Reconnection of a kinking flux rope triggering the ejection of a microwave and hard X-ray source. II. Numerical Modeling

Numerical simulations of the helical ($m\!=\!1$) kink instability of an arched, line-tied flux rope demonstrate that the helical deformation enforces reconnection between the legs of the rope if modes with two helical turns are dominant as a result of high initial twist in the range $\Phi\gtrsim6\pi$. Such reconnection is complex, involving also the ambient field. In addition to breaking up the original rope, it can form a new, low-lying, less twisted flux rope. The new flux rope is pushed downward by the reconnection outflow, which typically forces it to break as well by reconnecting with the ambient field. The top part of the original rope, largely rooted in the sources of the ambient flux after the break-up, can fully erupt or be halted at low heights, producing a "failed eruption." The helical current sheet associated with the instability is squeezed between the approaching legs, temporarily forming a double current sheet. The leg-leg reconnection proceeds at a high rate, producing sufficiently strong electric fields that it would be able to accelerate particles. It may also form plasmoids, or plasmoid-like structures, which trap energetic particles and propagate out of the reconnection region up to the top of the erupting flux rope along the helical current sheet. The kinking of a highly twisted flux rope involving leg-leg reconnection can explain key features of an eruptive but partially occulted solar flare on 18 April 2001, which ejected a relatively compact hard X-ray and microwave source and was associated with a fast coronal mass ejection.Comment: Solar Physics, in pres

Humpy LNRF-velocity profiles in accretion discs orbiting nearly extreme Kerr black holes. A possible relation to QPOs

Change of sign of the LNRF-velocity gradient has been found for accretion discs orbiting rapidly rotating Kerr black holes with spin a > 0.9953 for Keplerian discs and a > 0.99979 for marginally stable thick discs. Aschenbach (2004) has identified the maximal rate of change of the orbital velocity within the "humpy" profile with a locally defined critical frequency of disc oscillations, but it has been done in a coordinate-dependent form. We define the critical "humpy" frequency H in general relativistic, coordinate independent form, and relate the frequency defined in the LNRF to distant observers. At radius of its definition, so-called "humpy" radius r_h, the "humpy" frequency H is compared to the radial (R) and vertical (V) epicyclic frequencies and the orbital frequency of the disc. For Keplerian thin discs, we show that the epicyclic resonance radii r_31 and r_41 (with V:R = 3:1 or 4:1) are located in vicinity of r_h where efficient triggering of oscillations with frequencies ~ H could be expected. Asymptotically (for 1-a < 10^(-4)) the ratio of the epicyclic and Keplerian frequencies and the humpy frequency is nearly constant, i.e., almost independent of spin, being for the radial epicyclic frequency R:H ~ 3:2. For thick discs the situation is more complex due to dependence on distribution of the specific angular momentum l determining the disc properties. For l = const tori and 1-a < 10^(-6) the frequency ratios of the humpy frequency and the orbital and epicyclic frequencies are again nearly constant and independent of both a and l, being for the radial epicyclic frequency R:H close to 4. In the limiting case of very slender tori (l ~ l_ms) the epicyclic resonance radius r_41 ~ r_h for spin 1-a < 2x10^(-4).Comment: 11 pages,10 figures, 1 table. Accepted for publication in Astronomy and Astrophysic

How river rocks round: resolving the shape-size paradox

River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox: downstream shape change indicates substantial abrasion, while size change apparently rules it out. Here we use laboratory experiments and numerical modeling to show quantitatively that pebble abrasion is a curvature-driven flow problem. As a consequence, abrasion occurs in two well-separated phases: first, pebble edges rapidly round without any change in axis dimensions until the shape becomes entirely convex; and second, axis dimensions are then slowly reduced while the particle remains convex. Explicit study of pebble shape evolution helps resolve the shape-size paradox by reconciling discrepancies between laboratory and field studies, and enhances our ability to decipher the transport history of a river rock.Comment: 11 pages, 5 figure

Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model

The high-frequency quasi-periodic oscillations (HF QPOs) that appear in the X-ray fluxes of low-mass X-ray binaries remain an unexplained phenomenon. Among other ideas, it has been suggested that a non-linear resonance between two oscillation modes in an accretion disc orbiting either a black hole or a neutron star plays a role in exciting the observed modulation. Several possible resonances have been discussed. A particular model assumes resonances in which the disc-oscillation modes have the eigenfrequencies equal to the radial and vertical epicyclic frequencies of geodesic orbital motion. This model has been discussed for black hole microquasar sources as well as for a group of neutron star sources. Assuming several neutron (strange) star equations of state and Hartle-Thorne geometry of rotating stars, we briefly compare the frequencies expected from the model to those observed. Our comparison implies that the inferred neutron star radius "RNS" is larger than the related radius of the marginally stable circular orbit "rms" for nuclear matter equations of state and spin frequencies up to 800Hz. For the same range of spin and a strange star (MIT) equation of state, the inferrred radius RNS is roughly equal to rms. The Paczynski modulation mechanism considered within the model requires that RNS < rms. However, we find this condition to be fulfilled only for the strange matter equation of state, masses below one solar mass, and spin frequencies above 800Hz. This result most likely falsifies the postulation of the neutron star 3:2 resonant eigenfrequencies being equal to the frequencies of geodesic radial and vertical epicyclic modes. We suggest that the 3:2 epicyclic modes could stay among the possible choices only if a fairly non-geodesic accretion flow is assumed, or if a different modulation mechanism operates.Comment: 7 pages, 4 figures (in colour), accepted for publication in Astronomy & Astrophysic

Quasiperiodic oscillations in a strong gravitational field around neutron stars testing braneworld models

The strong gravitational field of neutron stars in the brany universe could be described by spherically symmetric solutions with a metric in the exterior to the brany stars being of the Reissner-Nordstrom type containing a brany tidal charge representing the tidal effect of the bulk spacetime onto the star structure. We investigate the role of the tidal charge in orbital models of high-frequency quasiperiodic oscillations (QPOs) observed in neutron star binary systems. We focus on the relativistic precession model. We give the radial profiles of frequencies of the Keplerian (vertical) and radial epicyclic oscillations. We show how the standard relativistic precession model modified by the tidal charge fits the observational data, giving estimates of the allowed values of the tidal charge and the brane tension based on the processes going in the vicinity of neutron stars. We compare the strong field regime restrictions with those given in the weak-field limit of solar system experiments.Comment: 26 pages, 6 figure

The origin of net electric currents in solar active regions

There is a recurring question in solar physics about whether or not electric currents are neutralized in active regions (ARs). This question was recently revisited using three-dimensional (3D) magnetohydrodynamic (MHD) numerical simulations of magnetic flux emergence into the solar atmosphere. Such simulations showed that flux emergence can generate a substantial net current in ARs. Another source of AR currents are photospheric horizontal flows. Our aim is to determine the conditions for the occurrence of net vs. neutralized currents with this second mechanism. Using 3D MHD simulations, we systematically impose line-tied, quasi-static, photospheric twisting and shearing motions to a bipolar potential magnetic field. We find that such flows: (1) produce both {\it direct} and {\it return} currents, (2) induce very weak compression currents - not observed in 2.5D - in the ambient field present in the close vicinity of the current-carrying field, and (3) can generate force-free magnetic fields with a net current. We demonstrate that neutralized currents are in general produced only in the absence of magnetic shear at the photospheric polarity inversion line - a special condition rarely observed. We conclude that, as magnetic flux emergence, photospheric flows can build up net currents in the solar atmosphere, in agreement with recent observations. These results thus provide support for eruption models based on pre-eruption magnetic fields possessing a net coronal current.Comment: 14 pages and 11 figures (Accepted in The Astrophysical Journal

LNRF-velocity hump-induced oscillations of a Keplerian disc orbiting near-extreme Kerr black hole: A possible explanation of high-frequency QPOs in GRS 1915+105

At least four high-frequency quasiperiodic oscillations (QPOs) at frequencies 41Hz, 67Hz, 113Hz, and 167Hz were reported in a binary system GRS 1915+105 hosting near-extreme Kerr black hole with a dimensionless spin a>0.98. We use the idea of oscillations induced by the hump of the orbital velocity profile (related to locally non-rotating frames - LNRF) in discs orbiting near-extreme Kerr black holes, which are characterized by a "humpy frequency" f_h, that could excite the radial and vertical epicyclic oscillations with frequencies f_r, f_v. Due to non-linear resonant phenomena the combinational frequencies are allowed as well. Assuming mass M=14.8M_sun and spin a=0.9998 for the GRS 1915+105 Kerr black hole, the model predicts frequencies f_h=41Hz, f_r=67Hz, (f_h+f_r)=108Hz, (f_v-f_r)=170Hz corresponding quite well to the observed ones. For black-hole parameters being in good agreement with those given observationally, the forced resonant phenomena in non-linear oscillations, excited by the "hump-induced" oscillations in a Keplerian disc, can explain high-frequency QPOs in GRS 1915+105 within the range of observational errors.Comment: 4 pages, 2 figures, accepted for publication in Astronomy and Astrophysics, added references, corrected typo

Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope

The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.Comment: V2: update to conform to the published article; new choice for internal inductance of torus; updated Fig. 2; new Figs. 3, 5, and