Interaction of Supernova Ejecta with Nearby Protoplanetary Disks

The early Solar System contained short-lived radionuclides such as 60Fe (t1/2 = 1.5 Myr) whose most likely source was a nearby supernova. Previous models of Solar System formation considered a supernova shock that triggered the collapse of the Sun's nascent molecular cloud. We advocate an alternative hypothesis, that the Solar System's protoplanetary disk had already formed when a very close (< 1 pc) supernova injected radioactive material directly into the disk. We conduct the first numerical simulations designed to answer two questions related to this hypothesis: will the disk be destroyed by such a close supernova; and will any of the ejecta be mixed into the disk? Our simulations demonstrate that the disk does not absorb enough momentum from the shock to escape the protostar to which it is bound. Only low amounts (< 1%) of mass loss occur, due to stripping by Kelvin-Helmholtz instabilities across the top of the disk, which also mix into the disk about 1% of the intercepted ejecta. These low efficiencies of destruction and injectation are due to the fact that the high disk pressures prevent the ejecta from penetrating far into the disk before stalling. Injection of gas-phase ejecta is too inefficient to be consistent with the abundances of radionuclides inferred from meteorites. On the other hand, the radionuclides found in meteorites would have condensed into dust grains in the supernova ejecta, and we argue that such grains will be injected directly into the disk with nearly 100% efficiency. The meteoritic abundances of the short-lived radionuclides such as 60Fe therefore are consistent with injection of grains condensed from the ejecta of a nearby (< 1 pc) supernova, into an already-formed protoplanetary disk.Comment: 57 pages, 16 figure

Singular Laplacian Growth

The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate Schwarz-Christoffel map. The equations of motion describe the motions of these singularities. Despite the typical fractal-like outcomes of Laplacian growth processes, the equations of motion are shown to be not particularly sensitive to initial conditions. It is argued that the sensitivity of this system derives from a novel cause, the non-uniqueness of solutions to the differential system. By a mechanism of singularity creation, every solution can become more complex, even in the absence of noise, without violating the growth law. These processes are permitted, but are not required, meaning the equation of motion does not determine the motion, even in the small.Comment: 8 pages, Latex, 4 figures, Submitted to Phys. Rev.

Model Simulations of a Shock-Cloud Interaction in the Cygnus Loop

We present optical observations and 2D hydrodynamic modeling of an isolated shocked ISM cloud. H$\alpha$ images taken in 1992.6 and 2003.7 of a small optical emission cloud along the southwestern limb of the Cygnus Loop were used to measure positional displacements of $\sim$ 0 \farcs 1 yr$^{-1}$ for surrounding Balmer dominated emission filaments and 0\farcs025 - \farcs055 yr$^{-1}$ for internal cloud emission features. These measurements imply transverse velocities of $\simeq$ 250 km s$^{-1}$ and $\simeq$ 80 -- 140 km s$^{-1}$ for ambient ISM and internal cloud shocks respectively. The complex shock structure visible within the cloud indicates that the cloud's internal density distribution is two phased: a smoothly varying background density which is populated by higher density clumps. We present model results for a shock interacting with a non-uniform ISM cloud. We find that this cloud can be well modeled by a smoothly varying power law core surrounded by a low density envelope with a Lorentzian profile. The lack of sharp density gradients in such a model inhibits the growth of Kelvin-Helmholtz instabilities, consistent with the cloud's appearance. Our model results also suggest that cloud clumps have densities $\sim$ 10 times the ambient ISM density and account for $\sim$ 30% of the total cloud volume. Moreover, the observed spacing of internal cloud shocks and model simulations indicate that the distance between clumps is $\sim$ 4 clump radii.Comment: To be published in Ap

Chandra View of the Dynamically Young Cluster of Galaxies A1367 I. Small-Scale Structures

The 40 ks \emph{Chandra} ACIS-S observation of A1367 provides new insights into small-scale structures and point sources in this dynamically young cluster. Here we concentrate on small-scale extended structures. A ridge-like structure around the center (``the ridge'') is significant in the \chandra\ image. The ridge, with a projected length of $\sim$ 8 arcmin (or 300 h$_{0.5}^{-1}$ kpc), is elongated from northwest (NW) to southeast (SE), as is the X-ray surface brightness distribution on much larger scales ($\sim$ 2 h$_{0.5}^{-1}$ Mpc). The ridge is cooler than its western and southern surroundings while the differences from its eastern and northern surroundings are small. We also searched for small-scale structures with sizes $\sim$ arcmin. Nine extended features, with sizes from $\sim$ 0.5$'$ to 1.5$'$, were detected at significance levels above 4 $\sigma$. Five of the nine features are located in the ridge and form local crests. The nine extended features can be divided into two types. Those associated with galaxies (NGC 3860B, NGC 3860 and UGC 6697) are significantly cooler than their surroundings (0.3 - 0.9 keV vs. 3 - 4.5 keV). The masses of their host galaxies are sufficient to bind the extended gas. These extended features are probably related to thermal halos or galactic superwinds of their host galaxies. The existence of these relatively cold halos imply that galaxy coronae can survive in cluster environment (e.g., Vikhlinin et al. 2001). Features of the second type are not apparently associated with galaxies. Their temperatures may not be significantly different from those of their surroundings. This class of extended features may be related to the ridge. We consider several possibilities for the ridge and the second type of extended features. The merging scenario is preferred.Comment: To appear in ApJ, Vol 576, 2002, Sep., a high-resolution version is in http://cfa160.harvard.edu/~sunm/a1367_a.ps.g

The Crustal Rigidity of a Neutron Star, and Implications for PSR 1828-11 and other Precession Candidates

We calculate the crustal rigidity parameter, b, of a neutron star (NS), and show that b is a factor 40 smaller than the standard estimate due to Baym & Pines (1971). For a NS with a relaxed crust, the NS's free-precession frequency is directly proportional to b. We apply our result for b to PSR 1828-11, a 2.5 Hz pulsar that appears to be precessing with period 511 d. Assuming this 511-d period is set by crustal rigidity, we show that this NS's crust is not relaxed, and that its reference spin (roughly, the spin for which the crust is most relaxed) is 40 Hz, and that the average spindown strain in the crust is 5 \times 10^{-5}. We also briefly describe the implications of our b calculation for other well-known precession candidates.Comment: 44 pages, 10 figures, submitted to Ap

Tails of the Unexpected: The Interaction of an Isothermal Shell with a Cloud

A new mechanism for the formation of cometary tails behind dense clouds or globules is discussed. Numerical hydrodynamical models show that when a dense shell of swept-up matter overruns a cloud, material in the shell is focussed behind the cloud to form a tail. This mode of tail formation is completely distinct from other methods, which involve either the removal of material from the cloud, or shadowing from a strong, nearby source of ionization. This mechanism is relevant to the cometary tails seen in planetary nebulae and to the interaction of superbubble shells with dense clouds.Comment: 6 pages, 6 figures, accepted for publication in MNRAS letter

New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps

We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth patterns are compared to those obtained by the best algorithms of direct numerical solutions. The fractal dimension of the patterns is discussed.Comment: Sumitted to Phys. Rev. Lett. Further details at http://www.pik-potsdam.de/~ander

Diffusion-limited aggregation as branched growth

I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A {\bf 46}, 7793 (1992)]. This leads to a result for the cluster dimensionality, D \approx 1.66, which is close to numerically obtained values. In addition, the multifractal exponent \tau(3) = D in this theory, in agreement with a proposed `electrostatic' scaling law.Comment: 13 pages, one figure not included (available by request, by ordinary mail), Plain Te

Iterated Conformal Dynamics and Laplacian Growth

The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes. We emphasize the fundamental difference between these processes: DLA is grown serially with constant size particles, while Laplacian patterns are grown by advancing each boundary point in parallel, proportionally to the gradient of the Laplacian field. We introduce a 2-parameter family of growth patterns that interpolates between DLA and a discrete version of Laplacian growth. The ultraviolet putative finite-time singularities are regularized here by a minimal tip size, equivalently for all the models in this family. With this we stress that the difference between DLA and Laplacian growth is NOT in the manner of ultraviolet regularization, but rather in their deeply different growth rules. The fractal dimensions of the asymptotic patterns depend continuously on the two parameters of the family, giving rise to a "phase diagram" in which DLA and discretized Laplacian growth are at the extreme ends. In particular we show that the fractal dimension of Laplacian growth patterns is much higher than the fractal dimension of DLA, with the possibility of dimension 2 for the former not excluded.Comment: 13 pages, 12 figures, submitted to Phys. Rev.

A mean-field kinetic lattice gas model of electrochemical cells

We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier work for neutral particles. We include the Poisson equation to account for the influence of the electric field on ion migration, and oxido-reduction processes on the electrode surfaces to allow for growth and dissolution. We confirm the viability of our approach by simulating (i) the electrochemical equilibrium at flat electrodes, which displays the correct charged double-layer, (ii) the growth kinetics of one-dimensional electrochemical cells during growth and dissolution, and (iii) electrochemical dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure