Agglomerative Algebras

This paper investigates a generalization of Boolean algebras which I call agglomerative algebras. It also outlines two conceptions of propositions according to which they form an agglomerative algebra but not a Boolean algebra with respect to conjunction and negation

Nonlinear Single-Armed Spiral Density Waves in Nearly Keplerian Disks

Single-armed, stationary density waves can propagate in very weakly self-gravitating gas disks dominated by a central mass. Examples include circumstellar disks of protostars and molecular disks in galactic nuclei. We explore the linear and nonlinear dynamics of such waves. Variational methods yield nonlinear versions of the dispersion relation, angular momentum flux, and propagation velocity in the tight-winding limit. The pitch angle increases with amplitude until the tight-winding approximation breaks down. We also find a series of nonlinear logarithmic spirals which is exact in the limit of small disk mass and which extends to large pitch angle.Comment: 16 pages, 3 figures. Uses mn.sty and mncite.sty. Accepted by MNRA

Understanding WASP-12b

The orbital period of the hot Jupiter WASP-12b is apparently changing. We study whether this reflects orbital decay due to tidal dissipation in the star, or apsidal precession of a slightly eccentric orbit. In the latter case, a third body or other perturbation would be needed to sustain the eccentricity against tidal dissipation in the planet itself. We have analyzed several such perturbative scenarios, but none is satisfactory. Most likely therefore, the orbit really is decaying. If this is due to a dynamical tide, then WASP-12 should be a subgiant without a convective core as Weinberg et al. (2017) have suggested. We have modeled the star with the MESA code. While no model fits all of the observational constraints, including the luminosity implied by the GAIA DR2 distance, main-sequence models are less discrepant than subgiant ones.Comment: 12 pages, 4 figure, submitted to MNRA

Ruling Out Bosonic Repulsive Dark Matter in Thermal Equilibrium

Self-interacting dark matter (SIDM), especially bosonic, has been considered a promising candidate to replace cold dark matter (CDM) as it resolves some of the problems associated with CDM. Here, we rule out the possibility that dark matter is a repulsive boson in thermal equilibrium. We develop the model first proposed by Goodman (2000) and derive the equation of state at finite temperature. Isothermal spherical halo models indicate a Bose-Einstein condensed core surrounded by a non-degenerate envelope, with an abrupt density drop marking the boundary between the two phases. Comparing this feature with observed rotation curves constrains the interaction strength of our model's DM particle, and Bullet Cluster measurements constrain the scattering cross section. Both ultimately can be cast as constraints on the particle's mass. We find these two constraints cannot be satisfied simultaneously in any realistic halo model---and hence dark matter cannot be a repulsive boson in thermal equilibrium. It is still left open that DM may be a repulsive boson provided it is not in thermal equilibrium; this requires that the mass of the particle be significantly less than a millivolt.Comment: 13 pages, 3 figures, 1 table, accepted MNRAS August 9 201

Stochastic Coagulation and the Timescale for Runaway Growth

We study the stochastic coagulation equation using simplified models and efficient Monte Carlo simulations. It is known that (i) runaway growth occurs if the two-body coalescence kernel rises faster than linearly in the mass of the heavier particle; and (ii) for such kernels, runaway is instantaneous in the limit that the number of particles tends to infinity at fixed collision time per particle. Superlinear kernels arise in astrophysical systems where gravitational focusing is important, such as the coalescence of planetesimals to form planets or of stars to form supermassive black holes. We find that the time required for runaway decreases as a power of the logarithm of the the initial number of particles. Astrophysical implications are briefly discussed.Comment: 16 pages, 4 figures, 1 appendi

Production of magnetic energy by macroscopic turbulence in GRB afterglows

Afterglows of gamma-ray bursts are believed to require magnetic fields much stronger than that of the compressed pre-shock medium. As an alternative to microscopic plasma instabilities, we propose amplification of the field by macroscopic turbulence excited by the interaction of the shock with a clumpy pre-shock medium, for example a stellar wind. Using a recently developed formalism for localized perturbations to an ultra-relativistic shock, we derive constraints on the lengthscale, amplitude, and volume filling factor of density clumps required to produce a given magnetic energy fraction within the expansion time of the shock, assuming that the energy in the field achieves equipartion with the turbulence. Stronger and smaller-scale inhomogeneities are required for larger shock Lorentz factors. Hence it is likely that the magnetic energy fraction evolves as the shock slows. This could be detected by monitoring the synchrotron cooling frequency if the radial density profile ahead of the shock, smoothed over clumps, is known.Comment: 24 pages, 3 figure

Hydrodynamic Photoevaporation of Protoplanetary Disks with Consistent Thermochemistry

Photoevaporation is an important dispersal mechanism for protoplanetary disks. We conduct hydrodynamic simulations coupled with ray-tracing radiative transfer and consistent thermochemistry to study photoevaporative winds driven by ultraviolet and X-ray radiation from the host star. Most models have a three-layer structure: a cold midplane, warm intermediate layer, and hot wind, the last having typical speeds $\sim 30~\mathrm{km\ s}^{-1}$ and mass-loss rates $\sim 10^{-9}~M_\odot~\mathrm{yr}^{-1}$ when driven primarily by ionizing UV radiation. Observable molecules including CO, OH and H2O re-form in the intermediate layer and survive at relatively high wind temperatures due to reactions being out of equilibrium. Mass-loss rates are sensitive to the intensity of radiation in energy bands that interact directly with hydrogen. Comparison with previous works shows that mass loss rates are also sensitive to the treatment of both the hydrodynamics and the thermochemistry. Divergent results concerning the efficiency of X-ray photoevaporation are traced in part to differing assumptions about dust and other coolants.Comment: 15 pages, 9 figures, submitted to Ap

Higher-Order Contingentism, Part 1: Closure and Generation

This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to the view itself, do not exist to be drawn. The paper begins with a non-technical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations