Optimized Grad – Shafranov Reconstruction of a Magnetic Cloud Using STEREO-Wind Observations

Abstract

We present results on the geometry of a magnetic cloud (MC) on 23 May 2007 from a comprehensive analysis of Wind and STEREO observations. We first apply a GradShafranov reconstruction to the STEREO-A plasma and magnetic field data, delivered by the PLASTIC and IMPACT instruments. We then optimize the resulting field map with the aid of observations by Wind, which were made at the very outer boundary of the cloud, at a spacecraft angular separation of 6°. For the correct choice of reconstruction parameters such as axis orientation, interval and grid size, we find both a very good match between the predicted magnetic field at the position of Wind and the actual observations as well as consistent timing. We argue that the reconstruction captures almost the full extent of the cross-section of the cloud. The resulting shape transverse to the invariant axis consists of distorted ellipses and is slightly flattened in the direction of motion. The MC axis is inclined at −58°to the ecliptic with an axial field strength of 12 nT. We derive integrated axial fluxes and currents with increased precision, which we contrast with the results from linear force- free fitting. The helical geometry of the MC with almost constant twist (≈1.5 turns AU −1 ) is not consistent with the linear force-free Lundquist model. We also find that the cloud is non-force-free (|J ⊥ |/|J | > 0.3) in about a quarter of the cloud cross sectional area, particularly in the back part which is interacting with the trailing high speed stream. Based on the optimized reconstruction we put forward preliminary guidelines for the improved use of single-spacecraft Grad -Shafranov reconstruction. The results also give us the opportunity to compare the CME direction inferred from STEREO/SECCHI observations by Mierla et al. (Solar Phys. 252, 385, 2008) with the three-dimensional configuration of the MC at 1 AU. This yields an almost radial CME propagation from the Sun to the Earth.

Magnetic cloud models with bent and oblate cross-section boundaries

“…We also confirm the results of Vandas & Romashets (2003) who derived an analytical solution of a linear force-free field contained inside an elliptical boundary. We find that the configuration of the core inherits the oblate shape of the boundary but with a significantly lower aspect ratio, in agreement with previous observations (e.g., Dasso et al 2005a;Liu et al 2008;Möstl et al 2009). …”

“…by a smoothing procedure). The method was recently tested successfully with MCs crossed by two spacecraft (Liu et al 2008;Möstl et al 2009). …”

“…Moreover, using combined observations of several spacecraft, some recent analyses have shown that the core of the MCs is significantly more circular than their oblate outer part (Liu et al 2008;Kilpua et al 2009;Möstl et al 2009). Still, the Lundquist solution is known to have difficulties in fitting the magnetic field strength, in particular it was found that it frequently overestimates the axial component of the field near the flux-rope axis (e.g., Gulisano et al 2005).…”

Does spacecraft trajectory strongly affect detection of magnetic clouds?

“…This approach only supposes a magnetostatic field invariant by translation along the straight axis (Hu & Sonnerup 2002;Sonnerup et al 2006). The method was tested successfully with MCs crossed by two spacecraft (Liu et al 2008;Kilpua et al 2009;Möstl et al 2009a). The results depend on the MC studied, ranging from nearly round to elongated cross sections (Hu et al 2005;Liu et al 2008;Möstl et al 2009a,b;Isavnin et al 2011;Farrugia et al 2011).…”

Dynamical evolution of a magnetic cloud from the Sun to 5.4 AU

“…This is used to test the technique by computing the magnetic field in the cross section from the data of one spacecraft and/or to have a more accurate reconstruction of the magnetic field Liu et al 2008;Kilpua et al 2009;Möstl et al 2009). …”