Three-Dimensional Magnetohydrodynamic Numerical Simulations of Coronal Loop Oscillations Associated with Flares

Miyagoshi, Takehiro; Yokoyama, T.; Shimojo, Masataka

doi:10.1093/pasj/56.1.207

Cited by 18 publications

(30 citation statements)

References 18 publications

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“…These authors considered a dipole magnetic field rather than the arcade studied here; however, it shares the property of being a symmetric but non-uniform field, so Alfvén waves may be supported by the flux surfaces defined by the field. Miyagoshi et al (2004) excited oscillations by applying a velocity field to the top of their loop in a way similar to our internal driver. For our internal excitation simulations, we find the period of oscillation is consistent with P k , whereas Miyagoshi et al (2004) described the period of oscillation in terms of the Alfvén speed at the loop top and found that P ∝ ρ 0.33 0 .…”

Section: Simulation With No Loop Structurementioning

confidence: 99%

“…Miyagoshi et al (2004) excited oscillations by applying a velocity field to the top of their loop in a way similar to our internal driver. For our internal excitation simulations, we find the period of oscillation is consistent with P k , whereas Miyagoshi et al (2004) described the period of oscillation in terms of the Alfvén speed at the loop top and found that P ∝ ρ 0.33 0 . Figure 10 shows the dependence on the period of oscillation on the density contrast.…”

Section: Simulation With No Loop Structurementioning

confidence: 99%

“…For example, Miyagoshi et al (2004) performed simulations for a 3D potential field and described the period of oscillation in terms of the Alfvén speed at the loop top rather than the kink speed. The interaction of fast MHD waves with 3D active regions was also modeled numerically by Ofman & Thompson (2002) for potential and force-free fields.…”

Section: Introductionmentioning

confidence: 99%

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Standing Kink Modes in Three-Dimensional Coronal Loops

Pascoe¹,

Moortel²

2014

ApJ

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So far, the straight flux tube model proposed by Edwin & Roberts is the most commonly used tool in practical coronal seismology, in particular, to infer values of the (coronal) magnetic field from observed, standing kink mode oscillations. In this paper, we compare the period predicted by this basic model with three-dimensional (3D) numerical simulations of standing kink mode oscillations, as the period is a crucial parameter in the seismological inversion to determine the magnetic field. We perform numerical simulations of standing kink modes in both straight and curved 3D coronal loops and consider excitation by internal and external drivers. The period of oscillation for the displacement of dense coronal loops is determined by the loop length and the kink speed, in agreement with the estimate based on analytical theory for straight flux tubes. For curved coronal loops embedded in a magnetic arcade and excited by an external driver, a secondary mode with a period determined by the loop length and external Alfvén speed is also present. When a low number of oscillations is considered, these two periods can result in a single, non-resolved (broad) peak in the power spectrum, particularly for low values of the density contrast for which the two periods will be relatively similar. In that case (and for this particular geometry), the presence of this additional mode would lead to ambiguous seismological estimates of the magnetic field strength.

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Section: Simulation With No Loop Structurementioning

confidence: 99%

Section: Simulation With No Loop Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Standing Kink Modes in Three-Dimensional Coronal Loops

Pascoe¹,

Moortel²

2014

ApJ

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“…More realistic, bipolar magnetic field (e.g. Miyagoshi et al 2004;McLaughlin & Ofman 2008;Selwa & Ofman 2009;Selwa et al 2011aSelwa et al ,b, 2013Pascoe & De Moortel 2014) or extrapolated magnetogram based magnetic field (e.g., Ofman 2007;Schmidt & Ofman 2010) and gravitationally stratified density structures were modeled with 3D MHD in order to study waves, clearly demonstrating the advantage of considering 3D realistic magnetic field topology on unambiguous determination of seismologically derived coronal magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional MHD modeling of vertical kink oscillations in an active region plasma curtain

Ofman

Parisi

Srivastava

2015

A&A

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Context. Observations on 2011 August 9 of an X 6.9-class flare in active region (AR) 11263 by the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SDO), were followed by a rare detection of vertical kink oscillations in a largescale coronal active region plasma curtain in EUV coronal lines. The damped oscillations with periods in the range 8.8-14.9 min were detected and analyzed recently. Aims. Our aim is to study the generation and propagation of the MHD oscillations in the plasma curtain taking into account realistic 3D magnetic and density structure of the curtain. We also aim at testing and improving coronal seismology for more accurate determination of the magnetic field than with standard method. Methods. We use the observed morphological and dynamical conditions, as well as plasma properties of the coronal curtain based on Differential Emission Measure (DEM) analysis to initialize a 3D MHD model of its vertical and transverse oscillations by implementing the impulsively excited velocity pulse mimicking the flare generated nonlinear fast magnetosonic propagating disturbance interacting with the curtain obliquely. The model is simplified by utilizing initial dipole magnetic field, isothermal energy equation, and gravitationally stratified density guided by observational parameters. Results. Using the 3D MHD model, we are able to reproduce the details of the vertical oscillations and study the process of their excitation by nonlinear fast magnetosonic pulse, propagation, and damping, finding agreement with the observations. Conclusions. We estimate the accuracy of simplified slab-based coronal seismology by comparing the determined magnetic field strength to actual values from the 3D MHD modeling results and demonstrate the importance of taking into account more realistic magnetic geometry and density for improving coronal seismology.

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“…Other works have also included the curvature of a loop in either 1D or 2D geometry, and even non-planar loops (Ruderman & Scott 2011). Rigorous 3D MHD simulations have also been performed (e.g., Miyagoshi et al 2004;Ofman 2009;Selwa & Ofman 2010).…”

Section: Introductionmentioning

confidence: 99%

Klein-Gordon equations for horizontal transverse oscillations in two-dimensional coronal loops

McKenzie

Webb

2012

A&A

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We present a theory for hydromagnetic waves in an axi-symmetric background magnetic field in which the wave equations for the horizontal transverse magnetic field and velocity perturbations can be transformed into Klein-Gordon (KG) equations. For harmonic time variations, the KG equations become a set of ordinary differential equations that can be solved along any individual field line, subject to boundary conditions at the two ends. The solutions provide the spatial (latitudinal) profiles of the transverse magnetic field and velocity oscillations, especially in the horizontal direction, along the field line. In particular, we examine the KG solutions for two background field geometries: a local dipole field line, and a stretched global dipole field line which may approximate coronal loop geometries in the solar corona. The results yield the oscillation frequencies in agreement with observations (periods on the order of minutes), and the spatial profiles which are characteristic of a propagating type near the center of the loop and a possible evanescent type towards the footpoints of the loop. The latter solution arises when the oscillation frequency is less than a critical cut-off frequency which varies spatially along the loop. The oscillation amplitude is also affected by an adiabatic growth/decay factor along the loop. We discuss the implications of our results and future applications to coronal loop oscillations.

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Three-Dimensional Magnetohydrodynamic Numerical Simulations of Coronal Loop Oscillations Associated with Flares

Cited by 18 publications

References 18 publications

Standing Kink Modes in Three-Dimensional Coronal Loops

Standing Kink Modes in Three-Dimensional Coronal Loops

Three-dimensional MHD modeling of vertical kink oscillations in an active region plasma curtain

Klein-Gordon equations for horizontal transverse oscillations in two-dimensional coronal loops

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