Microlensing in phase space II: Correlations analysis

Applications of the phase space approach to the calculation of the microlensing autocorrelation function are presented. The continuous propagation equation for a random star field with a Gaussian velocity distribution is solved in the leading non-trivial approximation using the perturbation technique. It is shown that microlensing modulations can be important in the interpretation of optical and shorter-wavelength light curves of pulsars, power spectra of active galactic nuclei and coherence estimates for quasi-periodic oscillations of dwarf novae and low-mass X-ray binaries. Extra scatter in the brightness of type Ia supernovae due to gravitational microlensing is shown to be of order up to 0.2 stellar magnitudes depending on the extent of the light curves.Comment: Accepted for publication in MNRAS. 17 pages, 8 figures. The first part of this little series is available at http://www.arxiv.org/abs/astro-ph/0604302 . Replaced to add a link to the first par

Identification of Very Red Counterparts of SiO Maser and OH/IR Objects in the GLIMPSE Survey

Using the 3.6/4.5/5.8/8.0 micron images with 1.2 arcsec pixel resolution from the Spitzer/GLIMPSE survey, we investigated 23 masing and 18 very red objects that were not identified in the 2MASS survey. Counterparts for all selected objects were found in the GLIMPSE images. Color indices in these IR bands suggest the presence of a high-extinction layer of more than a few tenths of a solar mass in front of the central star. Furthermore, radio observations in the SiO and H2O maser lines found characteristic maser-line spectra of the embedded objects, e.g., the SiO J=1-0 line intensity in the v=2 state stronger than that of the v=1 state, or very widespread H2O maser emission spectra. This indicates that these objects are actually enshrouded by very thick circumstellar matter, some of which cannot be ascribed to the AGB wind of the central star. Individually interesting objects are discussed, including two newly found water fountains and an SiO source with nebulosity.Comment: High resolution figures available at ftp://ftp.nro.nao.ac.jp/nroreport/no653.pdf.gz. ApJ No. 655 no.1 issue in pres

Correlation between Infrared Colors and Intensity Ratios of SiO Maser Lines

We present the results of SiO millimeter-line observations of a sample of known SiO maser sources covering a wide dust-temperature range. A cold part of the sample was selected from the SiO maser sources found in our recent SiO maser survey of cold dusty objects. The aim of the present research is to investigate the causes of the correlation between infrared colors and SiO maser intensity ratios among different transition lines. In particular, the correlation between infrared colors and SiO maser intensity ratio among the J=1-0 v=1, 2, and 3 lines are mainly concerned in this paper. We observed in total 75 SiO maser sources with the Nobeyama 45m telescope quasi-simultaneously in the SiO J=1-0 v=0, 1, 2, 3, 4 and J=2-1 v=1, 2 lines. We also observed the sample in the 29SiO J=1-0 v=0 and J=2-1 v=0, and 30SiO J=1-0 v=0 lines, and the H2O 6(1,6)-5(2,3) line. As reported in previous papers, we confirmed that the intensity ratios of the SiO J=1-0 v=2 to v=1 lines clearly correlate with infrared colors. In addition, we found possible correlation between infrared colors and the intensity ratios of the SiO J=1-0 v=3 to v=1&2 lines. Two overlap lines of H2O (i.e., 11(6,6) nu_2=1 -> 12(7,5) nu_2=0 and 5(0,5) nu_2=2 -> 6(3,4) nu_2=1) might explain these correlation if these overlap lines become stronger with increase of infrared colors, although the phenomena also might be explained by more fundamental ways if we take into account the variation of opacity from object to object.Comment: 49 pages, 7 figures, 3 tables, accepted for publication in ApJ. Full resolution version available at http://www.asiaa.sinica.edu.tw/~junichi/paper

On the Dominance of Trivial Knots among SAPs on a Cubic Lattice

The knotting probability is defined by the probability with which an $N$-step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as a function of $N$. In particular the characteristic length of the trivial knot that corresponds to a `half-life' of the knotting probability is estimated to be $2.5 \times 10^5$ on the cubic lattice.Comment: LaTeX2e, 21 pages, 8 figur

Topological entropy of a stiff ring polymer and its connection to DNA knots

We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula as a function of the thickness and length of the circular chain. The result is consistent with the viewpoint that for stiff polymers such as DNAs, the length and diameter of the chains should play a central role in their statistical and dynamical properties. Furthermore, we show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure

Microlensing in phase space I: Continuous propagation of variability moments

A method to calculate the statistical properties of microlensing light curves is developed. The approach follows works by Deguchi & Watson, Seitz & Schneider and Neindorf, attempting to clarify the ideas involved and techniques used in the calculations. The method is then modified to include scattering by multiple lensing planes along the line of sight and transition to a continuous limit of this treatment for average quantities is performed leading to a Fokker-Planck type equation. The equation is solved for a particular model of the random star field and microlensing effect on the flux temporal variability is extracted. Applications in astrophysically relevant situations are discussed.Comment: Accepted for publication in MNRAS. 15 pages, 4 figures. The second part of this little series is available at http://www.arxiv.org/abs/astro-ph/060419

Detection of Vibrationally Excited CO in IRC+10216

Using the Submillimeter Array we have detected the J=3-2 and 2-1 rotational transitions from within the first vibrationally excited state of CO toward the extreme carbon star IRC+10216 (CW Leo). The emission remains spatially unresolved with an angular resolution of ~2" and, given that the lines originate from energy levels that are ~3100 K above the ground state, almost certainly originates from a much smaller (~10^{14} cm) sized region close to the stellar photosphere. Thermal excitation of the lines requires a gas density of ~10^{9} cm^{-3}, about an order of magnitude higher than the expected gas density based previous infrared observations and models of the inner dust shell of IRC+10216.Comment: Accepted for publication in ApJ Letter

Magnetic susceptibility and low-temperature specific-heat of integrable 1-D Hubbard model under open-boundary conditions

The magnetic susceptibility and the low-temperature specific heat of the 1-dimensional Hubbard model under the integrable open-boundary conditions are discussed through the Bethe ansatz with the string hypothesis. The contributions of the boundary fields to both the susceptibility and the specific heat are obtained, and their exact expressions are analytically derived.Comment: 14 pages, Latex, No figures, to appear in J. Phys. A: Gen. & Mat

The emergence of localized vortex-wave interaction states in plane Couette flow

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall &amp; Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2}$ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall &amp; Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.</jats:p