The Sizes of 1720 MHz OH Masers: VLBA and MERLIN Observations of the Supernova Remnants W44 and W28

We have used the NRAO Very Long Baseline Array (VLBA) to image OH(1720 MHz) masers in the supernova remnants W28 and W44 at a resolution of 40 mas. We also used MERLIN to observe the same OH(1720 MHz) masers in W44 at a resolution of 290 x 165 mas. All the masers are resolved by these VLBA and MERLIN observations. The measured sizes range from 50 to 180 mas and yield brightness temperature estimates from 0.3--20 x 10**8 K. We investigate whether these measured angular sizes are intrinsic and hence originate as a result of the physical conditions in the supernova remnant shock, or whether they are scatter broadened sizes produced by the turbulent ionized gas along the line of sight. While the current data on the temporal and angular broadening of pulsars, masers and extragalactic soures toward W44 and W28 can be understood in terms of scattering, we cannot rule out that these large sizes are intrinsic. Recent theoretical modeling by Lockett et al. suggests that the physical parameters in the shocked region are indicative of densities and OH abundances which lead to estimates of sizes as large as what we measure. If the sizes and structure are intrinsic, then the OH(1720 MHz) masrs may be more like the OH(1612 MHz) masers in circumstellar shells than OH masers associated with HII regions. At two locations in W28 we observe the classical S-shapes in the Stokes V profiles caused by Zeeman splitting and use it to infer magnetic fields of order 2 milliGauss.Comment: 24 pages, 6 figures, accepted by Ap

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

1/fα1/f^\alpha spectra in elementary cellular automata and fractal signals

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays $1/f$ spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no $1/f$ spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce $1/f^{\alpha}$ spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics and computer sciences, there are various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included

OH (1720 MHz) Masers: A Multiwavelength Study of the Interaction between the W51C Supernova Remnant and the W51B Star Forming Region

We present a comprehensive view of the W51B HII region complex and the W51C supernova remnant (SNR) using new radio observations from the VLA, VLBA, MERLIN, JCMT, and CSO along with archival data from Spitzer, ROSAT, ASCA, and Chandra. Our VLA data include the first 400 cm (74 MHz) continuum image of W51 at high resolution (88 arcsec). The 400 cm image shows non-thermal emission surrounding the G49.2-0.3 HII region, and a compact source of non-thermal emission (W51B_NT) coincident with the previously-identified OH (1720 MHz) maser spots, non-thermal 21 and 90 cm emission, and a hard X-ray source. W51B_NT falls within the region of high likelihood for the position of TeV gamma-ray emission. Using the VLBA three OH (1720 MHz) maser spots are detected in the vicinity of W51B_NT with sizes of 60 to 300 AU and Zeeman effect magnetic field strengths of 1.5 to 2.2 mG. The multiwavelength data demonstrate that the northern end of the W51B HII region complex has been partly enveloped by the advancing W51C SNR and this interaction explains the presence of W51B_NT and the OH masers. This interaction also appears in the thermal molecular gas which partially encircles W51B_NT and exhibits narrow pre-shock (DeltaV 5 km/s) and broad post-shock (DeltaV 20 km/s) velocity components. RADEX radiative transfer modeling of these two components yield physical conditions consistent with the passage of a non-dissociative C-type shock. Confirmation of the W51B/W51C interaction provides additional evidence in favor of this region being one of the best candidates for hadronic particle acceleration known thus far.Comment: Accepted to Ap

Nongaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process

The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature (London) 428, 646 (2004)] defines a promising standard model of evolutionary game theory in finite populations for which analytical results are accessible. In this paper, we derive the stationary distribution of the Moran process population dynamics for arbitrary $2\times{}2$ games for the finite size case. We show that a nonvanishing background fitness can be transformed to the vanishing case by rescaling the payoff matrix. In contrast to the common approach to mimic finite-size fluctuations by Gaussian distributed noise, the finite size fluctuations can deviate significantly from a Gaussian distribution.Comment: 4 pages (2 figs). Published in Physical Review E (Rapid Communications

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

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