Evolutionary signatures in complex ejecta and their driven shocks

We examine interplanetary signatures of ejecta-ejecta interactions. To this end, two time intervals of inner-heliospheric (≤1AU) observations separated by 2 solar cycles are chosen where ejecta/magnetic clouds are in the process of interacting to form complex ejecta. At the Sun, both intervals are characterized by many coronal mass ejections (CMEs) and flares. In each case, a complement of observations from various instruments on two spacecraft are examined in order to bring out the in-situ signatures of ejecta-ejecta interactions and their relation to solar observations. In the first interval (April 1979), data are shown from Helios-2 and ISEE-3, separated by ~0.33AU in radial distance and 28° in heliographic longitude. In the second interval (March-April 2001), data from the SOHO and Wind probes are combined, relating effects at the Sun and their manifestations at 1AU on one of Wind's distant prograde orbits. At ~0.67AU, Helios-2 observes two individual ejecta which have merged by the time they are observed at 1AU by ISEE-3. In March 2001, two distinct Halo CMEs (H-CMEs) are observed on SOHO on 28-29 March approaching each other with a relative speed of 500kms<sup>-1</sup> within 30 solar radii. In order to isolate signatures of ejecta-ejecta interactions, the two event intervals are compared with expectations for pristine (isolated) ejecta near the last solar minimum, extensive observations on which were given by Berdichevsky et al. (2002). The observations from these two event sequences are then intercompared. In both event sequences, coalescence/merging was accompanied by the following signatures: heating of the plasma, acceleration of the leading ejecta and deceleration of the trailing ejecta, compressed field and plasma in the leading ejecta, disappearance of shocks and the strengthening of shocks driven by the accelerated ejecta. A search for reconnection signatures at the interface between the two ejecta in the March 2001 event was inconclusive because the measured changes in the plasma velocity tangential to the interface (Δν<sub>t</sub>) were not correlated with Δ(<i>B<sub>t</sub></i> /ρ). This was possibly due to lack of sufficient magnetic shear across the interface. The ejecta mergers altered interplanetary parameters considerably, leading to contrasting geoeffects despite broadly similar solar activity. The complex ejecta on 31 March 2001 caused a double-dip ring current enhancement, resulting in two great storms (<i>D<sub>st</sub></i>, corrected for the effect of magnetopause currents, <-450nT), while the merger on 5 April 1979 produced only a corrected <i>D<sub>st</sub></i> of ~-100nT, mainly due to effects of magnetopause currents

Interaction of a vortex ring with the free surface of ideal fluid

The interaction of a small vortex ring with the free surface of a perfect fluid is considered. In the frame of the point ring approximation the asymptotic expression for the Fourier-components of radiated surface waves is obtained in the case when the vortex ring comes from infinity and has both horizontal and vertical components of the velocity. The non-conservative corrections to the equations of motion of the ring, due to Cherenkov radiation, are derived.Comment: LaTeX, 15 pages, 1 eps figur

Lagrangian Variational Framework for Boundary Value Problems

A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is implemented through a Lagrangian framework that allows to account for (i) a variety of forces including dissipative acting at the boundary; (ii) a multitude of features of interactions between the boundary and the interior fields when the boundary fields may differ from the boundary limit of the interior fields; (iii) detailed pictures of the energy distribution and its flow; (iv) linear and nonlinear effects. We provide a number of elucidating examples of the structured boundary and its interactions with the system interior. We also show that the proposed approach covers the well known boundary value problems.Comment: 41 pages, 3 figure

Derivation of Boltzmann Principle

We present a derivation of Boltzmann principle $S_{B}=k_{B}\ln \mathcal{W}$ based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the nineteenth century with the works of Helmholtz and Boltzmann. Despite its simplicity, this argument has remained almost unknown. We present it in a modern, self-contained and accessible form. The approach constitutes an important link between classical mechanics and statistical mechanics

Halo-coronal mass ejections near the 23rd solar minimum: lift-off, inner heliosphere, and in situ (1 AU) signatures

International audienceThe extreme ultraviolet (EUV) signatures of a solar lift-off, decametric and kilometric radio burst emissions and energetic particle (EP) inner heliospheric signatures of an interplanetary shock, and in situ identification of its driver through solar wind observations are discussed for 12 isolated halo coronal mass ejections (H-CMEs) occurring between December 1996 and 1997. For the aforementioned twelve and the one event added in the discussion, it is found that ten passed several necessary conditions for being a "Sun-Earth connection". It is found that low corona EUV and Ha chromospheric signatures indicate filament eruption as the cause of H-CME. These signatures indicate that the 12 events can be divided into two major subsets, 7 related to active regions (ARs) and 5 unrelated or related to decayed AR. In the case of events related to AR, there is indication of a faster lift-off, while a more gradual lift-off appears to characterize the second set. Inner heliospheric signatures ? the presence of long lasting enhanced energetic particle flux and/or kilometric type II radio bursts ? of a driven shock were identified in half of the 12 events. The in situ (1 AU) analyses using five different solar wind ejecta signatures and comparisons with the bidirectional flow of suprathermal particles and Forbush decreases result in indications of a strong solar wind ejecta signatures for 11 out of 12 cases. From the discussion of these results, combined with work by other authors for overlapping events, we conclude that good Sun-Earth connection candidates originate most likely from solar filament eruptions with at least one of its extremities located closer to the central meridian than ~ 30° E or ~ 35° W with a larger extension in latitudinal location possible. In seven of the twelve cases it appears that the encountered ejecta was driving a shock at 1 AU. Support for this interpretation is found on the approximately equal velocity of the shock and the ejecta leading-edge. These shocks were weak to moderate in strength, and a comparison of their transit time with their local speed indicated a deceleration. In contradistinction with this result on shocks, the transit time versus the local speed of the ejecta appeared either to indicate that the ejecta as a whole traveled at constant speed or underwent a small amount of acceleration. This is a result that stands for cases with and without fast stream observations at their rear end. Seven out of twelve ejecta candidate intervals were themselves interplanetary magnetic cloud (IMC) or contained a previously identified IMC. As a by-product of this study, we noticed two good ejecta candidates at 1 AU for which observation of a H-CME or CME appears to be missing

Relationship between solar energetic oxygen flux and MHD shock Mach number

This study correlates the time-intensity profile of a magnetohydrodynamic (MHD) shock with the corresponding solar energetic oxygen for a coronal mass ejection (CME) event that occurred on October 28, 2003. The intensity of MHD shock, in terms of Mach number, is simulated using a 1.5D MHD code, whereas the solar energetic oxygen flux is observed by the Solar Isotope Spectrometer (SIS) on board the Advanced Composition Explorer (ACE) spacecraft. A good correlation (Pearson correlation coefficient: r = 0.70 – 0.84) is found between the forward fast-mode shock Mach number and the hourly-averaged, logarithmic oxygen differential energy flux for 7 energy channels (7.3 – 63.8 MeV). We suspect that the intensity-time profile of high energy SEP events is manifested by the strength (Mach number) of CME-driven propagation shocks. While further studies with more events are required to be more conclusive, this study result provides a direction for future studies or predictions of SEP fluxes

Does the Boltzmann principle need a dynamical correction?

In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived [M. Bianucci, R. Mannella, B. J. West, and P. Grigolini, Phys. Rev. E 51, 3002 (1995)] which differs from the one that follows from the Boltzmann principle S = k log (Omega(E)) via the thermodynamic relation 1/T= dS/dE by additional terms of "dynamical" character, which are argued to correct and generalize the Boltzmann principle for small systems (here Omega(E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker-Planck formalism of Bianucci et al. is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the "volume" entropy S = k log (Phi(E)) via the thermodynamic relation above for systems of any number of degrees of freedom (Phi(E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al. and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain (N~10) of quartic oscillators are also provided to further illustrate these facts.Comment: REVTeX 4, 10 pages, 2 figures. Accepted to J. Stat. Phy

A summary of WIND magnetic clouds for years 1995-2003: model-fitted parameters, associated errors and classifications

International audienceInterplanetary magnetic clouds (MCs) have been identified for the first 8.6 years of the WIND mission, and their magnetic field structures have been parameter-fitted by a static, force free, cylindrically-symmetric model (Lepping et al., 1990) with various levels of success. This paper summarizes various aspects of the results of the model fitting by providing: seven estimated model fit-parameter values for each of the 82 MCs found, their objectively determined quality estimates, closest approach vectors (in two coordinate frames), fit-parameter errors for the cases of acceptable quality (50 cases, or 61%), axial magnetic fluxes, axial current densities, and total axial current - as well as some examples of MC profiles for various conditions and "categories" for each case (e.g. Bz: N?S or S?N, etc.). MC quality is estimated from a quantitative consideration of a large set of parameters, such as the chi-squared of the model fit, degree of asymmetry of the B profile, and a comparison of two means of estimating radius. This set of MCs was initially identified by visual inspection of relevant field and plasma data. Each resulting MC candidate is then tested through the use of the MC parameter model, for various adjusted durations to determine the best fit, which helps to refine the boundary-times. The resulting MC set is called Set 1. Another, larger, set (Set 2) of MCs is identified through an automated program whose criteria are based on general MC plasma and field characteristics at 1AU determined through past experience. Set 1 is almost fully contained within Set 2, whose frequency of occurrence better matches that of the sunspot cycle than Set 1. The difference-set (Set 2-Set 1) is referred to as the magnetic cloud-like (MCL) set, whose members do not very well represent good flux ropes through modeling. We present a discussion of how a MC's front boundary is specifically identified in terms of multi-parameter considerations (i.e. any one or more of: increase in B, directional discontinuity, magnetic hole in B, drop in proton plasma beta, B-fluctuation level change, proton temperature drop, etc.), as well as through the application of the flux rope model. Also presented are examples of unusual MCs, as well as some commonly occurring relationships, such as the existence and frequency (approx. 1/2 the time) of upstream interplanetary shocks, and less frequent internal shocks