Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1211.1708

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy

Markus J. Aschwanden
View original source ↗Read source document ↗Export metadata ↓

Abstract

An analytical approximation of a nonlinear force-free magnetic field (NLFFF) solution was developed in Paper I, while a numerical code that performs fast forward-fitting of this NLFFF approximation to a line-of-sight magnetogram and coronal 3D loops has been described and tested in Paper II. Here we calculate the free magnetic energy $E_{\rm free}=E_{\rm N}-E_{\rm P}$, i.e. the difference of the magnetic energies between the nonpotential field and the potential field. A second method to estimate the free energy is obtained from the mean misalignment angle change $Δμ=μ_{\rm P}-μ_{\rm N}$ between the potential and nonpotential field, which scales as $E_{\rm free}/E_{\rm P} \approx \tan^2{(Δμ)}$. For four active regions observed with STEREO in 2007 we find free energies in the range of $q_{\rm free}=(E_{\rm free}/E_{\rm P}) \approx 1%-10%$, with an uncertainty of less than $\pm 2%$ between the two methods, while the free energies obtained from 11 other NLFFF codes exhibit a larger scatter of order $\approx\pm10%$. We find also a correlation between the free magnetic energy and the GOES flux of the largest flare that occurred during the observing period, which can be quantified by an exponential relationship, $F_{\rm GOES} \propto \exp{(q_{\rm free}/0.015)}$, implying an exponentiation of the dissipated currents.

Explore related subjects

astro-ph.SR

Keep this discovery

BibTeXRIS

Markus J. Aschwanden. 2012-11-07. A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy. https://doi.org/10.1007/s11207-012-0203-6

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Eclipse Properties and Superhump Evolution in the SU UMa-Type Dwarf Nova Z Cha

The advent of large-scale time-domain surveys provides both opportunities and challenges for understanding accretion disk evolution in cataclysmic variables (CVs). Using high-cadence photometry from the Transiting Exoplanet Survey Satellite (TESS), we investigate the eclipsing SU UMa-type dwarf nova Z Cha. Leveraging eclipses as a natural probe, we examine the evolution of the accretion disk through variations in eclipse depth, O--C of eclipse minima, and positive superhump (PSH) amplitude. During superoutbursts, all three quantities exhibit quasi-periodic modulations with a common period of $\sim$2 days, consistent with the precession period of an eccentric disk. We interpret these correlated variations as evidence of an eccentric, precessing disk: O--C traces the periodic shift of the system's brightness center, while eclipse depth and PSH amplitude vary with the orientation of the disk bulge relative to the line of sight. In quiescence (Sectors 13 and 93), PSHs with periods of $\sim$0.0762 days show linearly decreasing amplitudes and periods, indicating gradual shrinkage of the eccentric disk and a slowing precession. Remarkably, a coherent signal with a period of $\sim$0.0729~days ($\epsilon^{-}\approx-0.02$) appears in the same quiescent intervals. This signal may represent negative superhumps (NSHs) coexisting with PSHs, although an orbital sideband of the PSH cannot presently be excluded with the available data. If confirmed as NSHs, their coexistence with PSHs would challenge the classical tilted-disk model, and could be explained by retrograde apsidal precession of an eccentric disk, where the inner disk precesses retrogradely (NSHs) and the outer disk progradely (PSHs); this interpretation remains to be tested by further observations.

astro-ph.SR↗
arXiv2026

Classical Nova V1405 Cas Had $M_{\rm ejecta}$$>$$M_{\rm accreted}$ and so is Unlikely to be a Type Ia Supernova Progenitor

Nova 2021 Cassiopeia (V1405 Cas) was an ordinary J(175) neon nova with the white dwarf mass estimated to be $M_{\rm WD}$=0.60$\pm$0.10 $M_{\odot}$. I found an orbital period of $P$=0.1884 days, and have tracked 20 times of photometric minima from 2013--2025. I measure that $P$ increased from before to after the eruption with $P_{\rm pre}$=0.1883919$\pm$0.0000018 days and $P_{\rm post}$=0.1884043$\pm$0.0000018 days, for $\Delta P$/$P$=66$_{-18}^{+21}$ parts-per-million. With correction for the angular momentum loss by the binary during the eruption, I derive that the nova ejected $M_{\rm ejecta}$=7.5$\times$10$^{-4}$ $M_{\odot}$, with an extreme range of (2.9--40)$\times$10$^{-4}$ $M_{\odot}$. The mass accreted during the previous eruption cycle comes from the trigger mass, and is $M_{\rm accreted}$=(1.6$\pm$0.4)$\times$10$^{-4}$ $M_{\odot}$. V1405 Cas provides counterexamples against five claims about CV evolution that have dominated since the 1980s. First, V1405 Cas has positive $\dot{P}$, and this is contrary to the Magnetic Braking Model. Second, the $\Delta P$ is 20$\times$ too small to allow the system to fade into a hibernation state. Third, $M_{\rm WD}$ is decreasing over time, as shown by $M_{\rm ejecta}$$>$$M_{\rm accreted}$ and by being a neon nova. Fourth, V1405 Cas is not a Type Ia supernova progenitor, for the same reasons. Fifth, the orbital period of V1405 Cas increased by $+$75 ppm from 2013--2025, as a counterexample to the pervasive idea that cataclysmic variables are universally declining in period from evolution. V1405 Cas is the latest of recent measures of $\Delta P$ and $\dot{P}$ for 52 cataclysmic variables and 25 X-ray binaries that have together refuted all five claims.

astro-ph.SR↗
arXiv2026

A prolonged plateau-to-tail transition in the Type II supernova SN2025abyc

We present optical photometric and spectroscopic observations of the Type II supernova SN2025abyc. During the optically thick phase between approximately 10 and 70 d after explosion, its light curves show strongly wavelength-dependent decline rates of approximately 2.7, 2.1, 0.9, and 0.8 mag/100d in the g, c, r, and o bands, respectively. At approximately 70 d, the light curves begin to depart from their nearly linear plateau evolution and gradually transition toward the radioactive tail. A Fermi-Dirac fit to the well-sampled ATLAS o-band light curve yields a transition midpoint of t_PT ~ 100.5d. The interval between the end of the linear plateau and this transition midpoint is approximately 30 d, indicating a prolonged plateau-to-tail transition. This timescale is comparable to those measured for SN2013by, SN2013ej, and SN2014G. Spectroscopically, at +13 d post-explosion, the Halpha profile appears weak and broad, whereas Hbeta and Hgamma display clear P-Cygni profiles. This morphology can be explained by the normal early spectroscopic evolution of SNe II, although partial filling of the Halpha absorption trough by emission associated with circumstellar interaction cannot be excluded. SN2025abyc otherwise follows the general photospheric velocity evolution of SNe II, while remaining toward the high-velocity side of the comparison distribution in Halpha, Hbeta, and FeII. Exploratory light-curve modelling suggests a synthesized Ni mass of approximately 0.03-0.04 solar mass. We suggest that the extended circumstellar environment, Ni distribution, and hydrogen-envelope structure could all play a role in shaping the observed light-curve evolution, particularly the prolonged plateau-to-tail transition.

astro-ph.SR↗