diff --git "a/19FIT4oBgHgl3EQf4Su_/content/tmp_files/load_file.txt" "b/19FIT4oBgHgl3EQf4Su_/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/19FIT4oBgHgl3EQf4Su_/content/tmp_files/load_file.txt" @@ -0,0 +1,534 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf,len=533 +page_content='MNRAS 000, 1–7 (2023) Preprint 30 January 2023 Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='0 Formation of asymmetric arms in barred galaxies P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín,1⋆ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' García-Gómez,2 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Masdemont3 and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Romero-Gómez4 1 IUMA, Universidad de Zaragoza, Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' de Matemática Aplicada, Pedro Cerbuna, 12, 50009 Zaragoza, Spain 2D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='M, Universitat Rovira i Virgili, Avd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Països Catalans, 26, 43007 Tarragona, Spain 3IEEC & Universitat Politècnica de Catalunya, Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' de Matemàtiques, Diagonal 647, E08028 Barcelona, Spain 4Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, E08028 Barcelona, Spain Accepted XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Received YYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' in original form ZZZ ABSTRACT We establish a dynamical mechanism to explain the origin of the asymmetry between the arms observed in some barred disk galaxies, where one of the two arms emanating from the bar ends is very well defined, while the second one displays a ragged structure, extending between its ridge and the bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' To this purpose, we study the invariant manifolds associated to the Lyapunov periodic orbits around the unstable equilibrium points at the ends of the bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Matter from the galaxy center is transported along these manifolds to the periphery, forming this way the spiral arms that emanate from the bar ends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' If the mass distribution in the galaxy center is not homogeneous, because of an asymmetric bar with one side stronger than the other, or because of a non-centered bulge, the dynamics about the two unstable Lagrange points at the ends of the bar will not be symmetric as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' One of their invariant manifolds becomes more extended than the other, enclosing a smaller section and the escaping orbits on it are fewer and dispersed in a wider region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The result is a weaker arm, and more ragged than the one at the other end of the bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Key words: galaxies: kinematics and dynamics – galaxies: structure – galaxies: spiral 1 INTRODUCTION A high fraction of disk galaxies appear to be barred (74% to 85% in automatic classifications or 36% to 63% with alternative meth- ods (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2019)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' These authors also suggest that strongly barred galaxies, classified as SBs, are preponderant in late-type galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Most of these strongly barred galaxies appear to be asym- metric under a simple visual inspection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' They usually present a strong bar and two spiral arms emanating from the bar ends, and frequently some inner rings as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' However, a detailed visual in- spection of these galaxies, available in the STScI Digitized Sky Sur- vey or in the Sloan Digital Sky Survey (SDSS) (Bundy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2015), reveals that some barred galaxies exhibit important asymmetries in their spiral structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' While one of the two spiral arms is long and strongly defined, the second arm shows a ragged structure, and the matter is distributed irregularly between the ridge of the spiral arm and the bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' A non-symmetric distribution of matter in the galaxy disc can be a natural outcome, since disc galaxies may be formed through a combination of secular evolution and violent events, in- cluding smooth accretion, disc instabilities and minor and major mergers (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Tonini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 1 we show some examples of galaxies showing asymmetric discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In this paper we study the dynamic response of an asymmetric mass distribution on the orbital structure of barred galaxies, mod- elling the asymmetry of the central parts by a slightly off-centered bulge which, viewing the galaxy as a whole, represents a simple but realistic model of an asymmetric bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In this scenario, the Lagrange ⋆ E-mail: patricias@unizar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='es Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Images of some strongly barred galaxies showing the asymmetric spiral arm patterns in the R-filter from the STScI Digitized Sky Survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the top row we show the galaxies PGC 05849 (NGC 0613), PGC 12412 (NGC 1300) and in the bottom one PGC 15941 (NGC 1672) and PGC 54849 (NGC 5921).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' invariant points located at the bar ends will present also an asym- metric orbital structure, as initially shown in Colin & Athanassoula (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The new step in this work is to additionally study the unsta- ble periodic orbits around these Lagrange points and the associated unstable manifolds which provide escape routes for orbits which can transport material from the central regions to the outer parts of the discs (Romero-Gómez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' © 2023 The Authors arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='11385v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='GA] 26 Jan 2023 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='PGC 05849(R) PGC 12412 (R) PGC 15941 (R) PGC 54849 (R)2 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' These unstable manifolds are the backbones of the spiral arms ema- nating from the bar ends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the case of asymmetric Lagrange points, however, the unstable manifolds display also important differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The orbits following one of these manifolds are close together and can explain the presence of a strong spiral arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' On the other hand, the second manifold has a more open orbital structure, with its es- caping orbits dispersed in a wider zone, causing the ragged struc- ture of the second arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Thus, the orbital structure of the unstable Lagrange points is able to explain the asymmetric phenomenology present in some of the strongly barred galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The paper is organized as follows: in Section 2 we quantify the level of asymmetry in asymmetric barred galaxies using a two- dimensional Fourier transform method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In Sections 3 and 4 we de- scribe the asymmetric barred galaxy model used in this work and show the orbital analysis and invariant manifolds, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Dif- ferent approaches are summarized and conclusions are given in Sec- tion 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2 ANALYSIS OF THE BAR ASYMMETRY In this paper, we model the galactic asymmetric mass distribution using a classical galactic model with three symmetric components (disc, bar and bulge) but displacing slightly the bulge from the galaxy centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' This results in a total mass distribution biased to- wards one side of the bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Many barred galaxies show some kind of asymmetries in their inner mass distribution with one side of the bar stronger than the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' An example is the galaxy NGC 1300, studied by Patsis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' They generated a numerical model of the potential using K images of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The resultant model was clearly asymmetric, containing a bar with a stronger arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' This model was used to study the orbits associated with this asymmetric barred structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Many barred galaxies show similar asymmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Some of these galaxies are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In order to quantify these asymmetries, we can analyze in detail the mass distribution of one of the galaxies showing this phenomenology, namely the galaxy PGC 70419 (NGC 7479).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' For this purpose, we use a galaxy image from the SDSS survey in the infrared z-filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Assuming a constant M/L ratio, the light distribution is a good tracer of the mass distribu- tion in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The image is previously cleaned from background stars and then deprojected using the FFT method (García-Gómez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2004) giving a position angle (PA) of 38◦ and an inclination angle of 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The image is then decomposed in its Fourier components using a technique first introduced by Considère & Athanassoula (1982);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Iye et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (1982), and further developed by García-Gómez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' For deprojected image of the galaxy I(u,θ), where u = ln(r), we cal- culate the two-dimensional Fourier transform defined as A(p,m) = � umax umin � 2π 0 I(u,θ)ei(pu+mθ) dθdu (1) Where m is the azimuthal frequency, associated with the multiplicity of the structures, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', the number of arms while p is the radial fre- quency, associated to the pitch angle of the structure i, through the relation p = − m tan(i) (2) In this way, the m = 1 spectrum contains the spiral components with no symmetry, the m = 2 spectrum the components with a periodicity of π radians or bisymmetric signals, and so on for the rest of the m frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Each of the azimuthal components m = 1,2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' can be further decomposed in its radial components using a Gaussian fit to the modulus and keeping the phase constant as follows: | A(p,m) |= Ng � j=1 C j exp−(p− pj)2 2σ2 j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (3) In this relation, pj represents the central frequency of the Gaussian, σj its dispersion, and C j its amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The number of Gaussians used in each fit, Ng, will depend on the complexity of the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the upper panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2 we show the deprojected SDSS galaxy image of NGC 7479 using the z-filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Note that one of its arms is very pronounced, while the opposite arm appears diffuse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' On the left of the middle and lower panels of this figure we show the modulus of the Fourier spectrum of the m = 1 component which is associ- ated to the asymmetries in the light distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The modulus of the Fourier components are normalized to the modulus of the stronger component, which in this case is the m = 2 containing the bisymmet- ric signals of the strong bar and the spiral arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The m = 1 spectrum shown here contains the spiral components responsible for the asym- metries in the mass distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The relative low values of the m = 1 in this scale shows that the mass asymmetry is a second order effect for this galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In red we superpose two of the Gaussian components into which this signal is decomposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' These Gaussian components can be transformed back to obtain the density distribution associated to each particular spiral mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The density distributions of these spi- ral components are presented in the respective right panels in green, superposed on the galaxy image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The isocontours come from the normalized density corresponding to the Gaussian components and show that the asymmetries are related to the southern end of the bar and the strong arm emanating from its end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' This shows that the galaxy has an asymmetric mass distribution, biased to the southern part of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 3 CHARACTERISTICS OF THE GALACTIC MODEL The equations of motion of the classical galactic model (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Pfenniger 1984;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Skokos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Romero-Gómez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2016) describe the movement of a particle in a gravitational potential φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the rotating frame, the equations of motion are described by ¨r = −2(Ωp × ˙r)−Ωp ×(Ωp ×r)−∇φ, (4) where r = (x, y, z) is the position of the particle, φ is the total grav- itational potential of the system and Ωp is the angular velocity of the bar around the z-axis, Ωp = (0,0,Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The origin of the reference frame is located at the center of mass of the system and the frame is aligned with the main axis of the bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The potential model φ used in this paper is a combination of three analytical components: an axisymmetric Miyamoto-Nagai disc with potential φd (Miyamoto & Nagai 1975), an ellipsoid Ferrers bar with potential φb (Ferrers 1877) and a bulge structure represented by a Plummer spheroid potential φbl (Plummer 1911).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The total potential is the addition of these three components, φ = φd +φb +φbl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The disc potential is described by the equation φd = − GMd � R2 +(A+ � B2 +z2)2 , (5) were R2 = x2 + y2 is the cylindrical coordinate radius of the poten- tial in the disc plane, and z is the vertical distance over the disk component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The parameters G, Md, A and B denote the gravitational MNRAS 000, 1–7 (2023) Formation of asymmetric arms in barred galaxies 3 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Analysis of the m = 1 component of the SDSS galaxy image of NGC 7479 in the z-filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The upper panel shows the deprojected image of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' On the left of the middle and lower panels we show the modulus of the m = 1 component of the Fourier spectrum, and with red-dashed lines two Gaussian components fitted to this modulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the respective right panels, we show in green the density distribution associated to each of these single components superimposed on the galaxy image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' constant, the disc mass and the shape of the disc, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Tak- ing A = 0 the potential becomes the Plummer potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The bar is modelled by an ellipsoid with density function ρ = � ρ0(1−m2)nh, m ≤ 1 0, m > 1 (6) where m2 = x2/a2 + y2/b2 + z2/c2, a (semi-major axis), b (interme- diate axis) and c (semi-minor axis) determine the shape of the bar, nh is the homogeneity degree of the mass distribution (nh = 2 in our work) and ρ0 is the density at the origin (ρ0 = 105 32π GMb abc if nh = 2, where Mb is the bar mass).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The unit of length considered is the kpc, the time unit is ut = 2 × 106 yr, Ω is in [ut]−1, and the mass unit is uM = 2 × 1011M⊙, where M⊙ denotes the mass of the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' G stands for the gravitational constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In our model, we select a disc radius of A = 3 kpc, height B = 1 kpc and mass giving a value of GMd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='52 kpc3/u2 t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The dimensions of the bar are a = 6 kpc, b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5 kpc, c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='4 kpc, and its mass is such that GMb = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='4 kpc3/u2 t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The Plummer bulge with a radius B = 1 kpc and GMbl is set to have around 15% of the mass of the bar GMb, in order that G(Md + Mb + Mbl) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The bar pattern speed is fixed as Ω = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='0633 [ut]−1 (∼ 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='97 km/s/kpc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the rotating reference frame aligned with the main axis of the bar, the equations of motion given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (4) are written as the fol- lowing dynamical system: ��������� ¨x = 2Ω ˙y+Ω2 x−φx ¨y = −2Ω ˙x+Ω2 y−φy ¨z = −φz .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (7) The Jacobi first integral of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (4) (which can be regarded as the energy in the rotating frame) is given by CJ(x,y,z, ˙x, ˙y, ˙z) = −(˙x2 + ˙y2 + ˙z2)+Ω2 (x2 +y2)−2φ, (8) and the effective potential is defined by φeff = φ− 1 2 Ω2 (x2 +y2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The goal of this paper is to analyze which is the effect of an asym- metric distribution of mass in the central parts of the galaxy on the external spiral structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' To introduce this asymmetry, we displace the bulge potential along the x-axis (main axis of the bar) towards the equilibrium point placed at the right end of the bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The bulge center is then located at (xd,0,0) using several values for the displacement xd (in kpc), namely: (0,0,0), (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0), (1,0,0) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' We move the center of our potential model to the resulting center of mass of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The plot of the equal density contours of the resulting models are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Note that the displacement of the bulge along the main axis of the bar creates an asymmetry in the central part of the model and around the libration points L1 and L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The rotation curves of the model, defined as V2 rot = r dφ dr , where the potential is φ = φd +φb +φbl with the selected values of the parame- ters and for the above explained positions of the bulge displacement, are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The resulting rotation curve is reasonably flat in the outer parts, and displays only minor differences in the position of the maximum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 4 DYNAMICS OF THE MODELS The solutions of ∇φeff = 0 in rotating coordinates give five La- grangian equilibrium points of the model (Li, i = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=',5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Points L1 and L2 are linearly unstable points and lie on the x-axis at the ends of the bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Point L3 is linearly stable and it is placed on the origin of co- ordinates in the case of a symmetric model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Points L4 and L5 are also linearly stable and located out of the x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' A detailed explanation of the dynamics around these points can be found in Athanassoula et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (1983);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Romero-Gómez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (2006);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The regions where φeff > CJ are forbidden regions for a star of en- ergy CJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the plane, these regions are delimited by the zero velocity curves, which are defined by the level surfaces φeff = CJ intersected with z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 5 we show the zero velocity curves corresponding to an energy slightly above of that of the equilibrium point, CJ,Li +δ, for the models with off-centered bulges in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 4, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', setting the val- ues xd = 0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5, 1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' These zero velocity curves limit the inner and outer regions in the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the symmetric case (xd = 0), the en- ergy of both equilibrium points L1 and L2 is the same, CJ,L1 = CJ,L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' For the asymmetric cases, as xd grows CJ,L2 becomes smaller than CJ,L1, which makes the zero velocity curves related to L1 more open at the opposite point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Particular attention is given in this work to the unstable points L1 and L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' They are surrounded by planar and vertical families of Lyapunov periodic orbits, which are unstable in the neighborhood of the equilibrium point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The relevant family for the transport of matter between the inner and outer regions of the galaxy is the planar family (Romero-Gómez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 6 shows the (x, y) projection of the planar family for the models with xd = 0 (solid black line) and xd = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5 (dotted red line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The family around L2 is displayed at the left panel and that around L1 at the right one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In the symmetric case (xd = 0) both families coincide, in the asymmetric one (xd = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5) the family around L2 is smaller than the one around L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' These critical points are characterized by the superposition of a saddle and two harmonic oscillations in the rotating frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Conse- quently, for a given Jacobi constant, stable and unstable invariant MNRAS 000, 1–7 (2023) PGC70419 (z) NGC 7479 m=1 A=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='11 g= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='57 A m=1 A= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='09 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='86 =6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='86 A 10 0 10 p4 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 5 0 5 x 5 0 5 y 5 0 5 x 5 0 5 y 5 0 5 x 5 0 5 y 5 0 5 x 5 0 5 y Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Isodensity curves of the potential φ = φd +φb +φbl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Equilibrium points of the system are marked with a cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The Ferrers bar and the Plummer bulge are outlined by dotted black curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' From left to right: Bulge centered at (0,0,0), (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0), (1,0,0) and at (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 0 2 4 6 8 10 R [kpc] 0 50 100 150 Vrot [km/s] Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Rotation curve of the potential φ = φd + φb + φbl for the bulge centered at (0,0,0) (in blue), (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0) (in red), (1,0,0) (in magenta) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0) (in green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' manifolds emanate from the periodic Lyapunov orbit around each point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The stable manifold is defined as the set of orbits that asymp- totically tend to the periodic orbit forward in time, and the unstable manifold consists of those orbits which depart asymptotically from the periodic orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' These latter manifold drive the escape orbits that are responsible for the visible trajectories, in the form of arms and rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 7 shows the invariant manifolds associated to L1 and L2 for the set of models where xd = 0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5, 1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The effect of an asym- metric mass distribution, modelled by the displacement of the bulge, makes the exterior manifold that emanates from L2 to differ from the invariant manifold associated with L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The transit orbits trapped inside the manifolds are in charge of the transfer of matter, from the inner to the outer regions delimited by the zero velocity curves (Gidea & Masdemont 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Romero- Gómez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' As the dynamics of our system (4) takes place in a four dimensional phase space when we consider orbits with z = ˙z = 0 (the plane z = 0 is invariant), the intersection of the trajectories of the inner branch of the stable in- variant manifold of a Lyapunov orbit with the hyperplane S defined by the section x = 0 in phase space gives a closed curve in the (y, ˙y) projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Given a pair (y, ˙y) and an energy level, this lets us to de- fine a state on S by selecting (0,y,0, ˙x, ˙y,0), where ˙x is determined by the fixed energy level of the Lyapunov orbit and the orientation of the crossing, taking into account Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (8), ˙x = � −˙y2 +Ω2y2 −2φ(0,y,0)−(CJ,Li +δ), (9) with CJ,Li +δ the energy of the Lyapunov orbit around the point Li, i = 1,2, slightly above of that of the equilibrium point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The forward in time integration of initial conditions corresponding to (y, ˙y) points inside the closed curve establishes the trajectories of the particles confined inside the invariant manifold that transit from the inner to the outer region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' This procedure enables us to quantify the amount of matter trans- ferred inside each invariant manifold associated to any energy level and, consequently, from each spiral arm of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 8 repre- sents the (y, ˙y) projection of the intersection with the hyperplane S of the invariant manifolds arising from three orbits with different Ja- cobi constants in the Lyapunov family around L2 (top), and the same corresponding orbits for L1 (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The three closed curves are displayed with different colors, from red to yellow, according to the increasing Jacobi constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The initial conditions located inside each of the closed curves are marked with crosses of the same color as the curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' From left to right, the figure displays the (y, ˙y) projection for the models with bulge center ranging from (0,0,0) to (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The main feature to notice in this figure is the narrowing and stretching of the curves as the bulge moves away from the L2 equilibrium point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' This constriction marks the difference between initial conditions for the escape orbits related with L2 and those related to L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The initial conditions emanating from near L2 are more extended along the y- axis, resulting in a dispersion in space of the orbits enclosed by the manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' As we integrate forward in time these initial conditions, we obtain fewer escape orbits, and dispersed in a wider region, in comparison to those emanating near L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' So, the spiral arm defined by these orbits becomes more spread out and less bright.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The result of these integrations is exhibited in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 9 where it can be appreci- ated how the orbits inside the invariant manifolds develop the arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The orbits corresponding to the L1 point are more concentrated as the density of the bar increases in the region close to L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 5 DISCUSSION AND CONCLUSIONS The goal of this work is to analyze the relation between the asym- metric arms observed in certain barred galaxies and the mass distri- bution in the central part of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' We propose and show that there is a strong correlation between their asymmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The mod- els used to study this fact consist of a superposition of a bar and an off-centered bulge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The displacements of the bulge along the main axis of the bar introduce an increasing asymmetry in the central part of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' When the center of mass of the galaxy is displaced along the major axis of the bar, the zero velocity curves of the ef- fective potential become asymmetric: the one at the opposite side of the dispacement becomes more open (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' We show that this asymmetry between the zero velocity curves in their opening is carried to the orbits trapped by invariant manifolds around the Lagrangian equilibrium points L1 and L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' This orbits become asym- MNRAS 000, 1–7 (2023) Formation of asymmetric arms in barred galaxies 5 5 0 5 x 5 0 5 y 5 0 5 x 5 0 5 y 5 0 5 x 5 0 5 y 5 0 5 x 5 0 5 y Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Zero velocity curves for a Jacobi constant slightly above to that of L1 (blue) and for one slightly above to that of L2 (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Equilibrium points of the system are marked with a cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The Ferrers bar and the Plummer bulge are outlined by dotted black curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' From left to right: Bulge centered at (0,0,0), (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0), (1,0,0) and at (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 7 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5 6 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5 x 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='4 y 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5 6 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5 7 x 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='4 y Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Lyapunov family of periodic orbits around Li, i = 1, 2, for a range of values of the Jacobi constant in (CJ,Li, CJ,Li +10−4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Solid black line: (x, y) projection of the family around L2 (left) and L1 (right) for the symmetric model with bulge centered at (0,0,0), CJ,Li = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='2338, i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Dotted red line: (x, y) projection of the family around L2 (left) and L1 (right) for the asymmetric model with bulge centered at (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0), CJ,L2 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='2358, CJ,L1 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='2331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' metric as well, with the arm at the opposite side of the displacement wider and more spread out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' We quantify this effect by computing the fraction of orbits trapped by the manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The procedure consists in intersecting the manifold with a hyperplane and, inside the result- ing closed curve in the (y, ˙y) projection, obtaining the set of points with the same energy of the manifold as initial conditions that char- acterize the escaping orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Indeed, the above closed curve turns out to be the most relevant feature in order to predict the asymmetry of the arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' When the bulge is displaced along the main axis of the bar, causing an asym- metry in the density distribution of the model, the closed curves around the equilibrium point at the end of the less dense side of the bar, narrow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' This leads to a smaller measure of states in phase space that become initial conditions for escaping orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Moreover, these closed curves are more stretched, making the distribution of the points inside them more spread out in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Both aspects are responsible for the resulting ragged and dispersed spiral arms in the less dense end of the bar, while the arm associated with the denser end becomes brighter and well defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The dynamics of off-centered bars have been studied using ana- lytical models (Colin & Athanassoula 1989), showing how the La- grangian points vary as a function of the displacement with respect to the center of mass of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Łokas (2021) digs into the barred galaxies in the IllustrisTNG simulations to check how com- mon asymmetric and off-centered bars are and study its possible ori- gin, concluding that asymmetric bars are persistent in time and this asymmetric may be due to the interaction with a companion galaxy or due to the disc itself being asymmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In either case, no further development has been proposed to link the asymmetry in the bar with the one-armed dominant spiral structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 1, this is a quite common phenomenon in barred galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' In particular, the dynamics of NGC 1300 have been studied in detail by (Patsis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2010), including an orbital analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The iso- contours of a smooth K-band image (see their Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 1) show a clear asymmetric bar distribution leading to an asymmetry in the spiral arms, which is reproduced by the different orbital models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Other ex- amples of one armed dominated galaxies with an asymmetric bar may be: NGC 4027 (Phookun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 1992), the density contours show an asymmetric and off-centered bar leading to a mass distri- bution dominated by an m = 1 mode, though a weak counter-part is also clear;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' the Large Magellanic Cloud (de Vaucouleurs & Freeman 1972), showing a rotational asymmetry, which is confirmed by more recent studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Jiménez-Arranz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Niederhofer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 2022, and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' To sum up, we show that asymmetric arms are a common feature in barred galaxies and that there is a clear correlation between arm asymmetry and the displacement of the center of mass caused by an asymmetric central density distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Escaping orbits trapped in the invariant manifolds of an asymmetric bar distribution are asym- metric and the limiting case would be to have only one armed barred spiral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' ACKNOWLEDGEMENTS P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' thanks the Spanish Ministry of Economy grants PID2020- 117066GB-I00 and PID2021-123968NB-I00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' thanks MINECO-FEDER for the grant PID2021-123968NB-I00 and the Catalan government grant 2017SGR-1049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' thanks the Spanish Ministry of Science grant MICIU/FEDER RTI2018- 095076-B-C21, and the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia "María de Maeztu") grant CEX2019-000918-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sloan Foundation, the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Department of En- ergy Office of Science, and the Participating Institutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' SDSS (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='sdss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='org) acknowledges support and resources from the Cen- ter for High-Performance Computing at the University of Utah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' DATA AVAILABILITY The data underlying this article are available in the article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' MNRAS 000, 1–7 (2023) 6 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 10 0 10 x 10 5 0 5 10 y 10 0 10 x 10 5 0 5 10 y 10 0 10 x 10 5 0 5 10 y 10 0 10 x 10 5 0 5 10 y Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Unstable invariant manifolds associated to the Lyapunov periodic orbits of L1 and L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The position of the equilibrium points is marked with crosses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The bar and the bulge are outlined by dotted black curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The reference system is marked with a solid black line and the center of the bar with a dotted magenta line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' From left to right: Bulge centered at (0,0,0), (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0), (1,0,0) and at (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='6 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='4 y 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='02 0 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='4 y 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='02 0 Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' (y, ˙y) projection of the intersection of the plane S with the stable manifolds associated to three orbits with different Jacobi constant of the Lyapunov family around L2 (top) and L1 (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The intersection of each manifold is in a color, from red to yellow, according to the energy of the manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Initial conditions distributed inside each curve are marked with a cross with the same color as the curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' From left to right: Bulge centered at (0,0,0), (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0), (1,0,0) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Note that the axis limits are different but their scale and range length are constant in each row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Orbits resulting from the integration of the initial conditions of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Equilibrium points marked in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Bar and bulge outlined by dotted black curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' The reference system is marked with a solid black line and the center of the bar with a dotted magenta line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' From left to right: Bulge centered at (0,0,0), (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0), (1,0,0) and at (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='5,0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' REFERENCES Athanassoula E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Bienaymé O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Martinet L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Pfenniger D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1983, A&A, 127, 349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Bundy K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2015, ApJ, 798, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Colin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Athanassoula E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1989, A&A, 214, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Considère S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Athanassoula E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1982, A&A, 111, 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' de Vaucouleurs G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Freeman K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1972, Vistas Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 14, 163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Ferrers N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1877, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 14, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' García-Gómez C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Barberà C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Athanassoula E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Bosma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Whyte L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2004, A&A, 421, 595.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' García-Gómez C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Athanassoula E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Barberà C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Bosma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2017, A&A, 601, A132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Gidea M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Masdemont J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2007, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' of bifurcation and chaos, 17, 1151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Iye M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Okamura S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Hamabe M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Watanabe M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1982, ApJ, 256, 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Jiménez-Arranz Ó.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2022, preprint (arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='01728).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Lee Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Ann H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Park M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2019, ApJ, 872, 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Łokas E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2021, A&A, 655, A97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Miyamoto M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Nagai R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' 1975, PASJ, 27, 533.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Niederhofer F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2022, MNRAS, 512, 5423.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Patsis P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Kalapotharakos C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Grosbol P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2010, MNRAS, 408, 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Pfenniger D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1984, A&A, 134, 373.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Phookun B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Mundy L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Teuben P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Wainscoat R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1992, ApJ, 400, 516.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Plummer H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 1911, MNRAS, 71, 460.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Romero-Gómez M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Masdemont J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Athanassoula E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', García-Gómez C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2006, A&A, 453, 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Romero-Gómez M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Masdemont J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', García-Gómez C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Athanassoula E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', MNRAS 000, 1–7 (2023) 10 5 0 5 10 10 0 10 X10 5 0 5 10 10 0 10 X10 5 0 5 10 10 0 10 X10 5 0 5 10 10 0 10 XFormation of asymmetric arms in barred galaxies 7 2009, CNSNS, 14, 4123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Romero-Gómez M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Masdemont J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2016, A&A, 588, A76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Sánchez-Martín P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Masdemont J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Romero-Gómez M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2018, A&A, 618, A72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Skokos Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Patsis P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Athanassoula E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2002, MNRAS, 333, 847.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' Tonini C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Mutch S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Croton D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', Wyithe J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=', 2016, MNRAS, 459, 4109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' This paper has been typeset from a TEX/LATEX file prepared by the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'} +page_content=' MNRAS 000, 1–7 (2023)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FIT4oBgHgl3EQf4Su_/content/2301.11385v1.pdf'}