Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

Nonlinear Alfvén waves, discontinuities, proton perpendicular acceleration, and magnetic holes/decreases in interplanetary space and the magnetosphere: intermediate shocks?

International audienceAlfvén waves, discontinuities, proton perpendicular acceleration and magnetic decreases (MDs) in interplanetary space are shown to be interrelated. Discontinuities are the phase-steepened edges of Alfvén waves. Magnetic decreases are caused by a diamagnetic effect from perpendicularly accelerated (to the magnetic field) protons. The ion acceleration is associated with the dissipation of phase-steepened Alfvén waves, presumably through the Ponderomotive Force. Proton perpendicular heating, through instabilities, lead to the generation of both proton cyclotron waves and mirror mode structures. Electromagnetic and electrostatic electron waves are detected as well. The Alfvén waves are thus found to be both dispersive and dissipative, conditions indicting that they may be intermediate shocks. The resultant "turbulence" created by the Alfvén wave dissipation is quite complex. There are both propagating (waves) and nonpropagating (mirror mode structures and MDs) byproducts. Arguments are presented to indicate that similar processes associated with Alfvén waves are occurring in the magnetosphere. In the magnetosphere, the "turbulence" is even further complicated by the damping of obliquely propagating proton cyclotron waves and the formation of electron holes, a form of solitary waves. Interplanetary Alfvén waves are shown to rapidly phase-steepen at a distance of 1AU from the Sun. A steepening rate of ~35 times per wavelength is indicated by Cluster-ACE measurements. Interplanetary (reverse) shock compression of Alfvén waves is noted to cause the rapid formation of MDs on the sunward side of corotating interaction regions (CIRs). Although much has been learned about the Alfvén wave phase-steepening processfrom space plasma observations, many facets are still not understood. Several of these topics are discussed for the interested researcher. Computer simulations and theoretical developments will be particularly useful in making further progress in this exciting new area

High resolution infrared spectra of bulge globular clusters: Liller~1 and NGC 6553

Using the NIRSPEC spectrograph at Keck II, we have obtained echelle spectra covering the range 1.5-1.8um for 2 of the brightest giants in Liller 1 and NGC 6553, old metal rich globular clusters in the Galactic bulge. We use spectrum synthesis for the abundance analysis, and find [Fe/H]=-0.3 +/- 0.2 and [O/H]=+0.3 +/- 0.2 dex. The composition of the clusters is similar to that of field stars in the bulge and is consistent with a sceanrio in which the clusters formed early, with rapid enrichment. We have dificulty achieveing a good fit to the spectrum of NGC 6553 using either the low or the high values recently reported in the literature, unless unusually large, or no alpha-element enhancements are adopted, respectively.Comment: To appear in the Astronomical Journal, March 200

The Temperature Scale of Metal-Rich M Giants Based on TiO Bands: Population Synthesis in the Near Infrared

We have computed a grid of high resolution synthetic spectra for cool stars (2500<Teff<6000 K) in the wavelength range 6000 -- 10200A, by employing an updated line list of atomic and molecular lines, together with state-of-the-art model atmospheres. As a by-product, by fitting TiO bandheads in spectra of well-known M giants, we have derived the electronic oscillator strengths of the TiO gamma prime, delta, epsilon and phi systems. The derived oscillator strenghts for the gamma prime, epsilon and phi systems differ from the laboratory and ab initio values found in the literature, but are consistent with the model atmospheres and line lists employed, resulting in a good match to the observed spectra of M giants of known parameters. The behavior of TiO bands as a function of the stellar parameters Teff, log g and [Fe/H] is presented and the use of TiO spectral indices in stellar population studies is discussed.Comment: ApJ accepted, 27 pages + 11 figures, AASLatex v4.

Near-infrared Spectral Features in Single-aged Stellar Populations

Synthetic spectra for single-aged stellar populations of metallicities [M/H] = -0.5, 0.0 and +0.5, ages = 3 to 17 Gyrs, and initial mass function exponents x = 0.1 to 2.0 were built in the wavelength range 6000-10200 Angstrons. For such we have employed the grid of synthetic spectra described in Schiavon & Barbuy (1999), computed for the stellar parameters 2500 <= Teff <= 6000 K, -0.5 <= log g <= 5.0, [M/H] = -0.5, 0.0 and +0.5, and [alpha/Fe] = 0.0, together with the isochrones by Bertelli et al. (1994) and Baraffe et al. (1998). The behavior of the features NaI8190, CaII8662, TiO6600 and FeH9900 in the integrated spectra of single stellar populations were studied in terms of metallicity, initial mass function and age variations. The main conclusions are that the NaI doublet is an IMF-sensitive feature, which is however sensitive also to metallicity and age, whereas TiO, CaII and FeH are very sensitive to metallicity and essentially insensitive to IMF and age.Comment: 13 pages + 7 figures, ApJ accepte

DIGITAL 3D RECONSTRUCTION OF SCROVEGNI CHAPEL WITH MULTIPLE TECHNIQUES

The use of 3D digitization and modeling in documenting heritage sites has increased significantly over the past few years. This is mainly due to advances in laser scanning techniques, 3D modeling software, image-based-modeling techniques, computer power, and virtual reality. There are many approaches currently available. The most common remains based on surveying and CAD tools and/or traditional photogrammetry with control points and a human operator. This is very time consuming and can be tedious and lingering effort. Lately, modeling methods based on laser scanners data and more automated image-based techniques are becoming available. Initially, the goal of this work was to discuss advantages and disadvantages of those 3D modeling techniques applied to a cultural heritage building, i.e. the Scrovegni chapel in Padova, Italy, by comparing the geometry and visual quality of related models for asbuilt documentation, restoration and interactive visualization purposes. To this aim the chapel was imaged with a color digital camera and surveyed with both different kind of laser scanners and traditional topographic instrument. Unfortunately due to the long time wasted before all requested laser scanners were available from the dealers and difficulties encountered during the subsequent 3D modeling, due to the bad quality of some range data, at the present date only the range data model is available. Therefore in this paper we will discuss only the results obtained by generating a unique 3D model of the Scrovegni Chapel using four different laser scanners: Cyrax 2500, Mensi GS 100, Optech ILRIS 3D and Riegl LMS-Z210. In order to assess the performance of these sensors when applied for cultural heritage survey, data quality, geometric accuracy, sensor noise, ease of use, speed of data collection, will be the topics of this work. 1

The Nature of the Halo Population of NGC 5128 Resolved with NICMOS on the Hubble Space Telescope

We present the first infrared color-magnitude diagram (CMD) for the halo of a giant elliptical galaxy. The CMD for the stars in the halo of NGC 5128 (Centaurus A) was constructed from HST NICMOS observations of the WFPC2 CHIP-3 field of Soria et al. (1996) to a 50% completeness magnitude limit of [F160W]=23.8. This field is located at a distance of 08'50" (~9 kpc) south of the center of the galaxy. The luminosity function (LF) shows a marked discontinuity at [F160W]=20.0. This is 1-2 mag above the tip of the red giant branch (TRGB) expected for an old population (~12 Gyr) at the distance modulus of NGC 5128. We propose that the majority of stars above the TRGB have intermediate ages (~2 Gyr), in agreement with the WFPC2 observations of Soria et al. (1996). Five stars with magnitudes brighter than the LF discontinuity are most probably due to Galactic contamination. The weighted average of the mean giant branch color above our 50% completeness limit is [F110W]-[F160W]=1.22+-0.08 with a dispersion of 0.19 mag. From our artificial-star experiments we determine that the observed spread in color is real, suggesting a real spread in metallicity. We estimate the lower and upper bounds of the stellar metallicity range by comparisons with observations of Galactic star clusters and theoretical isochrones. Assuming an old population, we find that, in the halo field of NGC 5128 we surveyed, stars have metallicities ranging from roughly 1% of solar at the blue end of the color spread to roughly solar at the red end, with a mean of [Fe/H]=-0.76 and a dispersion of 0.44 dex.Comment: Accepted for publication in AJ, 23 pages of text, 13 figures, uses aastex v5.

An Abundance Analysis for Five Red Horizontal Branch Stars in the Extremely Metal Rich Globular Cluster NGC 6553

We provide a high dispersion line-by-line abundance analysis of five red HB stars in the extremely metal rich galactic globular cluster NGC 6553. These red HB stars are significantly hotter than the very cool stars near the tip of the giant branch in such a metal rich globular cluster and hence their spectra are much more amenable to an abundance analysis than would be the case for red giants. We find that the mean [Fe/H] for NGC 6553 is -0.16 dex, comparable to the mean abundance in the galactic bulge found by McWilliam & Rich (1994) and considerably higher than that obtained from an analysis of two red giants in this cluster by Barbuy etal (1999). The relative abundance for the best determined alpha process element (Ca) indicates an excess of alpha process elements of about a factor of two. The metallicity of NGC 6553 reaches the average of the Galactic bulge and of the solar neighborhood.Comment: 29 pages, 6 figures, accepted for publication in the Ap