Revealing the spiral arms through radial migration and the shape of the metallicity distribution function

MNRAS 463, 459–466 (2016) doi:10.1093/mnras/stw1997 Advance Access publication 2016 August 11 Revealing the spiral arms through radial migration and the shape of the metallicity distribution function L. A. Martinez-Medina,‹ B. Pichardo,‹ E. Moreno and A. Peimbert Instituto de Astronomı́a, Universidad Nacional Autónoma de México, A.P. 70–264, 04510 México, CDMX, Mexico Accepted 2016 August 5. Received 2016 August 5; in original form 2016 April 4 Recent observations show that the Milky Way’s metallicity distribution function (MDF) changes its shape as a function of radius. This new evidence of radial migration within the stellar disc sets additional constraints on Galactic models. By performing controlled test particle simulations in a very detailed, observationally motivated model of the Milky Way, we demonstrate that, in the inner region of the disc, the MDF is shaped by the joint action of the bar and spiral arms, while at outer radii the MDF is mainly shaped by the spiral arms. We show that the spiral arms are able to imprint their signature in the radial migration, shaping the MDF in the outskirts of the Galactic disc with a minimal participation of the bar. Conversely, this work has the potential to characterize some structural and dynamical parameters of the spiral arms based on radial migration and the shape of the MDF. Finally, the resemblance obtained with this approximation to the MDF curves of the Galaxy as seen by APOGEE, show that a fundamental factor influencing their shape is the Galactic potential. Key words: Galaxy: disc – Galaxy: evolution – Galaxy: kinematics and dynamics – Galaxy: structure. 1 I N T RO D U C T I O N An enormous effort has been dedicated, in the last decade, to the understanding of radial and vertical orbital stellar motions induced by the non-axisymmetric structures in the Galaxy (Sellwood & Binney 2002; Roškar et al. 2008; Bird, Kazantzidis & Weinberg 2012; Grand, Kawata & Cropper 2012a; Roškar et al. 2012; VeraCiro et al. 2014; Halle et al. 2015; Aumer, Binney & Schönrich 2016, and references therein). Particular attention has been paid to stellar migration and its effects on the chemical elements distribution in the Galaxy (Schönrich & Binney 2009; Minchev et al. 2011; Minchev, Chiappini & Martig 2013, 2014; Sánchez-Blázquez et al. 2014; Hayden et al. 2015; Loebman et al. 2016). The mechanism of radial migration, as defined by Sellwood & Binney (2002, hereafter SB02), is understood as the redistribution of angular momentum for stars that interact with the non-axisymmetric structure of the galaxy around the corotation (CR) resonance while keeping their orbital eccentricity unchanged. On the other hand, redistribution of angular momentum at radii different from CR will cause a dynamical heating of the stellar disc. Both mechanisms move stars to inner or outer radii, but radial migration does not leave a kinematic imprint on stellar orbits. It is worth noting that the  E-mail: (LAMM); (BP) term radial migration has been used differently by different authors1 (see for example the discussion by Vera-Ciro et al. 2014). Without the effect of stellar migration, a perfect correlation between age and metallicity of a star could be found for a given Galactic region, assuming the abundance of chemical elements was known in such region. Although this seems to approximate the case for the interstellar medium (ISM) in the Milky Way (MW) and other galaxies (Wilson & Rood 1994; Henry & Worthey 1999), it is known that, for example, in the solar neighbourhood, stars of a given age show a large dispersion in metallicity (Edvardsson et al. 1993). This effect is not readily explained by plain orbital excursions from epicycles corresponding at their birth place (SB02). More recently, Hayden et al. (2015) measure the metallicity distribution functions (MDFs) of the MW, from a sample of 69 919 red giants from the SDSS-III/APOGEE Data Release 12. They find that the shape of the mid-plane MDF changes systematically with radius, with a negatively skewed distribution at 3 < R < 7 kpc, to a roughly Gaussian distribution at the solar annulus, to a positively skewed shape in the outer Galaxy. Using a simple model they suggest that the reversal of MDF shape could be due to radial migration. However, a more complex model is needed to differentiate between the contribution of the different non-axisymmetric components of the Galaxy. 1 The results presented in this paper do not depend on the specific definition of radial migration.  C 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society ABSTRACT 460 L. A. Martinez-Medina et al. With detailed orbital studies performed in suitable observationally motivated potentials of the MW, we show here that the spiral arms can imprint their mark on the MDF. This paper is organized as follows. The galactic model, initial conditions, and methodology are described in Section 2. A study on radial migration and radial heating is presented on Section 3. The link between the MDF and the initial radial distribution is shown in Section 4. Finally, we present the discussion and conclusions in Sections 5 and 6. 2 THE GALAXY MODEL, NUMERICAL S I M U L AT I O N S A N D I N I T I A L C O N D I T I O N S (1) The model is fully adjustable. We are able to fit the whole axisymmetric and non-axisymmetric potential (i.e. spiral arms and bar), in three dimensions to our best understanding of the MW (or any other particular galaxy) from observations and models. (2) Rather than using a simple ad hoc model for a spiral perturbation, we employ a three-dimensional (3D) mass distribution for the spiral arms, from which we derive their gravitational potential and force fields. Our model is considerably faster, computationally speaking, than N-body simulations. (3) It allows us to study in great detail individual stellar orbital behaviour (e.g. resonant regions, vertical structure, chaotic and ordered behaviour, periodic orbits to estimate at some degree orbital self-consistency, etc.), without the resolution problems of N-body simulations. We have integrated test particle orbits in this 3D Galactic potential model. Our model is observationally motivated by the MW and suitable to explain several characteristics of the local kinematics due to the spiral arms and the bar (such as moving groups in the solar neighbourhood; e.g. Antoja et al. 2009). Although the one employed is a much better suited spiral model to represent the MW than any N-body simulation, we do not include any prescription of metallicity or ISM physics as in Loebman et al. (2016). In a future work, we will perform a more specific study of the spiral arms parameters, as well as implementing a metallicity prescription, to seek for a better fit to the APOGEE MDFs for the MW Galaxy, and search for some restrictions to the morphology and physical characteristics of the spiral arms. 2.1 The full Galactic model The Galactic m (...truncated)