An interesting example for spectral invariants

In "Illinois J. of Math. {\bf 38} (1994) 653--678", the heat operator of a Bismut superconnection for a family of generalized Dirac operators is defined along the leaves of a foliation with Hausdorff groupoid. The Novikov-Shubin invariants of the Dirac operators were assumed greater than three times the codimension of the foliation. It was then showed that the associated heat operator converges to the Chern character of the index bundle of the operator. In "J. K-Theory {\bf 1} (2008) 305--356", we improved this result by reducing the requirement on the Novikov-Shubin invariants to one half of the codimension. In this paper, we construct examples which show that this is the best possible result.Comment: Third author added. Some typos corrected and some material added. Appeared in Journal of K Theory, Volume 13, in 2014, pages 305 to 31

Magnetized Non-linear Thin Shell Instability: Numerical Studies in 2D

We revisit the analysis of the Non-linear Thin Shell Instability (NTSI) numerically, including magnetic fields. The magnetic tension force is expected to work against the main driver of the NTSI -- namely transverse momentum transport. However, depending on the field strength and orientation, the instability may grow. For fields aligned with the inflow, we find that the NTSI is suppressed only when the Alfv\'en speed surpasses the (supersonic) velocities generated along the collision interface. Even for fields perpendicular to the inflow, which are the most effective at preventing the NTSI from developing, internal structures form within the expanding slab interface, probably leading to fragmentation in the presence of self-gravity or thermal instabilities. High Reynolds numbers result in local turbulence within the perturbed slab, which in turn triggers reconnection and dissipation of the excess magnetic flux. We find that when the magnetic field is initially aligned with the flow, there exists a (weak) correlation between field strength and gas density. However, for transverse fields, this correlation essentially vanishes. In light of these results, our general conclusion is that instabilities are unlikely to be erased unless the magnetic energy in clouds is much larger than the turbulent energy. Finally, while our study is motivated by the scenario of molecular cloud formation in colliding flows, our results span a larger range of applicability, from supernovae shells to colliding stellar winds.Comment: 12 pages, 17 figures, some of them at low resolution. Submitted to ApJ, comments welcom

2MASS Studies of Differential Reddening Across Three Massive Globular Clusters

J, H, and K_S band data from the Two Micron All-Sky Survey (2MASS) are used to study the effects of differential reddening across the three massive Galactic globular clusters Omega Centauri, NGC 6388, and NGC 6441. Evidence is found that variable extinction may produce false detections of tidal tails around Omega Centauri. We also investigate what appears to be relatively strong differential reddening towards NGC 6388 and NGC 6441, and find that differential extinction may be exaggerating the need for a metallicity spread to explain the width of the red giant branches for these two clusters. Finally, we consider the implications of these results for the connection between unusual, multipopulation globular clusters and the cores of dwarf spheroidal galaxies (dSph).Comment: 40 pages, 14 figures. Accepted for publication in Oct. 2003 A

An ammonia spectral map of the L1495-B218 filaments in the Taurus molecular cloud. I. Physical properties of filaments and dense cores

We present deep NH3 observations of the L1495-B218 filaments in the Taurus molecular cloud covering over a 3° angular range using the K-band focal plane array on the 100 m Green Bank Telescope. The L1495-B218 filaments form an interconnected, nearby, large complex extending over 8 pc. We observed NH3 (1, 1) and (2, 2) with a spectral resolution of 0.038 km s−1 and a spatial resolution of 31''. Most of the ammonia peaks coincide with intensity peaks in dust continuum maps at 350 and 500 μm. We deduced physical properties by fitting a model to the observed spectra. We find gas kinetic temperatures of 8–15 K, velocity dispersions of 0.05–0.25 km s−1, and NH3 column densities of 5 × 1012 to 1 × 1014 cm−2. The CSAR algorithm, which is a hybrid of seeded-watershed and binary dendrogram algorithms, identifies a total of 55 NH3 structures, including 39 leaves and 16 branches. The masses of the NH3 sources range from 0.05 to 9.5 ${{M}_{\odot }}$. The masses of NH3 leaves are mostly smaller than their corresponding virial mass estimated from their internal and gravitational energies, which suggests that these leaves are gravitationally unbound structures. Nine out of 39 NH3 leaves are gravitationally bound, and seven out of nine gravitationally bound NH3 leaves are associated with star formation. We also found that 12 out of 30 gravitationally unbound leaves are pressure confined. Our data suggest that a dense core may form as a pressure-confined structure, evolve to a gravitationally bound core, and undergo collapse to form a protostar

Magnetic Fields in Large Diameter HII Regions Revealed by the Faraday Rotation of Compact Extragalactic Radio Sources

We present a study of the line-of-sight magnetic fields in five large-diameter Galactic HII regions. Using the Faraday rotation of background polarized radio sources, as well as dust-corrected H-alpha surface brightness as a probe of electron density, we estimated the strength and orientation of the magnetic field along 93 individual sight-lines through the HII regions. Each of the HII regions displayed a coherent magnetic field. The magnetic field strength (line-of-sight component) in the regions ranges from 2 to 6 microgauss, which is similar to the typical magnetic field strength in the diffuse interstellar medium. We investigated the relationship between magnetic field strength and electron density in the 5 HII regions. The slope of magnetic field vs. density in the low-density regime (0.8 < n_e < 30 per cubic cm) is very slightly above zero. We also calculated the ratio of thermal to magnetic pressure, beta_th, for each data point, which fell in the range 1.01 < beta_th < 25. Finally, we studied the orientation of the magnetic field in the solar neighborhood (d < 1.1 kpc) using our data from 5 HII regions along with existing measurements of the line-of-sight magnetic field strength from polarized pulsars whose distances have been determined from their annual parallax. We identify a net direction for the magnetic field in the solar neighborhood, but find no evidence for a preferred vertical direction of the magnetic field above or below the Galactic plane.Comment: Accepted to the Astrophysical Journal, June 4th 201

Giant Molecular clouds: what are they made from, and how do they get there?

We analyse the results of four simulations of isolated galaxies: two with a rigid spiral potential of fixed pattern speed, but with different degrees of star-formation induced feedback, one with an axisymmetric galactic potential and one with a `live' self-gravitating stellar component. Since we use a Lagrangian method we are able to select gas that lies within giant molecular clouds (GMCs) at a particular timeframe, and to then study the properties of this gas at earlier and later times. We find that gas which forms GMCs is not typical of the interstellar medium at least 50 Myr before the clouds form and reaches mean densities within an order of magnitude of mean cloud densities by around 10 Myr before. The gas in GMCs takes at least 50 Myr to return to typical ISM gas after dispersal by stellar feedback, and in some cases the gas is never fully recycled. We also present a study of the two-dimensional, vertically-averaged velocity fields within the ISM. We show that the velocity fields corresponding to the shortest timescales (that is, those timescales closest to the immediate formation and dissipation of the clouds) can be readily understood in terms of the various cloud formation and dissipation mechanisms. Properties of the flow patterns can be used to distinguish the processes which drive converging flows (e.g.\ spiral shocks, supernovae) and thus molecular cloud formation, and we note that such properties may be detectable with future observations of nearby galaxies.Comment: 13 pages, 8 figures, accepted for publication in MNRA

Gas Accretion is Dominated by Warm Ionized Gas in Milky Way-Mass Galaxies at z ~ 0

We perform high-resolution hydrodynamic simulations of a Milky Way-mass galaxy in a fully cosmological setting using the adaptive mesh refinement code, Enzo, and study the kinematics of gas in the simulated galactic halo. We find that the gas inflow occurs mostly along filamentary structures in the halo. The warm-hot (10^5 K 10^6 K) ionized gases are found to dominate the overall mass accretion in the system (with dM/dt = 3-5 M_solar/yr) over a large range of distances, extending from the virial radius to the vicinity of the disk. Most of the inflowing gas (by mass) does not cool, and the small fraction that manages to cool does so primarily close to the galaxy (R <~ 20 kpc), perhaps comprising the neutral gas that may be detectable as, e.g., high-velocity clouds. The neutral clouds are embedded within larger, accreting filamentary flows, and represent only a small fraction of the total mass inflow rate. The inflowing gas has relatively low metallicity (Z/Z_solar < 0.2). The outer layers of the filamentary inflows are heated due to compression as they approach the disk. In addition to the inflow, we find high-velocity, metal-enriched outflows of hot gas driven by supernova feedback. Our results are consistent with observations of halo gas at low z.Comment: 10 pages including 5 figures, submitted to Ap

Turbulent Control of the Star Formation Efficiency

Supersonic turbulence plays a dual role in molecular clouds: On one hand, it contributes to the global support of the clouds, while on the other it promotes the formation of small-scale density fluctuations, identifiable with clumps and cores. Within these, the local Jeans length \Ljc is reduced, and collapse ensues if \Ljc becomes smaller than the clump size and the magnetic support is insufficient (i.e., the core is ``magnetically supercritical''); otherwise, the clumps do not collapse and are expected to re-expand and disperse on a few free-fall times. This case may correspond to a fraction of the observed starless cores. The star formation efficiency (SFE, the fraction of the cloud's mass that ends up in collapsed objects) is smaller than unity because the mass contained in collapsing clumps is smaller than the total cloud mass. However, in non-magnetic numerical simulations with realistic Mach numbers and turbulence driving scales, the SFE is still larger than observational estimates. The presence of a magnetic field, even if magnetically supercritical, appears to further reduce the SFE, but by reducing the probability of core formation rather than by delaying the collapse of individual cores, as was formerly thought. Precise quantification of these effects as a function of global cloud parameters is still needed.Comment: Invited review for the conference "IMF@50: the Initial Mass Function 50 Years Later", to be published by Kluwer Academic Publishers, eds. E. Corbelli, F. Palla, and H. Zinnecke

Thermochemistry of Alane Complexes for Hydrogen Storage: A Theoretical and Experimental Comparison

Knowledge of the relative stabilities of alane (AlH3) complexes with electron donors is essential for identifying hydrogen storage materials for vehicular applications that can be regenerated by off-board methods; however, almost no thermodynamic data are available to make this assessment. To fill this gap, we employed the G4(MP2) method to determine heats of formation, entropies, and Gibbs free energies of formation for thirty-eight alane complexes with NH3-nRn (R = Me, Et; n = 0-3), pyridine, pyrazine, triethylenediamine (TEDA), quinuclidine, OH2-nRn (R = Me, Et; n = 0-2), dioxane, and tetrahydrofuran (THF). Monomer, bis, and selected dimer complex geometries were considered. Using these data, we computed the thermodynamics of the key formation and dehydrogenation reactions that would occur during hydrogen delivery and alane regeneration, from which trends in complex stability were identified. These predictions were tested by synthesizing six amine-alane complexes involving trimethylamine, triethylamine, dimethylethylamine, TEDA, quinuclidine, and hexamine, and obtaining upper limits of delta G for their formation from metallic aluminum. Combining these computational and experimental results, we establish a criterion for complex stability relevant to hydrogen storage that can be used to assess potential ligands prior to attempting synthesis of the alane complex. Based on this, we conclude that only a subset of the tertiary amine complexes considered and none of the ether complexes can be successfully formed by direct reaction with aluminum and regenerated in an alane-based hydrogen storage system.Comment: Accepted by the Journal of Physical Chemistry

The Frequency of Mid-Infrared Excess Sources in Galactic Surveys

We have identified 230 Tycho-2 Spectral Catalog stars that exhibit 8 micron mid-infrared extraphotospheric excesses in the MidCourse Space Experiment (MSX) and Spitzer Space Telescope Galactic Legacy MidPlane Survey Extraordinaire (GLIMPSE) surveys. Of these, 183 are either OB stars earlier than B8 in which the excess plausibly arises from a thermal bremsstrahlung component or evolved stars in which the excess may be explained by an atmospheric dust component. The remaining 47 stars have spectral classifications B8 or later and appear to be main sequence or late pre-main-sequence objects harboring circumstellar disks. Six of the 47 stars exhibit multiple signatures characteristic of pre-main-sequence circumstellar disks, including emission lines, near-infrared K-band excesses, and X-ray emission. Approximately one-third of the remaining 41 sources have emission lines suggesting relative youth. Of the 25 GLIMPSE stars with SST data at >24 microns, 20 also show an excess at 24 microns. Three additional objects have 24 micron upper limits consistent with possible excesses, and two objects have photospheric measurements at 24 microns. Six MSX sources had a measurement at wavelengths >8 microns. We modeled the excesses in 26 stars having two or more measurements in excess of the expected photospheres as single-component blackbodies. We determine probable disk temperatures and fractional infrared luminosities in the range 191 < T < 787 and 3.9x10^-4 < L_IR/L_* < 2.7x10^-1. We estimate a lower limit on the fraction of Tycho-2 Spectral Catalog main-sequence stars having mid-IR, but not near-IR, excesses to be 1.0+-0.3%.Comment: Accepted to Ap