On Deriving Mass & Energetics of Coronal Mass Ejections

1. On Deriving Mass & Energetics of Coronal Mass Ejections A Tutorial Angelos VourlidasNRL

2. Overview • The following questions will be addressed: • How can we derive information about CME mass/energetics? • What assumptions enter in the calculations? • What are the data analysis steps to extract quantitative CME information from white light images? • How good are the numbers? • Can we estimate the errors? How? • What can we do with this information? • What statistics tell us? • What correlations can we find?

3. Preliminaries • Height-time plots, online movies are constructed from UNCALIBRATED LASCO images. Calibrated images are rarely shown. • All necessary calibration tools exist in the LASCO Solarsoft distribution. • This talk is relevant to CME measurements ONLY. Coronal background densities, streamers and plumes must be treated differently. • Remember, a white light CME is defined as an brightnessincrease relative to the background

4. Calibrated C3 Image (Diff.) Our Objective ? Raw C3 Image

5. CME Mass/Energy Derivation Flow C3_massimg.pro cme_massimg2total.pro

6. Mass Calculations Primer Assumptions: • Emission is due to Thompson scattering of photospheric light from coronal electrons. • All mass is on the sky plane. • Plasma composition is 10% He, 90% H. Restrictions: • The 3D distribution of the background and CME electrons, Ne, is unknown. • The temperature of the ejected material is unknown (coronal should dominate). • Emission is optically thin.

7. Excess DN calibration Btotal Be No. of e- composition Mass Mass Calculations Primer Method:A coronagraph measures the total brightness along the line of sight. We can only measure excess brightness (ICME - IPREEVENT). Error Sources: exposure time(~0.15%)vignetting(~1%)photon noise(<1.4%) Phot. Calibration (0.73%) composition (6%) stars (cancel out) Cosmicrays (few pixels) solarrotation(not important for fast events) Streamer deflections (difficult to estimate) 3Dstructure (more on that later)

8. TORUS SECTOR ROI Best for automated calculations: Extent & Upper boundary from CME lists/ht measurements Best for flow calculations: Position at fixed distance Most common: Avoid streamers, planets, other CMEs Mass Calculation Methods • Several ways to obtain a “mass” for an event. • The choice depends on the objectives: • After the whole event? • After specific features (i.e., core)? • Flow measurements? “Typical” C3 Mass Image

9. Etotal mass Epot Ekin vCM or vfront Emag vesc Example Results — Single Event Etotal Mass EP vCM EK EM vesc More examples in Vourlidas et al (2000), Subramanian & Vourlidas (2004)

10. Real mass could be x2 larger How Good Are CME Mass Estimates?

11. CME mass could be 3x less PA Corrected Sky-Plane CME mass could be 5x larger Effect of CME-SkyPlane Distance on Mass Estimates? Sky-Plane PA Corrected By taking into account the source PA: - mass is accurate for <60, - Overestimated by only 3x for halos

12. CME Mass Database (Jan 1996 – Dec 2003) • Date/time • Width • Position Angle • Height of CME Front • Sector Area • Mass • Thanks to the hard work of Ed Esfandiari an up-to-date CME database has been created: • The CME information is taken from the CUA/NRL list. • The database includes full-frame mass images for every h-t data point in the CUA list (6385 events so far). • The mass is derived with the same method (sector) for all frames. • Energy and other calculations are also provided. • The following information is provided for every CME frame: • Mass density • Kinetic Energy • Potential Energy • Velocity (H-t) • Acceleration • Escape Velocity.

13. Results • The analysis of the mass database is based on : • Measurements at the point of maximum mass. (Need for a single “representative” number for each event). • Does not include events with: • < 5 h-t measurements (frames). • Width > 120°. • Negative mass. • Zero pixels in sector.

14. Results – Distributions

15. 31010gr/pixor 1.3104e/cm3/Rs Results – Average Mass • The constant mass density suggests that: • Only the CME width is needed to derive the mass • The bulk of the CME material originates at high altitudes where the corona is more uniform.

16. Results – Bimodal Distribution? Do we have “failed” and “successful” CME populations?

17. Results – Yearly Variations

18. Review • It is easy to calculate CME mass and energetics from the LASCO images (calibration/routines available since 1996). • The accuracy of the mass values is difficult to estimate without 3D information. Simple simulations suggest that masses could be underestimated by x2 (on average, well-behaved (aka non-halo) events). • Thousands of measurements of several dynamical parameters for almost all CMEs are now available. • Mass images for almost all CMEs are also available (for DIYers). • Preliminary analysis of the mass/energy data yielded a couple of very interesting results: • CME mass density = constant! • There may be 2 classes of CMEs; “failed” and “successful”. • CME mass/energy distributions are power-laws (like flares!).

19. BACKUPS

20. Solwind Exponential Fit (Jackson & Howard 1993) LASCO Power-law Fit,  =-1.8 (Vourlidas & Patsourakos 2004) Results – Mass Distribution

21. LASCO C3 Photometric Performance Courtesy of A. Thiernisien

22. Magnetic Energy Estimates • Problem:Direct measurement is not (currently) possibleexcept • Radio gyrosynchrontron emission from energetic electrons within the CME (Bastian et al. 2001). Only a handful cases so far. • Another Approach:1. Select fluxrope-like CMEs.2. Assume the fluxrope feature becomes the IP Magnetic Cloud.3. Assume magnetic flux, Φ is conserved (in the fluxrope).4. Use in-situ measurements of Φ to normalize the magnetic energy, EM.5. Use the coronagraph measurements of the fluxrope area, A and “length”, l to derive the evolution of EM.

23. Magnetic Energy Estimates • Relevant Equations: Assume fluxrope is cylindrical,B & A are measured/derived from in-situ observations  Φ. A is given by the no. of pixels in the LASCO imagesl is assumed equal to the height of the CM, l rCM.