Validation of the magnetic energy vs. helicity scaling in solar magnetic structures

We assess the validity of the free magnetic energy - relative magnetic helicity diagram for solar magnetic structures. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volume-calculation nonlinear force-free (NLFF) method applied to finite coronal magnetic structures and a surface-calculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic active-region cases obtained by three-dimensional magneto-hydrodynamic (MHD) simulations and observed active-region cases, which include both eruptive and noneruptive magnetic structures. The derived energy--helicity diagram shows a consistent monotonic scaling between relative helicity and free energy with a scaling index 0.84$\pm$0.05 for both data sets and calculation methods. It also confirms the segregation between noneruptive and eruptive active regions and the existence of thresholds in both free energy and relative helicity for active regions to enter eruptive territory. We consider the previously reported energy-helicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism

Validation and Benchmarking of a Practical Free Magnetic Energy and Relative Magnetic Helicity Budget Calculation in Solar Magnetic Structures

In earlier works we introduced and tested a nonlinear force-free (NLFF) method designed to self-consistently calculate the free magnetic energy and the relative magnetic helicity budgets of the corona of observed solar magnetic structures. The method requires, in principle, only a single, photospheric or low-chromospheric, vector magnetogram of a quiet-Sun patch or an active region and performs calculations in the absence of three-dimensional magnetic and velocity-field information. In this work we strictly validate this method using three-dimensional coronal magnetic fields. Benchmarking employs both synthetic, three-dimensional magnetohydrodynamic simulations and nonlinear force-free field extrapolations of the active-region solar corona. We find that our time-efficient NLFF method provides budgets that differ from those of more demanding semi-analytical methods by a factor of ~3, at most. This difference is expected from the physical concept and the construction of the method. Temporal correlations show more discrepancies that, however, are soundly improved for more complex, massive active regions, reaching correlation coefficients of the order of, or exceeding, 0.9. In conclusion, we argue that our NLFF method can be reliably used for a routine and fast calculation of free magnetic energy and relative magnetic helicity budgets in targeted parts of the solar magnetized corona. As explained here and in previous works, this is an asset that can lead to valuable insight into the physics and the triggering of solar eruptions.Comment: 32 pages, 14 figures, accepted by Solar Physic

Energy and helicity budgets of solar quiet regions

We investigate the free magnetic energy and relative magnetic helicity budgets of solar quiet regions. Using a novel non-linear force-free method requiring single solar vector magnetograms we calculate the instantaneous free magnetic energy and relative magnetic helicity budgets in 55 quiet-Sun vector magnetograms. As in a previous work on active regions, we construct here for the first time the (free) energy-(relative) helicity diagram of quiet-Sun regions. We find that quiet-Sun regions have no dominant sense of helicity and show monotonic correlations a) between free magnetic energy/relative helicity and magnetic network area and, consequently, b) between free magnetic energy and helicity. Free magnetic energy budgets of quiet-Sun regions represent a rather continuous extension of respective active-region budgets towards lower values, but the corresponding helicity transition is discontinuous due to the incoherence of the helicity sense contrary to active regions. We further estimate the instantaneous free magnetic-energy and relative magnetic-helicity budgets of the entire quiet Sun, as well as the respective budgets over an entire solar cycle. Derived instantaneous free magnetic energy budgets and, to a lesser extent, relative magnetic helicity budgets over the entire quiet Sun are comparable to the respective budgets of a sizeable active region, while total budgets within a solar cycle are found higher than previously reported. Free-energy budgets are comparable to the energy needed to power fine-scale structures residing at the network, such as mottles and spicules

A persistent quiet-Sun small-scale tornado. II. Oscillations

Recently, the characteristics, and dynamics of a persistent 1.7 h vortex flow, resembling a small-scale tornado, have been investigated with ground-base and space-based observations and for the first time in the Ha line centre. The vortex flow showed significant substructure in the form of several intermittent chromospheric swirls. We investigate the oscillatory behaviour of various physical parameters in the vortex area, with a 2D wavelet analysis performed within the vortex flow area and in a quiet-Sun region (for comparison), using the same high spatial and temporal resolution Ha and Ca II 8542 CRISP observations, as well as Doppler velocities and FWHM derived from the Ha line profiles. The vortex flow shows significant oscillatory power in the 3-5 min range that peaks around 4 min and behaves differently than the reference quiet-Sun region. Oscillations reflect the cumulative action of different components such as swaying motions, rotation, and waves. The derived swaying motion periods are in the range of 200-220 s, and the rotation periods are ~270 s for Ha and ~215 s for Ca II. Periods increase with atmospheric height and seem to decrease with radial distance from the vortex centre, suggesting a deviation from a rigid rotation. The behaviour of power within the vortex flow as a function of period and height implies the existence of evanescent waves and the excitation of different types of waves, such as magnetoacoustic (e.g. kink) or Alfven waves. The vortex flow seems to be dominated by two motions: a transverse (swaying) motion, and a rotational motion while oscillations point to the propagation of waves within it. Nearby fibril-like flows could play an important role in the rotational modulation of the vortex flow. Indirect evidence exists that the structure is magnetically supported while the central swirl seems to be acting as a "central engine" to the vortex flow

Chromospheric swirls I. Automated detection in Hα\alpha observations and their statistical properties

Chromospheric swirls are considered to play a significant role in the dynamics and heating of the upper solar atmosphere. It is important to automatically detect and track them in chromospheric observations and determine their properties. We applied a recently developed automated chromospheric swirl detection method to time-series observations of a quiet region of the solar chromosphere obtained in the H$\alpha$-0.2 \r{A} wavelength of the H$\alpha$ spectral line by the CRISP instrument at the Swedish 1-m Solar Telescope. The algorithm exploits the morphological characteristics of swirling events in high contrast chromospheric observations and results in the detection of these structures in each frame of the time series and their tracking over time. We conducted a statistical analysis to determine their various properties, including a survival analysis for deriving the mean lifetime. A mean number of 146 $\pm$ 9 swirls was detected within the FOV at any given time. The mean surface density is found equal to $\sim$0.08 swirls$$Mm$^{-2}$ and the occurrence rate is $\sim$10$^{-2}$ swirls$$Mm$^{-2}$ min$^{-1}$. These values are much higher than those previously reported from chromospheric observations. The radii of the detected swirls range between 0.5 and 2.5 Mm, with a mean value equal to 1.3 $\pm$ 0.3 Mm, which is slightly higher than previous reports. The lifetimes range between 1.5 min and 33.7 min with an arithmetic mean value of $\sim$8.5 min. A survival analysis of the lifetimes, however, using the Kaplan-Meier estimator in combination with a parametric model results in a mean lifetime of 10.3 $\pm$ 0.6 min. An automated method sheds more light on their abundance than visual inspection, while higher cadence, higher resolution observations will most probably result in the detection of a higher number of such features on smaller scales and with shorter lifetimes

Filament absorption study using THEMIS and SOHO/CDS-SUMER observations

A long filament has been observed with THEMIS/MSDP and SOHO/CDS-SUMER, during a coordinated campaign (JOPs 131/95) on May 5, 2000. THEMIS provided 2D Hα spectra, SUMER rasters in the L4 line and spectra of the whole Lymanseries and the Lymancon tinuum, CDS obtained rasters in several EUV lines (e.g., Mg X 624 ˚A, Si XII 520 ˚A, Ca X 557 ˚A and He I 584 ˚A). A large depression of coronal line emission in the CDS images corresponds to the absorption by the hydrogen Lyman continuum and represents the EUV filament. Non-LTE radiative transfer calculations allow to explain, in terms of opacities, the large width of the EUV filament compared to the width of the Hα filament itself. The optical thickness of the Lyman continuum is larger than that of Hα line by one to two orders of magnitude. This could be of great importance in the understanding of the filament formation, if we consider that cool material does exist in filament channels but is optically too thin to be visible in Hα images