucleon Knockout

The first spectroscopy of excited states in 52Ni (Tz=2) and 51Co (Tz=-3/2) has been obtained using the highly selective two-neutron knockout reaction. Mirror energy differences between isobaric analogue states in these nuclei and their mirror partners are interpreted in terms of isospin nonconserving effects. A comparison between large scale shell-model calculations and data provides the most compelling evidence to date that both electromagnetic and an additional isospin nonconserving interactions for J=2 couplings, of unknown origin, are required to obtain good agreement.Comment: Accepted for publication in Physical Review Letter