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The Dynamical Origin of the Local Arm and the Sun's Trapped Orbit

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The Dynamical Origin of the Local Arm and the Sun's Trapped Orbit Draft version May 15, 2017 Typeset using LATEX twocolumn style in AASTeX61 THE DYNAMICAL ORIGIN OF THE LOCAL ARM AND THE SUN'S TRAPPED ORBIT Jacques R. D. Lepine,´ 1 Tatiana A. Michtchenko,1 Douglas A. Barros,1 and Ronaldo S. S. Vieira1 1Universidade de S~aoPaulo, IAG, Rua do Mat~ao,1226, Cidade Universit´aria, 05508-090 S~aoPaulo, Brazil (Received ....; Revised ...; Accepted May 10, 2017) Submitted to ApJ ABSTRACT The Local arm of the Milky Way, a short spiral feature near the Sun whose existence is known for decades, was recently observed in detail with different tracers. Many efforts have been dedicated to elaborate plausible hypotheses concerning the origin of the main spiral arms of the Galaxy; however, up to now, no specific mechanism for the origin of the Local arm was proposed. Here we explain, for the first time, the Local arm as an outcome of the spiral corotation resonance, which traps arm tracers and the Sun inside it. We show that the majority of maser sources belonging to the Local arm, together with the Sun, evolve inside the corotation resonance, never crossing the main spiral arms but instead oscillating in the region between them. This peculiar behavior of the Sun could have numerous consequences to our understanding of the local kinematics of stars, the Galactic Habitable Zone, and the Solar System evolution. Keywords: Galaxy: disk, kinematics and dynamics, solar neighbourhood, structure | Galaxies: spiral arXiv:1705.04381v1 [astro-ph.GA] 11 May 2017 Corresponding author: Jacques L´epine [email protected], [email protected], [email protected], [email protected] 2 Lepine´ et al. 1. INTRODUCTION stability as \corotation zones"; the number of corotation The Milky Way is considered to be a Grand Design zones corresponds to the number of spiral arms adopted spiral galaxy, as most works on spiral arm tracers in- in the Galaxy model. Early theoretical studies on the dicate (Georgelin & Georgelin 1976; Levine et al. 2006; corotation dynamics in disk galaxies predicted a trapped 1 Hou et al. 2009; Hou & Han 2014; Reid et al. 2014). stellar mass inside such corotation zones (Contopoulos At regions not too far from the Sun, the geometry of 1973; Barbanis 1976). Moreover, it was recently found, the spiral structure is well known. The main features by means of magnetohydrodynamics simulations, that are the extended Sagittarius-Carina arm, which passes the gas also remains trapped in the corotation zones at an inner galactic radius (compared to the Sun), and (G´omezet al. 2013). the Perseus arm, at an outer radius. These arms are We have plenty of evidence that we live near the spiral corotation circle (Marochnik et al. 1972; Creze & Men- revealed by molecular clouds, H II regions, OB stellar associations, and open clusters, among other tracers nessier 1973; Marochnik 1983; Mishurov & Zenina 1999; (Georgelin & Georgelin 1976; Hou & Han 2014; Bobylev L´epineet al. 2001; Dias & L´epine 2005; L´epineet al. & Bajkova 2014; Reid et al. 2014). The most accu- 2011). A direct measurement of the corotation radius rate picture of the spiral arms in the Galactic plane is was made by Dias & L´epine(2005) by using a sample of given by maser sources associated with star forming re- open clusters with known distances, ages and space ve- gions, whose distances are obtained by recent Very Long locities. Integrating the orbits to the past towards their Baseline Interferometry (VLBI) parallax measurements birthplaces, the authors followed the time displacement (Reid et al. 2014); in this case, the calculation of the of the spiral arms and determined the corotation radius distances needs no assumption about the rotation curve as RCR = (1:06 ± 0:08)R0, where R0 is the galactocen- and interstellar extinction. Inside the solar circle, the tric radius of the Sun. Observations also show that the position of the arms with respect to the Sun can be de- Sun lies in the vicinity of the Local arm, at a distance termined by the directions of lines of sight tangent to smaller than 500 pc (e.g. Hou & Han 2014, among oth- them (Vall´ee 2016). ers). Owing to the fact that the Sun is close to both Midway between the Sagittarius-Carina and Perseus the corotation circle and the Local arm, we elaborate a arms, and close to the Sun, there is a short structure, the hypothesis on the origin of the Local arm and present it Local arm (or Orion Spur; see Xu et al. 2013; Bobylev in this paper. & Bajkova 2014; Hou & Han 2014; Reid et al. 2014; Xu Within the context of a spiral structure with a well- et al. 2016), which is also precisely traced by the VLBI defined corotation radius, we build a Galactic potential maser sources and other tracers (Hou & Han 2014). model which is composed by an axisymmetric compo- Even though this arm is known for decades (Morgan nent and a perturbation term due to a four-armed spiral et al. 1952, 1953; Bok et al. 1970; Georgelin & Georgelin structure. For observationally constrained physical and 1976) and extensively studied by observational means, dynamical parameters, the model gives rise to four coro- there was no explanation for its origin up to now. tation zones. One of these lies between the Sagittarius- The main arms are usually interpreted as the crowding Carina and Perseus spiral arms encompassing the posi- of successive stellar orbits of different radii that produces tion of the Sun; it will be hereafter referred to as the increased stellar densities and creates elongated valleys \local corotation zone". The closeness to the corotation of gravitational potential (Kalnajs 1973; Contopoulos & radius and the superposition of the banana-shaped re- Grosbol 1986; Junqueira et al. 2013). The self-consistent gion over the Local arm position in the Galactic plane portrait of the Galaxy shows the spiral pattern rotat- allow us to presume a natural connection between ob- ing with a constant angular velocity (the pattern speed servational and dynamical phenomena, namely the Lo- cal arm and the local corotation zone. This conjecture Ωp), similar to a rigid body. The pattern speed Ωp deter- mines the corotation circle, at which stars and gas rotate is supported by the results of recent gas simulations, around the galactic center with the same average veloc- which show that the `Local arms' form consistently in ity of the spiral arm pattern; the average velocity of the the gas density response to the action of an external stars is given by the rotation curve, which is relatively spiral potential (Li et al. 2016). Moreover, the reported flat for the Milky Way (Clemens 1985; Sofue et al. 2009). Around the corotation circle, the islands of orbital sta- 1 We make clear that our references throughout the paper bility appear in the form of banana-like regions in the to \being inside the corotation resonance/island/zone" actually effective potential maps; they are associated with the mean being located in the island of trapped orbits, not lying at a smaller radius with respect to the corotation radius. corotation resonance (Contopoulos 1973; Michtchenko et al. 2017). Hereafter, we will refer to these islands of The dynamical origin of the Local arm 3 corotation radius of those simulations shows that these body simulations was sufficiently large, e.g. 3 × 106 par- arms are relatively close to the corotation circle. ticles. From the observational point of view, Mart´ınez- We look for evidence that the mass trapped inside the Garc´ıa& Gonz´alez-L´opezlira(2013) analyzed azimuthal local corotation zone actually forms the Local arm, and age/color gradients across spiral arms for a sample of 13 that the Sun probably evolves inside this zone. Using normal or weakly barred galaxies, and verified that at a sample of young objects (maser sources) associated to least 50% of the objects show signatures of long-lived the Local arm, we study their dynamics by performing patterns. numerical integrations of the equations of motion. Our It must be emphasized that the existence of the coro- results show that the majority of these objects do not es- tation zone needs no assumption about the lifetime of cape from the local corotation zone, indicating that their the Galactic spiral structure. Indeed, once a spiral mode orbits are trapped inside it. Since these objects are iden- emerges in the Galactic disk, the corotation zones ap- tified as tracers of the Local arm, we can propose that pear instantaneously as a natural consequence of the the Local arm is an outcome of the resonant dynam- spiral arms perturbation (Contopoulos 1973). Never- ics induced by perturbations due to the main galactic theless, the knowledge of the timescale is necessary to spiral arms on a background axisymmetric disk. The distinguish between the quasi-steady or transient nature trapping mechanism is similar to the one observed in of the main spiral arms; the Local arm structure, with the Solar System of the Jupiter Trojan asteroids, which its current features, also depends on this timescale. are trapped in the L4,L5 Lagrangian solutions for the The organization of this paper is as follows: In Sec- Sun-Jupiter system (Murray & Dermott 1999, Chapter tion2 we describe the sample of objects used to trace 3). Thus, knowing the mechanism which originates the the Local arm. In Section3 we introduce the model of Local arm, we can elaborate a scenario for its formation the Galactic disk and the potential of the spiral arms. and evolution. In Section4 we present the topology of the Hamilto- To simulate the evolution of the objects inside the Lo- nian and resulting energy levels.
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