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Keywords:

  • switch-on shock;
  • Rankine-Hugoniot relations;
  • magnetic cloud

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Observations of a Switch-on Shock
  5. 3. Summary and Discussion
  6. Acknowledgments
  7. References
  8. Supporting Information

[1] A possible interplanetary switch-on shock event prior to a trailing magnetic cloud was observed on August 1, 2002 at 1 AU. We fit the data with the Rankine-Hugoniot (R-H) relations based on both oblique and switch-on shock models. It is found that both models are consistent with the observed data, and the best fit solutions of the two models are close to one another. For the oblique shock model, the best fit upstream shock normal angle, θBN1 (= cos−1(Bt1/B1)), is as small as 5.55°. The shock has the following characteristics: (1) plasma density, plasma temperature, and the magnetic field strength all increase across the shock, (2) protons are thermalized very efficiently across the shock, but it is not the case for electrons, (3) the fast-mode Mach number is greater than unity in the preshock region and less than unity in the postshock region, and (4) from the oblique shock model we find that the normal Alfvén Mach number is very close to unity in the postshock region, while from the switch-on shock model we obtain a solution of unity normal Alfvén Mach number. Our results clearly demonstrate the MHD character of a fast shock propagating along the ambient magnetic field.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Observations of a Switch-on Shock
  5. 3. Summary and Discussion
  6. Acknowledgments
  7. References
  8. Supporting Information

[2] According to the ideal MHD theory, there exist three types of linear MHD wave: fast magnetosonic, Alfvén (intermediate), and slow magnetosonic waves. If we define state 1 as the state upon which the fluid velocity is super-fast–magnetosonic, state 2 upon which the fluid velocity is sub-fast–magnetosonic and super-Alfvénic, state 3 upon which the fluid velocity is sub-Alfvénic and super-slow–magnetosonic, and state 4 upon which the fluid velocity is sub-slow–magnetosonic, the entropy-satisfying jump relations then include 1 [RIGHTWARDS ARROW] 2, 1 [RIGHTWARDS ARROW] 3, 1 [RIGHTWARDS ARROW] 4, 2 [RIGHTWARDS ARROW] 3, 2 [RIGHTWARDS ARROW] 4, and 3 [RIGHTWARDS ARROW] 4 transitions. The 1 [RIGHTWARDS ARROW] 2 and 3 [RIGHTWARDS ARROW] 4 shocks are fast and slow shocks, respectively. The other four transitions are called intermediate shocks [Wu, 1990]. In addition, as the upstream flow velocity is equal to the normal Alfvén speed, the transverse component of the downstream magnetic field vanishes, producing a switch-off shock [Daughton et al., 2001; Feng et al., 2008]. Thus, switch-off shock is an extreme of the 3 [RIGHTWARDS ARROW] 4 slow shock and 2 [RIGHTWARDS ARROW] 4 intermediate shock [Wu, 1990]. In contrary to the switch-off shock, a switch-on shock has a vanished transverse component of the upstream magnetic field, and on its downstream side the flow speed is equal to the normal Alfvén speed. Switch-on shock is an extreme of the 1 [RIGHTWARDS ARROW] 2 fast shock and 1 [RIGHTWARDS ARROW] 3 intermediate shock.

[3] From the Rankine-Hugoniot (R-H) relations, the switch-on shock solution can be obtained in a narrow range of the upstream parameters. When the upstream region has a very low beta plasma (β ≪ 1) with an adiabatic condition (γ = 5/3), a parallel shock will generate a non-zero downstream tangential magnetic field with 1 < MA < 2. Here, MA is the Alfvén Mach number (MA = V1/VA, where V1 is the upstream velocity seen in the shock frame). Beyond this range, the parallel shock is purely hydrodynamic; the downstream magnetic field does not ‘switch-on’. For higher beta plasma, the possibility of the existence of a switch-on shock becomes lower [Kantrowitz and Petschek, 1966; De Sterck and Poedts, 1999]. However, in the two-fluid model, if one considers the electron heat conduction, the range for the switch-on shock solution can be extended [Kennel and Edmiston, 1988].

[4] A switch-on shock propagates parallel to ambient magnetic fields. From the linear wave theory, it is known that magnetic compression cannot happen in the direction exactly parallel to the background magnetic field. However, if one considers second-order perturbation, the compression can then occur [Omidi et al., 1990]. Switch-on shock is expected to form from linearly-polarized Alfvénic wave train. Some authors argue that if the leading wave disturbs the ambient magnetic field and produces a tiny nonzero transverse magnetic field, then the trailing wave can propagate in a slightly oblique direction relative to the magnetic field. In such a condition, the magnetic field can be compressed [Kantrowitz and Petschek, 1966; Kennel and Edmiston, 1988]. The existence of switch-on shocks have been confirmed in numerical simulations [e.g., Kan and Swift, 1983; Omidi et al., 1990].

[5] A switch-on shock is expected to develop as a low Alfvén Mach number (between 1 to 2) shock in a low beta plasma and likely to be observed in interplanetary space [Kennel and Edmiston, 1988]. If a fast CME moves from the sun in a low-beta corona, it may induce a switch-on shock at some magnetic field topology [De Sterck et al., 1998]. To our knowledge, a switch-on shock has been reported as a part of Earth's bow shock [Farris et al., 1994]. However, no switch-on shock preceding a CME has been reported to date. In this paper, we report a switch-on shock prior to a magnetic cloud. The shock was observed by Wind at 1 AU on August 1, 2002. It has a low upstream plasma beta (β < 0.2).

2. Observations of a Switch-on Shock

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Observations of a Switch-on Shock
  5. 3. Summary and Discussion
  6. Acknowledgments
  7. References
  8. Supporting Information

2.1. Data and Method of Analysis

[6] In the analysis, we consider the contributions of both the protons and alpha particles to the plasma mass. The magnetic field data are obtained from the Magnetic Field Investigation (MFI) magnetometer, and the proton, electron and alpha particle data are obtained from the 3-Dimension Plasma (3DP) analyzer. Description of the instruments on board Wind is given by Lepping et al. [2005] and Lin et al. [1995]. The data have a time resolution of 3 s except in the case of electron data where a 92-second average is used.

[7] For an ideal MHD shock, the coplanarity theorem requires that the up- and down-stream magnetic fields (B1 and B2) and the shock normal vector n lie on a coplanar plane. The shock normal vector can therefore be obtained as follows [Colburn and Sonnet, 1966]:

  • equation image

On the basis of it, one can define an orthogonal shock coordinate system. Provided that s denotes a unit vector perpendicular to the coplanar plane, it can be obtained by s = ±(B1 × B2)/∣(B1 × B2)∣. Thus, the third coordinate, t, can be obtained from t = ±n × s. As a result, the ts plane is just the shock front, and both the up- and down-stream magnetic fields lie on the nt plane.

[8] To study an observed shock, it is important to fit the measured magnetic fields and plasma data on both sides of the shock to the R-H relations. The main task of shock fitting is to find a reliable shock frame of reference. In searching for a shock frame, identification of shock normal vector, n, is crucial. Here we apply a shock fitting procedure based on the Monte Carlo calculation proposed recently by Lin et al. [2006]. The procedure finds optimized (best fit) shock coordinates (n, t, and s). Viñas and Scudder [1986] had proposed a least-squares approach to determine an optimized shock normal vector using a subset of the R-H relations. The approach was then modified by Szabo [1994] to include the whole set of the R-H relations. The Monte Carlo shock fitting (MSF) procedure also considers the whole set of the R-H relations. The numerical scheme of the MSF procedure is different from that of Viñas and Scudder [1986]. Moreover, with the procedure the tangential vector of shock can simultaneously be found together with the shock normal vector. The shock tangential vector plays a more role for MHD shocks than for hydrodynamic shocks, since for the MHD shock, the plasma flow is deflected toward the shock tangential direction. More detailed descriptions about the MSF procedure are given by Lin et al. [2006].

2.2. Identification Based on the R-H Relations

2.2.1. Estimate of the Shock Using Oblique Shock Model

[9] The shock was observed by Wind at ∼0519:28 UT on August 1, 2002, when Wind was located at (20.9, 86.5, 4.8) RE in the GSE coordinate system. The shock is found prior to a magnetic cloud, and it may be a product in the leading medium as the medium is pushed and compressed by the trailing magnetic cloud. A magnetic cloud is defined empirically in terms of its magnetic field and plasma having the following properties: (1) a high magnetic field strength compared to the ambience, (2) a smooth change in field direction as observed by a spacecraft passing through the cloud, and (3) a low proton temperature compared to the ambient proton temperature [Burlaga et al., 1981; Burlaga, 1991]. Figure 1 shows the magnetic field and proton temperature data of the magnetic cloud as well as the leading shock. It can be seen that the event satisfies the three criterions mentioned above. In addition, this event was identified as a magnetic cloud by R. P. Lepping et al. (http://lepmfi.gsfc.nasa.gov/mfi/mag_cloud_pub1.html), Jian et al. [2006], Lepping et al. [2005], Wu et al. [2006], Wu and Lepping [2007]. Figure 2 shows 13 minutes of the magnetic field and plasma data of this shock observed by Wind. From top to bottom the panels show the magnitude of the total magnetic field (∣B∣), the x, y, z components of the magnetic field (Bx, By, Bz), the x, y, z components of the proton speed (Vx, Vy, Vz), the proton density (Np), the proton and electron temperatures (Tp), respectively. It can be seen from Figure 2 that the proton number density Np, the proton and electron temperatures Tp and Te, and the total magnetic field strength ∣B∣ increase across the discontinuity. As can also be seen, the protons are thermalized to a very high temperature across the shock in comparison to the unperturbed state. However, it is not the case for the electrons. In addition, across the shock the proton velocity ∣V∣ (not shown here) also increases by 112 km/s. All these jump signatures are consistent with the requirements for a fast shock.

image

Figure 1. Interplanetary magnetic field and proton temperature data measured by the Wind spacecraft during the 1–2 August 2002 Magnetic cloud passages. FB and RB are the estimated front and rear boundaries, respectively.

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image

Figure 2. The interplanetary magnetic field and plasma data measured by Wind in GSE coordinate system on 1 August 2002.

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[10] The selected up- and down-stream intervals for fitting are indicated by the vertical lines in Figure 2. The selection of the intervals representative of the up- and down-stream regions is difficult and important, and a certain amount of subjectivity seems unavoidable. We try to select the intervals which are close to the transition layer and in which the magnetic field and plasma are relatively stable in order to reduce the effect of waves as well as the disturbances associated with the other structures.

[11] Table 1 lists the observed mean values and standard deviations of the magnetic field vector B, the solar wind velocity vector V, and the number density N. Subscripts 1 and 2 refer to the up- and down-stream variables, respectively. Note that the density N is an effective plasma number density calculated from N = Np + 4Na, where Np is the proton number density and Na is the number density of alpha particles. From the optimized solution obtained by the MSF procedure, we have the corresponding shock parameters. They are listed in Table 1. These parameters are the shock normal vector n, the other two axes of the shock coordinate system t and s, the plasma beta (β), the normal Alfvén-Mach number (MAN = Vn/VA), the fast-mode Mach number (MF = Vn/Vf) in the upstream/downstream region, and the shock normal angle, θBN1 = cos−1(B1n/B1), between the shock normal and the upstream magnetic field vector. Here, VA = Bn/(μ0ρ)1/2 is the Alfvén speed based on the magnetic field component normal to the shock front, Vn is the normal component of the bulk velocity to the shock front and measured in the shock frame of reference, and Vf is the speed of the fast-magnetosonic wave in the direction of the shock normal.

Table 1. Observed and Model Solution of the 1 August 2002 Discontinuity Event
ParameterObserved ValuesaFast Shock Model SolutionSwitch-on Shock Model Solution
  • a

    The SD of B1 is (0.72, 0.96, 0.88), the SD of B2 is (0.51, 0.88, 0.70), the SD of N1 and N2 are 0.23 and 0.33, the SD of V1 and V2 are (11.3, 12.5, 12.6) and (6.0, 8.2, 5.2),the SD of β1 and β2 are 0.014 and 0.127.

B1 (nT)(5.79, −4.88, −3.36)(6.69, −4.77, −3.36)(6.84, −4.36, −3.76)
B2(5.98, −0.66, −11.76)(6.17, −1.01, −12.22)(5.45, −1.30, −11.75)
N1, N2 (cm−3)3.30, 7.183.11, 7.133.25, 6.99
V1 (km/s)(−385.3, 4.8, −47.4)(−385.1, 5.6, −48.8)(−385.1, 5.6, −48.8)
V2 (km/s)(−471.5, 96.3, −94.8)(−464.6, 91.7, −88.2)(−467.9, 78.1, −82.5)
β1, β20.167, 0.6520.161, 0.6950.154, 0.624
n(−0.701, 0.643, 0.308)(−0.762, 0.578, 0.291)(−0.765, 0.488, 0.421)
t(0.019, 0.449, −0.893)(−0.054, 0.390, −0.919)(−0.232, 0.400, −0.887)
s(−0.713, −0.620, −0.327)(−0.644,−0.717,−0.266)(−0.601, −0.776, −0.193)
MAN1, MNA21.559, 1.0621.608, 1.0631.465, 1.000
MF1, MF21.549, 0.5921.600, 0.5771.465, 0.594
θBN16.40°5.55°0.00°

[12] As can be seen in Table 1, the best fit values are close to the observed means, namely, the data can be interpreted as an oblique fast shock (with small shock normal angle). The shock solution demonstrates the following properties: (1) the fast-mode Mach number is greater than unity in the preshock state and less than unity in the postshock state, (2) the normal Alfvén-Mach number (MAN) is greater than unity in the preshock state and almost equal to unity in the postshock state, and (3) the shock normal angle (θBN1) is very small. Figure 3a shows the magnetic field profiles in the shock coordinates. It can be seen that the tangential component of the upstream magnetic field (Bt) is nearly vanished. However, across the shock the tangential component of the magnetic field is “switched-on” significantly. In addition, it can also be seen that the normal component (Bn) is nearly constant across the shock, while the other component (Bs) is nearly zero.

image

Figure 3. The observed magnetic fields on 1 August 2002 in the shock coordinate system, (a) the fast shock model, and (b) the switch-on model.

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2.2.2. Estimate of the Shock Using the Switch-on Model

[13] In order to have a more comprehensive understanding of whether the shock is switch-on or not, we modify the MSF procedure based on a switch-on model, and we apply it to analyze the data independently. For a switch-on shock, the shock normal is parallel to the upstream magnetic field. Therefore, in the modified procedure, we calculate the shock normal by

  • equation image

with the Monte Carlo calculation. Therefore, we have a zero degree shock normal angle, θBN1. The other two coordinates are then obtained by

  • equation image

Here, t represents the tangential direction of the shock.

[14] For a switch-on shock, u (≡Bt1/Bt2) [RIGHTWARDS ARROW] ∞ and θBN1 = 0°, there are some uncertain situations in the values of the calculated velocity and plasma betas in equations (8) to (11) of Lin et al. [2006]. The expressions of these parameters should be modified to

  • equation image
  • equation image
  • equation image
  • equation image

Since in the modified procedure the shock normal is not obtained by the magnetic coplanarity theorem, the normal magnetic fields B1·n and B2·n do not have to be equal to one another. For finding an optimized solution for the divergence free condition of the magnetic field, we add a term in the loss function for the normal magnetic field. The term is expressed as equation image. Here, we calculate the error, σbn, using the standard errors of the up- and down-stream magnetic field. It is calculated as

  • equation image

[15] Employing the modified fitting procedure, we obtain a best fit solution which satisfies the R-H relations for a switch-on shock. Table 1 lists the best fit shock parameters. In addition, Figure 3b shows the magnetic field profiles in the optimized switch-on shock coordinates. As can be seen in Table 1 and Figure 3, the solution of this modified procedure is close to the data as well. We also find that the solutions of the two independent analyses based on oblique and switch-on shocks are close to one another. Therefore, we suggest that the spacecraft may have observed a switch-on shock.

3. Summary and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Observations of a Switch-on Shock
  5. 3. Summary and Discussion
  6. Acknowledgments
  7. References
  8. Supporting Information

[16] In this study, an interplanetary switch-on shock is identified by fitting the R-H relations. This shock was observed by Wind on August 1, 2002 at 1 AU. The shock is found prior to a magnetic cloud. We investigate this shock using two independent analyses. For one analysis, we apply the MSF procedure for oblique shock proposed by Lin et al. [2006]. For the other one, we also apply the MSF procedure but based on the switch-on shock model. We find that the two models can fit the observed data well, and their solutions are close to one another. The observed magnetic field and plasma data satisfy the R-H relations well. We believe that this event is a switch-on shock.

[17] The upstream parameters of this shock are within the domain of switch-on shock expected by the ideal MHD regime. This shock has a low upstream plasma beta of less than 0.2 (β1 = 0.154). The fast and Alfvén Mach numbers are 1.465, which is at a mid point of the theoretical Mach-number domain for a switch-on shock (1–2 for low beta case). Note that here for θBN1 = 0°, the characteristic speeds of fast and Alfvén mode are equal. Therefore, a switch-on shock has the same upstream fast and Alfvén Mach number. In addition, the downstream normal Alfvén Mach numbers calculated by the two models are unity to almost unity, respectively, which also agrees with the criterion of a switch-on shock. In our analysis, we find that this shock propagates and is compressed in the direction of (−0.77, 0.49, 0.42) (GSE), which is in the direction of the spiral IMF at 1 AU. If the compression is made by the following magnetic cloud, geometrically the shock front should be at the limb side of the whole magnetic cloud structure. The association of the switch-on shock and the CME is an interesting problem and can be investigated in future.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Observations of a Switch-on Shock
  5. 3. Summary and Discussion
  6. Acknowledgments
  7. References
  8. Supporting Information

[18] This work was supported by National Nature Science Foundation of China (NSFC) under grants 40804034, 10425312, 10603014, and 40574065 and by a Project Supported by the Specialized Research Fund for State Key Laboratories. This work was also supported by the National Science Council (NSC) (Taiwan) grants NSC 97-2111-M-008-012-MY3 and NSC 97-2811-M-008-039, the National Space Organization (NSPO) grant 97-NSPO(B)-SP-FA07-01, and the Ministry of Education grant “Aim for the Top University” to the National Central University. The authors thank NASA/GSFC for the use of Wind MFI and 3DP obtained via the CDA Web page. The authors also thank Ann Fellows for improving the writing of the paper.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Observations of a Switch-on Shock
  5. 3. Summary and Discussion
  6. Acknowledgments
  7. References
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Observations of a Switch-on Shock
  5. 3. Summary and Discussion
  6. Acknowledgments
  7. References
  8. Supporting Information
FilenameFormatSizeDescription
grl25754-sup-0001-t01.txtplain text document1KTab-delimited Table 1.

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