Energy variations at the onset of the tearing instability

Abstract

The resistive instability of a simple one-dimensional current sheet model has been investigated both in the long and in the short wavelength approximation. For the linear phase of the instability it is possible to derive, by means of an expansion technique, an analytical expression for the growth rate and for the perturbation itself. The variations of each kind of energy (magnetic, kinetic and dissipated energies, Poynting vector, work against pressure gradients and magnetic forces) are then exactly computed. Different behaviour of the System is obtained for different wavelengths. In particular, the driving energy for the instability is found to come from different regions: for high wavenumber α there is a decrease of the magnetic energy in the inner resistive region where the reconnection occurs, whereas for low-α modes the magnetic energy decreases in the outer ideal region. Moreover, the amount of Joule dissipation is found to increase with decreasing α so that the low-α regime is the most efficient.

A Multiwavelength Perspective of Flares on HR 1099: 4 Years of Coordinated Campaigns

“…The flux spectrum is increasing at low frequencies, but turns over at higher frequencies, with a maximum between 2 and 5 GHz. This behavior is consistent with optically thick emission at low frequencies and optically thin conditions at high frequencies, a pattern that has been seen during the rise and peak of flares on other active binaries (Feldman et al 1978;Klein & Chiuderi-Drago 1987;Torricelli-Ciamponi et al 1998). In the limits of small and large optical depth, the frequency dependence of the effective temperature and absorption coefficient can be combined to estimate the range of spectral indices α between flux measurements at adjacent frequencies.…”

The variable XMM-Newton spectrum of Markarian 766

“…The seed UV photons could be produced either by an accretion disk (Haardt et al 1997) or from low temperature (T ∼ 3 10 5 K) thermal emission in the corona itself Torricelli-Ciamponi & Courvoisier 1995). In Mrk 766 the broad Fe Kα line seen in the EPIC spectra provides strong evidence for the presence of a cool, optically thick accretion disk (Tanaka et al 1995).…”

Soft X-ray spectral variations of the narrow-line Seyfert 1 galaxy Markarian 766

“…These pairs down scatter the γ‐ray radiation and produce the observed X‐ray spectrum, including the soft X‐ray excess (Zdziarski et al 1990). Both these models predict that in the variability of a single source the power‐law slope is softer when the power‐law flux is higher (Done & Fabian 1989; Torricelli‐Ciamponi & Courvoisier 1995), as observed in Markarian 766.…”

“…However, in current models (e.g. Torricelli‐Ciamponi & Courvoisier 1995), the change in spectral index with power‐law flux is brought about by a change in the relativistic electron energy spectrum, not by a change in the number of soft photons, and hence there is no expectation that the soft flux should change first. This would explain how the power law varies when there is no detectable soft‐excess variability, and is consistent with the behaviour of HR hard in all the observations.…”