Earth's magnetosphere and outer radiation belt under sub-Alfvénic solar wind

The interaction between Earth's magnetic field and the solar wind results in the formation of a collisionless bow shock 60,000–100,000 km upstream of our planet, as long as the solar wind fast magnetosonic Mach (hereafter Mach) number exceeds unity. Here, we present one of those extremely rare instances, when the solar wind Mach number reached steady values <1 for several hours on 17 January 2013. Simultaneous measurements by more than ten spacecraft in the near-Earth environment reveal the evanescence of the bow shock, the sunward motion of the magnetopause and the extremely rapid and intense loss of electrons in the outer radiation belt. This study allows us to directly observe the state of the inner magnetosphere, including the radiation belts during a type of solar wind-magnetosphere coupling which is unusual for planets in our solar system but may be common for close-in extrasolar planets.

Panel (a) shows the proton density as derived from Wind 3DP (black) and from Wind SWE through nonlinear fit (red) and moment calculation (blue). Panel (b) shows the Wind 3DP proton density as compared to that measured by Geotail (shifted by 48 min) and by ACE (shifted by 9 minutes). Panel (c) shows the density of alpha particles as measured by Wind. These measurements validate the use of Wind 3DP in this study and confirm that from 17 to 24 UT on January 17 the solar wind density was below 1 cm -3 .  Lopez et al. (1987). Panels l-s: End of the sheath and beginning of the ejecta in the minimum variance coordinates. The panels show the proton density (panel l), the i, j and k components of the velocity (panels m-o), the i, j and k components of the magnetic field (panel p-r), and the total magnetic field strength (panel s). (a)

Supplementary Note 1-White-light observation of the CME:
The 2013 January 13 CME is observed by LASCO C2 and C3 coronagraphs (Brueckner et al., 1995) as well as white-light imagers part of the SECCHI suite (Howard et al., 2008) onboard STEREO, as shown in Supplementary Figure 1. In fact, the CME can be tracked using J-map (Davies et al., 2009) until January 17 by STEREO-A/SECCHI and until January 15 by STEREO-B/SECCHI. STEREO-B measurements analyzed with the self-similar expanding fitting technique (SSEF: Davies et al., 2013) give a Earth-directed CME with a speed of ~470 km.s -1 (assuming a constant propagation speed) and a predicted arrival time on January 17 at 02:50 UT. This fitting result was obtained independently of the current study as part of a large survey undertaken under the HELCATS European project and further confirms that this CME is indeed the one which impacted Wind around 00:00 UT on January 17. Although white-light images show a dark cavity (see for example top right panel of Supplementary Figure 1), the remote observations do not give any indication that the density inside the CME will be so low when the CME reaches 1 AU.

Supplementary Note 2-Solar Wind Density:
In the main text, we use the Wind spacecraft 3-D plasma analyzer (3DP: Lin et al., 1995) analysis of the proton density to obtain the upstream solar wind proton density. In order to ascertain that instrumental effects are not the cause of the low-density period, we compare this density to that: i) obtained from the Solar Wind Experiment (SWE: Ogilvie et al., 1995) derived both through a non-linear fitting of the proton distribution function and from moment analysis. ii) obtained from ACE Solar Wind Electron Proton Alpha Monitor (SWEPAM: McComas et al., 1998) iii) obtained from Geotail Comprehensive Plasma Instrumentation / Solar Wind Analyzed (CPI/ SWA: Frank et al., 1994). In addition, we looked at the density of alpha particles obtained from Wind/3DP to make sure that the ratio of alpha to proton remains low.
Supplementary Figure 2 shows the comparison of the proton (and alpha for the last panel) density as measured by different spacecraft/methods, illustrating that all methods and instruments return a proton density below 0.4 cm -3 from 18:15UT to 00UT, except for the 30-minute period centered around 20:30UT, when the density was greater than 1 cm -3 . During the period of low density, the density of alpha particles is extremely low, reaching below 0.02 cm -3 . This shows that the alpha particles remain around the typical proportion of 5% (or 20% by mass) of the solar wind composition. These comparisons validate the Wind/3DP density measurements and confirm that the period of interest was indeed sub-Alfvénic, and is not due to an instrumental failure or defect.
We further confirmed the low density by plotting (not shown here) the thermal noise receiver data from Wind (Meyer-Vernet et al., 1998). It shows the plasma line dropping to value under 10 kHz around 17:30 UT, before a data gap. This is another, independent confirmation that the density of the solar wind was indeed very low at this time.

Supplementary Note 3-Planarity of the magnetic field in the CME sheath and pressure tensor
We performed a minimum variance analysis (MVA, Sonnerup and Cahill, 1967) on the magnetic field on January 17 from 00:00 UT to 16:00 UT. The ratio of intermediate to minimum eigenvalues is 7.8, indicating that the field is indeed planar. The normal to the plane is found to be (0.9183, 0.2315, -0.3210) in GSM coordinates, i.e. primarily in the Sun-Earth direction (x-direction). In this coordinate system, Bn is equal to 0.6 ± 2.6 nT, much smaller than the other two components, which have magnitudes of the order of 10 nT, and consistent with Bn ~ 0 nT. Overall, this planar structure is tangent to the magnetopause.
Supplementary Figure 4 shows a close-up to the sheath and the beginning of the ejecta, including the magnetic field in the MVA coordinate system. There are strong correlation between non-radial components of the velocity (Vy and Vz) and of the magnetic field (By and Bz) especially during the late part of the sheath around 13:00UT. This further confirm the planarity of this structure.
Next, we determine, for the same period, corresponding to the dense sheath preceding the magnetic ejecta, the total pressure tensor, in order to identify stresses onto the magnetopause.
The total pressure tensor (total momentum flux tensor) is given by equation: Piαβ = (P + B 2 /(2 μ0 ))δαβ + ρ Vα Vβ + Bα Bβ/μ0, where α and β are running indices, ρ is the proton mass density, P the thermal pressure, B the magnetic field and V the velocity. Using the coordinates i, j, k with Bk = 0, derived from the minimum variance of the field (see previous section), the component of momentum flux normal to the discontinuity plane is: Pik,k = ρ Vk 2 + P + (Bi 2 + Bj 2 )/ (2 μ0 ).
Note that at the moment of impact, vector k is normal to both the discontinuity as well as to the magnetopause, so that Pik,k represents the pressure normal to the boundary. During the first 13 hours of January 17, the dayside magnetopause at low latitudes can be modeled as a tangential discontinuity, since the field is northward (this excludes the cusp region). The components of the momentum flux in the magnetopause plane are given by: Pk,β = ρ Vk Vβ, where β = i, j. Supplementary Figure 5 shows the quantity Πk,k (≡ ρ Vk 2 + P) and Pk,k (red trace), followed by Πki, and Πkj. It is clear from the first panel that the magnetic tension forces are negligible for these considerations.
Considering the changes in the pressure components, we see that (last panel) the Pk,i is not negligible in comparison with the normal pressure in the top panel. So considerable tangential stresses were also applied to the magnetopause. These stresses dropped significantly around 14:30 UT (at Wind, corresponding to ~15:30 UT at the magnetopause) and became negligible around 16:30 UT.