System on board the Solar and Heliospheric Observatory spacecraft located at Lagrangian point ... back from the upstream to the downstream solar wind plasma.
The Astrophysical Journal, 601:L99–L102, 2004 January 20 䉷 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.
HYDROMAGNETIC WAVE EXCITATION UPSTREAM OF AN INTERPLANETARY TRAVELING SHOCK K. Bamert,1 R. Kallenbach,2 N. F. Ness,3 C. W. Smith,4 T. Terasawa,5 M. Hilchenbach,6 R. F. Wimmer-Schweingruber,7 and B. Klecker8 Received 2003 January 20; accepted 2003 December 10; published 2004 January 19
ABSTRACT Using data of the Highly Suprathermal Time-Of-Flight sensor of the Charge, Element, and Isotope Analysis System on board the Solar and Heliospheric Observatory spacecraft located at Lagrangian point L1 near Earth, we have measured proton spectra in the energy range 60 keV–2 MeV associated with the Bastille Day coronal mass ejection of 2000 July 14–16. For the same event, the power spectral densities of the magnetic field fluctuations in the solar wind have been measured with the magnetometer on board the Advanced Composition Explorer in the frequency range from about 0.05 mHz to 0.5 Hz. Within 0.11 AU upstream of the main shock, the flux of protons in the energy range 150 keV–2 MeV decreases much more rapidly with distance from the shock than is expected from diffusion in typical solar wind magnetic turbulence. In the same upstream region, the excitation of hydromagnetic waves in the frequency range 0.25–3 mHz and with power spectral density levels of up to 100 times the typical levels in the ambient solar wind is observed. Subject headings: acceleration of particles — interplanetary medium — shock waves — Sun: coronal mass ejections (CMEs) — waves is located near the Solar and Heliospheric Observatory (SOHO) at Langrangian point L1. For the same upstream plasma region, the proton spectra in the energy range 60–2000 keV are derived from data of the Charge, Element, and Isotope Analysis System (CELIAS) Highly Suprathermal Time-Of-Flight (HSTOF) sensor (Hovestadt et al. 1995; Bamert et al. 2002) on board SOHO. The spatial distribution of the proton flux in the energy range 0.25–1 MeV near the shock IPS2 indicates a strong preenergized ion population in the downstream magnetic turbulence region. This population presumably supplies seed ions for injection into first-order Fermi acceleration at the shock IPS2. The left panels of Figure 2 show the proton spectra at distances z p 0.0, 0.022, 0.066, and 0.11 AU upstream of the shock. The central field of view of the HSTOF sensor is directed 37⬚ west of the direction to the Sun in the ecliptic plane. The angular acceptance is Ⳳ2⬚ in heliolongitude and Ⳳ17⬚ in heliolatitude. The angle between the central field of view of the HSTOF sensor and the ambient magnetic field B 0 is at most 50⬚ (Smith et al. 2001). The spectra are plotted as a function of the wavenumber k in units of the wavenumber k 1 MeV of an Alfve´n wave that resonates with a proton at 1 MeV energy and at zero pitch angle, k 1 MeV ≈ Q p /v1 MeV, with v1 MeV ≈ 1.38 # 10 7 m s⫺1. In the range of proton energies analyzed here, the frequencies of the waves that gyroresonate with the protons is small compared to the proton gyrofrequency. The latter is fgyro; p p Q p /2p p eB 0 /2pm p (e: elementary charge; m p: proton mass) and is about ≈0.14 Hz upstream of the shock (0.022 AU ! z ! 0.11 AU; see Table 1 for the values of B 0). This results in k 1 MeV ≈ 6.37 # 10⫺8 m⫺1 or f1 MeV ≈ k 1 MeVVA/2p ≈ 1 mHz, assuming a mean Alfve´n speed VA ≈ 104 km s⫺1 for 0.022 AU ≤ z ≤ 0.11 AU (Table 1). The proton spectra right at the shock obey a power law Fp (k, z p 0) p F0 (k/k 1 MeV ) b, with b ≈ 4.9 and F0 ≈ 3 # 10⫺4 s3 km⫺6 sr⫺1. In the right panels of Figure 2, the power spectral densities of the magnetic field fluctuations are displayed for the same distances z p 0.0, 0.022, 0.066, and 0.11 AU upstream of the shock as for the proton spectra. The scale of wavenumbers k p 2pfA/VA of all panels refers to Alfve´n waves propagating parallel within about 30⬚ to the ambient magnetic field in antisunward direction. The local Alfve´n speeds VA and the correction
1. INTRODUCTION
First-order Fermi acceleration of ions or electrons at an interplanetary shock requires scattering of the particles forth and back from the upstream to the downstream solar wind plasma and vice versa. By this means, a particle gains a speed increment of the order of the difference between the upstream and downstream bulk plasma speeds during each bounce. While the turbulence downstream of interplanetary shocks driven by coronal mass ejections (CMEs) efficiently scatters ions, the capability of the upstream plasma of scattering ions is less obvious. We present an analysis of data associated with the Bastille Day event during the time period 2000 July 14–16. This analysis is aimed at testing the hypothesis that the upstream waves that scatter energetic protons in course of the first-order Fermi process are generated by these protons themselves (Lee 1983). 2. OBSERVATIONS
An overview of spacecraft data recorded during the Bastille Day event is given in Figure 1. In this Letter, power spectral densities of magnetic field fluctuations with frequencies between 0.05 mHz and 0.5 Hz in the frame of the plasma within 0.11 AU upstream of the main shock IPS2 (Fig. 2, right panels) are calculated from data of the magnetometer on board the Advanced Composition Explorer (ACE; Smith et al. 1998), which 1 Physikalisches Institut, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland. 2 International Space Science Institute, Hallerstrasse 6, CH-3012 Bern, Switzerland. 3 Bartol Research Institute, University of Delaware, 217 Sharp Laboratory, Newark, DE 19716. 4 Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Morse Hall, 39 College Road, Durham, NH 03824-3525. 5 University of Tokyo, Department of Earth and Planetary Science, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan. 6 Max-Planck-Institut fu¨r Aeronomie, Postfach 20, D-37189 KatlenburgLindau, Germany. 7 Institut fu¨r Experimentelle und Angewandte Physik, University of Kiel, Leibnizstrasse 11, D-24118 Kiel, Germany. 8 Max-Planck-Institut fu¨r extraterrestrische Physik, Giessenbachstrasse Postfach 1603, D-85740 Garching, Germany.
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2.5k 1 MeV above dB˜ 2 (k, ⬁). The range of k-numbers between 0.25k 1 MeV and 2.5k 1 MeV corresponds to the range of k-numbers or proton speeds, respectively, where the proton phase-space density is much below the level that would be expected, if there were no increase of the wave power with decreasing z at 0 AU ! z ! 0.11 AU. At k-numbers larger than 2.5k 1 MeV, the power spectral density looks like a Kolmogorov cascade with a spectral index of ⫺5/3 up to k ≈ k diss. Right at the shock in the downstream plasma, the power spectral density is quite high and follows a power law over the full analyzed frequency range, dB˜ 2 (k, 0) ≈ 10 8 nT2 m (k/k 1 MeV )⫺5/3. 3. DISCUSSION
Fig. 1.—Overview of the Bastille Day event. For the time period 2000 July 14–16 (day of year 196–198), we show from top to bottom: the energetic proton flux in three energy ranges derived from CELIAS/HSTOF data, the proton density from proton monitor (PM) data of SOHO/CELIAS (Carrington Rotation Web site; http://umtof.umd.edu/pm/crn), the magnetic field strength from level 2 data of the MAG experiment on board ACE (see http://www .srl.caltech.edu/ACE/ASC/level2/lvl2DATA_MAG.html), the calculated Alfve´n speed [VA p B0 /(m0mp Np)1/2], and the solar wind speed (dashed line) also taken from the PM Web site. The two interplanetary shocks IPS1 and IPS2 are marked by dashed lines. The boundaries of the magnetic clouds of this event are indicated by dash-dotted lines. In addition, we have marked the onsets of the X-flare observed at 1024 UT on 2000 July 14 by the EUV Imaging Telescope on SOHO and the Earth-directed halo CME observed at 1054 UT by the Large Angle and Spectrometric Coronagraph Experiment on SOHO, leaving the Sun at a speed of about 1775 km s⫺1.
factors c c for the Doppler shift of the wave frequency fA between the local plasma frame and the spacecraft frame are listed in Table 1. The calibration of the wavenumber scale appears reasonable because the wavenumber, where the power spectra break from the typical inertial range with a Kolmogorov-type spectral index of ⫺5/3 to the dissipation range with typical spectral index ⫺7/2, is at k diss ≈ Q p /VA ≈ 75k 1 MeV, consistent with the results of Leamon et al. (1998). An explicit determination of the kvector of the plasma waves and their specific type, however, is not possible with a single spacecraft measurement. Far upstream of the shock, at z 1 0.11 AU (evaluated at z p 0.21 AU for k K k 1 MeV), the power spectral density of the magnetic field fluctuations is of Kolmogorov type, dB˜ 2 (k, ⬁) ≈ 2 # 10 5 nT2 m (k/k 1 MeV )⫺5/3. If only this level of turbulence were present at z ≤ 0.11 AU, the proton spectra would approximately evolve as indicated by the dash-dotted lines in the left panels of Figure 2. These dash-dotted lines are calculated using the scattering mean free paths shown for large z in Figure 3. The observed phase-space density, however, is far below the level indicated by the dash-dotted lines, in particular for k ! 2.5k 1 MeV, i.e., for E p 1 150 keV. As a matter of fact, for z ≤ 0.11 AU upstream of the shock, the power spectral density of the magnetic field fluctuations increases above dB˜ 2 (k, ⬁) with decreasing distance to the shock and at frequencies fA 1 0.25 mHz corresponding to k ≈ 0.25k 1 MeV. At a distance z ≈ 0.022 AU, this enhancement is most pronounced. The power spectral density is almost flat in the range from about k p 0.25k 1 MeV and k ≈ 2.5k 1 MeV, which results in an enhancement of almost 2 orders of magnitude at k ≈
We compare our observations to the predictions of the theory of coupled hydromagnetic wave excitation and ion acceleration at interplanetary traveling shocks by Lee (1983), which is based on quasi-linear theory (QLT). The spatial diffusion coefficient is derived from the pitch angle diffusion coefficient Dmm; s p pQ s2 (1 ⫺ m2 ) dB˜ 2 (kkres; s ) /FmFvB 02, where the subscript s denotes the species of ions with charge qs p Q s e and mass m s ≈ A s m p with angular gyrofrequency Q s. The parameter m p cos v characterizes the ion’s pitch angle v with respect to the ambient magnetic field B 0. The quantity dB˜ 2 (kkres; s ) denotes the power spectral density of the magnetic field fluctuations in units of nT2 m. The wavenumber kkres; s denotes the field-aligned component of the wavevector k that resonates with an ion of species s with zero pitch angle at speed v, Q s p kkres; s v. In this Letter, we drop the index “res” and use simply k ≈ kkres; s. We constrain ourselves to the interaction between the major species, the protons, and the hydromagnetic waves. The theory by Lee (1983) assumes an asymmetry proportional to the parameter m in the distribution function of the energetic protons entering the upstream plasma. These protons amplify the antisunward propagating hydromagnetic waves, i.e., the waves with k 1 0. Their relative power spectral density P(k, z) p dB˜ 2 (k)/B 02 and the omnidirectional phase-space density of the protons Fp (k, z) are related by a growth factor gp (k) ∝ k⫺6 (Lee 1983): P(k, z) p gp (k)Fp (k, z) ⫹ P(k, z p ⬁).
(1)
The phase-space density of the protons solves the above equation and the transport equation simultaneously (Lee 1983): Fp (k, z) p
Fp (k, 0) , [1 ⫹ g(k)] exp [h(k)z] ⫺ g(k)
g(k) p
gp (k)Fp (k, 0) , P(k, ⬁)
h(k) p
VP(k, ⬁) , k p (k)
(2)
where V is the mean upstream solar wind bulk speed and k p (k) p Q p k⫺3/8p. With V, B 0, and dB˜ 2 (k, ⬁) from our data set, we obtain h(k) ≈ 1.65 (k/k 1 MeV ) 4/3 AU⫺1. The growth parameter gp (k) (Lee 1983), rewritten in SI units, is gp (k) ≈ 3p 2 Q 5p /b (b ⫺ 2) k 6NpVVA. This yields in our case gp (k) ≈ 5 # 10 7 (k/k 1 MeV )⫺6 km6 s⫺3 m. Two sets of functions Fp (k, z) and P(k, z) have been fitted to the data. One applied the theory by Lee (1983) as is, except that prefactors gp0 and h 0 of gp (k) and h(k) have been varied
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Fig. 2.—Left panels: Phase-space densities of energetic protons measured with the SOHO/CELIAS/HSTOF sensor at different distances upstream of the main shock of the Bastille Day event. The speed of the protons can be derived by the relation v p v1 MeVk1 MeV/k , where v1 MeV p 1.38 # 107 m s⫺1. Right panels: Power spectral densities of the magnetic field fluctuations for locations corresponding to the left panels. Details of the plotted fit functions are described in the text. The free parameters h0 and gp0 of these functions are adjusted to both the proton data and the power spectral densities by least-square fits. The label “cutoff” denotes the fit function with a cutoff in gp(k) at k p 3.3k1 MeV.
to fit the data. The second set of functions additionally contained a sharp fitted cutoff in gp (k) of the form gp; c (k) p gp (k) exp [⫺(k/k c ) 9.5 ] for k 1 k c ≈ 3.3k 1 MeV, i.e., for E p 1 Ec ≈ 90 keV. This cutoff is at considerably higher energy than the cutoff suggested by Lee (1983) that accounts for the injection threshold to first-order Fermi acceleration. Both fits resulted in h 0 ≈ 1.2. This factor presumably becomes even larger, if a decomposition of the magnetic field fluctuations into transverse and longitudinal fluctuations is performed. This means that mean free paths for protons are somewhat shorter than predicted by QLT. The wave growth factor
gp (k) derived from the data is similar to that predicted by Lee (1983), gp0 ≈ 1. The cutoff in gp (k) at k c ≈ 3.3k 1 MeV accounts for the enhancement of the proton phase-space density Fp (k, z) at locations 0.022 AU ! z ! 0.11 AU (Fig. 2, left panels) in the energy range below 150 keV (at k 1 2.5k 1 MeV) above the level predicted by the theory of Lee (1983). On the other hand, the power spectral density P(k, z) of the magnetic fluctuations for k 1 2.5k 1 MeV does not drop according to the cutoff in gp (k). It rather follows a Kolmogorov-type cascade up to k ≈ k diss. Depending on the range in wavenumbers, the power spectral density level of the magnetic field fluctuations in the
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TABLE 1 Shock Properties UT
Dt (UT)
z (AU)
Vsw (km s⫺1)
VA (km s⫺1)
cca
B0 (nT)
14.25–15.75 . . . . . . 12.75–14.25 . . . . . . 11.25–12.75 . . . . . . 9.75–11.25 . . . . . . .
0 0.75 2.25 3.75
0 0.022 0.066 0.11
789 577 558 592
236 114 103 96
4.01 5.56 5.88 6.55
29 10 10 9
a Correction factor for the Doppler shift: cc p (Vsw /VA) cos f with cos f p 0.9, f denoting the angle between the solar wind flow with speed Vsw and the ambient magnetic field B0. The Alfve´n speed is VA p B0 / (m0mpNp)1/2 (m0: permeability of the vacuum; Np: bulk proton density).
downstream plasma right at the shock is by far more than a factor of 10 above the upstream level at z p 0.022 AU, while the transmission coefficient of McKenzie & Westphal (1969) predicts a 10-fold enhancement. The proton mean free paths for several ranges of proton energies as a function of the distance upstream of the shock are displayed in Figure 3. These mean free paths are derived from l k p 3 v2/8pQ 2p P(k, z). The plots of Figure 3 suggest that the waves generated by the upstream energetic protons are capable of scattering these energetic protons back to the shock.
Fig. 3.—Proton scattering mean free paths upstream of the main shock of the Bastille Day event for various energies derived from the fit functions described in the text. The plotted mean free paths are a factor of 1.2 smaller than predicted by QLT. As noted in the text, a decomposition of the magnetic fluctuations into parallel and transverse components would yield the result that QLT overestimates the mean free paths even more than by a factor of 1.2.
4. CONCLUSIONS
an asymmetry is not the only feature of energetic particle distribution functions that may cause wave amplification (Berezhko 1990; Ng, Reames, & Tylka 2003). The process of hydromagnetic wave excitation upstream of interplanetary shocks will further be explored.
Correlated observations of ions in the energy range from 60 to 2000 keV and of magnetic field fluctuations in the frequency range from 0.05 mHz to 0.5 Hz suggest that the theory of Lee (1983) on coupled hydromagnetic wave excitation and ion acceleration at interplanetary traveling shocks cannot account for all phenomena of wave-particle interaction in the upstream plasma. A better understanding of these phenomena could be provided by instruments that measure the full angular distribution of protons in the energy range above 100 keV. In fact,
CELIAS is a joint effort of five hardware institutions under the direction of the Max-Planck-Institut fu¨r extraterrestrische Physik (MPE; prelaunch) and the University of Bern (UoB; postlaunch). The MPE is the prime hardware institution for the HSTOF sensor. The UoB provided the entrance system. The DPU was provided by the Technical University of Braunschweig. This work is funded by the Swiss National Science Foundation and by INTAS grant WP 270.
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Lee, M. A. 1983, J. Geophys. Res., 88, 6109 McKenzie, J. F., & Westphal, K. O. 1969, Planet. Space Sci., 17, 1029 Ng, C. K., Reames, D. V., & Tylka, A. J. 2003, ApJ, 591, 461 Smith, C. W., Acun˜a, M. H., Burlaga, L. F., L’Heureux, J., Ness, N. F., & Scheifele, J. 1998, Space Sci. Rev., 86, 613 Smith, C. W., et al. 2001, Sol. Phys., 204, 227
