Bipolar Expansion Research Articles

Kinematic properties and ages of extended fast, neutral gas around η Carinae: tracing the pre-eruption bipolar wind

ABSTRACT We present proper-motion measurements and long-slit spectroscopy of the Mg ii nebula around η Carinae obtained with the Wide Field Camera 3 and Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope. Detailed kinematics of the Mg ii-emitting material constrain the geometry and history of mass-loss from η Car, and provide estimated ejection dates, assuming linear, ballistic motions. These measurements show that the neutral gas immediately outside the Homunculus – i.e. material into which the Homunculus is now expanding – was expelled over several decades prior to the Great Eruption, thus representing unshocked pre-eruption stellar wind. Material outside the Homunculus is therefore not part of a Hubble-like flow from the Great Eruption itself. This result discriminates between versions of merger-in-a-triple models for η Car. The STIS spectrum of Mg ii-emitting gas along the projected outflow axis displays radial velocities consistent with bipolar expansion, redshifted several hundred km s−1 towards the northwest, similarly blueshifted towards the southeast, and with low internal velocity dispersion. The η Car system was therefore losing mass in a relatively fast, low-density polar wind for several decades that probably traces the critical inspiral phase preceding a merger event.

Paleoecology and evolutionary response of planktonic foraminifera to the mid-Pliocene Warm Period and Plio-Pleistocene bipolar ice sheet expansion

Abstract. The Pliocene-Recent is associated with many important climatic and paleoceanographic changes, which have shaped the biotic and abiotic nature of the modern world. The closure of the Central American Seaway and the development and intensification of Northern Hemisphere ice sheets had profound global impacts on the latitudinal and vertical structure of the oceans, triggering the extinction and radiation of many marine groups. In particular, marine calcifying planktonic foraminifera, which are highly sensitive to water column structure, exhibited a series of extinctions as global temperatures fell. By analyzing high-resolution (∼ 5 kyr) sedimentary records from the Eastern Equatorial Pacific Ocean, complemented with global records from the novel Triton dataset, we document the biotic changes in this microfossil group, within which three species displayed isochronous co-extinction, and species with cold-water affinity increased in dominance as meridional temperature gradients steepened. We suggest that these changes were associated with the terminal stages of the closure of the Central American Seaway, where following the sustained warmth of the mid-Pliocene Warm Period, bipolar ice sheet expansion initiated a world in which cold- and deep-dwelling species became increasingly more successful. Such global-scale paleoecological and macroevolutionary variations between the Pliocene and the modern icehouse climate would suggest significant deviations from pre-industrial baselines within modern and future marine plankton communities as anthropogenic climate forcing continues.

Numerical solution of bipolar fuzzy initial value problem

Differential equations occur in many fields of science, engineering and social science as it is a natural way of modeling uncertain dynamical systems. A bipolar fuzzy set model is useful mathematical tool for addressing uncertainty which is an extension of fuzzy set model. In this paper, we study differential equations in bipolar fuzzy environment. We introduce the concept gH-derivative of bipolar fuzzy valued function. We present some properties of gH-differentiability of bipolar fuzzy valued function by considering different types of differentiability. We consider bipolar fuzzy Taylor expansion. By using Taylor expansion, Euler method is presented for solving bipolar fuzzy initial value problems. We discuss convergence analysis of proposed method. We describe some numerical examples to see the convergence and stability of the method and compute global truncation error. From numerical results, we see that for small step size Euler method converges to exact solution.

Spatial and Temporal Variations of Particulate Organic Carbon Sinking Flux in Global Ocean from 2003 to 2018

The monitoring of particulate organic carbon (POC) flux at the bottom of the euphotic layer in global ocean using remote sensing satellite data plays an important role in clarifying and evaluating the ocean carbon cycle. Based on the in situ POC flux data, this paper evaluated various estimation models. The global ocean POC flux from 2003 to 2018 was calculated using the optimal model, and its temporal and spatial variation characteristics were analyzed. In general, the annual average of global ocean POC flux is about 8.5–14.3 Gt C yr − 1 for period of 2003–2018. In the spatial dimension, the POC flux in the mid-latitude ocean (30–60°) is higher than that in the low-latitude (0–30°). The POC flux in Continental Margins with water depth less than 2000 m accounted for 30% of global ocean, which should receive more attention in global carbon cycle research. In the time dimension, the global POC flux decreases year by year generally, but the POC flux abnormally decreases during El Niño and increases during La Niña. In addition, due to global warming, sea ice melting, and bipolar sea area expansion, POC flux in high-latitude oceans (60–90°) is increasing year by year.

Redshift-space distortions from vector perturbations. II. Anisotropic signal

We study the impact on the galaxy correlation function of the presence of a vector component in the tracers' peculiar velocities, in the case in which statistical isotropy is violated. We present a general framework - based on the bipolar spherical harmonics expansion - to study this effect in a model independent way, without any hypothesis on the origin or the properties of these vector modes. We construct six new observables, that can be directly measured in galaxy catalogs in addition to the standard monopole, quadrupole and hexadecapole, and we show that they completely describe any deviations from isotropy. We then perform a Fisher analysis in order to quantify the constraining power of future galaxy surveys. As an example, we show that the SKA2 would be able to detect anisotropic rotational velocities with amplitudes as low as 1% of that of the vorticity generated during shell-crossing in standard dark matter scenarios.

Hu 1-2: a metal-poor bipolar planetary nebula with fast collimated outflows

We present narrow-band optical and near-IR imaging and optical long-slit spectroscopic observations of Hu1-2, a Galactic planetary nebula (PN) with a pair of [N II]-bright, fast-moving (> 340 km/s) bipolar knots. Intermediate-dispersion spectra are used to derive physical conditions and abundances across the nebula, and high-dispersion spectra to study the spatio-kinematical structure. Generally Hu1-2 has high He/H (~0.14) and N/O ratios (~0.9), typical of Type I PNe. On the other hand, its abundances of O, Ne, S, and Ar are low as compared with the average abundances of Galactic bulge and disc PNe. The position-velocity maps can be generally described as an hour-glass shaped nebula with bipolar expansion, although the morphology and kinematics of the innermost regions cannot be satisfactorily explained with a simple, tilted equatorial torus. The spatio-kinematical study confines the inclination angle of its major axis to be within 10 degrees of the plane of sky. As in the irradiated bow-shocks of IC4634 and NGC7009, there is a clear stratification in the emission peaks of [O III], H_alpha, and [N II] in the northwest (NW) knot of Hu1-2. Fast collimated outflows in PNe exhibit higher excitation than other low-ionization structures. This is particularly the case for the bipolar knots of Hu1-2, with He II emission levels above those of collimated outflows in other Galactic PNe. The excitation of the knots in Hu1-2 is consistent with the combined effects of shocks and UV radiation from the central star. The mechanical energy and luminosity of the knots are similar to those observed in the PNe known to harbor a post-common envelope (post-CE) close binary central star.

A 3D kinematic study of the northern ejecta ‘jet’ of the Crab nebula

We present [O III] 4959,5007 emission line spectra (FWHM = 40 km/s) of the Crab Nebula's northern ejecta `jet'. These data, along with a recent [O III] image of the Crab, are used to build 3-dimensional models of the jet and adjacent remnant nebulosity to better understand the jet's properties and possible formation. We find that the jet's radial velocities range from -190 to +480 km/s with transverse velocities from 1600 to 2650 km/s from base to tip. The jet appears virtually hollow in [O III] emission with the exception of some material at the jet's base where the it connects with the remnant. Our 3D reconstructions indicate that the jet is elliptical in shape and slightly funnel-like rather than a straight cylindrical tube as previously thought. At the base of the jet we find evidence for a significant opening or "channel" in the Crab's main nebula shell. Our analysis of the jet's expansion properties and location supports the theory that the jet may simply represent the highest velocity component of the Crab's N-S bipolar expansion.

Convergence of the bipolar expansion for the coulomb potential

The bipolar expansion of the Coulomb potential, which underlies the multipole moment expansion for interacting charge distributions, converges like a geometric series for separated charges, but converges at best only conditionally when the charges interpenetrate. This article shows how the order of summation affects the sum. Evidence is presented for simpler series when the geometry is linear. © 2014 Wiley Periodicals, Inc.

Modelling the Late-time Hubble Space Telescope Imaging of the Outburst of the Recurrent Nova RS Ophiuchi (2006)

AbstractThe nebular remnant of RS Ophiuchi was modelled using combined HST/ACS imaging and ground-based spectroscopy on day 155 after outburst as a two component bipolar expansion with a low velocity innermost hour-glass over density and a more extended high velocity dumbbell structure. The model was evolved to a much later date, day 455 after outburst, when second epoch HST images were secured. However, due to the lack of simultaneous ground-based spectroscopy the evolved model was much harder to constrain. One suggestion put forward was that the dumbbell structure expanded linearly while the inner hour-glass showed signs of deceleration. Archival data in the form of ground-based spectroscopy on day 415 were subsequently obtained. These new data suggest indeed that a non-linear expansion of the system occurred.

Cryptic variation and recent bipolar range expansion within the Stumped-Toed Gecko Gehyra mutilata across Indian and Pacific Ocean islands

With an impressively wide distribution, Gehyra mutilata is present on almost all Indian and Pacific Ocean islands and in large regions of Southeast Asia and Indonesia. Mitochondrial sequence data (~500 bp) from individuals covering large parts of its (mainly insular) distribution reveals deep cryptic variation and strong geographic structure, with two well differentiated lineages. Molecular data also reveals that the wide Indian and Pacific insular distribution of Gehyra is very recent and, at least across the Indian Ocean islands, most probably the result of human- aided dispersal, as no variation within this lineage was found. Further research is needed to determine geographic patterns of variation across Southeast Asia, the level of genetic variation, and possible mechanisms of speciation. If recognized as distinct taxa, the binomen Gehyra insulensis should be resurrected, and applied to the ‘Pacific lineage’.

Optical Imaging and Spectroscopy of the Galactic Supernova Remnant 3C 58 (G130.7+3.1)

We present a comprehensive imaging and spectroscopic survey of optical emission knots associated with the young Galactic supernova remnant 3C 58. Hα images show hundreds of clumpy filaments and knots arranged in a complex structure covering a nearly circular area roughly 400'' in diameter. A quite different emission structure is seen in [O III], where the brightest features are less clumpy and largely confined to the remnant's northwest quadrant. Measured radial velocities of over 450 knots reveal two distinct kinematic populations; one with average and peak expansion velocities of 770 and 1100 km s−1, respectively, forming a thick shell, and the other showing |v| ≤ 250 km s−1. High-velocity knots (|v| ≥ 500 km s−1) exhibit a strong bipolar expansion pattern with redshifted and blueshifted knots located in northeastern and southwestern regions, respectively. These knots also show strong [N II]/Hα line emission ratios, suggesting enhanced N/H. In contrast, the slower expanding knot population shows much lower [N II]/Hα line ratios and likely represents circumstellar mass loss material from the 3C 58 progenitor. Proper-motion estimates using images spanning a 28 yr time interval suggest positional shifts of between 0.5'' and 2.0'', implying proper motions of 0.02''-0.07'' yr−1. These values agree with previous estimates but are much less than the ≈0.2'' yr−1 expected if 3C 58 were associated with historic guest star of 1181 CE.

Early Infrared Spectral Development of V1187 Scorpii (Nova Scorpii 2004 No. 2)

We report on an unprecedented infrared time series of spectra of V1187 Sco, a very fast ONeMg nova. The observations covered a 56 day period (2004 August 6-September 30) starting 2 days after the nova's peak brightness. Time evolution of the spectra revealed changing line strengths and profiles on timescales of less than a day to weeks as the nova evolved from early postmaximum to early coronal phases. When our ground-based optical and Spitzer Space Telescope data were combined, the wavelength coverage of 0.38-36 μm allowed an accurate spectral energy distribution to be derived when it was about 6 weeks after outburst. Developing double structure in the He I lines showed them changing from narrow to broad in only a few days. Using the O I lines in combination with the optical spectra, we derived a reddening of E(B - V) = 1.56 ± 0.08 and a distance of 4.9 ± 0.5 kpc. Modeling of the ejected material strongly suggested that it was geometrically thick with ΔR/R = 0.8-0.9 (more of a wind than a shell) and a low filling factor of order a few percent. The line shapes were consistent with a cylindrical jet, bipolar, or spherical Hubble flow expansion with a maximum speed of about -3000 km s-1. The central peak appeared to be more associated with the spherical component, while the two peaks (especially in Hβ) suggested a ring with either a lower velocity component or with its axis inclined to the line of sight.

Bipolar outflow on the asymptotic giant branch – the case of IRC+10011

Near-infrared imaging of the asymptotic giant branch (AGB) star IRC+10011 (= CIT3) reveals the presence of a bipolar structure within the central ∼0.1 arcsec of a spherical dusty wind. We show that the image asymmetries originate from ∼10 −4 Mof swept-up wind material in an elongated cocoon whose expansion is driven by bipolar jets. We perform detailed 2D radiative transfer calculations with the cocoon modelled as two cones extending to ∼1100 au within an opening angle of ∼30 ◦ , embedded in a wind with the standard r −2 density profile. The cocoon expansion started 200 yr ago, while the total lifetime of the circumstellar shell is ∼5500 yr. Similar bipolar expansion, at various stages of evolution, has been recently observed in a number of other AGB stars, culminating in jet breakout from the confining spherical wind. The bipolar outflow is triggered at a late stage in the evolution of AGB winds, and IRC+10011 provides its earliest example thus far. These new developments enable us to identify the first instance of symmetry breaking in the evolution from AGB to planetary nebula.

An alternative multipolar expansion for intermolecular potential functions.

We have derived a new multipolar expansion for intermolecular potential-energy functions with applications in molecular physics, theoretical chemistry, and mathematical physics. The new formulation employs a separation of radial and angular terms with a simple index structure that leads to computational efficiency and ease of physical interpretation. For the case of the Coulomb interaction, we compare the present formulation with two conventional multipole expansions: the Cartesian tensor and the irreducible spherical tensor expansions. The new formalism leads to efficient numerical algorithms that are useful for general applications beyond intermolecular potentials. In addition to the electrostatic Coulomb interaction, we illustrate the formalism with applications to special function theory and a bipolar expansion involved in potential theory.

Sexual behaviour, auxosporulation and chloroplast dynamics in a marine Amphora (Bacillariophyceae) studied in culture

Chloroplast, mating behaviour, and auxosporulation are described for Amphora cf. proteus Gregory. The interphase chloroplast is butterfly-shaped and lies with its central part, containing a flat discoid pyrenoid, pressed against the ventral side of the girdle. Chloroplast division is longitudinal and begins and ends before mitosis and cytokinesis. Over the cell cycle, no rotations or lateral translocations of the chloroplast were noticed. A. cf. proteus is the first species of this genus in which sexual reproduction and breeding behaviour have been studied in clonal cultures. The cells isolated exhibited strictly dioecious behaviour, reproducing only in mixed cultures of sexually compatible clones. Sexual reproduction in A. cf. proteus is morphologically and behaviourally isogamous. Each gametangium forms two functional gametes, which do not rearrange within the gametangium, and two small aborted cells. The aborted cells are produced after an unequal cytokinesis accompanying meiosis II; the second cytokinesis during gametogenesis represents a phenomenon hitherto unknown in pennate diatoms. Auxospore development takes place by bipolar expansion. The expansion is unequal on the two long sides of the auxospore, so that the auxospore becomes curved and dorsiventral. The auxospore forms a transverse and longitudinal perizonium.

The Mysterious Ring in the Open Cluster NGC 3572: Planetary Nebula or Photoevaporating Globule?

ABSTRACTWe discuss optical and infrared emission from the putative planetary nebula in the young open cluster NGC 3572. Velocity images of [N ii] λ6583 obtained with the Rutgers/CTIO Fabry‐Perot interferometer reveal that most gas in the nebula is expanding at velocities ≲5 km s -1, with marginal evidence for bipolar expansion. A few outer condensations are seen at faster redshifted velocities, but their origin is uncertain. Optical spectra reveal a spatial excitation gradient, with higher excitation in a diffuse outer halo and low excitation in the bright inner nebula, suggesting that the nebula is externally ionized by hot stars in the open cluster and that the nebula and cluster are therefore equidistant. The nebula coincides with an infrared source detected by the MSX and IRAS satellites and has a spectral energy distribution implying a total mass of 5–10 M⊙. MSX also reveals diffuse infrared emission associated with the cluster, and its morphology implies a connection with the ring nebula. We discuss two very different interpretations of this object—it is either a strange planetary nebula or (more probably) a young photoevaporating globule left over from the molecular cloud that formed the cluster.

Applications of the modified Faddeev equations: t + dμ -

We present calculations of the cross-sections for elastic as well as for muon transfer in t + dμ- collisions below the tμ-(n = 2) threshold. The appropriate mass-scaled Jacobi coordinates are used in the direct and rearrangement channels. The K-matrix elements are obtained from the solution of multichannel Faddeev equations in the configuration space formulation. A bipolar expansion and spline representation are used in the numerical solution of the modified Faddeev equations.

The modified Faddeev equation and multichannel positron-hydrogen scattering calculation

A bipolar spherical harmonics expansion of the modified Faddeev equation is used to calculate the K-matrices of the e++H scattering for up to five open channels and for total angular momentum L4. Partial cross sections and differential cross sections including hydrogen production channels are reported. Comparison with previous calculations are made whenever feasible. Good agreement is observed.

Note on the computation of the multiple tensor in spherical harmonics

A simple formula for the spherical multipole tensor which has better scaling behaviour than those based on a cartesian formulation is presented. The interaction energy calculation scales O ( L 4) for a multipole expansion up to rank L. A new derivation of the bipolar multipole expansion for well-separated charge distributions is given.

Optical and UV Observations of Supernova Remnants

Recent observations of the galactic supernova remnants the Crab Nebula, SN 1006, Cas A, and the Cygnus Loop are reviewed. New studies of the Crab Nebula suggest its progenitor may have had appreciable mass loss in the form of a circumstellar disk resulting in both a bipolar expansion and formation of the synchrotron ‘bays'. Unusually high proper motion knots near to and possibly directed away from the pulsar also have been reported. In the Cas A remnant, a NE jet of ejecta appears to be a plume of mantle material with expansion velocities up to 12000 km s-1 or nearly twice that seen in the main ejecta shell. HST observations of the sdOB star located behind SN 1006 indicate symmetrically expanding Fe II ejecta out to 8100 km s-1. Lastly, deep images of the Cygnus Loop reveal emission structures similar to those seen in 2D & 3D shocked cloud simulations.