The Sun in 4D: Understanding magnetic eruptions in the solar atmosphere
Dr. Peter Gallagher, Dr. James McAteer, Jason Byrne, Paul Conlon, Shane Maloney Astrophysics Research Group, School of Physics, Trinity College Dublin www.physics.tcd.ie/astrophysics
The STEREO mission was launched on October 2006 from Cape Canaveral in Florida onboard a Delta II rocket. The mission consists of two spacecraft with identical imaging suites drifting away from the Earth at opposite directions with a speed of about 22.5 degrees per year (see Figure 1). The two satellites will obtain simultaneous observations of the constantly changing solar atmosphere with ever-changing perspectives. SECCHI is a suite of remote sensing telescopes on STEREO, which consists of two white light coronagraphs, an EUV imager and a Heliospheric Imager. Researchers in Trinity’s Astrophysics Research Group (ARG) are using these three instruments to study the changing morphology and kinematics of solar storms, from the inner solar atmosphere to the orbit of the Earth. This is the first time that this region of space – the inner heliosphere – has been studied with such high temporal and spatial resolution (see Figure 2).
Figure 1: The STEREO spacecrafts give two different perspectives on CMEs reupting from the sun. One spacecraft travels ahead of the Earth, the other behind. Figure 2: Two combined extreme-ultraviolet images obtained by the STEREO satellite. The images show plasma temperatures of approximately 1.5 million degrees K. The TCHPC visualization facility is being used to study spatial and temporal variability of the solar atmosphere.
Coronal mass ejections (CMEs) are spectacular eruptions of plasma and magnetic fields in the lower atmosphere of the Sun. Despite nearly thirty years of study, the basic physics that expels these plasma clouds into the solar system is still not well understood. Several theoretical models have been proposed to describe the observed properties of CMEs. The three-dimensional magnetic flux-rope model assumes that the kinematics of an erupting flux-rope can be described using a force-balance equation, which includes gas pressure, gravity and the Lorentz force1. The flux-rope acceleration was found to be dependent on its geometrical properties, such as its width and radius. An alternative to the flux-rope model is the so-called magnetic breakout model in which the CME eruption is triggered by magnetic reconnection between the overlying field and a neighbouring magnetic flux system2. The breakout model is based on numerically solving the equations of ideal magnetohydrodynamics in three-dimensions. It starts by shearing a potential field configuration (Figure 3), which adds magnetic pressure to the inner flux system and causes it to expand and distort the overlying field, eventually forming a thin current sheet. The current sheet then grows causing reconnection to begin, and thus releasing some of the restraining overlying flux. This produces an increase in the rate of outward expansion which in turn drives a faster rate of breakout reconnection, yielding the positive feedback required for explosive eruption.
Figure 3: Theoretical model of magnetic fields in the solar corona. Measurements of the magnetic filed on the Sun's surface are used as a boundary condition to the model4.
In order to make a detailed comparison between observations and theory, ARG researchers are developing advanced image processing techniques to automatically measure the fundamental properties of CMEs3. These include basic morphological properties, such as size, width and curvature, but also kinematic parameters, such as position, velocity and acceleration. Once these are extracted from two unique perspectives, they can be combined and used to study the true three-dimensional morphology and kinematics of CMEs.
Our approach relies on decomposing an image into a spectrum of scales. Larger features, such as the Sun itself, appear at large length-scales, whereas CME edges, for example, are visible at short length-scales. This decomposition is achieved using the multiscale properties of the wavelet transform. In its continuous form, the wavelet transform of a signal, I(r), can be written as
r − x
¥ ∫ dr ,,
where (r) is the mother wavelet, s is a term describing scale at a position r, and w(s,x) are the wavelet coefficients of the image. The mother wavelet can take several forms, depending on the application and include the Morlet, Paul and Mexican hat. For convenience, we use wavelets that are the first derivatives of a smoothing function, where the smoothing function is a discrete cubic spline approximation of a Gaussian. Once the wavelet transform is applied to the images, the edges of the CME are calculated using the local maxima of the image gradient at each scale.
Figure 4: Top sequence of unprocessed coronagraph images containing a faint CME. Bottom: previous sequence with the CME visible and edges detected via the wavelet transform5.
Figure 4 shows a series of coronagraph images containing a faint CME. Our algorithm detects points of sharp variation in an image by calculating the modulus of the gradient vector convolved with a Gaussian. This gives curves in the image parallel to the direction of maximum change – a property particularly useful for tracking CMEs and other moving features in solar image sequences. Although the dynamic range of the images in Figure 4 is high, there is a significantly varying background which makes faint objects difficult to identify. Applying our multiscale methods, the faint eruption can be detected and its edges identified without the need for background subtraction.
In the future, these advanced image processing techniques will be of great benefit to real-time data analysis from other missions akin to STEREO6. Current data rates from existing spacecraft are low enough to make human analysis of images possible (~1 GByte/day). This will not be the case for missions such as NASA’s Solar Dynamics Observatory (SDO), which will be launched in late 2008. SDO has a projected data rates of ~1 TByte/day that will make an interactive analysis unfeasible. The multiscale methods developed by ARG will therefore naturally lend themselves to the real-time identification and characterisation of CMEs observed by future ESA and NASA satellites.
Acknowledgements This research is funded by Science Foundation Ireland and IRCSET.
- Chen, J., Marque, C., Vourlidas, A., Krall, J., Schuck, P. W., “The Flux-Rope Scaling of the Acceleration of Coronal Mass Ejections and Eruptive Promiences”, Astrophysical Journal, 649, 452, 2006.
- MacNeice, P, Antiochos, S. K., Phillips, P, Spicer, D. S., DeVore, C. R., Olson, K., “A Numerical Study of the Breakout Model of Coronal Mass Ejection Initiation”, Astrophysical Journal, 614, 1038, 2004.
- Byrne, J, Gallagher, P. T., McAteer, R. T. J., Young, C. A., “Multiscale Detection and Characterisation of Coronal Mass Ejections”, submitted, Astronomy & Astrophysics, 2008.
- Conlon, P, Gallagher, P. T., “The 3D Magnetic Topology of Flaring Active Regions”, submitted, Astronomy & Astrophysics, 2008.
- Young, C. A., Gallagher, P. T., “Multiscale Structure of Coronal Mass Ejections”, Journal of Solar Physics, accepted, 2008.
- Gallagher, P. T., et al., “Solar Activity Monitoring”, in Space Weather: Research Towards Applications in Europe (Ed. J. Lillensten), Springer, 2007.