NoRH Visit February, 2005 Angelos Vourlidas, NRL
On Deriving Mass & Energetics of Coronal Mass Ejections
Angelos VourlidasNRL
A Tutorial
NoRH Visit February, 2005 Angelos Vourlidas, NRL
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?
NoRH Visit February, 2005 Angelos Vourlidas, NRL
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 brightness increase relative to the background
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Our Objective
Raw C3 Image Calibrated C3 Image (Diff.)
?
NoRH Visit February, 2005 Angelos Vourlidas, NRL
CME Mass/Energy Derivation Flow
C3_massimg.pro
cme_
mas
sim
g2to
tal.p
ro
NoRH Visit February, 2005 Angelos Vourlidas, NRL
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.
NoRH Visit February, 2005 Angelos Vourlidas, NRL
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)
Cosmic rays (few pixels) solar rotation (not important for fast events)Streamer deflections (difficult to estimate) 3D structure (more on that later)
Mass Calculations Primer
Excess DN calibration Btotal Be No. of e- composition Mass
NoRH Visit February, 2005 Angelos Vourlidas, NRL
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
SECTOR
Best for automated calculations:
Extent & Upper boundary from CME lists/ht
measurements
TORUS
Best for flow calculations:Position at fixed distance
ROI
Most common:Avoid streamers, planets,
other CMEs
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Example Results — Single Event
EM
EK
EP
Etotal Mass
vesc
vCM
Emag
Epot
Ekin
Etotal
vesc
vCM or vfront
mass
More examples in Vourlidas et al (2000), Subramanian & Vourlidas (2004)
NoRH Visit February, 2005 Angelos Vourlidas, NRL
How Good Are CME Mass Estimates?
Real mass could be x2 larger
NoRH Visit February, 2005 Angelos Vourlidas, NRL
PA Corrected
Sky-Plane
Effect of CME-SkyPlane Distance on Mass Estimates?
CME mass could be 5x larger
CME mass could be 3x less
Sky-Plane
PA Corrected
By taking into account the source PA: - mass is accurate for <60, - Overestimated by only 3x for halos
NoRH Visit February, 2005 Angelos Vourlidas, NRL
CME Mass Database (Jan 1996 – Dec 2003)
1. Date/time
2. Width
3. Position Angle
4. Height of CME Front
5. Sector Area
6. Mass
7. Mass density
8. Kinetic Energy
9. Potential Energy
10. Velocity (H-t)
11. Acceleration
12. Escape Velocity.
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:
NoRH Visit February, 2005 Angelos Vourlidas, NRL
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.
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Results – Distributions
Parameter LASCO Solwind
<Ekin> (ergs) 4.3 1030 3.5 1030
<Mass> (gr) 1.7 1015 4.1 1015
Total Mass (gr) 4.1 1018 3.9 1018
Mass Flux (gr/day) 3.6 1015 7.5 1015
Duty cycle 81.7% 66.5%
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Results – Average Mass
The constant mass density suggests that:1. Only the CME width is needed to derive
the mass2. The bulk of the CME material originates at
high altitudes where the corona is more uniform.
31010 gr/pix
or 1.3104 e/cm3/Rs
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Results – Bimodal Distribution?
Do we have “failed” and “successful” CME
populations?
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Results – Yearly Variations
NoRH Visit February, 2005 Angelos Vourlidas, NRL
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!).
NoRH Visit February, 2005 Angelos Vourlidas, NRL
BACKUPS
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Results – Mass Distribution
Solwind Exponential Fit (Jackson & Howard 1993)
LASCO
Power-law Fit, =-1.8 (Vourlidas & Patsourakos 2004)
NoRH Visit February, 2005 Angelos Vourlidas, NRL
LASCO C3 Photometric Performance
Courtesy of A. Thiernisien
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Magnetic Energy Estimates
• Problem:Direct measurement is not (currently) possible except
• 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.
NoRH Visit February, 2005 Angelos Vourlidas, NRL
Magnetic Energy Estimates
• Relevant Equations:
22
8
1
8
1AB
A
ldVBE
fluxrope
M
2
8
1
A
lEM
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.
tfEM