The Magnetic Nature of Coronal Mass Ejections High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer. The Solar Corona • Hot, tenuous, fully ionized, highly conducting plasma: Parameter photosphere Inner corona Outer corona Electron density (cm-3) 21017 1 10 9 1 10 7 Temperature (K) 5 103 1000 2106 1 10 6 10 0.1 3 0.07 7 Magnetic Field (G) Plasma p /( B 2 / 8 ) Yohkoh SXT May 11, 2000 • The macroscopic behavior of the solar atmosphere as a continuous ionized gas (or plasma) can be well described by the theory of magneto-hydrodynamics (MHD): • a simplified form of the Maxwell equations in the non-relativistic limit • Ohm’s law • the perfect gas law • equations of mass continuity, motion, and energy. Evolution of the large scale coronal magnetic field • The MHD induction equation: V ~ 100km/s, L ~ 100 Mm, ~ 1 m 2 /s, Rm ~ 1013 ! • The perfectly conducting limit or the large length scale limit: ignore the diffusive term – frozen-in evolution: magnetic field lines behave as if frozen into the plasma and are carried along with it. – Conservation of magnetic helicity: linkage of magnetic flux in a closed field is conserved. H m 21 2 Evolution of the large scale coronal magnetic field • The Lorentz force: force due to tension force due to pressure • In the lower solar corona, 1 , magnetic energy dominates and the magnetic field is very close to being a force-free field: J B 0 J is parallel to B, or B B • Minimum energy state: a potential field B 0, or B and 2 0 Evolution of the large scale coronal magnetic field • The coronal magnetic field evolves quasi-statically through force-free equilibria as it is driven at the foot points by continual motions and flux emergence at the photosphere. ph 1, cor 1 ph ~ 10 9 cor C ph , V Ap h ~ 10 2 V Aco r – in the photosphere, pressure dominates, plasma moves magnetic field; in the corona, magnetic field dominates and tries to relax to a force free state – photosphere is much heavier and has a much longer dynamic time scale compared to the corona. Thus coronal magnetic field can adjust quickly to new force-free equilibria in response to the slow perturbations on the photosphere. – For fast dynamic evolution of magnetic fields in the corona, photosphere acts as an inertially line-tying lower boundary. – force-free evolution while preserving the frozen-in constraint often leads to the formation of magnetic tangential discontinuities or current sheets in the corona. Magnetic current sheet and magnetic reconnection Priest (1982) • A current sheet is a magnetic tangential discontinuity across which total pressure is continuous. • Frozen-in evolution outside, inside current sheet, magnetic diffusion becomes important and magnetic energy is dissipated. • A steady state is established with Vi / l , the magnetic field being brought towards the current sheet reconnects at the central current sheet and the plasma along with a weaker reconnected field are ejected from the two ends of the sheet. Spontaneous formation of current sheets Low and Wolfson (1988) • A coronal potential field (a) is subject to a converging displacement of its foot-points on the photosphere and the new potential field it tries to relax to is (c), which is not accessible due to the frozen-in constraint. Instead it evolves to the field (b) in which a current sheet is formed. Reconnection in the current sheet then allows the transition to the (c) field. Prominences/Filaments • Dense, cool plasma suspended in the much hotter and rarer corona: 11 -3 • T ~ 8000K, n ~ 10 cm , B ~ 10 G • Supported by magnetic field against gravity. • Form along polarity inversion lines with magnetic field direction having a small angle relative to the PIL. • Active prominences: form in active regions; higher field strength, temperature and density, shorter life time • Quiescent prominences: in decaying active regions or boundaries between decaying active regions, can be extremely long and extremely long lived. Three-part structure of coronal helmet streamers • The flux rope model: the cavity in the helmet corresponds to the cross-section of a magnetic flux rope containing helical field lines with a strong axial field component whose magnetic pressure supports the low density cavity, and the filament mass is supported in the lower dipped portion of the helical field lines. from Low (2001) Hemispheric dependence of magnetic twist • Coronal soft X-ray observations: soft X-ray images of solar active regions sometimes show hot plasma of S or inverse-S morphology called “sigmoids”,with the northern hemisphere preferentially showing inverse-S shapes and the southern hemisphere preferentially showing forward-S shapes: Pevtsov, Canfield, & Latushko (2001) Soft-x ray observation from Yohkoh Canfield et al. (1999) Active regions are significantly more likely to produce flares or CMEs if they are associated with sigmoid structures. • Sigmoid shaped filaments in association with X-ray sigmoids: Gibson et al. 2002 Hemispheric dependence of magnetic twist • Solar Active Regions: Vector magnetic field observations show that solar active regions on the photosphere show a small but statistically significant trend for left handed twist in the northern hemisphere and right handed twist in the southern hemisphere (Pevtsov et al. 1994, 1995, 2001): J z / Bz Pevtsov, Canfield, & Latushko (2001) 203 regions in cycle 22 263 regions in cycle 23 • Twisted magnetic flux ropes as CME precursors: – contain free magnetic energy – dipped field lines support prominence material against gravity – current sheet formation along the “bald-patch” separatrix surface (BPSS) of a line-tied flux rope X-ray sigmoids (Titov & Demoulin 1999; Low and Berger 2003; Fan & Gibson 2004; Gibson et al. 2004): Gibson et al. (2004) Observational properties of CMEs • CMEs are large-scale ejections of mass and magnetic flux from the lower corona into interplanetary space: Three-part structure of a CME in white light Yohkoh SXT, Mar. 8, 1999 • Energetics: For a fast and large CME Estimates of coronal energy sources mass ~ 1016 g, speed ~ 1000 km/s kinetic energy ~ 1032 erg kinetic (m p nV 2 / 2) : ~ 10-5 erg/cm 3 work done against gravity ~ 1031 erg thermal (nkT ) : ~ 0.1 erg/cm 3 heating and radiation ~ 1032 erg gravitatio nal (m p ngh) : ~ 50 erg/cm 3 in prominence s volume of source region ~ 1030 cm 3 magnetic ( B 2 / 8 ) : ~ 400 erg/cm 3 energy density ~ 100 erg/cm 3 Observational properties of CMEs • Sigmoid Cusp Sigmoid: recurring eruptions Yohkoh SXT images from June 6 through June 7, 2000 From http://solar.physics.montana.edu/nuggets/2000/000609/000609.html Observational properties of CMEs • Sigmoid Cusp Sigmoid: recurring eruptions Gibson et al. (2002) A unified picture for solar eruptions • CMEs, prominence eruptions, and large two-ribbon flares are closely related and may in fact be different manifestations of a single physical process, the disruption of a large-scale coronal magnetic field structure. • The eruptions are caused by a loss of stability or equilibrium of the coronal magnetic field which contains free magnetic energy that has been built up over time through continual emergence of new flux and shuffling of field-line foot-points at the photosphere. Forbes (2000) The Aly-Sturrock constraint • The magnetic energy of a force-free magnetic field with all its field lines anchored to the boundary cannot exceed the energy of the fully open magnetic field (Aly 1984; Sturrock 1991; Low & Smith 1993): Em Eopen • Ways around the constraint: – CMEs do not open all the field lines – An ideal eruptive process causes the formation of a current sheet where magnetic reconnection allows the ejection of a magnetic flux rope. – Presence of detached magnetic flux rope – Non-force free field: the weight of cold prominence mass Low (2000) Some representative models • All models are based on the principle that CMEs are driven by the sudden release of the free magnetic energy stored in pre-eruptive coronal magnetic fields. – Resistive MHD models: where magnetic reconnection in a current sheet plays an important role in triggering the CME onset and in sustaining the eruption. – Ideal resistive hybrid: where eruption is triggered by an ideal loss of equilibrium of the magnetic field but that subsequent formation of a current sheet and magnetic reconnection is crucial for sustaining the eruption and allowing a magnetic flux rope to escape. – Non-force free models: the weight of the prominence mass plays a important role in building up the magnetic energy to exceed that of the open-field limit, and that a sudden drop of the prominence weight triggers the eruption. Resistive models Mikic and Linker (1994) Resistive models Antiochos et al. (1994): the break out model • During the initial quasi-static evolution, the gradual shearing of the inner arcade field and its confinement by the overlying un-sheared arcade build up free magnetic energy. • Reconnection at the current sheet weakens the confinement such that a run-away expansion of the central sheared field takes place. The end state is a partially open field where the sheared arcade field expands to infinity while the overlying un-sheared field moves out of the way by reconnection and remains closed. Ideal resistive hybrid models Lin et al. (1998): loss of equilibrium of a twisted flux rope • Initial force-free equilibrium: a flux rope suspended in the corona confined by an external dipole field • As the strength of the dipole field is reduced, there exists a sequence of force-free equilibria with increasing height of the flux rope until the nose point, where the force balance can no-longer be maintained and the flux rope jumps to an equilibrium at a higher height of lower magnetic energy, and containing a current sheet. • Subsequent reconnection in the current sheet at a sufficiently fast rate is then necessary to sustain a smooth escape of the flux rope. Ideal resistive hybrid models Fan and Gibson (2006): 2D axisymmetric MHD simulations of loss of equilibrium of coronal flux rope Case C: emergence stopped at t=112 Case A: emergence stopped at t=118 Flux emergence stops at t=118 Ideal resistive hybrid models Fan and Gibson (2007): eruption of 3D line-tied flux rope due to the torus instability Confined flux rope Loss of equilibrium Ideal resistive hybrid models Fan and Gibson (2007): eruption of 3D line-tied flux rope due to the helical kink instability Confined flux rope Loss of equilibrium • kink motions in eruptions: • Formation of sigmoid shaped current sheet during eruption Fan and Gibson (2007) • post-eruption state: Case T: t=136 Case K: t=135 Fan and Gibson (2007) Summary • It is fairly certain that CMEs are driven by the free magnetic energy stored in the twisted magnetic fields (with field aligned current) in the corona. However the detailed form of the twisted fields for CME precursor structures and the triggering mechanisms for CME onset are not clear. • Models and simulations of CMEs are still using highly idealized field structures and invoking very artificial lower boundary conditions to represent the driving perturbations on the photosphere. Also simulations of the dynamic evolutions are critically effected by the process of magnetic reconnection whose physics are not well represented in current numerical simulations. • New observations from Hinode, STEREO, and upcoming new instruments that directly measures the coronal magnetic fields will provide important input for constraining and distinguishing between models. • It has been argued that CMEs are an inevitable consequence of the accumulation of magnetic helicity on the Sun, and they are means by which helicity can be removed, which may have important implications for the working of the solar dynamo (e.g. Zhang and Low 2005).