# Presentation: 513110

## The Proper Treatment of the CME Brightness: A New Methodology and Implications for Future Observations.

- With the complement of the coronagraphs and imagers in the SECCHI suite, we will follow a coronal mass ejection continuously from the Sun to Earth for the first time. The comparison, however, of the CME emission among the various instruments is not as easy as one might think. This is because the coronagraphs record the Thomson scattered emission from the CME plasma which has a rather sensitive dependence on the geometry between the observer and the scattering plasma. Here, we describe the proper treatment of the Thomson scattered emission and the implications that arise in comparing CME emission over a large range of elongation angles. More details can be found in Vourlidas & Howard (2006).

**The Proper Treatment of the CME Brightness:**** A New Methodology and Implications for Future Observations.**
- Angelos Vourlidas, Russ Howard *Naval Research Laboratory*

***ABSTRACT***

***3. Comparison to Standard Assumption***

***5. SECCHI Analysis***

***4. Implications***

-  The emission recorded by white light coronagraphs originates by Thomson scattering of the photospheric light by the electrons within a CME or other coronal structure.
-  The emission is composed of radial, Ir and tangential, It components. They are derived from the equations in **Fig. 1**. They depend on two angles: (1) the **angle ****χ**, between the line of sight and the radial through the scattering electron, and (2) the **elongation ****Ω**, of the solar limb as seen by the scattering electron.
-  The actual observables are the total **B = I****t**** + I****r**, and polarized **pB = I****t**** – I****r** brightness.
-  The emission is maximum when the LOS is normal to the radius through the scattering electron, χ = 90o. This is commonly called the *plane-of-the-sky* and corresponds to the plane of the solar limb as seen by the observer.

- However, the location of the maximum scattering does not lie on a plane but on a spherical surface (we call it **“Thomson Surface”**) centered half-way between Sun and observer. To treat the brightness of CMEs self-consistently over large elongations (as is the case for SECCHI), we need to make two adjustments:
- The lines of sight should not be assumed parallel to the Sun-observer line.
- The analysis should be made relative to the Thomson surface and not the plane of the sky.
**But what do these changes in the brightness calculation imply for past and future CME analysis?**

- The default assumption for brightness measurements has been to equate the plane of the solar limb to the maximum scattering plane But this is assumption is not correct (the “Thomson surface” is the correct plane). **Where does this assumption break down?**
**Fig. 3** shows that the standard assumption easily holds for brightness calculations **out to at least 70 R****sun**.
**There is no need to reexamine past work/results.**
- This formulation allows us to explore the behavior of the CME brightness over large elongations. **What are the implications?**

- The SECCHI coronagraphs will observe CMEs over the full range of elongations we have considered here. Therefore, we need to apply the full scattering treatment to the analysis of all 4 SECCHI coronagraphs to derive consistent results. This implies the following:
- The solar limb is no longer the plane of maximum scattering. The Thomson surface is.
- The CME mass will be calculated assuming that all electrons are on the Thomson surface.
- Projected quantities will be given as a function of elongation.

- The “Thomson surface” presents us with a changing plane of maximum scattering instead of the constant plane-of-the-sky. **What is the brightness effect on CMEs ejected at different longitudes?**
- In **Fig. 4**, we plot the brightness versus elongation for a single electron propagating radially at various heliocentric longitudes (the solar limb is at 0o). The plot indicates that:
-  The brightness of CMEs originating at the solar limb drops sharply beyond about > 150 **R****sun****. **They might not be detected by heliospheric imagers.
-  CMEs originating at intermediate angles tend to reach the same brightness for > 30  **R****sun**.

- Since the true extent of a CME is unknown, the total mass was always calculated assuming that is concentrated on the plane of the sky. The effect of this assumption on the masses has been discussed by Vourlidas et al (2000). **How does the new methodology affect the masses?**
- In **Fig. 5**, we show the result for the simple case of a CME of zero width propagating radially along the given latitudes (the limb is at 0o). The y-axis gives the ratio of the “real” to the derived mass under the standard assumption that all mass is on the surface of maximum scattering.

***6. Example Application***

- A simple example can help clarify how the mass analysis of SECCHI images could make use of the concepts we outlined here.
- Each image (COR1/2, HI1/2) is calibrated in MSB. A preevent image is subtracted to provide an excess brightness image (Fig 6a).
- The CME mass is calculated assuming that all electrons are on the Thomson surface. The elongation of the derived center of mass is used to as the location of the derived mass.
- The masses are normalized (Fig. 6b).
- The normalized masses are plotted on a plot similar to Fig. 5 containing parametric curves for several ejection longitudes.
- We expect that the SECCHI masses will closely follow one of the curves, therefore revealing the most likely propagation angle of the particular CME.

*** ******References***

- Billings, D.E. 1966, Guide to the Solar Corona
- Vourlidas, A et al, 2000, ApJ, 534, 456
- Vourlidas, A. & Howard, R.A., 2006, ApJ, submitted

-  **Figure 1**:  Thomson scattering formulas and geometry (from Billings (1996), page 148).

-  **Figure 3**: Range of validity of the plane-of-the-sky assumption currently used for CME brightness calculations. The ratio Blimb/B0 is the ratio of the brightness calculated using the assumption over the brightness derived from the correct treatment.

-  **Figure 4**: The brightness of a single electron as a function of elongation for various distances from the solar limb (located at 0o). The plot refers to front side angles only.

***1. Thomson Scattering Facts***

***2. Scattering Geometry***

-  **Figure 2**: The proper geometry for Thomson scattering calculations..

-  **Figure 5**: The underestimation of the mass of a CME having zero width and propagating radially from a given latitude as a function of elongation.

-  **Figure 6a**: Simulated single-electron CME. The stars represent the brightness measurements from the SECCHI telescopes.

-  **Figure 6b**: Derived masses from the SECCHI telescopes. They are normalized to maximum mass.

-  **Figure 6c**: The normalized masses are plotted on parametric curves (Fig. 4). The estimation of the ejection longitude of a CME might be possible..