Compression of Dense and Regular Point Clouds

We present a simple technique for single-rate compression of point clouds sampled from a surface, based on a spanning tree of the points. Unlike previous methods, we predict future vertices using both a linear predictor, which uses the previous edge as a predictor for the current edge, and lateral predictors that rotate the previous edge 90 degrees left or right about an estimated normal. By careful construction of the spanning tree and choice of prediction rules, our method improves upon existing compression rates when applied to regularly sampled point sets, such as those produced by laser range scanning or uniform tesselation of higherorder surfaces. For less regular sets of points, the compression rate is still generally within 1.5 bits per point of other compression algorithms

Star Formation from Galaxies to Globules

The empirical laws of star formation suggest that galactic-scale gravity is involved, but they do not identify the actual triggering mechanisms for clusters in the final stages. Many other triggering processes satisfy the empirical laws too, including turbulence compression and expanding shell collapse. The self-similar nature of the gas and associated young stars suggests that turbulence is more directly involved, but the small scale morphology of gas around most embedded clusters does not look like a random turbulent flow. Most clusters look triggered by other nearby stars. Such a prominent local influence makes it difficult to understand the universality of the Kennicutt and Schmidt laws on galactic scales. A unified view of multi-scale star formation avoids most of these problems. Ambient self-gravity produces spiral arms and drives much of the turbulence that leads to self-similar structures, while localized energy input from existing clusters and field supernovae triggers new clusters in pre-existing clouds. The hierarchical structure in the gas made by turbulence ensures that the triggering time scales with size, giving the Schmidt law over a wide range of scales and the size-duration correlation for young star fields. The efficiency of star formation is determined by the fraction of the gas above a critical density of around 10^5 m(H2)/cc. Star formation is saturated to its largest possible value given the fractal nature of the interstellar medium.Comment: accepted for ApJ, 42 pages, Dannie Heineman prize lecture, January 200

Magnetic fields in barred galaxies. IV. NGC 1097 and NGC 1365

We present 3.5cm and 6.2cm radio continuum maps in total and polarized intensity of the barred galaxies NGC 1097 and NGC 1365. Both galaxies exhibit radio ridges roughly overlapping with the massive dust lanes in the bar region. The contrast in total intensity across the radio ridges is compatible with compression and shear of an isotropic random magnetic field. The contrast in polarized intensity is significantly smaller than that expected from compression and shearing of the regular magnetic field; this could be the result of decoupling of the regular field from the dense molecular clouds. The regular field in the ridge is probably strong enough to reduce significantly shear in the diffuse gas (to which it is coupled) and hence to reduce magnetic field amplification by shearing. This contributes to the misalignment of the observed field orientation with respect to the velocity vectors of the dense gas. Our observations, for the first time, indicate that magnetic forces can control the flow of the diffuse interstellar gas at kiloparsec scales. The total radio intensity reaches its maximum in the circumnuclear starburst regions, where the equipartition field strength is about 60\mu G, amongst the strongest fields detected in spiral galaxies so far. The regular field in the inner region has a spiral shape with large pitch angle, indicating the action of a dynamo. Magnetic stress leads to mass inflow towards the centre, sufficient to feed the active nucleus in NGC 1097. We detected diffuse X-ray emission, possibly forming a halo of hot gas around NGC 1097.Comment: 32 pages with 45 PostScript figures. Accepted for publication in A&A; Typos corrected 12/10/200

Interstellar MHD Turbulence and Star Formation

This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic motions in the roughly isothermal cold atomic and molecular components. Within this context, we discuss: i) the production and statistical distribution of turbulent density fluctuations in both isothermal and polytropic media; ii) the nature of the clumps produced by thermal instability, noting that, contrary to classical ideas, they in general accrete mass from their environment; iii) the density-magnetic field correlation (or lack thereof) in turbulent density fluctuations, as a consequence of the superposition of the different wave modes in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio (MFR) in density fluctuations as they are built up by dynamic compressions; v) the formation of cold, dense clouds aided by thermal instability; vi) the expectation that star-forming molecular clouds are likely to be undergoing global gravitational contraction, rather than being near equilibrium, and vii) the regulation of the star formation rate (SFR) in such gravitationally contracting clouds by stellar feedback which, rather than keeping the clouds from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as per referee's recommendation

Radial Profiles of Star Formation in the Far Outer Regions of Galaxy Disks

Star formation in galaxies is triggered by a combination of processes, including gravitational instabilities, spiral wave shocks, stellar compression, and turbulence compression. Some of these persist in the far outer regions where the column density is far below the threshold for instabilities, making the outer disk cutoff somewhat gradual. We show that in a galaxy with a single exponential gas profile the star formation rate can have a double exponential with a shallow one in the inner part and a steep one in the outer part. Such double exponentials have been observed recently in the broad-band intensity profiles of spiral and dwarf Irregular galaxies. The break radius in our model occurs slightly outside the threshold for instabilities provided the Mach number for compressive motions remains of order unity to large radii. The ratio of the break radius to the inner exponential scale length increases for higher surface brightness disks because the unstable part extends further out. This is also in agreement with observations. Galaxies with extended outer gas disks that fall more slowly than a single exponential, such as 1/R, can have their star formation rate scale approximately as a single exponential with radius, even out to 10 disk scale lengths. Halpha profiles should drop much faster than the star formation rate as a result of the rapidly decreasing ambient density.Comment: To appear in ApJ. Available from ftp.lowell.edu/pub/dah/papers/sfouterdisks