Dependence of the Walén test on the density estimate: A Cluster case study

A. Blăgău (1,2), B. Klecker (1), G. Paschmann (1), O. Marghitu (2, 1), M. Scholer (1), S. Haaland (1), T. Phan (3), L. M. Kistler (4), C. Mouikis (4) and H. Reme (5)

(1) Max-Planck-Institut für extraterrestrische Physik, Garching, Germany(2) Institute for Space Sciences, Bucharest, Romania(3) Space Science Lab., University of California at Berkeley, USA(4) Space Science Center, University of New Hampshire, Durham, USA(5) CESR, Toulouse, France

ABSTRACT: The experimental check of the tangential momentum balance (Walén test) at the magnetopause is often performed without exploiting the full density information collected along the satellite track. Instead, one uses the density, ρ, measured at a reference point in the magnetosheath, and the anisotropy factor, α, measured during the entire crossing, together with the relation ρ(1-α)=const., which holds for a rotational discontinuity. This approach has often been used because, in the presence of heavier ions, ion instruments that do not resolve mass provide better estimates of the pressure anisotropy than of mass density.The CIS ion spectrometers on the Cluster spacecraft allow for a continuous monitoring of the plasma composition, with an increased accuracy in the calculation of the ion moments. In this study we focus on a particular reconnection event, when both He+ and O+ ions were present. We investigate the possibility of processing the full information available from CIS during this traversal, in order to get accurate density estimates; particular attention is given to minimize the errors of instrumental origin. We explore the impact of using these mass density estimates on the Wal\'en test, and discuss the consequences for a rotational discontinuity.

INTRODUCTION: The aim of this study is two-fold: - to estimate the Oxygen moments and it's influence on the Walén test for a case when the magnetopause forms a rotational discontinuity (RD) (case from 26. Jan 2001). - to experimentally check the relation (1-)=const. - a relation often used in performing such test - in two cases: in the presence of Oxygen (26. Jan 2001) and in the absence of it (5 July 2001). is plasma density and the pressure anisotropy factor

The event of 26th of January has two important particularities: it is rich in Oxygen ions and it is a case of stable RD structure which, due to the magnetopause (MP) movement, is sampled many times by the CLUSTER constellation. This case has been studied before (T.D.Phan, et. al. 2004), where the authors were able to predict the plasma velocity changes at the MP for a long time-period, encompassing more than 10 crossings, using the magnetic field and the shear-stress balance equation. In order to do this and also in performing the Walen test for the individual crossings, the authors used the relation (1-)=const. toghether with the density measurered in a reference point.

When testing the Walén relation, we use HIA on-board moments because of several reasons:- they offer a better angular, energetic and time resolution- because of an on-board dead-time correction they are not affected by high rates in the magnetosheath (MS).The disadvantage in using HIA lies in the inability to separate different ions that, when present, are contaminating the data.In the general plot for this case, the Oxygen spectrogram is also shown, although we have instrument uncertainties that compromises the measurements.  One way to see whether we truly have Oxygen counts is to use the auxiliary product P28 which sends all the information for a limited number of events in each spin (48 events). In the figure from left we plotted the energy channel versus time-of-flight (TOF) channel for the events collected during 3 hours. The vertical lines indicate the allocated TOF regions for different species. The Oxygen counts are clearly seen in the last TOF interval at energies higher than 2keV.

First method 

We evaluate the CODIF Oxygen moments in two ways. In the first method (investigated by C. Mouikis), we used another auxiliary product, P27, that monitors different instrument rates, and estimate it's saturation limit by considering it a non-paralysable counter. The time resolution for P27 is 34 spin periods so we expect that our correction will not be good in cases when high variations in the data are present. After applying this correction, we take into account the so called spill-over background effect (the presence of false Oxygen counts (i.e. protons) at times of high proton fluxes). This effect could be estimated by looking at Oxygen TOF channels during times when we know that no such ions should be present (well outside the magnetosphere, for example).

In figure from right we present the proton moments from CODIF after the saturation correction was applied in contrast with HIA on-board moments. Also the un-corrected CODIF moments are shown.

Second method We assumed that the satellites sampled a time-stationary structure in general (as indicated in the introduction) and used the CODIF product P28. Due to the poor statistics of events collected during each spin, we divided the MP region in five sub-intervals, according to the magnetic field orientation. All P28 events for both CLUSTER1 and CLUSTER3 were summed for each such sub-intervals. Then, for each HIA energy channel we evaluate the oxygen counts relative to proton counts fraction from the TOF distribution.

The division of the magnetopause region in five subintervals was made by close inspection of the magnetic field rotation.

One such a collection of events for the time when CLUSTER1 is in the magnetosheath is presented. The Oxygen branch is clearly identifiable.

By comparing the un-corrected and corrected Oxygen moments we arrive at the following conclusion (see figures below):- the un-corrected moments are strongly contaminated during MP crossings, and cannot be used.- in the first method an over-correction was obtained, due to the uncertainties in estimations for the proton flux at high rates. So in the magnetosheath the moments are not reliable.- in the second method, an over-estimation was obtained, mainly due to the poor statistics that characterize product P28. We expect that the uncertainties come from the low energy channels

We took another case (5th of July 2001) where there are no significant Oxygen ions and chrcked whether (1-)=const. is experimentally supported. In this way we exclude the possible influence the presence of heavy ions could have on the density and on the alpha factor. Also in this case the relation could not be experimentally verified.

 The table presents the different results obtained in performing the Walén test and in determining the deHoffmann-Teller frame on one of the RD crossings:- the first row, refers to the case when the (1-)=const. relation was used. Systematically, this method yields closer to unity values for all the crossings in this event.- the second row refers to the situation when we use (1-)=const. As in the previous case, the Oxygen contamination of HIA measurements was neglected.- the third and the fourth row presents the results when we take into accounts the Oxygen moments estimated by the two methods and combine them with HIA on-board moments in order to obtain the total-fluid moments.

 When we experimentally checked the (1-)=const. relation we computed the parallel and perpendicular temperatures by using explicitly the direction of the magnetic field (not, as usually is done, by diagonalization of the pressure tensor). This has a significant influence on the pressure anisotropy factor alpha.We conclud that the relation could not be experimentally proved and that it is dominated by the effect of density variation

CONCLUSIONS: 1) The methods we used to estimate the Oxygen moments need certainly some refinements; still the Walén test seems not so sensible to the presence of heavy ions in the MP2) The reason why (1-) is not experimentally verified is still unknown, despite we have examined 'clear' rotational discontinuities.

References:T.D. Phan et.al, Ann. Geophys., 22, 2355-2376G. Paschmann et.al., J.Geophys.Res, 91, 11099-11115C. Mouikis, CIS Meeting presentation, Paris, Sep. 2003