Strength of Coronal Mass Ejection- driven Shocks Near the Sun and Its Importance in Predicting Solar Energetic Particle Events Chenglong Shen 1, Yuming Wang 1,2, ∗, Pinzhong Ye 1, X. P. Zhao 3, Bin Gui 1, and S. Wang 1 1 CAS Key Laboratory of Basic Plasma Physics, School of Earth & Space Sciences., University of Science & Technology of China, Hefei, Anhui , P. R. China. 2 Department of Computational and Data Sciences, George Mason University, Fairfax, VA 22030, USA 3 W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA ( ∗ Author for correspondence) To be published in ApJ: doi: /’521716’ Please the author for preprints

Abstract Coronal shocks are an important structure without direct observations in solar and space physics. The strength of shocks plays a key role in shock causing phenomena, 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 1D global models are used. Two events, a relatively slow CME on 2001 September 15 and a very fast CME on 2000 June 15, are selected to illustrate the calculation process. The calculation results suggest that the slow CME drove a strong shock with Mach number of 3.43~4.18 while the fast CME drove a weak shock with Mach number of 1.90~3.21. This is consistent with the radio observations that a stronger and longer DH type II radio burst is found during the first event and a shorter type II during the second event. Particularly, the calculation results explain the observational fact that the slow CME produced a major SEP event while 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 m p is proton mass with the mean molecular weight (Priest 1982). Radio observations from Wind/Waves are adopted because the frequency range is 1 – 14 MHz corresponding to the heliocentric distance from 2 – 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 θ and φ are the latitude and longitude of the source region of a CME, which is determined by examining SOHO/EIT movies, H measure is the measured height in LASCO images and H heliocentric distance is corrected height. This step applies two assumptions: (1) the type II radio bursts are generated at the noses of CME driven shocks, (2) the shock standoff distance is relatively small near 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.

A comparison between a relatively slow CME and a fast CME Proton flux CME h-t curve CME onsets derived from EIT data and the h-t curve Radio emission Soft X-ray

Radio emission and coronal field for the slow and fast CMEs Large variation in magnetic field strength at the same height

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.

Type II-like emission Another case: An extremely fast CME without SEP on 1999 June 28 No SEP Source region location Loc: N27W43, V CME =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.