Residual Velocity Field Research Articles

Gas dynamics in the barred Seyfert galaxy NGC 4151 -- I. HI streaming shocks and inflow along the bar

We present sensitive, high-resolution observations of neutral hydrogen (H i) in the unusually gas-rich, oval distortion of the Seyfert galaxy NGC 4151. The gas dynamics of the oval are found to be consistent with those of a kinematically weak bar, fully confirming previous suggestions for the presence of a fat bar, and, for the first time, individual gaseous features in the bar are spatially resolved. In particular, the two bright regions close to the leading edges of the bar in NGC 4151 exhibit kinematics strikingly similar to the signature of bar shocks seen in gas-dynamical simulations, and demonstrate how strong the gaseous response may be even in such a weak bar potential. The residual velocity field, showing deviations from circular motion, is largely consistent with streaming in a bar potential, and, in addition, clearly shows that inflow is concentrated in narrow regions originating in the shocks. This inflow may represent an early stage in the fuelling process of the AGN. The presence and properties of the shocks in NGC 4151 indicate that, in addition to the x1 orbits, the family of x2 orbits exists and is of significant extent in the bar of NGC 4151, with gas streaming from the shocks making the transition between the two families. We therefore suggest that the circumnuclear ellipse, identified optically by previous authors and associated with gas flowing in x2 orbits, has formed as a natural consequence of the gas flows in the bar without the requirement for a second, inner bar. Observations of H i were previously thought to be ill-suited to the study of bar shocks because of limitations in angular resolution and sensitivity. However, our observations show that, following recent instrumental enhancements, such measurements are now feasible, albeit at the limits of instrumental capability.

A three-dimensional model of tidal currents in the mouth of the Tagus estuary

Three-dimensional simulations of barotropic tides are used to investigate the complex circulation at the mouth of the Tagus estuary. Comparison with field data shows that elevations are well represented in the main area of interest, but velocities are slightly over-predicted due to a simplified treatment of intertidal flats. Model results show the existence of strong velocity phase lags (up to 1.75 hours for the semi-diurnal constituents) between the shallow areas and the deep channel. These phase lags are partially responsible for the generation by advective accelerations of a strong residual velocity field (velocities reach 0.5 m s −1) with well defined eddies. The interaction between the residual and tidal velocity fields in turn generates strong chaotic stirring. Localized sigma coordinates (LSC), a recently proposed method which allows the number of nodes per vertical to vary horizontally, are used for the first time in a three-dimensional application. A previously proposed criterion for the horizontal distribution of the total number of vertical nodes is shown to be inadequate when advective accelerations are important. However, with an alternative criterion, the use of LSC reduces maximum errors by a factor of two relative to traditional sigma coordinates.

Measuring non-axisymmetry in spiral galaxies

We present a method for measuring small deviations from axisymmetry of the potential of a filled gas disc. The method is based on a higher order harmonic expansion of the full velocity field of the disc. This expansion is made by first fitting a tilted-ring model to the velocity field of the gas disc and subsequently expanding the velocity field along each ring into its harmonic terms. We use epicycle theory to derive equations for the harmonic terms in a distorted potential. The phase of each component of the distortion can vary with radius. We show that if the potential has a distortion of harmonic number m, the velocity field as seen on the sky exhibits an m − 1 and m + 1 distortion. As is to be expected, the effects of a global elongation of the halo are similar to an m = 2 spiral arm. The main difference is that the phase of the spiral arm can vary with radius. Our method allows a measurement of ϵ pot sin 2 ϕ2, where épot is the elongation of the potential and ϕ2 is one of the viewing angles. The advantage of this method over previous approaches to measure the elongations of disc galaxies is that, by using Hi data, one can probe the potential at radii beyond the stellar disc, into the regime where dark matter is thought to be the dominant dynamical component. The method is applied to the spiral galaxies NGC 2403 and 3198 and the harmonic terms are measured up to ninth order. The residual velocity field of NGC 2403 shows some spiral-like structures. The harmonic analysis indicates that the m = 3 term is dominant, with an average value of ∼0.02 υ c. This is consistent with an average ellipticity of the potential of ϵpot sin 2 ϕ2 = 0.064 ± 0.003, but spiral arms may couple significantly to this result. In the harmonic analysis of the kinematics of NGC 3198 the m= 2 and m= 3 terms are strongest (∼0.01υc). The inferred average elongation of the potential is 0.019 ± 0.003. Since the amplitude of the elongation is coupled to the viewing angles and may be influenced by spiral arms, more galaxies should be examined to separate these effects from true elongation in a statistical way.

Atomic hydrogen in the spiral galaxy NGC 3631

New high-resolution, high-sensitivity Westerbork Synthesis Radio Telescope H i synthesis observations of the spiral galaxy NGC 3631 are presented. In the total atomic hydrogen map, the spiral arms are well distinguished from the interarm regions, while the sensitivity allows detection of H i in all but a few isolated regions of the areas between the spiral arms. Most of the atomic hydrogen is located within the optical disc, but the H i extends to some 1.5Ropt. The H i follows the spiral arms, and streaming motions of up to ∼ 15 km s−1 (projected) can be identified from the velocity field. Assuming a constant inclination angle of 17°, a rotation curve is derived which is declining slightly in the outer parts of the disc. An analysis of a residual velocity field, obtained after the subtraction of an axisymmetric model based on the rotation curve, confirms the existence of streaming motions near the spiral arms in an otherwise undisturbed disc.

On Tidal Rectification, Friction, and Geostrophic Degeneracy

The indeterminacy of a frictionless, tidally rectified flow is a fundamental feature of the dynamics involved and cannot, indeed must not, be removed by the expedient of a coordinate transformation. This indeterminacy can only be removed by either specifying the flow in some manner at some time, or by the inclusion of friction. Tidal rectification for the general case of nonzero friction has been investigated in several studies in both the Eulerian and Lagrangian views, and leads to consistent schemes whereby the residual velocity field may be determined.

Space geodetic measurement of crustal deformation in central and southern California, 1984–1992

We estimate the velocity field in central and southern California using Global Positioning System (GPS) observations from 1986 to 1992 and very long baseline interferometry (VLBI) observations from 1984 to 1991. Our core network includes 12 GPS sites spaced approximately 50 km apart, mostly in the western Transverse Ranges and the coastal Borderlands. The precision and accuracy of the relative horizontal velocities estimated for these core stations are adequately described by a 95% confidence ellipse with a semiminor axis of approximately 2 mm/yr oriented roughly north‐south, and a semimajor axis of approximately 3 mm/yr oriented east‐west. For other stations, occupied fewer than 5 times, or occupied during experiments with poor tracking geometries, the uncertainty is larger. These uncertainties are calibrated by analyzing the scatter in three types of comparisons: (1) multiple measurements of relative position (“repeatability”), (2) independent velocity estimates from separate analyses of the GPS and VLBI data, and (3) rates of change in baseline length estimated from the joint GPS+VLBI solution and from a comparison of GPS with trilateration. The dominant tectonic signature in the velocity field is shear deformation associated with the San Andreas and Garlock faults, which we model as resulting from slip below a given locking depth. Removing the effects of this simple model from the observed velocity field reveals residual deformation that is not attributable to the San Andreas fault. Baselines spanning the eastern Santa Barbara Channel, the Ventura basin, the Los Angeles basin, and the Santa Maria Fold and Thrust Belt are shortening at rates of up to 5 ± 1, 5 ± 1, 5 ± 1, and 2 ± 1 mm/yr, respectively. North of the Big Bend, some compression normal to the trace of the San Andreas fault can be resolved on both sides of the fault. The rates of rotation about vertical axes in the residual geodetic velocity field differ by up to a factor of 2 from those inferred from paleomagnetic declinations. Our estimates indicate that the “San Andreas discrepancy” can be resolved to within the 3 mm/yr uncertainties by accounting for deformation in California between Vandenberg (near Point Conception) and the westernmost Basin and Range. Strain accumulation of 1–2 mm/yr on structures offshore of Vandenberg is also allowed by the uncertainties. South of the Transverse Ranges, the deformation budget must include 5 mm/yr between the offshore islands and the mainland.

A new way to locate corotation resonances in spiral galaxies

Kinematical information over the entire disk of a spiral galaxy can be used in a new way to locate the position of the corotation resonance. The spiral residual velocity field has a global appearance that is distinctly different inside and outside the corotation resonance radius. Inside the corotation radius, the spiral velocity field shows a single spiral feature (that is, a single approaching-receding spiral arm pair). Outside the corotation radius, there are three spiral features (approaching-receding arm pairs). The corotation radius is located where this morphological change occurs. The effect is a consequence of geometric phase. It should apply generally, regardless of the functional form of the velocity perturbation due to a spinal arm, if the spiral structure is wave-based

Residual circulation in shallow estuaries: 2. Weakly stratified and partially mixed, narrow estuaries

Long‐wave theory is used herein to analyze circulation in weakly stratified and partially mixed estuaries. Unlike the highly stratified systems considered in part 1, the flows considered here have only a minimal tidal‐frequency internal wave component. These estuaries may therefore be modeled as the sum of weakly interacting barotropic and baroclinic modes. The dominant factors driving the residual flow are finite amplitude barotropic effects in weakly stratified estuaries and a combination of barotropic effects and steady horizontal density gradient forcing in partially mixed estuaries. The dominant vertical exchange mechanism in the weakly stratified case is bottom boundary‐induced turbulence, and that in partially mixed estuaries is believed to be random internal wave interactions. A model of the Columbia River Estuary under weakly stratified conditions accurately predicts the observed residual velocity and salinity fields, and the tidal amplitude at which a transition to a highly stratified state takes place. The partially mixed state is unstable in the Columbia River Estuary because the tides and buoyancy input are both too strong.

Galaxien vom Magellanschen Typ

In the first part of this paper the morphological structure of Magellanic type galaxies (Irr I) is investigated. The galaxies of Magellanic type present a basic pattern consisting of a disk, a bar, stellar arms, rudimentary or well developed, spiral filaments and condensations in the disk. With the help of this pattern a well-defined classification scheme is set up. The subgroup of Irr II-systems consists of normal galaxies which are more or less tidally disturbed. Bursts of star formation have a great influence on structure and colour of irregular galaxies. Using the ESO-B Atlas, 580 galaxies of Magellanic type (out of a sample of 3187 galaxies) were classified; 57 are new SB(s)m systems (prototype Large Magellanic Cloud). The sample shows dominant bar structures at the classification stages d-, dm-, and m. A striking feature is the asymmetric position of bar and disk. This asymmetry is a general characteristic of galaxies of types SBd-SBm IB. The asymmetry can be discribed by a relative displacement parameter $$\tilde \Lambda $$ = 0.78 ±0.15, defined as the quotient of small and great distance of the bar center to the optical edge of the disk. The displacement cannot be explained by tidal interaction with neighbouring galaxies. In the second part of the paper the kinematics and dynamics of the Large Magellanic Cloud (LMC) as the nearest and best-known example of a galaxy of Magellanic type is investigated. The main structural features of the LMC are disk, bar, rudimentary and well developed stellar arms as well as spiral filaments (not necessarily connected with density waves); the γ-structure is a broken up ring structure. Embedded into these features are young, asymmetrically located spiral arm filaments. As an explanation for these structures stochastic start formation in an ordered chain reaction is proposed. The pattern of the spiral arm filaments is determined by the rotation curve. The morphological peculiarities of the LMC can also be detected in other galaxies of that type. The mean absolute displacement of the centers of bar and disk, determined from 18 galaxies, is Λ = 800 pc. The displacement between the bar center and the symmetry center of the rotation curve is of the same order. The presently known radial velocities of planetary nebulae, star clusters, Hi and Hii regions and stars belonging to the LMC have been collected in a catalogue as the basis of a discussion of the kinematics and dynamics of the LMC. Contrary to earlier work, we have used, for the first time, the radial velocities of objects of all subgroups together by a proper weighting scheme. Thus the basic kinematics and dynamics of the LMC has been deduced. The radial velocity field shows no central symmetry; it is characterized by large scale (2–3 kpc) disturbances. By comparison with the velocity field of other galaxies three main disturbances are identified: an oval distortion of the velocity field in the bar region, a radial velocity field around 30 Doradus, and disturbances connected with a warp or material above the disk in the southern quadrants. The results of a detailed numerical analysis of these three facts can be summed up as follows: The mean velocity dispersion of population I objects is 10.5 km s-1 of population II objects 16.0 km s-1. Red and blue globular clusters show different kinematical behavior. By comparison of eight mass models, taking into consideration thickness effects and controlled by surface photometric data, the mass of the LMC is found to be (0.5 ± 0.1) × 1010 $$\mathfrak{M}_ \odot $$ (assuming the inclination 33°, the systemic velocity 46.9 km s-1, and the distance 56 kpc). Dynamically, the LMC can be described by a dominating disk potential with an additional bar potential as a disturbance. The mass of the bar is 0.6 × 109 $$\mathfrak{M}_ \odot $$ . The stable neutral point of such a configuration can be found in the residual velocity field. The absorption feature crossing the bar coincides with the maximum velocity gradient of the computed radial velocity field in the plane of the system.