Critical phenomena and renormalization-group theory

Astronomical data analysis software and systems

Non-perturbative renormalization flow in quantum field theory and statistical physics

The size of a planet is an observable property directly connected to the physics of its formation and evolution. We used precise radius measurements from the California-Kepler Survey to study the size distribution of 2025 Kepler planets in fine detail. We detect a factor of ≥2 deficit in the occurrence rate distribution at 1.5–2.0 R⊕. This gap splits the population of close-in (P < 100 days) small planets into two size regimes: R_p < 1.5 R⊕ and R_p = 2.0-3.0 R⊕, with few planets in between. Planets in these two regimes have nearly the same intrinsic frequency based on occurrence measurements that account for planet detection efficiencies. The paucity of planets between 1.5 and 2.0 R⊕ supports the emerging picture that close-in planets smaller than Neptune are composed of rocky cores measuring 1.5 R⊕ or smaller with varying amounts of low-density gas that determine their total sizes.

/pdf/the-california-kepler-survey-iii-a-gap-in-the-radius-4a0vsnybgl.pdf

The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets*

The EUV Imaging Spectrometer (EIS) on Hinode will observe solar corona and upper transition region emission lines in the wavelength ranges 170 – 210 A and 250 – 290 A. The line centroid positions and profile widths will allow plasma velocities and turbulent or non-thermal line broadenings to be measured. We will derive local plasma temperatures and densities from the line intensities. The spectra will allow accurate determination of differential emission measure and element abundances within a variety of corona and transition region structures. These powerful spectroscopic diagnostics will allow identification and characterization of magnetic reconnection and wave propagation processes in the upper solar atmosphere. We will also directly study the detailed evolution and heating of coronal loops. The EIS instrument incorporates a unique two element, normal incidence design. The optics are coated with optimized multilayer coatings. We have selected highly efficient, backside-illuminated, thinned CCDs. These design features result in an instrument that has significantly greater effective area than previous orbiting EUV spectrographs with typical active region 2 – 5 s exposure times in the brightest lines. EIS can scan a field of 6×8.5 arc min with spatial and velocity scales of 1 arc sec and 25 km s−1 per pixel. The instrument design, its absolute calibration, and performance are described in detail in this paper. EIS will be used along with the Solar Optical Telescope (SOT) and the X-ray Telescope (XRT) for a wide range of studies of the solar atmosphere.

http://www.rxollc.com/windt/papers/2007_SolPhys_243_19.pdf

The EUV Imaging Spectrometer for Hinode

The ideal helical kink instability of a force-free coronal magnetic flux rope, anchored in the photosphere, is studied as a model for solar eruptions. Using the flux rope model of Titov and D?moulin as the initial condition in MHD simulations, both the development of helical shape and the rise profile of a confined (or failed) filament eruption (on 2002 May 27) are reproduced in very good agreement with the observations. By modifying the model such that the magnetic field decreases more rapidly with height above the flux rope, a full (or ejective) eruption of the rope is obtained in very good agreement with the developing helical shape and the exponential-to-linear rise profile of a fast coronal mass ejection (CME) on 2001 May 15. This confirms that the helical kink instability of a twisted magnetic flux rope can be the mechanism of the initiation and the initial driver of solar eruptions. The agreement of the simulations with properties that are characteristic of many eruptions suggests that they are often triggered by the kink instability. The decrease of the overlying field with height is a main factor in deciding whether the instability leads to a confined event or to a CME.

https://iopscience.iop.org/article/10.1086/462412/pdf

Confined and Ejective Eruptions of Kink-unstable Flux Ropes

The expansion instability of a toroidal current ring in low-beta magnetized plasma is investigated. Qualitative agreement is obtained with experiments on spheromak expansion and with essential properties of solar coronal mass ejections, unifying the two apparently disparate classes of fast and slow coronal mass ejections.

The Torus instability

We analyze the physical mechanisms that form a three-dimensional coronal flux rope and later cause its eruption. This is achieved by a zero-β magnetohydrodynamic (MHD) simulation of an initially potential, asymmetric bipolar field, which evolves by means of simultaneous slow magnetic field diffusion and sub-Alfvenic, line-tied shearing motions in the photosphere. As in similar models, flux-cancellation-driven photospheric reconnection in a bald-patch (BP) separatrix transforms the sheared arcades into a slowly rising and stable flux rope. A bifurcation from a BP to a quasi-separatrix layer (QSL) topology occurs later on in the evolution, while the flux rope keeps growing and slowly rising, now due to shear-driven coronal slip-running reconnection, which is of tether-cutting type and takes place in the QSL. As the flux rope reaches the altitude at which the decay index –∂ln B/∂ln z of the potential field exceeds ~3/2, it rapidly accelerates upward, while the overlying arcade eventually develops an inverse tear-drop shape, as observed in coronal mass ejections (CMEs). This transition to eruption is in accordance with the onset criterion of the torus instability. Thus, we find that photospheric flux-cancellation and tether-cutting coronal reconnection do not trigger CMEs in bipolar magnetic fields, but are key pre-eruptive mechanisms for flux ropes to build up and to rise to the critical height above the photosphere at which the torus instability causes the eruption. In order to interpret recent Hinode X-Ray Telescope observations of an erupting sigmoid, we produce simplified synthetic soft X-ray images from the distribution of the electric currents in the simulation. We find that a bright sigmoidal envelope is formed by pairs of -shaped field lines in the pre-eruptive stage. These field lines form through the BP reconnection and merge later on into -shaped loops through the tether-cutting reconnection. During the eruption, the central part of the sigmoid brightens due to the formation of a vertical current layer in the wake of the erupting flux rope. Slip-running reconnection in this layer yields the formation of flare loops. A rapid decrease of currents due to field line expansion, together with the increase of narrow currents in the reconnecting QSL, yields the sigmoid hooks to thin in the early stages of the eruption. Finally, a slightly rotating erupting loop-like feature (ELLF) detaches from the center of the sigmoid. Most of this ELLF is not associated with the erupting flux rope, but with a current shell that develops within expanding field lines above the rope. Only the short, curved end of the ELLF corresponds to a part of the flux rope. We argue that the features found in the simulation are generic for the formation and eruption of soft X-ray sigmoids.

https://iopscience.iop.org/article/10.1088/0004-637X/708/1/314/pdf

Formation of Torus-Unstable Flux Ropes and Electric Currents in Erupting Sigmoids

The force-free coronal loop model by Titov & Demoulin (1999) is found to be unstable with respect to the ideal kink mode, which suggests this instability as a mechanism for the initiation of flares. The long-wavelength ( m= 1) mode grows for average twists � > 3.5� (at a loop aspect ratio of≈ 5). The threshold of instability increases with increasing major loop radius, primarily because the aspect ratio then also increa ses. Numerically obtained equilibria at subcritical twist are very close to the approximate analytical equilibrium; they do not show indications of sigmoidal shape. The growth of kink perturbations is eventually slowed down by the surrounding potential field , which varies only slowly with radius in the model. With this field a global eruption is not obtained in the ideal MHD limit. Kink perturbations with a rising loop apex lead to the formation of a vertical current sheet below the apex, which does not occur in the cylindrical approximation.

/pdf/ideal-kink-instability-of-a-magnetic-loop-equilibrium-5d57r63x9q.pdf

Ideal kink instability of a magnetic loop equilibrium

We simulate the twisting of an initially potential coronal flux tube by photospheric vortex motions, centred at two photospheric flux concentrations, using the compressible zero-beta ideal MHD equations. A twisted flux tube is formed, surrounded by much less twisted and sheared outer flux. Under the action of continuous slow driving, the flux tube starts to evolve quasi-statically along a sequence of force-free equilibria, which rise slowly with increasing twist and possess helical shape. The flux bundle that extends from the location of peak photospheric current density ( slightly displaced from the vortex centre) shows a sigmoidal shape in agreement with observations of sigmoidal soft X-ray loops. There exists a critical twist, above which no equilibrium can be found in the simulation and the flux tube ascends rapidly. Then either stable equilibrium ceases to exist or the character of the sequence changes such that neighbouring stable equilibria rise by enormous amounts for only modest additions of twist. A comparison with the scalings of the rise of flux in axisymmetric geometry by Sturrock et al. ( 1995) suggests the former. Both cases would be observed as an eruption. The critical end-to-end twist, for a particular set of parameters describing the initial potential field, is found to lie in the range 2.5pi < Phi(c) < 2.75pi. There are some indications for the growth of helical perturbations at supercritical twist. Depending on the radial profiles of the photospheric flux concentration and vortex velocity, the outer part or all of the twisted flux expands from the central field line of the flux tube. This effect is particularly efficient in the dynamic phase, provided the density is modeled realistically, falling off sufficiently rapidly with height. It is expected to lead to the formation of a cavity in which the twisted flux tube is embedded, analogous to the typical structure of coronal mass ejections.

/pdf/the-evolution-of-twisting-coronal-magnetic-flux-tubes-4xtt2txur1.pdf

Tibor Torok

Papers

Confined and Ejective Eruptions of Kink-unstable Flux Ropes

The Torus instability

Formation of Torus-Unstable Flux Ropes and Electric Currents in Erupting Sigmoids

Ideal kink instability of a magnetic loop equilibrium

The evolution of twisting coronal magnetic flux tubes