Planetesimal formation by the streaming instability in a photoevaporating disk

Recent years have seen growing interest in the streaming instability as a candidate mechanism to produce planetesimals. However, these investigations have been limited to small-scale simulations. We now present the results of a global protoplanetary disk evolution model that incorporates planetesimal formation by the streaming instability, along with viscous accretion, photoevaporation by EUV, FUV, and X-ray photons, dust evolution, the water ice line, and stratified turbulence. Our simulations produce massive (60-130 $M_\oplus$) planetesimal belts beyond 100 au and up to $\sim 20 M_\oplus$ of planetesimals in the middle regions (3-100 au). Our most comprehensive model forms 8 $M_\oplus$ of planetesimals inside 3 au, where they can give rise to terrestrial planets. The planetesimal mass formed in the inner disk depends critically on the timing of the formation of an inner cavity in the disk by high-energy photons. Our results show that the combination of photoevaporation and the streaming instability are efficient at converting the solid component of protoplanetary disks into planetesimals. Our model, however, does not form enough early planetesimals in the inner and middle regions of the disk to give rise to giant planets and super-Earths with gaseous envelopes. Additional processes such as particle pileups and mass loss driven by MHD winds may be needed to drive the formation of early planetesimal generations in the planet forming regions of protoplanetary disks.Comment: 20 pages, 12 figures; accepted to Ap

Massive stars as thermonuclear reactors and their explosions following core collapse

Nuclear reactions transform atomic nuclei inside stars. This is the process of stellar nucleosynthesis. The basic concepts of determining nuclear reaction rates inside stars are reviewed. How stars manage to burn their fuel so slowly most of the time are also considered. Stellar thermonuclear reactions involving protons in hydrostatic burning are discussed first. Then I discuss triple alpha reactions in the helium burning stage. Carbon and oxygen survive in red giant stars because of the nuclear structure of oxygen and neon. Further nuclear burning of carbon, neon, oxygen and silicon in quiescent conditions are discussed next. In the subsequent core-collapse phase, neutronization due to electron capture from the top of the Fermi sea in a degenerate core takes place. The expected signal of neutrinos from a nearby supernova is calculated. The supernova often explodes inside a dense circumstellar medium, which is established due to the progenitor star losing its outermost envelope in a stellar wind or mass transfer in a binary system. The nature of the circumstellar medium and the ejecta of the supernova and their dynamics are revealed by observations in the optical, IR, radio, and X-ray bands, and I discuss some of these observations and their interpretations.Comment: To be published in " Principles and Perspectives in Cosmochemistry" Lecture Notes on Kodai School on Synthesis of Elements in Stars; ed. by Aruna Goswami & Eswar Reddy, Springer Verlag, 2009. Contains 21 figure

Stellar Dynamics of Extreme-Mass-Ratio Inspirals

Inspiral of compact stellar remnants into massive black holes (MBHs) is accompanied by the emission of gravitational waves at frequencies that are potentially detectable by space-based interferometers. Event rates computed from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due to uncertaintities about the rate coefficients. Here we present results from direct integration of the post-Newtonian N-body equations of motion descrbing dense clusters of compact stars around Schwarzschild MBHs. These simulations embody an essentially exact (at the post-Newtonian level) treatment of the interplay between stellar dynamical relaxation, relativistic precession, and gravitational-wave energy loss. The rate of capture of stars by the MBH is found to be greatly reduced by relativistic precession, which limits the ability of torques from the stellar potential to change orbital angular momenta. Penetration of this "Schwarzschild barrier" does occasionally occur, resulting in capture of stars onto orbits that gradually inspiral due to gravitational wave emission; we discuss two mechanisms for barrier penetration and find evidence for both in the simulations. We derive an approximate formula for the capture rate, which predicts that captures would be strongly disfavored from orbits with semi-major axes below a certain value; this prediction, as well as the predicted rate, are verified in the N-body integrations. We discuss the implications of our results for the detection of extreme-mass-ratio inspirals from galactic nuclei with a range of physical properties.Comment: 28 pages, 16 figures. Version 2 is significantly revised to reflect new insights into J and Q effects, to be published late

K-Theory of non-linear projective toric varieties

By analogy with algebraic geometry, we define a category of non-linear sheaves (quasi-coherent homotopy-sheaves of topological spaces) on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.Comment: v2: Final version, to appear in "Forum Mathematicum". Minor changes only, added more cross-referencing and references for toric geometr