Operations on integral lifts of K(n)

This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence that operations on lifts of the functors K(n) to cohomology theories with values in modules over valuation rings of local number fields, indexed by Lubin-Tate groups of such fields, are extensions of the groups of automorphisms of the indexing group laws, by the exterior algebras on the normal bundle to the orbits of the group laws in the space of lifts.Comment: \S 2.0 hopefully less cryptic. To appear in the proceedings of the 2015 Nagoya conference honoring T Ohkawa. Comments very welcome

Planets Rapidly Create Holes in Young Circumstellar Discs

Recent spectral observations by the Spitzer Space Telescope (SST) reveal that some discs around young ($\sim {\rm few} \times 10^6$ yr old) stars have remarkably sharp transitions to a low density inner region in which much of the material has been cleared away. It has been recognized that the most plausible mechanism for the sharp transition at a specific radius is the gravitational influence of a massive planet. This raises the question of whether the planet can also account for the hole extending all the way to the star. Using high resolution numerical simulations, we show that Jupiter-mass planets drive spiral waves which create holes on time scales $\sim 10$ times shorter than viscous or planet migration times. We find that the theory of spiral-wave driven accretion in viscous flows by Takeuchi et al. (1996) can be used to provide a consistent interpretation of the simulations. In addition, although the hole surface densities are low, they are finite, allowing mass accretion toward the star. Our results therefore imply that massive planets can form extended, sharply bounded spectral holes which can still accommodate substantial mass accretion rates. The results also imply that holes are more likely than gaps for Jupiter mass planets around solar mass stars.Comment: accepted by Ap

Radial migration in galactic disks caused by resonance overlap of multiple patterns: Self-consistent simulations

We have recently identified a new radial migration mechanism resulting from the overlap of spiral and bar resonances in galactic disks. Here we confirm the efficiency of this mechanism in fully self-consistent, Tree-SPH simulations, as well as high-resolution pure N-body simulations. In all barred cases we clearly identify the effect of spiral-bar resonance overlap by measuring a bimodality in the changes of angular momentum in the disk, dL, whose maxima are near the bar's corotation and outer Lindblad resonance. This contrasts with the smooth distribution of dL for a simulation with no stable bar present, where strong radial migration is induced by multiple spirals. The presence of a disk gaseous component appears to increase the rate of angular momentum exchange by about 20%. The efficiency of this mechanism is such that galactic stellar disks can extend to over 10 scale-lengths within 1-3 Gyr in both Milky Way size and low-mass galaxies (circular velocity ~100 km/s). We also show that metallicity gradients can flatten in less than 1 Gyr rendering mixing in barred galaxies an order of magnitude more efficient than previously thought.Comment: replaced with accepted version: 5 pages, 5 figures (one new figure added), minor change

Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case

The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a compact Lie group and the Chern character is explicitly computed in the case of SU(2). For large euclidean time, the character form is localized on a D-brane.Comment: Version 2: Essentially simplified proof of the main result using a map from twisted K-theory to gerbes modulo the twisting gerbe; references added + minor correction

Cyclic cocycles on twisted convolution algebras

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to a construction of Mathai and Stevenson. When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras. The results in this article were originally published in the author's Ph.D. thesis.Comment: 39 page

Do Proto-Jovian Planets Drive Outflows?

We discuss the possibility that gaseous giant planets drive strong outflows during early phases of their formation. We consider the range of parameters appropriate for magneto-centrifugally driven stellar and disk outflow models and find that if the proto-Jovian planet or accretion disk had a magnetic field of >~ 10 Gauss and moderate mass inflow rates through the disk of less than 10^-7 M_J/yr that it is possible to drive an outflow. Estimates based both on scaling from empirical laws observed in proto-stellar outflows and the magneto-centrigugal disk and stellar+disk wind models suggest that winds with mass outflow rates of 10^-8 M_J/yr and velocities of order ~ 20 km/s could be driven from proto-Jovian planets. Prospects for detection and some implications for the formation of the solar system are briefly discussed.Comment: AAS Latex, accepted for Ap

Outer edges of debris discs: how sharp is sharp?

Ring-like features have been observed in several debris discs. Outside the main ring, while some systems exhibit smooth surface brightness profiles (SB) that fall off roughly as r**-3.5, others display large luminosity drops at the ring's outer edge and steeper radial SB profiles. We seek to understand this diversity of outer edge profiles under the ``natural'' collisional evolution of the system, without invoking external agents such as planets or gas. We use a statistical code to follow the evolution of a collisional population, ranging from dust grains (submitted to radiation pressure) to planetesimals and initially confined within a belt (the 'birth ring'). The system typically evolves toward a "standard" steady state, with no sharp edge and SB \propto r**-3.5 outside the birth ring. Deviations from this standard profile, in the form of a sharp outer edge and a steeper fall-off, occur only when two parameters take their extreme values: 1) When the birth ring is so massive that it becomes radially optically thick for the smallest grains. However, the required disc mass is here probably too high to be realistic. 2) When the dynamical excitation of the dust-producing planetesimals is so low ( <0.01) that the smallest grains, which otherwise dominate the total optical depth, are preferentially depleted. This low-excitation case, although possibly not generic, cannot be ruled out by observations. Our "standard" profile provides a satisfactory explanation for a large group of debris discs with outer edges and SB falling as r**-3.5. Systems with sharper outer edges, barring other confining agents, could still be explained by ``natural'' collisional evolution if their dynamical excitation is very low. We show that such a dynamically-cold case provides a satisfactory fit for HR4796AComment: Accepted for publication in A&A (abstract truncated here, full version in the pdf file); v2: typos corrected + rephrasing title of Section 5.1.2; v3 :final technical change