Star formation history in the central region of the barred galaxy NGC 4245

We have investigated the gas and stellar kinematics and the stellar population properties at the center of the early-type galaxy NGC 4245 with a large-scale bar by the method of two-dimensional spectroscopy. The galaxy has been found to possess a pronounced chemically decoupled compact stellar nucleus, which is at least a factor of 2.5 richer in metals than the stellar population of the bulge, and a ring of young stars with a radius of 300 pc. Star formation goes on in the ring even now; its location corresponds to the inner Lindblad resonance of the large-scale bar. According to Hubble Space Telescope data, the mean stellar age in the chemically decoupled nucleus is significantly younger than that within 0″.25 of the center. It may be concluded that we take the former ultracompact star formation ring with a radius of no more than 100 pc located at the inner Lindblad resonance of the now disappeared nuclear bar as the chemically decoupled nucleus. On the whole, the picture of star formation at the center of this gas-poor galaxy is consistent with theoretical predictions of the consequences of the secular evolution of a stellar-gaseous disk under the action of a bar or bars.     

On the stability of dust orbits in mean-motion resonances perturbed by from an interstellar wind

Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange’s planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting–Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances.     

Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems.     

Signatures of recent star formation in ring S0 galaxies

We present a study of the stellar populations of ring and/or arm-like structures in a sample of S0 galaxies using GALEX far- and near-ultraviolet imaging and SDSS optical data. Such structures are prominent in the UV and reveal recent star formation. We quantitatively characterize these rejuvenation events, estimating the average age and stellar mass of the ring structures, as well as of the entire galaxy. The mass fraction of the UV-bright rings is a few percent of the total galaxy mass, although the UV ring luminosity reaches 70% of the galaxy luminosity. The integrated colors of these S0s locates them in the red sequence (NGC 2962) and in the so-called green valley. We suggest that the star formation episodes may be induced by different triggering mechanisms, such as the inner secular evolution driven by bars, and interaction episodes.     

Orbital motion of a massive object in a dense stellar system

In this paper we show the positional oscillation of a massive object in a dense stellar system by numerical N -body simulations. We found that the central massive object, which at first is placed at rest at the centre of the surrounding spherical stellar system, promptly departs from the centre and rotates in accordance with the rotation of the stellar system, if the stellar system has an appreciable rotation. This oscillatory motion continues for a long time because of the absence of dynamical friction. Such a long-lasting oscillation may explain the asymmetric structure observed in the centres of M31 and NGC 4486B, may cause the secular flow of gaseous elements distributed in the central regions of galaxies on to the massive object, and may ignite activity in the centres of galaxies.     

Local stellar stability. II

The existence proof of continuous spectra of eigenvaluess developed in the framework of the function space ofq-regularizations (Perdang, 1976) is extended in this paper by relaxing the severe restrictions previously imposed o the mathematical structure of the stellar stability equations. It is stressed that these local modes depend on the variable system in terms of which the linearized stellar structure equations are set up. We therefore search for a systematic procedure to select the most satisfactory system to analyze Local Stability. Our procedure is illustrated in great detail in the case of nonradial adiabatic stability. Moreover when applied to nonadiabatic perturbations it reveals the existence of two new types of local instability which seem to prevail in the majority of stars in a thermonuclear burning phase: (a) a nonrdial local secular instability; (b) a radial local nuclear instability. Numerical test calculations exhibit that the latter helps us to understand certain evolutionary features of stars, in particular it provides an interpretation of Hayashiet al.'s (1962) rule.     

Star formation history in the central region of the barred galaxy NGC 7177

Using the method of two-dimensional spectroscopy, we have investigated the kinematics and distribution of the gas and stars at the center of the early-type spiral galaxy NGC 7177 with a mediumscale bar as well as the change in the mean age of the stellar population along the radius. A classical picture of radial gas inflow to the galactic center along the shock fronts delineated by dust concentration at the leading edges of the bar has been revealed. The gas inflow is observed down to a radius R = 1″.5−2″, where the gas flows at the inner Lindblad resonance concentrate in an azimuthally highly inhomogeneous nuclear star formation ring. The bar in NGC 7177 is shown to be thick in z coordinate—basically, it has already turned into a pseudo-bulge as a result of secular dynamical evolution. The mean stellar age inside the star formation ring, in the galactic nucleus, is old, ∼10 Gyr.Outside, at a distance R = 6″−8″ from the nucleus, the mean age of the stellar population is ∼2 Gyr. If we agree that the bar in NGC 7177 is old, then, obviously, the star formation ring has migrated radially inward in the last 1–2 Gyr, in accordance with the predictions of some dynamical models.     

Vibrational stability of stars in thermal imbalance: A solution in terms of asymptotic expansions

The solution of the partial differential equation describing the ‘non-isentropic’ oscillations of a star in thermal imbalance has been obtained in terms of asymptotic expansions up to the first order in the parameterII/t _s, whereII is the adiabatic pulsation period for the fundamental mode andt _s , a secular time scale of the order of the Kelvin-Helmholtz time. Use has been made of the zeroth order ‘isentopic’ solution derived in I. The solution obtained allows one to derive unambiguously a general integral expression for the coefficient of vibrational stability for arbitrary stellar models in thermal imbalance. The physical interpretation of this stability coefficient is discussed and its generality and its simplicity are stressed. Application to some simple analytic stellar models in homologous and nonhomologous contraction enables one to recover, in a more straightforward manner, results obtained by Coxet al. (1973). Aizenman and Cox (1974) and Davey (1974). Finally, we emphasize that the inclusion of the effects of thermal imbalance in the stability calculations of realistic evolutionary sequences of stellar models, not considered up to now by the other authors, is quite easy and straightforward with the simple formula derived here.     

The local axisymmetric instability criterion in a thin, rotating, multicomponent disc

Purely gravitational perturbations are considered in a thin rotating disc composed of gas and several stellar components. The dispersion relation for the axisymmetric density waves propagating through the disc is found and the criterion for the local axisymmetric stability of the whole system is formulated. In the appropriate limit of two-component gas we confirm the findings of Jog & Solomon and extend consideration to the case when one component is collisionless. Gravitational stability of the Galactic disc in the solar neighbourhood based on the multicomponent instability condition is explored using recent measurements of the stellar composition and kinematics in the local Galactic disc obtained by the Hipparcos satellite.     

The accelerated Kepler problem

The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.     

Gauss's method for secular dynamics, softened

We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular dynamical evolution of nearly Keplerian systems such as stellar clusters surrounding black holes in galactic nuclei, cometary clouds or planetesimal discs. We illustrate its accuracy, efficiency and versatility on a variety of configurations. In particular, we examine a secularly unstable system of counterrotating discs, and follow the unfolding and saturation of the instability into a global, uniformly precessing, lopsided  ( m = 1)  mode.     

Stellar populations of classical and pseudo-bulges for a sample of isolated spiral galaxies

In this paper we present the stellar population synthesis results for a sample of 75 bulges in isolated spiral Sb-Sc galaxies, using the spectroscopic data from the Sloan Digital Sky Survey and the STARLIGHT code. We find that both pseudo-bulges and classical bulges in our sample are predominantly composed of old stellar populations, with mean mass-weighted stellar age around 10 Gyr. While the stellar population of pseudo-bulges is, in general, younger than that of classical bulges, the difference is not significant, which indicates that it is hard to distinguish pseudo-bulges from classical bulges, at least for these isolated galaxies, only based on their stellar populations. Pseudo-bulges have star formation activities with relatively longer timescale than classical bulges, indicating that secular evolution is more important in this kind of systems. Our results also show that pseudo-bulges have a lower stellar velocity dispersion than their classical counterparts, which suggests that classical bulges are more dispersion-supported than pseudo-bulges.     

Three-body planetary problem: study of KAM stability for the secular part of the Hamiltonian

The Hamiltonian representing the average over the mean-motion angles (i.e. the secular part) of the three-body planetary problem is considered. An efficient algorithm constructing invariant tori for the trajectories in phase space is provided. To give a possible practical application, we consider a toy-model including the main terms of the secular part of a hypothetic Sun-Jupiter-Saturn system having eccentricities and inclinations equal to 1/20 of the true ones. The scheme of a KAM proof of the stability of the model is sketched. The proof is “computer assisted”.     

Potential of a gaussian ring. A new approach

A fundamentally new approach to an elliptic Gaussian ring has been developed. It has been ascertained that it can be produced from a uniform plane elliptic disk by mass balayage into an elementary homothetic layer with the center of homothety at an ellipse focus. An advantage of new interpretation is in the fact that the spatial potential of a Gaussian ring is expressed in terms of the potential of a uniform elliptic disk, well-known in the finite form, and its derivatives. A general formula for the potential of a two-dimensional homothetic layer has been derived with this purpose. As a result, the potential of a Gaussian ring is represent-able in a simple analytical form in terms of standard complete elliptic integrals in both elliptic and Cartesian coordinates. The mass asymmetry along the ring is considered explicitly. The potential formulas are verified numerically and have no singular points at ellipse foci. Particular cases are considered; the 3D potential surface and system of equipotentials are constructed. Knowledge of the potential extends the range of application of a Gaussian ring in the problem of calculation of secular perturbations in celestial mechanics.     

Radiative steady-state colliding stellar wind models: are they correct?

The properties of radiative steady-state colliding stellar winds in binary systems are studied. It is shown that the presence of a singularity at the stagnation point has a major influence on the structure of these flows. This problem is of great importance if their stability properties are considered. None of the existing models treats this mathematical problem properly, and special efforts must be undertaken in the future in order to come to a firm conclusion about the physical nature of possible instabilities. At the moment, neither numerical nor analytical models can be considered to be of acceptable accuracy in the case of highly radiative steady-state colliding stellar winds.     

Motion of dust in mean motion resonances with planets

Effect of stellar electromagnetic radiation on the motion of spherical dust particle in mean motion orbital resonances with a planet is investigated. Planar circular restricted three-body problem with the Poynting–Robertson (P–R) effect yields monotonic secular evolution of eccentricity when the particle is trapped in the resonance. Planar elliptic restricted three-body problem with the P–R effect enables nonmonotonous secular evolution of eccentricity and the evolution of eccentricity is qualitatively consistent with the published results for the complicated case of interaction of electromagnetic radiation with nonspherical dust grain. Thus, it is sufficient to allow either nonzero eccentricity of the planet or nonsphericity of the grain and the orbital evolutions in the resonances are qualitatively equal for the two cases. This holds both for exterior and interior mean motion orbital resonances. Evolutions of argument of perihelion in the planar circular and elliptical restricted three-body problems are shown. Numerical integrations show that an analytic expression for the secular time derivative of the particle’s argument of perihelion does not exist, if only dependence on semimajor axis, eccentricity and argument of perihelion is admitted. Connection between the shift of perihelion and oscillations in secular eccentricity is presented for the planar elliptic restricted three-body problem with the P–R effect. Period of the oscillations corresponds to the period of one revolution of perihelion. Change of optical properties of the spherical grain with the heliocentric distance is also considered. The change of the optical properties: (i) does not have any significant influence on the secular evolution of eccentricity, (ii) causes that the shift of perihelion is mainly in the same direction/orientation as the particle motion around the Sun. The statements hold both for circular and noncircular planetary orbits.     

Methods of Laser,Non-Linear,and Fiber Optics in Studying Fundamental Problems of Astrophysics

Precise measurements of Doppler shifts of lines in stellar spectra allowing the radial velocity to be measured are an important field of astrophysical studies. A remarkable feature of the Doppler spectroscopy is the possibility to reliably measure quite small variations of the radial velocities (its acceleration, in fact) during long periods of time. Influence of a planet on a star is an example of such a variation. Under the influence of a planet rotating around a star, the latter demonstrates periodic motion manifested in the Doppler shift of the stellar spectrum. Precise measurements of this shift made it possible to indirectly discover planets outside the Solar system (exoplanets). Along with this, searching for Earth-type exoplanets within the habitable zone is an important challenge. For this purpose, accuracy of spectral measurements has to allow one to determine radial velocity variations at the level of centimeters per second during the timespans of about a year. Suchmeasurements on the periods of 10–15 years also would serve as a directmethod for determination of assumed acceleration of the Universe expansion. However, the required accuracy of spectroscopic measurements for this exceeds the possibilities of the traditional spectroscopy (an iodine cell, spectral lamps). Methods of radical improvement of possibilities of astronomical Doppler spectroscopy allowing one to attain the required measurement accuracy of Doppler shifts are considered. The issue of precise calibration can be solved through creating a system of a laser optical frequency generator of an exceptionally high accuracy and stability.     

“Anti-glitches” in the Quark–Nova model for AXPs I

In the Quark–Nova model, Anomalous X-ray Pulsars (AXPs) are quark stars surrounded by a degenerate iron-rich Keplerian ring (a few stellar radii away). AXP bursts are caused by accretion of chunks from the inner edge of the ring following magnetic field penetration. For bright bursts, the inner disk is prone to radiation induced warping which can tilt it into counter-rotation (i.e. retrograde). For AXP 1E2259+586, the 2002 burst satisfies the condition for the formation of a retrograde inner ring. We hypothesize the 2002 burst reversed the inner ring setting the scene for the 2012 outburst and “anti-glitch” when the retrograde inner ring was suddenly accreted leading to the basic observed properties of the 2012 event.     

Rings in the Planetesimal Disk of beta Pictoris

The nearby main-sequence star beta Pictoris is surrounded by an edge-on disk of dust produced by the collisional erosion of larger planetesimals. Here we report the discovery of substructure within the northeast extension of the disk midplane that may represent an asymmetric ring system around beta Pic. We present a dynamical model showing that a close stellar flyby with a quiescent disk of planetesimals can create such rings, along with previously unexplained disk asymmetries. Thus we infer that beta Pic's planetesimal disk was highly disrupted by a stellar encounter in the last hundred thousand years.     

Angular momentum loss and transfer in close binaries: effects on a human time-scale?

The orbital periods of binaries are known to great accuracy, their changes produce an easily detectable cumulative effect and many systems have been observed for more than a century. In tidally locked late-type binaries the orbital period changes are often related to structural or evolutionary changes. The study of the orbital period secular evolution can therefore provide information on phenomena taking place on timescales very short when compared to the typical stellar evolutionary scales, but still much longer than the human lifetime. This paper focuses on the dynamical evolution due to magnetic braking in late-type close binaries and on the detectability of angular momentum transfer among the stellar layers.