Stochastic differential equations for evolutionary dynamics with demographic noise and mutations

We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, $\mu$, are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For $\mu N\ll1$ this limits the use of SDE's, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a Rock-Scissors-Paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review

Database management and analysis of fisheries in Illinois: Final report, 1 March 1999-28 February 2002

Issued May 2002; F-69-RReport issued on: May 200

The Nature of the Nuclear H2O Masers of NGC 1068: Reverberation and Evidence for a Rotating Disk Geometry

We report new (1995) Very Large Array observations and (1984 - 1999) Effelsberg 100m monitoring observations of the 22 GHz H2O maser spectrum of the Seyfert 2 galaxy NGC 1068. The sensitive VLA observations provide a registration of the 22 GHz continuum emission and the location of the maser spots with an accuracy of ~ 5 mas. Within the monitoring data, we find evidence that the nuclear masers vary coherently on time-scales of months to years, much more rapidly than the dynamical time-scale. We argue that the nuclear masers are responding in reverberation to a central power source, presumably the central engine. Between October and November 1997, we detected a simultaneous flare of the blue-shifted and red-shifted satellite maser lines. Reverberation in a rotating disk naturally explains the simultaneous flaring. There is also evidence that near-infrared emission from dust grains associated with the maser disk also responds to the central engine. We present a model in which an X-ray flare results in both the loss of maser signal in 1990 and the peak of the near-infrared light curve in 1994. In support of a rotating disk geometry for the nuclear masers, we find no evidence for centripetal accelerations of the redshifted nuclear masers; the limits are +/- 0.006 km/s/year, implying that the masers are located within 2 degrees of the kinematic line-of-nodes. We also searched for high velocity maser emission like that observed in NGC 4258. In both VLA and Effelsberg spectra, we detect no high velocity lines between +/- 350 km/s to +/- 850 km/s relative to systemic, arguing that masers only lie outside a radius of ~ 0.6 pc (1.9 light years) from the central engine (assuming a distance of 14.4 Mpc).Comment: 62 pages, 19 figure

The magnetic field of IRAS 16293-2422 as traced by shock-induced H2O masers

Shock-induced H2O masers are important magnetic field tracers at very high density gas. Water masers are found in both high- and low-mass star-forming regions, acting as a powerful tool to compare magnetic field morphologies in both mass regimes. In this paper, we show one of the first magnetic field determinations in the low-mass protostellar core IRAS 16293-2422 at volume densities as high as 10^(8-10) cm^-3. Our goal is to discern if the collapsing regime of this source is controlled by magnetic fields or other factors like turbulence. We used the Very Large Array (VLA) to carry out spectro-polarimetric observations in the 22 GHz Zeeman emission of H2O masers. From the Stokes V line profile, we can estimate the magnetic field strength in the dense regions around the protostar. A blend of at least three maser features can be inferred from our relatively high spatial resolution data set (~ 0.1"), which is reproduced in a clear non-Gaussian line profile. The emission is very stable in polarization fraction and position angle across the channels. The maser spots are aligned with some components of the complex outflow configuration of IRAS 16293-2422, and they are excited in zones of compressed gas produced by shocks. The post-shock particle density is in the range of 1-3 x 10^9 cm^-3, consistent with typical water masers pumping densities. Zeeman emission is produced by a very strong line-of-sight magnetic field (B ~ 113 mG). The magnetic field pressure derived from our data is comparable to the ram pressure of the outflow dynamics. This indicates that the magnetic field is energetically important in the dynamical evolution of IRAS 16293-2422.Comment: 7 pages, 6 figures, accepted for publication in A&

VLA+PT Astrometry of 46 Radio Stars

We have used the Very Large Array (VLA), linked with the Pie Town Very Long Baseline Array antenna, to determine astrometric positions of 46 radio stars in the International Celestial Reference Frame (ICRF). Positions were obtained in the ICRF directly through phase referencing of the stars to nearby ICRF quasars whose positions are accurate at the 0.25 mas level. Radio star positions are estimated to be accurate at the 10 mas level, with position errors approaching a few milli-arcseconds for some of the stars observed. Our measured positions were combined with previous measurements taken from as early as 1978 to obtain proper motion estimates for all 46 stars with average uncertainties of ~1.7 mas/yr. We compared our radio star positions and proper motions with the Hipparcos Catalogue data, and find consistency in the reference frames produced by each data set on the 1-sigma level, with errors of ~2.7 mas per axis for the reference frame orientation angles at our mean epoch of 2003.78. No significant spin is found between our radio data frame and the Hipparcos Celestial Reference Frame (HCRF) with largest rotation rates of +0.55 and -0.41 mas/yr around the x and z axes, respectively, with 1-sigma errors of 0.36 mas/yr. Thus, our results are consistent with a non-rotating Hipparcos frame with respect to the ICRF.Comment: 29 pages, 8 figures, accepted for publication in the Astronomical Journa

Subarcsecond mid-infrared and radio observations of the W3 IRS5 protocluster

Observations at mid-infrared (4.8-17.65 um) and radio (0.7-1.3 cm) wavelengths are used to constrain the structure of the high-mass star-forming region W3 IRS5 on 0.1'' (200 AU) scales. Two bright mid-infrared sources are detected, as well as diffuse emission. The bright sources have associated compact radio emission and probably are young high-mass stars. The measured sizes and estimated temperatures indicate that these sources together can supply the observed far-infrared luminosity. However, an optically thick radio source with a possible mid-infrared counterpart may also contribute significant luminosity; if so, it must be extremely deeply embedded. The infrared colour temperatures of 350-390 K and low radio brightness suggest gravitational confinement of the H II regions and ongoing accretion at a rate of a few 10^-8 M0/yr or more. Variations in the accretion rate would explain the observed radio variability. The low estimated foreground extinction suggests the existence of a cavity around the central stars, perhaps blown by stellar winds. At least three radio sources without mid-infrared counterparts appear to show proper motions of ~100 km/s, and may be deeply embedded young runaway OB stars, but more likely are clumps in the ambient material which are shock-ionized by the OB star winds.Comment: Accepted by A&A; 14 pages, 7 b/w figure

The Extreme Scattering Event Toward 1741-038: H I Absorption

We report multi-epoch VLA H I absorption observations of the source 1741-038 (OT-068) before and during an extreme scattering event (ESE). Observations at four epochs, three during the ESE, were obtained. We find no changes in the equivalent width, maximum optical depth, or velocity of maximum optical depth during the ESE, but we do find a secular trend of decreasing maximum optical depth between our observations and ones by other observers a decade prior. The resulting limit on the H I column density change during the ESE for a structure with a spin temperature T_s is 6.4 x 10^{17} cm^{-2} (T_s/10 K). Tiny-scale atomic structures (TSAS), with a column density N_H ~ 3 x 10^{18} cm^{-2}, are ruled out marginally by this limit, though geometric arguments may allow this limit to be relaxed. Galactic halo molecular clouds, that are opaque in the H I line, cannot be excluded because the observed velocity range covers only 25% of their allowed velocity range.Comment: 9 pages, LaTeX2e with AASTeX5.0; 4 PostScript figures in 4 files; accepted for publication in the ApJ, vol. 546, 2001 January

Polarization Observations of 1720 MHz OH Masers toward the Three Supernova Remnants W28, W44, and IC443

(abridged) - We present arcsecond resolution observations from the VLA of the satellite line of the hydroxyl molecule (OH) at 1720.53 MHz toward three Galactic supernova remnants: W28, W44 and IC443. All of our observations are consistent with a model in which the OH(1720 MHz) is collisionally excited by H2 molecules in the postshock gas heated by a non-dissociative shock. Supernova remnants with OH(1720 MHz) maser emission may be promising candidates to conduct high energy searches for the sites of cosmic ray acceleration.Comment: ApJ Let (accepted). Hardcopies available from [email protected]

Critical number of atoms in an attractive Bose-Einstein condensate on an optical plus harmonic traps

The stability of an attractive Bose-Einstein condensate on a joint one-dimensional optical lattice and an axially-symmetric harmonic trap is studied using the numerical solution of the time-dependent mean-field Gross-Pitaevskii equation and the critical number of atoms for a stable condensate is calculated. We also calculate this critical number of atoms in a double-well potential which is always greater than that in an axially-symmetric harmonic trap. The critical number of atoms in an optical trap can be made smaller or larger than the corresponding number in the absence of the optical trap by moving a node of the optical lattice potential along the axial direction of the harmonic trap. This variation of the critical number of atoms can be observed experimentally and compared with the present calculation.Comment: Latex with 7 eps figures, Accepted in Journal of Physics

High resolution radio observations of the colliding-wind binary WR140

Milli-arcsecond resolution Very Long Baseline Array (VLBA) observations of the archetype WR+O star colliding-wind binary (CWB) system WR140 are presented for 23 epochs between orbital phases 0.74 and 0.97. At 8.4 GHz, the emission in the wind-collision region (WCR) is clearly resolved as a bow-shaped arc that rotates as the orbit progresses. We interpret this rotation as due to the O star moving from SE to approximately E of the WR star, which leads to solutions for the orbit inclination of 122+/-5 deg, the longitude of the ascending node of 353+/-3 deg, and an orbit semi-major axis of 9.0+/-0.5 mas. The distance to WR140 is determined to be 1.85+/-0.16 kpc, which requires the O star to be a supergiant. The inclination implies the mass of the WR and O star to be 20+/-4 and 54+/-10 solar masses respectively. We determine a wind-momentum ratio of 0.22, with an expected half-opening angle for the WCR of 63 deg, consistent with 65+/-10 deg derived from the VLBA observations. Total flux measurements from Very Large Array (VLA) observations show the radio emission from WR140 is very closely the same from one orbit to the next, pointing strongly toward emission, absorption and cooling mechanism(s) that are controlled largely by the orbital motion. The synchrotron spectra evolve dramatically through the orbital phases observed, exhibiting both optically thin and optically thick emission. We discuss a number of absorption and cooling mechanisms that may determine the evolution of the synchrotron spectrum with orbital phase.Comment: Accepted by ApJ, to appear in v623, April 20, 2005. 14 pages, 13 figs, requires emulateapj.cls. A version with full resolution figs can be obtained from http://www.drao.nrc.ca/~smd/preprint/wr140_data.pd