We show that a black-hole binary with an external companion can undergo Lidov-Kozai cycles that cause a close pericenter passage, leading to a rapid merger due to gravitational-wave emission. This scenario occurs most often for systems in which the companion has mass comparable to the reduced mass of the binary and the companion orbit has semi-major axis within a factor of ∼ 10 of the binary semi-major axis. Using a simple population-synthesis model and 3-body simulations, we estimate the rate of mergers in triple black hole systems in the field to be about six per Gpc 3 per year in the absence of natal kicks during black hole formation. This value is within the low end of the 90% credible interval for the total black-hole black-hole merger rate inferred from the current LIGO results. There are many uncertainties in these calculations, the largest of which is the unknown distribution of natal kicks. Even modest natal kicks of 40 km s −1 will reduce the merger rate by a factor of 40. A few percent of these systems will have eccentricity greater than 0.999 when they first enter the frequency band detectable by aLIGO (above 10 Hz). 4(1) (Peters 1964). Here a is the semi-major axis of the black-hole binary, M = m 1 + m 2 is the sum of the individual masses, and µ = m 1 m 2 /(m 1 + m 2 ) is the reduced mass of the system. Equation (1)

We investigate the rotational emission from dust grains that rotate around non-principal axes. We argue that in many phases of the interstellar medium, the smallest grains, which dominate spinning dust emission, are likely to have their nutation state (orientation of principal axes relative to the angular momentum vector) randomized during each thermal spike. We recompute the excitation and damping rates associated with rotational emission from the grain permanent dipole, grain-plasma interactions, infrared photon emission and collisions. The resulting spinning dust spectra generally show a shift towards higher emissivities and peak frequencies relative to previous calculations. and similarly for E JK and E KK . We may then investigate the mean rate of change of J:Here, the contributions from J, K and − J, − K nearly cancel. They differ only due to the presence of first-order terms (in J, K) in equation (69); these give

Detections of planets in eccentric, close (separations of ∼ 20 AU) binary systems such as α Cen or γ Cep provide an important test of planet formation theories. Gravitational perturbations from the companion are expected to excite high planetesimal eccentricities resulting in destruction, rather than growth, of objects with sizes of up to several hundred km in collisions of similar-size bodies. It was recently suggested that gravity of a massive axisymmetric gaseous disk in which planetesimals are embedded drives rapid precession of their orbits, suppressing eccentricity excitation. However, disks in binaries are themselves expected to be eccentric, leading to additional planetesimal excitation. Here we develop secular theory of eccentricity evolution for planetesimals perturbed by the gravity of an elliptical protoplanetary disk (neglecting gas drag) and the companion. For the first time we derive an expression for the disturbing function due to an eccentric disk, which can be used for a variety of other astrophysical problems. We obtain explicit analytical solutions for planetesimal eccentricity evolution neglecting gas drag and delineate four different regimes of dynamical excitation. We show that in systems with massive ( 10 −2 M ⊙ ) disks, planetesimal eccentricity is usually determined by the gravity of the eccentric disk alone, and is comparable to the disk eccentricity. As a result, the latter imposes a lower limit on collisional velocities of solids, making their growth problematic. In the absence of gas drag this fragmentation barrier can be alleviated if the gaseous disk rapidly precesses or if its own self-gravity is efficient at lowering disk eccentricity.

We develop a self-consistent model for the equilibrium gas temperature and size-dependent dust temperature in cold, dense pre-stellar cores, assuming an arbitrary power-law size distribution of dust grains. Compact analytical expressions applicable to a broad range of physical parameters are derived and compared with predictions of the commonly used standard model. It is suggested that combining the theoretical results with observations should allow us to constrain the degree of dust evolution and the cosmic-ray ionization rate in dense cores, and to help in discriminating between different regimes of cosmic-ray transport in molecular clouds. In particular, assuming a canonical MRN distribution of grain sizes, our theory demonstrates that the gas temperature measurements in the pre-stellar core L1544 are consistent with an ionization rate as high as ∼ 10 −16 s −1 , an order of magnitude higher than previously thought.

Understanding the cosmic ray (CR) ionization rate is crucial in order to simulate the dynamics of, and interpret the chemical species observed in molecular clouds. Calculating the CR ionization rate requires both accurate knowledge of the spectrum of MeV to GeV protons at the edge of the cloud as well as a model for the propagation of CRs into molecular clouds. Some models for the propagation of CRs in molecular clouds assume the CRs to stream freely along magnetic field lines, while in others they propagate diffusively due to resonant scattering off of magnetic disturbances excited by MHD turbulence present in the medium. We discuss the conditions under which CR diffusion can operate in a molecular cloud, calculate the local CR spectrum and ionization rate in both a free-streaming and diffusive propagation model, and highlight the different results from the two models. We also apply these two models to the propagation through the ISM to obtain the spectrum seen by Voyager 1, and show that such a spectrum favors a diffusive propagation model.