Turbulence-Induced Relative Velocity Of Dust Particles. III. The Probability Distribution

Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, tau(p1) and tau(p2), of two particles of arbitrary sizes. The friction time of the particles included in the simulation ranges from 0.1 tau(eta) to 54T(L), where tau(eta) and T-L are the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of tau(p1), the PDF shape is the fattest for equal-size particles (tau(p2) = tau(p1)), and becomes thinner at both tau(p2) tau(p1). Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in (1/2) less than or similar to f less than or similar to 1, the PDF fatness first increases with the friction time tau(p,h) of the larger particle, peaks at tau(p,h) similar or equal to tau(eta), and then decreases as tp, h increases further. For 0 > T-L). These features are successfully explained by the Pan & Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanetary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem.Astronom

Orbital Deflection of Comets by Directed Energy

Cometary impacts pose a long-term hazard to life on Earth. Impact mitigation techniques have been studied extensively, but they tend to focus on asteroid diversion. Typical asteroid interdiction schemes involve spacecraft physically intercepting the target, a task feasible only for targets identified decades in advance and in a narrow range of orbits---criteria unlikely to be satisfied by a threatening comet. Comets, however, are naturally perturbed from purely gravitational trajectories through solar heating of their surfaces which activates sublimation-driven jets. Artificial heating of a comet, such as by a laser, may supplement natural heating by the Sun to purposefully manipulate its path and thereby avoid an impact. Deflection effectiveness depends on the comet's heating response, which varies dramatically depending on factors including nucleus size, orbit and dynamical history. These factors are incorporated into a numerical orbital model to assess the effectiveness and feasibility of using high-powered laser arrays in Earth orbit and on the ground for comet deflection. Simulation results suggest that a diffraction-limited 500 m orbital or terrestrial laser array operating at 10 GW for 1% of each day over 1 yr is sufficient to fully avert the impact of a typical 500 m diameter comet with primary nongravitational parameter A1 = 2 x 10^-8 au d^-2. Strategies to avoid comet fragmentation during deflection are also discussed.Comment: 13 pages, 12 figures; AJ, in pres

A Definitive Optical Detection of a Supercluster at z = 0.91

We present the results from a multi-band optical imaging program which has definitively confirmed the existence of a supercluster at z = 0.91. Two massive clusters of galaxies, CL1604+4304 at z = 0.897 and CL1604+4321 at z = 0.924, were originally observed in the high-redshift cluster survey of Oke, Postman & Lubin (1998). They are separated by 4300 km/s in radial velocity and 17 arcminutes on the plane of the sky. Their physical and redshift proximity suggested a promising supercluster candidate. Deep BRi imaging of the region between the two clusters indicates a large population of red galaxies. This population forms a tight, red sequence in the color--magnitude diagram at (R-i) = 1.4. The characteristic color is identical to that of the spectroscopically-confirmed early-type galaxies in the two member clusters. The red galaxies are spread throughout the 5 Mpc region between CL1604+4304 and CL1604+4321. Their spatial distribution delineates the entire large scale structure with high concentrations at the cluster centers. In addition, we detect a significant overdensity of red galaxies directly between CL1604+4304 and CL1604+4321 which is the signature of a third, rich cluster associated with this system. The strong sequence of red galaxies and their spatial distribution clearly indicate that we have discovered a supercluster at z = 0.91.Comment: Accepted for publication in Astrophysical Journal Letters. 13 pages, including 5 figure

The Observations of Redshift Evolution in Large-Scale Environments (ORELSE) Survey. I. The Survey Design and First Results on CL 0023+0423 at z = 0.84 and RX J1821.6+6827 at z = 0.82

We present the Observations of Redshift Evolution in Large-Scale Environments (ORELSE) Survey, a systematic search for structure on scales greater than 10 h^(–1)_70 Mpc around 20 well-known clusters at redshifts of 0.6 < z < 1.3. The goal of the survey is to examine a statistical sample of dynamically active clusters and large-scale structures in order to quantify galaxy properties over the full range of local and global environments. We describe the survey design, the cluster sample, and our extensive observational data covering at least 25' around each target cluster. We use adaptively smoothed red galaxy density maps from our wide-field optical imaging to identify candidate groups/clusters and intermediate-density large-scale filaments/walls in each cluster field. Because photometric techniques (such as photometric redshifts, statistical overdensities, and richness estimates) can be highly uncertain, the crucial component of this survey is the unprecedented amount of spectroscopic coverage. We are using the wide-field, multiobject spectroscopic capabilities of the Deep Multiobject Imaging Spectrograph to obtain 100-200+ confirmed cluster members in each field. Our survey has already discovered the Cl 1604 supercluster at z ≈ 0.9, a structure which contains at least eight groups and clusters and spans 13 Mpc × 100 Mpc. Here, we present the results on the large-scale environments of two additional clusters, Cl 0023+0423 at z = 0.84 and RX J1821.6+6827 at z = 0.82, which highlight the diversity of global properties at these redshifts. The optically selected Cl 0023+0423 is a four-way group-group merger with constituent groups having measured velocity dispersions between 206 and 479 km s^–1. The galaxy population is dominated by blue, star-forming galaxies, with 80% of the confirmed members showing [O II] emission. The strength of the Hδ line in a composite spectrum of 138 members indicates a substantial contribution from recent starbursts to the overall galaxy population. In contrast, the X-ray-selected RX J1821.6+6827 is a largely isolated, massive cluster with a measured velocity dispersion of 926 ± 77 km s^(–1). The cluster exhibits a well-defined red sequence with a large quiescent galaxy population. The results from these two targets, along with preliminary findings on other ORELSE clusters, suggest that optical selection may be more effective than X-ray surveys at detecting less-evolved, dynamically active systems at these redshifts

Galois covers of the open p-adic disc

This paper investigates Galois branched covers of the open $p$-adic disc and their reductions to characteristic $p$. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is determined by arithmetic and geometric properties of the generic fiber and its characteristic zero specializations. As applications, we derive a criterion for good reduction in the abelian case, and give an arithmetic reformulation of the local Oort Conjecture concerning the liftability of cyclic covers of germs of curves.Comment: 19 pages; substantial organizational and expository changes; this is the final version corresponding to the official publication in Manuscripta Mathematica; abstract update