The standard flare model in three dimensions

Aulanier, G.; Démoulin, P.; Schrijver, Carolus J.; Janvier, Miho; Pariat, É.; Schmieder, B.

doi:10.1051/0004-6361/201220406

Cited by 202 publications

(159 citation statements)

References 68 publications

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“…Knowledge of the largest flares and solar proton events (SPEs) that the Sun can produce is important for both practical and theoretical reasons (Cliver & Svalgaard 2004;Riley 2012;Schrijver et al 2012;Aulanier et al 2013). Here we consider a recent report of what is possibly the largest SPE during the last ∼10 4 yr.…”

Section: Introductionmentioning

confidence: 99%

On a Solar Origin for the Cosmogenic Nuclide Event of 775 A.D.

Cliver

Tylka

Dietrich

et al. 2014

ApJ

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We explore requirements for a solar particle event (SPE) and flare capable of producing the cosmogenic nuclide event of 775 a.d., and review solar circumstances at that time. A solar source for 775 would require a >1 GV spectrum ∼45 times stronger than that of the intense high-energy SPE of 1956 February 23. This implies a >30 MeV proton fluence (F 30 ) of ∼8 × 10 10 proton cm −2 , ∼10 times larger than that of the strongest 3 month interval of SPE activity in the modern era. This inferred F 30 value for the 775 SPE is inconsistent with the occurrence probability distribution for >30 MeV solar proton events. The best guess value for the soft X-ray classification (total energy) of an associated flare is ∼X230 (∼9 × 10 33 erg). For comparison, the flares on 2003 November 4 and 1859 September 1 had observed/inferred values of ∼X35 (∼10 33 erg) and ∼X45 (∼2 × 10 33 erg), respectively. The estimated size of the source active region for a ∼10 34 erg flare is ∼2.5 times that of the largest region yet recorded. The 775 event occurred during a period of relatively low solar activity, with a peak smoothed amplitude about half that of the second half of the 20th century. The ∼1945-1995 interval, the most active of the last ∼2000 yr, failed to witness a SPE comparable to that required for the proposed solar event in 775. These considerations challenge a recent suggestion that the 775 event is likely of solar origin.

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Section: Introductionmentioning

confidence: 99%

On a Solar Origin for the Cosmogenic Nuclide Event of 775 A.D.

Cliver

Tylka

Dietrich

et al. 2014

ApJ

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“…maximum energy that can be released in a flare or in a CME (Emslie et al 2012;Aulanier et al 2013, and references therein).…”

Section: Introductionmentioning

confidence: 99%

“…is indebted to the NLFFF Consortium for stimulating discussions and collaborations. The research leading to these results has received funding from the European Commission's Seventh Framework Program (FP7/2007-2013 under the grant agreement eHeroes (project n • 284461, www.eheroes.eu). S.M.…”

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confidence: 99%

Accuracy of magnetic energy computations

Valori

Démoulin

Pariat

et al. 2013

A&A

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118

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Context. For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, the free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. A trustworthy estimation of the magnetic energy is therefore needed in three-dimensional (3D) models of the solar atmosphere, e.g., in coronal fields reconstructions or numerical simulations. Aims. The expression of the energy of a system as the sum of its potential energy and its free energy (Thomson's theorem) is strictly valid when the magnetic field is exactly solenoidal. For numerical realizations on a discrete grid, this property may be only approximately fulfilled. We show that the imperfect solenoidality induces terms in the energy that can lead to misinterpreting the amount of free energy present in a magnetic configuration. Methods. We consider a decomposition of the energy in solenoidal and nonsolenoidal parts which allows the unambiguous estimation of the nonsolenoidal contribution to the energy. We apply this decomposition to six typical cases broadly used in solar physics. We quantify to what extent the Thomson theorem is not satisfied when approximately solenoidal fields are used. Results. The quantified errors on energy vary from negligible to significant errors, depending on the extent of the nonsolenoidal component of the field. We identify the main source of errors and analyze the implications of adding a variable amount of divergence to various solenoidal fields. Finally, we present pathological unphysical situations where the estimated free energy would appear to be negative, as found in some previous works, and we identify the source of this error to be the presence of a finite divergence. Conclusions. We provide a method of quantifying the effect of a finite divergence in numerical fields, together with detailed diagnostics of its sources. We also compare the efficiency of two divergence-cleaning techniques. These results are applicable to a broad range of numerical realizations of magnetic fields.

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“…If we assume that the same relation between spatial scales is valid in the solar corona current sheet, then Δy can be estimated as ∼10 2 −10 4 km from numerical modeling (e.g. Aulanier et al 2013) and observations (e.g. Ciaravella & Raymond 2008;Liu et al 2010).…”

Section: Discussionmentioning

confidence: 99%

Preferential acceleration of heavy ions in the reconnection outflow region

Artemyev

Zimbardo

Ukhorskiy

et al. 2014

A&A

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Context. Many observations show that heating in the solar corona should be more effective for heavy ions than for protons. Moreover, the efficiency of particle heating also seems to be larger for a larger particle electric charge. The transient magnetic reconnection is one of the most natural mechanisms of charged particle acceleration in the solar corona. However, the role of this process in preferential acceleration of heavy ions has still yet to be investigated. Aims. In this paper, we consider charged particle acceleration in the reconnection outflow region. We investigate the dependence of efficiency of various mechanisms of particle acceleration on particle charge and mass. Methods. We take into account recent in situ spacecraft observations of the nonlinear magnetic waves that have originated in the magnetic reconnection. We use analytical estimates and test-particle trajectories to study resonant and nonresonant particle acceleration by these nonlinear waves. Results. We show that resonant acceleration of heavy ions by nonlinear magnetic waves in the reconnection outflow region is more effective for heavy ions and/or for ions with a larger electric charge. Nonresonant acceleration can be considered as a combination of particle reflections from the front of the nonlinear waves. Energy gain for a single reflection is proportional to the particle mass, while the maximum possible gain of energy corresponds to the classical betatron heating. Conclusions. Small-scale transient magnetic reconnections produce nonlinear magnetic waves propagating away from the reconnection region. These waves can effectively accelerate heavy ions in the solar corona via resonant and nonresonnat regimes of interactions. This mechanism of acceleration is more effective for ions with a larger mass and/or with a larger electric charge.

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The standard flare model in three dimensions

Cited by 202 publications

References 68 publications

On a Solar Origin for the Cosmogenic Nuclide Event of 775 A.D.

On a Solar Origin for the Cosmogenic Nuclide Event of 775 A.D.

Accuracy of magnetic energy computations

Preferential acceleration of heavy ions in the reconnection outflow region

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