Chin-Chun Wu1, Simon Plunkett1, Kan Liou2, Angelos Vourlidas1, Murray Dryer3, S. T. Wu4, Richard A. Mewald5

1Space Science Division, Naval Research Laboratory

2Space Department, Applied Physics Laboratory

3Emeritus, NOAA, Boulder, CO, USA

4CSPAR, University of Alabama, Huntsville, Alabama, USA

5California Institute of Technology, Pasadena, CA, USA

INTERPRETATION OF THE TIME-INTENSITY PROFILE OF THE 15 MARCH 2013 SOLAR ENERGETIC PARTICLE EVENT WITH GLOBAL MHD

SIMULATION

ISSI, Bern, Switzerland, 2014-01-20ISSI, Bern, Switzerland, 2014-01-20

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The coronal mass ejection (CME) event on March 15, 2013 is one of the few solar events in cycle 24 that produced a large solar energetic particle (SEP) event and severe geomagnetic activity. SEP observations from the ACE spacecraft show a complex time-intensity profile that is not easily understood with current SEP theories. In this study, we employ a global three-dimensional (3-D) magnetohydrodynamic (MHD) simulation to help interpret the observations. The simulation is based on the H3DMHD code and incorporates extrapolations of photospheric magnetic field as the inner boundary condition at 2.5 solar radii (Rs). A Gaussian-shaped velocity pulse is imposed at the inner boundary as a proxy of the CME. It is found that the time-intensity profile of the high-energy (> 10MeV) SEPs can be explained by the evolution of the CME-driven shock and its interaction with the heliospheric current sheet and the non-uniform solar wind. Specifically, we demonstrate that the shock Mach number at the well-connected shock location is correlated (r ≥ 0.8) with the concurrent proton SEP fluxes with energies greater than 10 and 30 MeV. This study demonstrates that global MHD simulation, despite the limitation implied by its physics-based ideal fluid continuum assumption, can be a useful tool for SEP data analysis.

ABSTRACT

CASE : CME ON MARCH 15, 2013SOURCE LOCATION: N09W02(CME) /N09E06 (FLARE)SPEED: ~1000 KM/S (STEREO COR2A/B) 06:54UT

IMAGES OF STEREO-A COR2

IMAGES OF STEREO-B COR2

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Images of the 15 March 2013 CME from COR2-B (left), C3 (middle), and COR2-A (right). The observation times are shown on the images. The white arrows indicate the white light shock front and the black arrow indicated the erupting flux rope (see Vourlidas et al 2013, for details). The lack of sharp shock signatures in COR2-B indicates that the shock is expanding towards the spacecraft (eastwards). Venus is the bright planet with the saturation streaks in the C3 images.

ESTIMATED CME SPEED FROM COR2A

IN-SITU SOLAR WIND PARAMETERS: WIND

SH

OC

K

MCL

ICME

Discontinuity

Density

Velocity

Thermal speed

IMF Bz

ƟB

BTOTAL

φB

Dst

beta

SOLAR ENERGETIC PARTICLES (SEPs) at STEREO

STEREO-B STEREO-A

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Intensity-time profile of solar energetic proton integral flux by the Solar Isotope Spectrometer (SIS) on board the Advanced Composition Explorer (ACE) spacecraft for 2 energy ranges: 10-30 MeV (blue-dotted line) and 30-80 MeV (red-dashed line) during the period 15-19 March 2013.

SEPs at ACE

SIMULATION RESULTS AT 18 AND 215 SOLAR RADII

ICME crosses HCS

CME source location and Earth are at different side of heliospheric current sheet

Earth

Source location

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Solar wind speed (Vsolar-wind) on surface of angular cone at 7.5ºS that is centered at the Sun’s center. The solid circle is at 1 AU (215 Rs). Earth is located at helio-longitude, φ = 0º; thus, the east limb (relative to Earth) is at the top, 90ºE, and the west limb is at the bottom, 90ºW. The outer boundary is at 345 Rs. Symbols “@” and “*” mean positions of STEREO-A and –B, respectively. Red dots mean upstream of IP shocks. White dashed curves show the possible location of the HCS for which the magnetic field in the r-direction is zero.

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(Left panel) Comparison of H3DMHD simulated (red) and situ measurement data from ACE (black) result with ACE. Panels from top to bottom, and B are proton temperature (Tp), proton speed (V), proton density (Np), and magnetic field strength (B), respectively. (Right panel)

Comparisons of observed ACE in situ measurements (black) with H3DMHD simulated results at different latitudinal locations: 12.5 ºN (orange dash-dot-dot-dot-dashed lines), 7.5ºN (blue dash-dotted lines), 2.5ºN (dark-brown dotted lines), 2.5ºS (purple dashed lines), 7.5ºS (red solid lines), and 12.5ºS (green solid lines). Vertical blue-dashed lines indicate the arrival of the IP shock at ACE.

• STEREO-B observed SEPs right after the CME eruption

• STEREO-A did not observe SEPs

• ACE observed SEPs ~10 hours after the CME onset

• Why there are two sharp SEP enhancements at ACE?

DISCUSSION

DISCUSSION• First SEP enhancement at ACE: after ICME

(or shock) crossed the heliospheric current sheet (HCS).

• SEPs propagated along the magnetic field lines which were well connected to ACE.

FAST WAVE PROFILE NEAR ECLIPTIC PLANE

Low speed fast wave

High speed fast wave

ICME propagated into low speed fast wave region

DISCUSSION

• Second SEP enhancement at ACE: after ICME (or shock) propagated into a low speed fast-mode wave region.

• Increased shock strength by shock propagating into low speed (fast wave) region.

DISCUSSION

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Cfast = Speed of Fast WaveΔt = t2 - t1

Δr = r2 - r1

Vshock = Δr/ΔtMfast-shock = |Vshock-Vsolar-wind|/Cfast

t = t1

t = t2

Schematic illustration for the wave tracing method (adapted from Figure 1 of Wu et al. [2012b]).

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Color coded fast-mode shock Mach number in the solar ecliptic plane for the CME event on 15 Mach 2013. The upstream location of the shock at six different times are labeled and represented by contour lines. The location of the Sun and the Earth are marked as “■”and “+” signs. The dotted curve represents the cobpoints (assuming a classical Parker quiet-Sun IMF).

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Left panel: the simulated radial profile of fast-mode shock Mach number in the solar ecliptic plane for the 15 March 2013 CME epoch. The upstream location of the shock at six different times are labeled and represented by contour lines. The location of the Sun and the Earth are marked as “■”and “+” signs, respectively. The dotted curve represents the cobpoints (assuming a classical Parker quiet-Sun IMF). Right panel: variation of Mach number (blue curve) marked as dots on the left panel, and the location (black-dotted curve, r- distance away from the Sun.)

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(a) Solar energetic proton integral flux acquired by the Solar Isotope Spectrometer (SIS) on board the Advanced Composition Explorer (ACE) spacecraft for 10-30 MeV (red) and 30-80 MeV (blue) during the period 15-19 March 2013.The simulated fast-mode shock Mach number at the COBpoints is also plotted (black). (b) Scatter plots showing the relationship between the hourly integral fluxes of SEPs and fast-mode shock Mach numbers for the two energy ranges. The Pearson correlation coefficient “r” and linearly fitted line are provided.

* The shock Mach number drops substantially from its peak value near the Sun thus back streaming SEP may not contribute to the observed flux at 1 AU. This view is consistent with the ACE observations.

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Left panels show the Intensity-time profile of solar energetic particles integral flux (hourly resolution) by the Solar Isotope Spectrometer (SIS) on board the Advanced Composition Explorer (ACE) spacecraft for Helion (4He) and Oxygen particles with energy ranges 3.43-41.19 and 7.30-89.79 MeV, respectively during the period 15-19 March 2013. Middle/right panels show correlation coefficients (c.c.s’) between IP shocks’ Mach number and measured/r2-scaled SEP integral flux with different time shift (or delay time from 0 to 15 hours).

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Time delay for getting best correlation coefficients between time profiles of Mach number and SEP intensities. Left and right panels show results for 4He and O SEPs.

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Correlation coefficients between Mach number of IP shocks and measured/scaled 4He intensities.

Scaled with r 0 r -1 r -2 r -3 r -4

3.43-4.74 MeV 0.034 0.166 0.310 0.456 0.522

4.74-6.13 MeV 0.126 0.266 0.410 0.550 0.556

6.13-7.29 MeV 0.209 0.360 0.513 0.631 0.579

7.29-9.72 MeV 0.300 0.448 0.595 0.713 0.720

9.72-13.59 MeV 0.411 0.565 0.691 0.746 0.686

13.59-17.96 MeV 0.586 0.718 0.800 0.816 0.770

17.96-29.35 MeV 0.696 0.777 0.808 0.797 0.757

29.35-41.19 MeV 0.378 0.472 0.545 0.583 0.584

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Correlation coefficients between Mach number of IP shocks and measured/scaled Oxygen SEP intensities.

Scaled with r 0 r -1 r -2 r -3 r -4

7.30-9.99 MeV 0.275 0.429 0.581 0.709 0.766

9.99-13.07 MeV 0.422 0.577 0.717 0.815 0.838

13.07-15.63 MeV 0.544 0.691 0.785 0.877 0.607

15.63-20.97 MeV 0.635 0.743 0.808 0.820 0.774

20.97-29.42 MeV 0.758 0.831 0.854 0.829 0.751

29.42-38.94 MeV 0.655 0.676 0.648 0.592 0.517

38.94-63.77 MeV 0.527 0.561 0.499 0.344 0.169

63.77-89.78 MeV 0.091 0.115 0.061 -0.004 -0.049

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Best correlation coefficient for Mach number vs. time-delayed SEP intensities of 4He particles

Scaled with r0 r-1 r-2 r-3 r-4

3.43-4.74 MeV 0.918a (11)b 0.928 (10) 0.886 (9) 0.780 (7) 0.616 (5)

4.74-6.13 MeV 0.921 (11) 0.913 (09) 0.835 (7) 0.732 (5) 0.559 (1)

6.13-7.29 MeV 0.918 (10) 0.895 (8) 0.841 (6) 0.763 (5) 0.586 (2)

7.29-9.72 MeV 0.920 (9) 0.893 (7) 0.839 (6) 0.755 (2) 0.720 (0)

9.72-13.59 MeV 0.870 (7) 0.854 (5) 0.791 (4) 0.750 (1) 0.686 (0)

13.59-17.96 MeV 0.749 (7) 0.739 (4) 0.800 (0) 0.816 (0) 0.770 (0)

17.96-29.35 MeV 0.729 (5) 0.777 (0) 0.808 (0) 0.797 (0) 0.757 (0)

29.35-41.19 MeV 0.437 (3) 0.489 (3) 0.545 (0) 0.583 (0) 0.584 (0)a Best correlation coefficient picked from 15 delay-time c.c.s’. b Delay-time required (unit in hours).

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Best correlation coefficient for Mach number vs. time-delayed SEP intensities of Oxygen SEPs

Scaled with r 0 r -1 r -2 r -3 r -4

7.30-9.99 MeV 0.925a (9b) 0.902 (8) 0.851(6) 0.769 (4) 0.766 (0)

9.99-13.07 MeV 0.911(8) 0.881 (7) 0.821(5) 0.815 (0) 0.838 (0)

13.07-15.63 MeV 0.877 (7/6) 0.846 (5) 0.813 (3/2) 0.805 (1) 0.715 (1)

15.63-20.97 MeV 0.870 (5) 0.845 (4) 0.815 (1) 0.820 (0) 0.774 (0)

20.97-29.42 MeV 0.819 (4) 0.831(0) 0.854 (0) 0.829 (0) 0.751 (0)

29.42-38.94 MeV 0.655 (0) 0.696 (0) 0.648 (0) 0.592 (0) 0.517 (0)

38.94-63.77 MeV 0.527 (0) 0.561(0) 0.499 (0) 0.344 (0) 0.254 (3)

63.77-89.78 MeV 0.112 (1) 0.143 (1) 0.102 (1) 0.049 (1) 0.009 (1)a Best correlation coefficient picked from 15 delay-time c.c.s’. b Delay-time required (unit in hours).

SUMMARY• Sector boundary is an important factor for the

propagation of SEPs.

• Time-profile of shock strength (Mfast) and intensity of SEPs are well correlated.

• Background solar wind plays an important factor on the variation of IP shock strength.

• Global MHD simulation can provide a tool to link the general observations of SEP events observed at 1 AU to their solar sources, as well as to identify the origins of shock formation due to CME and CME/CIR interactions.

Acknowledgement We thank the Wind and ACE PI teams and National Space Science Data Center at Goddard Space Flight Center, National Aeronautics and Space Administration for management and providing solar wind plasma and magnetic field data, STEREO and LASCO PI teams for providing coronal images, and Kyoto University for providing geomagnetic activity index (Dst). We also thank Dr. Y. M. Wang (NRL) who provided derived solar magnetic fields at 2.5 RSUN. This study is supported partially by ONR 6.1 (CCW, SP), NASA (AV), and NSF base program (KL), AGS1153323 (STW). The Caltech effort was supported by NASA grants NNX13A66G and NNX11A075G. The Hakamada-Akasofu-Fry solar wind model version 2 (HAFv2) was provided to NRL/SSD by a software license from Exploration Physics International, Inc. (EXPI).

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