We construct a combinatorial model of an A-infinity-operad which acts simplicially on the cobar resolution (not just its total space) of a simplicial set with respect to a ring R.

Tilman Bauer Assaf Libman

A translation of Paul Ehrenfest's 1933 paper, entitled "Phase transitions in the usual and generalized sense, classified according to the singularities of the thermodynamic potential" is presented. Some historical commentary about the paper's context is also given.

Tilman Sauer

The Einstein Archives contain a considerable collection of calculations in the form of working sheets and scratch paper, documenting Einstein's scientific preoccupations during the last three decades of his life until his death in 1955. This paper provides a brief description of these documents and some indications of what can be expected from a more thorough investigation of these notes.

Tilman Sauer

In this note, we point attention to and briefly discuss a curious manuscript of Einstein, composed in 1938 and entitled "Unified Field Theory," the only such writing, published or unpublished, carrying this title without any further specification. Apparently never intended for publication, the manuscript sheds light both on Einstein's modus operandi as well as on the public role of Einstein's later work on a unified field theory of gravitation and electromagnetism.

Tilman Sauer Tobias Schütz

As a generalization of the ring spectrum of topological modular forms, we construct a graded ring spectrum of topological Jacobi forms, $\operatorname{TJF}_*$. This is constructed as the global sections of a sheaf of $E_\infty$-ring spectra on the stacky universal elliptic curve using circle-equivariant $\operatorname{TMF}$. Complete calculations of its homotopy at odd primes and partial results at $p=2$ are given.

Tilman Bauer Lennart Meier

We examine the longitudinal distribution of the stars escaping from a cluster along tidal tails. Using both theory and simulations, we show that, even in the case of a star cluster in a circular galactic orbit, when the tide is steady, the distribution exhibits maxima at a distance of many tidal radii from the cluster.

Andreas H. W. Küpper Andrew Macleod Douglas C. Heggie

Aerosol particles experience significant photophoretic forces at low pressure. Previous work assumed the average particle temperature to be very close to the gas temperature. This might not always be the case. If the particle temperature or the thermal radiation field differs significantly from the gas temperature (optically thin gases), given approximations overestimate the photophoretic force by an order of magnitude on average with maximum errors up to more than three magnitudes. We therefore developed a new general approximation which on average only differs by 1 % from the true value.

C. Loesche G. Wurm T. Jankowski M. Kuepper

A one dimensional sublimation model for cometary nuclei is used to derive size limits for the nuclei of sungrazing comets, and to estimate oxygen ion fluxes at 1 AU from their evaporation. Given that none of the ~300 sungrazers detected by the SOlar and Heliospheric Observatory (SOHO) was observed after disappearing behind the sun, and that small nuclei with a radius of ~3.5m could be observed, it is assumed that all SOHO sungrazers were completely destroyed. For the case that sublimation alone is sufficient for destruction, the model yields an upper size limit as a function of nuclear density, albedo and perihelion distance. If the density of the nuclei is that typical of porous ice (600kg/m^3), the maximum size is 63m. These results confirm similar model calculations by Weissman (1983). An analytical expression is derived that approximates the model results well. We discuss possible modifications of our results by different disruption mechanisms. While disruption by thermal stress does not change the upper size limits significantly, they may be somewhat increased by tidal disruption (up to 100m for a density of 600kg/m^3) dependent on the isotropy of the sublimation process and the tensile strength of the comet. Implications for the Kreutz family of sungrazers are discussed. Oxygen ions from the sublimation of sungrazing comets form a tail. Fluxes from this tail are sufficiently high to be measured at 1 AU by particle detectors on spacecraft, but the duration of a tail crossing is only about half an hour. Therefore the probability of a spacecraft actually encountering a tail of an evaporating sungrazer is only of the order of two percent per year.

M. Iseli M. Kueppers W. Benz P. Bochsler

Context: In 2004 asteroid (2867) Steins has been selected as a flyby target for the Rosetta mission. Determination of its spin period and the orientation of its rotation axis are essential for optimization of the flyby planning. Aim: Measurement of the rotation period and light curve of asteroid (2867) Steins at a phase angle larger than achievable from ground based observations, providing a high quality data set to contribute to the determination of the orientation of the spin axis and of the pole direction. Methods: On March 11, 2006, asteroid (2867) Steins was observed continuously for 24 hours with the scientific camera system OSIRIS onboard Rosetta. The phase angle was 41.7 degrees, larger than the maximum phase angle of 30 degrees when Steins is observed from Earth. A total of 238 images, covering four rotation periods without interruption, were acquired. Results: The light curve of (2867) Steins is double peaked with an amplitude of $\approx$ 0.23 mag. The rotation period is 6.052 $\pm$ 0.007 hours. The continuous observations over four rotation periods exclude the possibility of period ambiguities. There is no indication of deviation from a principal axis rotation state. Assuming a slope parameter of G = 0.15, the absolute visual magnitude of Steins is 13.05 $\pm$ 0.03.

M. Kueppers S. Mottola S. C. Lowry M. F. A'Hearn C. Barbieri M. A. Barucci S. Fornasier O. Groussin P. Gutierrez S. F. Hviid H. U. Keller P. Lamy

A novel way of looking at the evolution of star clusters is presented. With a dynamical temperature, given by the mean kinetic energy of the cluster stars, and a dynamical luminosity, which is defined as the kinetic energy of the stars leaving the cluster in analogy to the energy of photons emitted by a star, the dissolution of star clusters is studied using a new dynamical temperature-luminosity diagram for star clusters. The investigation contains a parameter-space study of open clusters of up to N = 32768 single-mass stars with different initial density distributions, half-mass radii, tidal conditions and binary fractions. The clusters show a strong correlation between dynamical temperature and dynamical luminosity and most of the investigated cluster families share a common sequence in such a dynamical temperature-luminosity diagram. Deviations from this sequence are analyzed and discussed. After core collapse, the position of a cluster within this diagram can be defined by three parameters: the mass, the tidal conditions and the binary fraction. Due to core collapse all initial conditions are lost and the remaining stars adjust to the given tidal conditions. Binaries as internal energy sources influence this adjustment. A further finding concerns the Lagrange radii of star clusters: Throughout the investigated parameter space nearly all clusters show a constant half-mass radius for the time after core collapse until dissolution. Furthermore, the ratio of half-mass radius to tidal radius evolves onto a common sequence which only depends on the mass left in the cluster.

Andreas H. W. Kuepper Pavel Kroupa Holger Baumgardt