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To be published in ApJ: doi:10.1086/â€™521716â€™ Please email the author for preprints

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Strength of Coronal Mass Ejection-driven Shocks Near the Sun and Its Importance in Predicting Solar Energetic Particle Events

Chenglong Shen1, Yuming Wang1,2,âˆ—, Pinzhong Ye1, X. P. Zhao3, Bin Gui1, and S. Wang1

1CAS Key Laboratory of Basic Plasma Physics, School of Earth & Space Sciences.,University of Science & Technology of China, Hefei, Anhui 230026, P. R. China.([email protected], [email protected])

2Department of Computational and Data Sciences, George Mason University, Fairfax, VA22030, USA

3W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA94305, USA

(âˆ— Author for correspondence)

To be published in ApJ: doi:10.1086/â€™521716â€™

Please email the author for preprints

Abstract

Coronal shocks are an important structure without direct observationsin solar and space physics. The strength of shocks plays a key role in shockcausingphenomena, such as radio bursts, SEP generation and so on. Radio emissions are one of the first signals of solar eruptions and interplanetary disturbances that could be recorded near the Earth, and SEP events are an important effect of space weather. Therefore, how to accurately evaluate the strength of coronal shocks is extremely important and interesting.

This work will present an improved method of calculating Alfven speed and shock strength (i.e., fast-mode magnetosonic Mach number) near the Sun (above 2 Rs). In the method, observations as many as possible rather than 1Dglobal models are used. Two events, a relatively slow CME on 2001 September15 and a very fast CME on 2000 June 15, are selected to illustrate the calculationprocess. The calculation results suggest that the slow CME drove a strong shockwith Mach number of 3.43~4.18 while the fast CME drove a weak shock withMach number of 1.90~3.21. This is consistent with the radio observationsthat a stronger and longer DH type II radio burst is found during the first event anda shorter type II during the second event. Particularly, the calculation resultsexplain the observational fact that the slow CME produced a major SEP eventwhile the fast CME did not. Through the comparison between the two events,the importance of shock strength in predicting SEP events is addressed.

Calculation process: Step 1

Calculation of the local plasma density at the height of type II radio burst

emitted by using the data of type II radio burst.

The fundamental component of type IIs is used to calculate the local plasma density as

where mpis proton mass with the mean molecular weight (Priest 1982).

Radio observations from Wind/Waves are adopted because the frequency range is 1 â€“ 14 MHz corresponding to the heliocentric distance from 2 â€“ 10 Rs within which shocks are most

efficient for energetic particle generation (Kahler 1994; Cliver et al. 2004) that is we interested in. The type IIs in this range could be called decameter-hectometric (DH) type IIs.

Calculation process: step 2

Calculation of the heliocentric distance where type II radio burst emitted and the speed of shocks at that time by using SOHO/LASCO.

The LASCO height-time profile of the CME responsible for the investigated type II radio burst is used to deduce the emission height. For the CMEs not originating from limb, the following formula is applied to correct the projection effect:

where Î¸ and Ï† are the latitude and longitude of the source region of a CME, which is determined by examining SOHO/EIT movies, Hmeasureis the measured height in LASCO images and Hheliocentric distance is corrected height.

This step applies two assumptions: (1) the type II radiobursts are generated at the noses of CME driven shocks, (2) the shock standoff distance isrelatively smallnear the Sun, and can be therefore ignored. For DH type IIs, both assumptions are reasonable (Gopalswamy et al. 2005; Cho et al. 2005; Vourlidas et al. 2003; Ciaravella et al. 2006).

Calculation process: step 3

Calculation of the background magnetic field strength at the shock by the CSSS model (Zhao & Hoeksema 1995; Zhao et al. 2002).

The model is used to extrapolate the coronal field with the bottom boundary adopted from the WSO (Wilcox Solar Observatory) synoptic charts.

An error of 20 percent of magnetic filed strength is taken into account to make our calculation results more reliable.

Calculation process: step 4

Calculation of the Alfven speed and fast-mode magnetosonic Mach number.

Alfven speed

Fast-mode magnetosonic speed

Fast-mode magnetosonic Mach number

are plasma density, shock speed, magnetic field strength, respectively, and have obtained through step 1 to 3.

is ignored since it is generally about 150 km/s at 5 Rs, the solar radius, and even smaller below that height (Sheeley et al. 1997) that is much less than shock speeds typically of several hundreds km/s.

is sound speed that related to temperature. In our work, an isothermal atmosphere is assumed because the coronal temperature is typically at the order of one million Kelvin throughout the IP space.

Proton flux

CME h-t curve

Soft X-ray

Radio emission

CME onsets derived from EIT data and the h-t curve

A comparison between a relatively slow CME and a fast CME

Large variation in magnetic field strength at the same height

Radio emission and coronal field for the slow and fast CMEs

Results:

Slow CME drove a strong shock, while the fast CME drove a weak shock.

The results are consistent with radio observations and SEP observations.

Large variation in plasma density

Compared with ideal models (one fold Newkirk density model and )

The results from ideal models are contrary to the observed facts.

Complements:

A comparison between the Mach number and the intensity of radio emissions as a function of height.

The figure shows that the intensity of radio emissions proportionally varies as the Mach number changes.

Another case: An extremely fast CME without SEP on 1999 June 28

No SEP

Source region location

Type II-like emission

Loc: N27W43, VCME=1586 km/s. The calculation suggests a Mach Number<1.56.

- Conclusions & discussions
- The variations of the plasma density and magnetic field strength of background solar wind are significant (could be about 2 orders) with the time and/or location (even at the same height).
- Alfven speeds and Mach number calculated based on 1-D global models of density and coronal magnetic field may largely deviate from the facts. Our calculations give more reliable results.
- Neither CME speed nor kinematic energy could correctly reflect the real strength of potential shocks. Fast CMEs are not necessary to drive a strong shock, and slow CMEs are also not necessary to drive a weak shock.
- To correctly predict SEP events, one needs to evaluate the real shock strength rather than using CME speed as a proxy.
- Presence of shock seems not to be the sufficient condition of SEP generation. There may be a threshold in strength, only above which the shock is able to accelerate energetic protons efficiently.