Ultraharmonic Resonance Research Articles

Closing the gap: secular evolution of bar-induced dark gaps in the presence of thick discs

ABSTRACT The presence of dark gaps, a preferential light deficit along the bar minor axis, is observationally well known. The properties of dark gaps are thought to be associated with the properties of bars, and their spatial locations are often associated with bar resonances. However, a systematic study, testing the robustness and universality of these assumptions, is still largely missing. Here, we investigate the formation and evolution of bar-induced dark gaps using a suite of N-body models of (kinematically cold) thin and (kinematically hot) thick discs with varying thick disc mass fractions and different thin-to-thick disc geometries. We find that dark gaps are a natural consequence of the trapping of disc stars by the bar. The properties of dark gaps (such as strength and extent) are well correlated with the properties of bars. For stronger dark gaps, the fractional mass-loss along the bar minor axis can reach up to ${\sim} 60\!-\!80$ per cent of the initial mass contained, which is redistributed within the bar. These trends hold true irrespective of the mass fraction in the thick disc and the assumed disc geometry. In all our models harbouring slow bars, none of the resonances (corotation, inner Lindblad resonance, and 4:1 ultraharmonic resonance) associated with the bar correspond to the location of dark gaps, thereby suggesting that the location of dark gaps is not a universal proxy for these bar resonances, in contrast with earlier studies.

Evolution of dark gaps in barred galaxies

Context. Recent studies show that barred galaxies have a light deficit, called a dark gap (DG), in the direction of the bar minor axis with respect to the major axis. The properties of these DGs might be related to the properties of the bars and to the location of some resonances of the galaxies. Aims. We have analyzed the evolution of the DGs properties in the barred galaxy of the GALAKOS simulation to compare them with those from real galaxies and infer conclusions about the evolutionary status of the bars. Methods. The DGs were measured by using the bar and the interbar surface brightness profiles from the Fourier decomposition of the light of the galaxies. We characterized them by two parameters: the prominence of the DG (Δμmax), and its location in the galaxy (RDG). Results. In the GALAKOS simulation, both Δμmax and RDG evolve with time. Thus, the DGs are more prominent and are located at larger radii as the bar evolves. In addition, RDG is smaller than the bar radius (Rb) at all time steps of the simulation, being always Rb/RDG > 1.2. About 90% of the real galaxies show Rb/RDG > 1.2 similar to the GALAKOS simulation. For these objects, the ratio of the corrotation radius (RCR) and the DG radius is RCR/RDG ≈ 1.8. This is similar to the expected ratio of the corrotation resonance (CR) and the ultraharmonic resonance (UHR) radius. This indicates a link between the DGs and the UHR of these galaxies. The remaining 10% of the galaxies show Rb/RDG < 1.2 and RCR/RDG ≈ 1. In these cases, the DG would be linked with the CR of the galaxy. We have found that the bar in GALAKOS, as well as real bars in galaxies, can be located in distinct places on the RCR/h − Rb/h plane based on the prominence of their DGs. In particular, galaxies with high values of Δμmax are located at RCR/h and Rb/h larger than 1.5. The simulated bar turned to be a slow rotator when Δμmax was larger than 0.8. When this occurs, RCR/h and Rb/h are larger than 2.0 and 1.5, respectively, for the GALAKOS bar. Conclusions. The location of the DG seems to be a robust signature of the location of the galaxy resonances. In addition, the prominence of the DG could be used as indicators of the amount of angular momentum exchange by the bar and other galactic components. Galaxies with Δμmax > 0.8 would be candidates for slow bar rotators. In addition, flat bars would be more evolved or would have exchanged more angular momentum than exponential bars.

Photometric Signature of Ultraharmonic Resonances in Barred Galaxies

Bars may induce morphological features, such as rings, through their resonances. Previous studies suggested that the presence of “dark gaps,” or regions of a galaxy where the difference between the surface brightness along the bar major axis and that along the bar minor axis is maximal, can be attributed to the location of bar corotation. Here, using GALAKOS, a high-resolution N-body simulation of a barred galaxy, we test this photometric method’s ability to identify the bar corotation resonance. Contrary to previous work, our results indicate that “dark gaps” are a clear sign of the location of the 4:1 ultraharmonic resonance instead of bar corotation. Measurements of the bar corotation can indirectly be inferred using kinematic information, e.g., by measuring the shape of the rotation curve. We demonstrate our concept on a sample of 578 face-on barred galaxies with both imaging and integral field observations and find that the sample likely consists primarily of fast bars.

Multi-parametric Dynamic Analysis of a Rolling Bearings System

A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.

On the threshold of 1/2 order subharmonic emissions in the oscillations of ultrasonically excited bubbles

The pressure threshold for 1/2 order subharmonic (SH) emissions and period doubling during the oscillations of ultrasonically excited bubbles is thought to be minimum when the bubble is sonicated with twice its resonance frequency (fr). This estimate is based on studies that simplified or neglected the effects of thermal damping. In this work, the nonlinear dynamics of ultrasonically excited bubbles is investigated accounting for the thermal dissipation. Results are visualized using bifurcation diagrams as a function of pressure. Here we show that, and depending on the gas, the pressure threshold for 1/2 order SHs can be minimum at a frequency between 0.5fr≤f≤0.6fr. In this frequency range, the generation of 1/2 order SHs are due to the occurrence of 5/2 order ultra-harmonic resonance. The stability of such oscillations is size dependent. For an air bubble immersed in water, only bubbles bigger than 1 μm in diameter are able to emit non-destructive SHs in these frequency ranges.

Stellar Migration in Galaxy Disks Using the Chirikov Diffusion Rate

Abstract We are reexamining the problem of stellar migration in disk galaxies from a diffusion perspective. We use for the first time the formulation of the diffusion rates introduced by Chirikov, applied to both energy, E, and angular momentum, L z , in self-consistent N-body experiments. We limit our study to the evolution of stellar disks well after the formation of the bar, in a regime of adiabatic evolution. We show that distribution functions of Chirikov diffusion rates have similar shapes, regardless of the simulations, but different slopes for energy and angular momentum. Distribution functions of derived diffusion timescales, T D , also have the same form for all simulations, but are different for T D (E) and T D (L z ). Diffusion timescales are strongly dependent on L z . in a L z range roughly delimited by the set of stellar bar resonances (between the ultraharmonic resonance and the outer Lindblad resonance). Only particles with low L z have , i.e., the simulation length. In terms of mass fraction, 35%–42% turn out to diffuse energy in a characteristic timescale shorter than 10 Gyr, i.e., simulations length, while 60%–64% undergo the diffusion of the angular momentum on the same timescale. Both the diffusion of L z and E are important to grasp the full characterization of the radial migration process, and we show that depending on the spatial region considered, one or the other diffusion dominates.

Inner and outer rings are not strongly coupled with stellar bars

Rings are distinctive features of many disc galaxies and their location and properties are closely related to the disc dynamics. In particular, rings are often associated to stellar bars, but the details of this connection are far from clear. We have studied the frequency and dimensions of inner and outer rings in the local Universe as a function of disc parameters and the amplitude of non-axisymmetries. We used the 1320 not highly inclined disc galaxies (i < 65°) from the S4G survey. The ring fraction increases with bar Fourier density amplitude: this can be interpreted as evidence for the role of bars in ring formation. The sizes of inner rings are positively correlated with bar strength: this can be linked to the radial displacement of the 1/4 ultraharmonic resonance while the bar grows and the pattern speed decreases. The ring’s intrinsic ellipticity is weakly controlled by the non-axisymmetric perturbation strength: this relation is not as strong as expected from simulations, especially when we include the dark matter halo in the force calculation. The ratio of outer-to-inner ring semi-major axes is uncorrelated with bar strength: this questions the manifold origin of rings. In addition, we confirm that (i) ∼1/3 (∼1/4) of the galaxies hosting inner (outer) rings are not barred; (ii) on average, the sizes and shapes of rings are roughly the same for barred and non-barred galaxies; and (iii) the fraction of inner (outer) rings is a factor of 1.2−1.4 (1.65−1.9) larger in barred galaxies than in their non-barred counterparts. Finally, we apply unsupervised machine learning (self-organising maps, SOMs) to show that, among early-type galaxies, ringed or barred galaxies cannot be univocally distinguished based on 20 internal and external fundamental parameters. We confirm, with the aid of SOMs, that rings are mainly hosted by red, massive, gas-deficient, dark-matter poor, and centrally concentrated galaxies. We conclude that the present-day coupling between rings and bars is not as robust as predicted by numerical models, and diverse physical mechanisms and timescales determine ring formation and evolution.

The effect of high viscosity on the evolution of the bifurcation set of a periodically excited gas bubble

In this study, a nonlinear investigation of a periodically driven gas bubble in glycerine is presented. The bifurcation structure of the bubble oscillator (Keller–Miksis equation) is explored in the pressure amplitude-frequency parameter plane of the excitation by means of initial (high resolution bi-parametric plots) and boundary value problem solvers at various ambient temperatures. The range of the applied temperature covers two orders of magnitude difference in the liquid viscosity which is the main damping factor of the system. Therefore, the evolution of the harmonic and ultraharmonic resonances are presented starting with an overdamped behaviour (there are no resonances in the parameter space) and ending up with a fully developed bifurcation superstructure. The results reveal a complex period bubbling mechanism organized in a Farey-tree; inside each bubble a fine substructure of alternating chaotic and periodic bands exist. The description of the bifurcation structure presented throughout the paper can help to understand the mechanism of dissipation on the behaviour of nonlinear systems in more detail.

The galactic branches as a possible evidence for transient spiral arms

With the use of a background Milky-Way-like potential model, we performed stellar orbital and magnetohydrodynamic (MHD) simulations. As a first experiment, we studied the gaseous response to a bisymmetric spiral arm potential: the widely employed cosine potential model and a self-gravitating tridimensional density distribution based model called PERLAS. Important differences are noticeable in these simulations, while the simplified cosine potential produces two spiral arms for all cases, the more realistic density based model produces a response of four spiral arms on the gaseous disk, except for weak arms -i.e. close to the linear regime- where a two-armed structure is formed. In order to compare the stellar and gas response to the spiral arms, we have also included a detailed periodic orbit study and explored different structural parameters within observational uncertainties. The four armed response has been explained as the result of ultra harmonic resonances, or as shocks with the massive bisymmetric spiral structure, among other. From the results of this work, and comparing the stellar and gaseous responses, we tracked down an alternative explanation to the formation of branches, based only on the orbital response to a self-gravitating spiral arms model. The presence of features such as branches, might be an indication of transiency of the arms.

油气悬架车辆振动非线性特性分析与仿真研究<br>Nonlinear Characteristics Analysis and Simulation on Vibration for Vehicle with Hydro-Pneumatic Suspensions

建立了二自由度汽车油气悬架系统模型,分析了油气悬架和车身模型的非线性特性。运用AMEsim仿真软件，通过模型对不同的激振频率的时域和频谱响应分析，验证了油气悬架非线性振动模型的正确性。仿真结果表明，系统产生了接近激振频率分数（或整数倍）的频率分量，造成亚谐波（或超谐波）共振，导致系统振动不稳定。 The non-linear characteristics of hydro-pneumatic suspension and car body model are analyzed in this paper, and two-degree-of-freedom vibration model of hydro-pneumatic suspension is modeled. Dynamic time domain and frequency response to different vibration frequency verify the correctness of the non-linear model by AMEsim simulation software. Results show that the unstable vibration state is due to subharmonic or ultraharmonic resonance produced by the frequency components which are close to the fraction or the integer times of excitation frequency in the system.

Molecular gas in NUclei of GAlaxies (NUGA)

In this paper we create a complete gravity torque map of the disk of the LINER/Seyfert 1.9 galaxy NGC 4579. We quantify the efficiency of angular momentum transport and search for signatures of secular evolution in the fueling process from r ∼ 15 kpc down to the inner r ∼ 50 pc around the active galactic nucleus (AGN). We use both the 1− 0a nd 2−1 line maps of 12 CO obtained with the Plateau de Bure Interferometer (PdBI) as part of the NUclei of Galaxies-(NUGA)-project. The CO(1−0) and CO(2−1) PdBI maps at 2.0 �� × 1.3 �� and 1.0 �� × 0.6 �� resolution, respectively, include the short spacing correction provided by IRAM-30 m data. We derive the stellar potential from an NIR (K band) wide field image of the galaxy. The K-band image, which reveals a large-scale stellar bar and a weak nuclear oval, together with a high-resolution Hi map of NGC 4579 obtained with the Very Large Array (VLA), allow us to extend the gravity torque analysis to the outer r ≥ 2 kpc disk. The bulk of the gas response traced by the new CO PdBI+30 m maps of NGC 4579 presented here follows the expected gas flow pattern induced by the bar potential in the presence of two inner Lindblad resonances (ILR) at r ∼ 500 pc and r ∼ 1.3 kpc. The morphology of the outer disk traced by Hi suggests that the neutral gas is currently piling up in a pseudo-ring formed by two winding spiral arms that are morphologically decoupled from the bar structure. The pseudo-ring is located inside the bar corotation (rCR ∼ 6 kpc) and close to the predicted position of the ultra harmonic resonance (UHR) (rUHR ∼ 3.8 kpc). The derived gravity torque budget in NGC 4579 shows that inward gas flow is occurring on different spatial scales in the disk. In the outer disk, the decoupling of the spiral allows the gas to efficiently populate the UHR region, and thus produce net gas inflow on intermediate scales. The corotation barrier seems to be overcome by secular evolution processes. The gas in the inner disk (r ≤ 2 kpc) is efficiently funneled by gravity torques down to r ∼ 300 pc. Closer to the AGN (r < 200 pc), gas feels negative torques due to the combined action of the large-scale bar and the inner oval. The two m = 2 modes act in concert to produce net gas inflow down to r ∼ 50 pc, providing clear smoking gun evidence of inward gas transport on short dynamical timescales (∼1−3 rotation periods).

Resonance‐related Spiral Substructure in a Galactic Gaseous Disk

We use high resolution 2D hydrodynamic simulations to study the formation of spiral substructure in the gaseous disk of a galaxy. The obtained gaseous response is driven by a self-consistent non-axisymmetric potential obtained from an imposed spiral mass distribution. We highlight the importance of ultraharmonic resonances in generating these features. The temporal evolution of the system is followed with the parallel ZEUS-MP code, and we follow the steepening of perturbations induced by the spiral potential until large-scale shocks emerge. These shocks exhibit bifurcations that protrude from the gaseous arms and continue to steepen until new shocks are formed. When the contribution from the spiral potential relative to the axisymmetric background is increased from our default value, spurs protrude from the main arms after several revolutions of the gaseous disk. Such spurs overlap on top of the aforementioned shocks. These results support the hypothesis that a complicated gaseous response can coexist with an orderly spiral potential term, in the sense that the underlying background potential can be smooth yet drive a gaseous response that is far more spatially complex.

The distribution of stellar population age in galactic bars

Recent analysis of stellar populations in barred galaxies have focused on the spatial distribution of stellar population ages and metallicities. However, barred galaxies are complex objects where dynamical instabilities play a leading role in shaping any spatial distribution. The age distribution of stellar populations should thus be analyzed from the two points of view of stellar population evolution and dynamical secular evolution. Chemodynamical simulations of single barred galaxies with simple but realistic star formation and feedback recipes are used to produce face-on mass-weighted maps of stellar population ages. Luminosity-weighted maps in V-band are also displayed after calibrating the simulation with mass-to-light ratios provided by a synthesis population model. It is shown that inside a stellar bar two persistent diametrically opposed regions display a mean age lower than the surrounding average. These two low-age regions are due to the accumulation of young stellar populations trapped on elliptical-like orbits along the bar, near the ultra-harmonic resonance. Age gradients along the bar major-axis are comparable to recent observations. Another low-age region is the outer ring located near the Outer Lindblad Resonance, but the presence and strength of this structure is very time-dependent.

Chemodynamical models of barred galaxies

The use of chemodynamical simulations of disc galaxies calibrated in B and K bands allows us to compare the location of Ultra Harmonic Resonance (UHR) and corotation (CR) with photometrically estimated bar lengths. We apply several observational criteria to determine bar lengths. We show that the minimum of ellipticity located just outside the bulk of the bar is correlated with CR whereas the location of UHR can be approximated using the end of the position-angle plateau of bar isophotes. We give evidence that the classification of slow/fast bars, based on the ratio = R CR /R bar could increase from 1 (fast bar) to 1.4 (slow bar) just by a change of method.

Chemodynamical models of barred galaxies

The use of chemodynamical simulations of disc galaxies calibrated in B and K bands allows us to compare the location of Ultra Harmonic Resonance (UHR) and corotation (CR) with photometrically estimated bar lengths. We apply several observational criteria to determine bar lengths. We show that the minimum of ellipticity located just outside the bulk of the bar is correlated with CR whereas the location of UHR can be approximated using the end of the position-angle plateau of bar isophotes. We give evidence that the classification of slow/fast bars, based on the ratio = R CR /R bar could increase from 1 (fast bar) to 1.4 (slow bar) just by a change of method.

The length of stellar bars in SB galaxies and N-body simulations

We have investigated the accuracy and reliability of six methods used to determine the length of stellar bars in galaxies or N-body simulations. All these methods use ellipse fitting and Fourier decomposition of the surface brightness. We have applied them to N-body simulations that include stars, gas, star formation, and feedback. Stellar particles were photometrically calibrated to make B and K-band mock images. Dust absorption is also included. We discuss the advantages and drawbacks of each method, the effects of projection and resolution, as well as the uncertainties introduced by the presence of dust. The use of N-body simulations allows us to compare the location of Ultra Harmonic Resonance (UHR or 4/1) and corotation (CR) with measured bar lengths. We show that the minimum of ellipticity located just outside the bulk of the bar is correlated with the corotation, whereas the location of the UHR can be approximated using the phase of the fitted ellipses or the phase of the m=2 Fourier development of the surface brightness. We give evidence that the classification of slow/fast bars, based on the ratio R = Rcr/Rbar could increase from 1 (fast bar) to 1.4 (slow bar) just by a change of method. We thus conclude that one has to select the right bar-length estimator depending on the application, since these various estimators do not define the same physical area.

Evolution of Stellar Bars in Live Axisymmetric Halos: Recurrent Buckling and Secular Growth

Evolution of stellar bars in disk galaxies is accompanied by dynamical instabilities and secular changes. Following the vertical buckling instability, the bars are known to weaken dramatically and develop a pronounced boxy/peanut shape when observed edge-on. Using high-resolution N-body simulations of stellar disks embedded in live axisymmetric dark matter halos, we have investigated the long-term changes in the bar morphology, specifically the evolution of the bar size, its vertical structure, and the exchange of angular momentum. We find that following the initial buckling, the bar resumes its growth from deep inside the corotation radius and follows the ultraharmonic resonance thereafter. We also find that this secular bar growth triggers a spectacular secondary vertical buckling instability that leads to the appearance of characteristic boxy/peanut/X-shaped bulges. The secular bar growth is crucial for the recurrent buckling to develop. Furthermore, the secondary buckling is milder, persists over a substantial period of time, ~3 Gyr, and can have observational counterparts. Overall, the stellar bars show recurrent behavior in their properties and evolve by increasing their linear and vertical extents, both dynamically and secularly. We also demonstrate explicitly that the prolonged growth of the bar is mediated by continuous angular momentum transfer from the disk to the surrounding halo and that this angular momentum redistribution is resonant in nature: a large number of lower resonances trap disk and halo particles, and this trapping is robust, in broad agreement with the earlier results in the literature.

Nonlinear analysis on the coupling process of electromagnetic vibrator and earth

The linear model based on the hydraulic pressure vibrator has been no longer adaptable to the electromagnetic vibrator. In order to realize the effective transmission of the limited energy from the vibrator to the ground, it is important to study the coupling model of the electromagnetic vibrator and the earth. In this paper, a nonlinear restore term was introduced to the coupling model because of the existence of a large amount of harmonics in the vibrator baseplate. The nonlinear vibration analysis was applied to the model by the multiscale method. In the course of energy transmission from the vibrator to the ground, ultraharmonic resonance was used to explain the generation of harmonics. An improved scheme was advanced to select the cross correlation reference signal in the vibrator seismic exploration. Good application results were obtained in field experiments.

Branch, Spur, and Feather Formation in Spiral Galaxies

We use hydrodynamic simulations to investigate the response of geometrically thin, self-gravitating, singular isothermal disks of gas to imposed rigidly rotating spiral potentials. By minimizing reflection-induced feedback from boundaries, and by restricting our attention to models where the swing parameter X ~ 10, we minimize the swing amplification of global normal modes even in models where Toomre's Qg ~ 1-2 in the gas disk. We perform two classes of simulations: short-term ones over a few galactic revolutions where the background spiral forcing is large, and long-term ones over many galactic revolutions where the spiral forcing is considerably smaller. In both classes of simulations, the initial response of the gas disk is smooth and mimics the driving spiral field. At late times, many of the models evince substructure akin to the so-called branches, spurs, and feathers observed in real spiral galaxies. We comment on the parts played respectively by ultraharmonic resonances, reflection off internal features produced by nonlinear dredging, and local, transient, gravitational instabilities within spiral arms in the generation of such features. Our simulations reinforce the idea that spiral structure in the gaseous component becomes increasingly flocculent and disordered with the passage of time, even when the background population of old disk stars is a grand-design spiral. We speculate that truly chaotic behavior arises when many overlapping ultraharmonic resonances develop in reaction to an imposed spiral forcing that has itself a nonlinear, yet smooth, wave profile.

An Hαstudy of the kinematics of NGC 3627

We report here on the first observations in the Hα line to investigate the kinematics of the spiral galaxy NGC 3627, the brightest member of the Leo Triplet. The velocity field observed at high angular resolution shows signatures of non-circular motion. They can be attributed to dynamical perturbations due to the bar and to external interactions. In particular, we confirm the presence of an inner ring recently detected in CO observations (Regan et al. 2002). We find a corotation radius significantly smaller than that derived in previous studies and we show that the inner ring location is consistent with the ultra-harmonic resonance induced by the bar pattern speed. We also show that a warped tilted-ring model can be fitted to the outer parts of the southern, receding half of the disc, which is inclined by some 15 ◦ relative to the inner parts of the galaxy.