Distributions of Constant Directional Derivatives and a Model of Spiral Galaxy Arms

Image analysis of over one hundred nearby galaxies (He, 2003) indicates that for any spiral galaxy image of small inclination there is evidence of two orthogonalsets of iso-ratio curves in different scales which, like curvilinear coordinate lines, expand over different galaxy components. This result sets a constraint on galaxy patterns and a general model equation which carries this constraint is given in its geometric form in He (2003). In the current paper the author reformulates the geometric equation into one quasilinearsystem of 3 partial differential equations with 3 dependents (the tangent direction of one set of iso-ratio curves and the two ratio profiles along the two sets of iso-ratio curves respectively). With one profile assumed to be a nonzero constant, there are two dependents and the system of two partial differential equations is a hyperbolic one. The author uses the standard method of characteristics and the boundary condition of ideal arms which are found by setting the above constant to be zero, to solve the hyperbolic system. This provides one analytic method to model galaxy patterns. Its varying parameters will be useful for galacticarm classification and for investigation of galaxy structure.     

Geometry of Spiral Galaxy Arms

The previous work (He, 2001) on image analysis of over one hundred nearby galaxies indicates that for any spiral galaxy image of small inclination there is evidence of two sets of iso-ratio curves in different scales which, like curvilineal coordinate lines, expand over different galaxy components. This result sets constraint on galaxy patterns and a general equation which carries this constraint is presented in the current paper. The equation has clear geometrical meaning. Its much simplified version which applies to galaxy arms, when solved, may be a guidance to understanding galaxy patterns. This revised version was published online in July 2006 with corrections to the Cover Date.     

A symmetry-induced model of elliptical galaxy patterns

Sérsic (Atlas de Galaxias Australes, Observatorio Astronómico, 1968) generalized the de Vaucouleurs law which follows the projected (observed) one dimensional radial profile of elliptical galaxies closely and Dehnen (Mon. Not. R. Astron. Soc. 265:250, 1993) proposed an analytical formula of the 3-dimensional light distributions whose projected line profile resembles the de Vaucouleurs law. This paper is involved to recover the Dehnen model and generalize the model to account for galaxy elliptical shapes by means of curvilinear coordinate systems and employing a symmetry principle. The symmetry principle maps an orthogonal coordinate system to a light distribution pattern. The coordinate system for elliptical galaxy patterns turns out to be the one which is formed by the complex-plane reciprocal transformation Z=1/W. The resulting spatial (3-dimensional) light distribution is spherically symmetric and has infinite gradient at its center, which is called spherical-nucleus solution and is used to model galaxy central area. We can make changes of the coordinate system by cutting out some column areas of its definition domain, the areas containing the galaxy center. The resulting spatial (3-dimensional) light distributions are axisymmetric or triaxial and have zero gradient at the center, which are called elliptical-shape solutions and are used to model global elliptical patterns. The two types of logarithmic light distributions are added together to model full elliptical galaxy patterns. The model is a generalization of the Dehnen model. One of the elliptical-shape solutions permits realistic numerical calculation and is fitted to all R-band elliptical images from Frei et al. (Astron. J. 111:174, 1996) galaxy sample. The fitting is satisfactory. This suggests that elliptical galaxy patterns can be represented in terms of a few basic parameters.     

A grid of chemical evolution models as a tool to interpret spiral and irregular galaxies data

We present a generalization of the multiphase chemical evolution model (CEM) applied to a wide set of theoretical galaxies with different masses and evolutionary rates. This generalized set of models has been computed using the so-called universal rotation curve from Persic, Salucci & Steel to calculate the radial mass distribution of 44 theoretical protogalaxies. This distribution is a fundamental input which, besides its own effect on the galaxy evolution, defines the characteristic collapse time-scale or gas infall rate on to the disc. We have adopted 10 sets of values, between 0 and 1, for the molecular cloud and star formation efficiencies, as corresponding to their probability nature, for each one of the radial distributions of total mass. Thus, we have constructed a biparametric grid of models, depending on those efficiency sets and on the rotation velocity, whose results are valid in principle for any spiral or irregular galaxy. The model results provide the time-evolution of different regions of the disc and the halo along galactocentric distance, measured by the gas (atomic and molecular) and stellar masses, the star formation rate (SFR) and chemical abundances of 14 elements, for a total of 440 models. This grid may be used to estimate the evolution of a given galaxy for which only present time information, such as radial distributions of elemental abundances, gas densities and/or star formation, which are the usual observational constraints of chemical evolution models (CEMs), is available.     

How can spirals persist?

The image of a spiral galaxy is one of the most tantalizing images in nature. It demands that we ask: why do so many galaxies present this morphology? We currently have two main schools of thought concerning galaxy morphology, one based on gravitational effects and the other based on electromagnetic effects. The older gravitational models can explain how spirals might form, but they also predict that the spirals would quickly disintegrate. And the observed pervasiveness of spirals seems to imply not only their formation, but also their persistence over time. The newer plasma cosmology model is an improvement in that it explains how spirals might form and persist so long as plasma persists. But the formation of charge-neutral stars seems to return the scenario to the gravitational domain, and to subsequent dissolution. Clearly we need an additional idea to account for pervasive and persistent spiral galaxy structure. The present paper attempts to uncover a previously unrecognized gravitational mechanism that can serve as a viable candidate for sustaining persistent spiral galaxy structure.     

Stellar and gas dynamics of late-type barred-spiral galaxies: NGC 3359, a test case

We study the dynamics of a model for the late-type barred-spiral galaxy NGC 3359 by using both observational and numerical techniques. The results of our modelling are compared with photometric and kinematical data. The potential used is estimated directly from observations of the galaxy. It describes with a single potential function, a barred-spiral system with an extended spiral structure. Thus, the study of the dynamics in this potential has an interest by itself. We apply orbital theory and response models for the study of the stellar component, and smoothed particle hydrodynamics for modelling the gas. In particular, we examine the pattern speed of the system and the orbital character (chaotic or ordered) of the spiral arms. We conclude that the spiral pattern rotates slowly, in the sense that its corotation is close to or even beyond the end of the arms. Although a single, slow pattern speed could, under certain assumptions, characterize the whole disc, the comparison with the observational data indicates that probably the bar and the spirals have different angular velocities. In our two pattern speeds model, the best fit is obtained with a bar ending close to its 4:1 resonance and a more slowly rotating spiral. Assuming an 11 Mpc distance to the galaxy, a match of our models with the observed data indicates a pattern speed of about  39 km s⁻¹ kpc⁻¹  for the bar and about  15 km s⁻¹ kpc⁻¹  for the spiral. We do not find any indication for a chaotic character of the arms in this barred-spiral system. The flow in the region of the spirals can best be described as a regular 'precessing-ellipses flow'.     

Origin of the Cartwheel Galaxy: Disk Instability?

The linear theory and N-body simulations are used to present a new, alternative model of the galaxy A0035-324 (the “Cartwheel”), which is the most striking example of the relatively small class of ring galaxies. The model is based on the gravitational Jeans-type instability of both axisymmetric (radial) and nonaxisymmetric (spiral) small-amplitude gravity perturbations (e.g., those produced by spontaneous disturbances) of a dynamically cold subsystem (identified as the gaseous component) of an isolated disk galaxy. The simplified model of a galaxy is used in which stars (and a dark matter, if it exists at all) do not participate in the disk collective oscillations and just form a background charge. In the theory presented here, a case for both purely radial solutions and purely spiral solutions to the equations of motion of an infinitesimally thin gaseous disk is made, which is associated with both a radial density wave and a dominant spiral density wave which propagate outwards creating a rough ring and a number of spiral arms. Through three-dimensional numerical simulation of a collisionless set of many particles, I associate these gravitationally unstable axisymmetric waves and nonaxisymmetric waves with growing clumps of matter which take on the appearance of a ring and spokes of mass blobs.     

Evolutionary synthesis models for galaxy transformation in clusters

The galaxy population in rich local galaxy clusters shows a ratio of one quarter elliptical galaxies, two quarters S0 galaxies, and one quarter spiral galaxies. Observations of clusters at redshift 0.5 show a perspicuously different ratio, the dominant galaxy type are spiral galaxies with a fraction of two quarters while the number of S0 galaxies decreases to a fraction of one quarter (Dressler et al. 1997). This shows an evolution of the galaxy population in clusters since redshift 0.5 and it has been suspected that galaxy transformation processes during the infall into a cluster are responsible for this change. These could be merging, starburst or ram-pressure stripping. We use our evolutionary synthesis models to describe various possible effects of those interactions on the star formation of spiral galaxies infalling into clusters. We study the effects of starbursts of various strengths as well as of the truncation of star formation at various epochs on the color and luminosity evolution of model galaxies of various spectral types. As a first application we present the comparison of our models with observed properties of the local S0 galaxy population to constrain possible S0 formation mechanisms in clusters. Application to other types of galaxies is planned for the future. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stellar Population Analysis of Galaxies based on Genetic Algorithms

We present a new method for determining the age and relative contribution of different stellar populations in galaxies based on the genetic algorithm. We apply this method to the barred spiral galaxy NGC 3384, using CCD images in U, B, V, R and I bands. This analysis indicates that the galaxy NGC 3384 is mainly inhabited by old stellar population (age >109yr). Some problems were encountered when numerical simulations are used for determining the contribution of different stellar populations in the integrated color of a galaxy. The results show that the proposed genetic algorithm can search efficiently through the very large space of the possible ages.     

Galaxies with “rows”: A new catalog

Galaxies with “rows” in Vorontsov-Velyaminov’s terminology stand out among the variety of spiral galactic patterns. A characteristic feature of such objects is the sequence of straight-line segments that forms the spiral arm. In 2001 A. Chernin and co-authors published a catalog of such galaxies which includes 204 objects from the Palomar Atlas. In this paper, we supplement the catalog with 276 objects based on an analysis of all the galaxies from the New General Catalogue and Index Catalogue. The total number of NGC and IC galaxies with rows is 406, including the objects of Chernin et al. (2001). The use of more recent galaxy images allowed us to detect more “rows” on average, compared with the catalog of Chernin et al. When comparing the principal galaxy properties we found no significant differences between galaxies with rows and all S-typeNGC/IC galaxies.We discuss twomechanisms for the formation of polygonal structures based on numerical gas-dynamic and collisionless N-body calculations, which demonstrate that a spiral pattern with rows is a transient stage in the evolution of galaxies and a system with a powerful spiral structure can pass through this stage. The hypothesis of A. Chernin et al. (2001) that the occurrence frequency of interacting galaxies is twice higher among galaxies with rows is not confirmed for the combined set of 480 galaxies. The presence of a central stellar bar appears to be a favorable factor for the formation of a system of “rows”.     

On the role of the magnetic field in a wave theory of the spiral structure of galaxies

The spiral waves in a model galaxy consisting of the differentially rotating interstellar gas and Population I are considered. The instability of spiral waves in the presence of differential rotation and magnetic field is found. This instability may lead as well as the Landau-instability found by Marochnik and Suchkov (1968, 1969) to the formation of an observable spiral pattern in a short time. It may play a definitive role in the spiral structure formation in galaxies with weak Population II.     

Grand-Design Spirals in the Core of NGC 5248

We report the detection of a bisymmetric nuclear spiral structure in the spiral galaxy NGC 5248.The two red spiral arms can be followed for about 3 arcsec, before they appear to end inside the radius of the circumnuclear starburst `ring' at about 5.5 arcsec or 400 pc distance from the nucleus. We combine our near-infrared Canada–France–Hawaii Telescope adaptive optics images with traditional near-infrared and optical images and show that spiral structure is present in this galaxy at spatial scales reaching from a hundred parsecs to 15 kpc. Comparison with a Hubble Space Telescope ultraviolet image shows how the starburst ring is related to the nuclear spiral structure. We also show a two-dimensional H_α velocity field that reveals no evidence for systematic streaming motions near the nuclear spiral or the starburst ring, nor for a rapidly rising rotation curve. This revised version was published online in July 2006 with corrections to the Cover Date.     

Leading spiral arms,retrograde galaxy encounters and massive halos

We study, theoretically and with N-body simulations, the formation of spiral patterns in retrograde galaxy encounters. A one-armed leading spiral dominates in a disk if the tidal perturbation from the companion is large and the disk is surrounded by a massive halo. Otherwise, a trailing pattern forms. The leading arm is made up of particles in slightly elongated orbits whose turning points outline the arm. The arm rotates opposite to the disk rotation. We have found one spiral galaxy, NGC4622, with a leading arm near its nucleus. From the literature, we find that very few spirals, if any, in a sample of strongly perturbed galaxies have leading arms. A possible reason for this is that few spiral galaxies have a halo with larger mass than the disk within the visible disk.     

Automatic morphological classification of galaxy images

We describe an image analysis supervised learning algorithm that can automatically classify galaxy images. The algorithm is first trained using manually classified images of elliptical, spiral and edge-on galaxies. A large set of image features is extracted from each image, and the most informative features are selected using Fisher scores. Test images can then be classified using a simple Weighted Nearest Neighbour rule such that the Fisher scores are used as the feature weights. Experimental results show that galaxy images from Galaxy Zoo can be classified automatically to spiral, elliptical and edge-on galaxies with an accuracy of ∼90 per cent compared to classifications carried out by the author. Full compilable source code of the algorithm is available for free download, and its general-purpose nature makes it suitable for other uses that involve automatic image analysis of celestial objects.     

Morphology of star formation regions in irregular galaxies

The location of H  II regions, which indicates the locus of present star formation in galaxies, is analysed for a large collection of 110 irregular galaxies (Irr) imaged in Hα and nearby continuum. The analysis is primarily by visual inspection, although a two-dimensional quantitative measure is also employed. The two different analyses yield essentially identical results. H  II regions appear preferentially at the edges of the light distribution, predominantly on one side of the galaxy, contrary to what is expected from stochastic self-propagating star formation scenarios. This peculiar distribution of star-forming regions cannot be explained by a scenario of star formation triggered by an interaction with extragalactic gas, or by a strong one-armed spiral pattern.     

Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

In the presence of a strong   m = 2  component in a rotating galaxy, the phase-space structure near corotation is shaped to a large extent by the invariant manifolds of the short-period family of unstable periodic orbits terminating at L ₁ or L ₂. The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine–Gordon equation. Numerical examples are given in an N -body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar–spiral pattern.     

Testing the nature of S0 galaxies using planetary nebula kinematics in NGC 1023

We investigate the manner in which lenticular galaxies are formed by studying their stellar kinematics: an S0 formed from a fading spiral galaxy should display similar cold outer disc kinematics to its progenitor, while an S0 formed in a minor merger should be more dominated by random motions. In a pilot study, an attempt to distinguish between these scenarios, we have measured the planetary nebula (PN) kinematics of the nearby S0 system NGC 1023. Using the Planetary Nebula Spectrograph, we have detected and measured the line-of-sight velocities of 204 candidate planetary nebulae (PNe) in the field of this galaxy. Out to intermediate radii, the system displays the kinematics of a normal rotationally supported disc system. After correction of its rotational velocities for asymmetric drift, the galaxy lies just below the spiral galaxy Tully–Fisher relation, as one would expect for a fading system. However, at larger radii the kinematics undergo a gradual but major transition to random motion with little rotation. This transition does not seem to reflect a change in the viewing geometry or the presence of a distinct halo component, since the number counts of PNe follow the same simple exponential decline as the stellar continuum with the same projected disc ellipticity out to large radii. The galaxy's small companion, NGC 1023A, does not seem to be large enough to have caused the observed modification either. This combination of properties would seem to indicate a complex evolutionary history in either the transition to form an S0 or in the past life of the spiral galaxy from which the S0 formed. More data sets of this type from both spirals and S0s are needed in order to definitively determine the relationship between these types of system.     

Chaotic spiral galaxies

We study the role of asymptotic curves in supporting the spiral structure of a N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions on the unstable asymptotic manifolds of the main unstable periodic orbits follow the shape of the periodic orbits for an initial interval of time and then they are diffused outwards along the spiral structure of the galaxy. Chaotic orbits having small deviations from the unstable periodic orbits, stay close and along the corresponding unstable asymptotic manifolds, supporting the spiral structure for more than 10 rotations of the bar. Chaotic orbits of different Jacobi constants support different parts of the spiral structure. We also study the diffusion rate of chaotic orbits outwards and find that the orbits that support the outer parts of the galaxy are diffused outwards more slowly than the orbits supporting the inner parts of the spiral structure.     

Structure and Dynamics of NGC 1300

The isophotal profiles and colour maps of a sample of 12 spiral galaxies allowed us to analyse the different structural components that compose them. These components were parameterized by performing a decomposition of the galaxy brightness profiles. Inferring the geometry for each component, we have obtained the spatial mass distribution and the gravitational potential for each object. Here we present the detailed analysis for one of the galaxies in the sample, the barred galaxy NGC 1300. This revised version was published online in July 2006 with corrections to the Cover Date.