Radial migration of the Sun in the Milky Way: a statistical study

MNRAS 446, 823–841 (2015) doi:10.1093/mnras/stu2094 Radial migration of the Sun in the Milky Way: a statistical study C. A. Martı́nez-Barbosa,‹ A. G. A. Brown† and S. Portegies Zwart‡ Leiden Observatory, Leiden University, PO Box 9513 Leiden, NL-2300 RA, the Netherlands Accepted 2014 October 7. Received 2014 September 30; in original form 2014 July 4 ABSTRACT Key words: Sun: general – Galaxy: kinematics and dynamics – open clusters and associations: general – solar neighbourhood. 1 I N T RO D U C T I O N The study of the history of the Sun’s motion within the Milky Way gravitational field is of great interest to the understanding of the origins and evolution of the Solar system (Adams 2010) and the study of past climate change and extinction of species on the earth (Feng & Bailer-Jones 2013). The determination of the birth radius of the Sun is of particular interest in the context of radial migration and in the quest for the siblings of the Sun (Portegies Zwart 2009; Brown, Portegies Zwart & Bean 2010). The work in this paper is motivated by the possibility in the near future of combining large amounts of phase-space data collected by the Gaia mission (Lindegren et al. 2008) with data on the chemical compositions of stars (such as collected by the Gaia-ESO survey; Gilmore et al. 2012) in order to search for the remnants of the Sun’s birth cluster. Our approach is to guide the search for the Sun’s siblings by understanding in detail the process of cluster disruption in the Galactic potential, using state of the art simulations. One of the initial conditions of such simulations is the birth location, in practice the birth radius, of the Sun’s parent cluster. In this paper, we present a parameter study of the Sun’s past orbit in a set of fully analytical Galactic potentials and we determine the most likely birth radius of the Sun and by  E-mail: † E-mail: ‡ E-mail: how much the Sun might have migrated radially within the Milky Way over its lifetime. The displacement of stars from their birth radii is a process called radial migration. This can be produced by different processes: interaction with transient spiral structure (Sellwood & Binney 2002; Minchev & Quillen 2006; Roškar et al. 2008), overlap of the dynamical resonances corresponding to the bar and spiral structure (Minchev & Famaey 2010; Minchev et al. 2011), interference between spiral density waves that produce short-lived density peaks (Comparetta & Quillen 2012), and interaction of the Milky Way disc with in-falling satellites (Quillen et al. 2009; Bird, Kazantzidis & Weinberg 2012). Since radial migration is a natural process in the evolution of Galactic discs, it is very likely that the Sun has migrated from its formation place to its current position in the Galaxy. Wielen (1996) argued that the Sun was born at a Galactocentric distance of 6.6 ± 0.9 kpc; roughly 2 kpc nearer to the Galactic Centre. He based his conclusions on the observation that the Sun is more metal rich by 0.2 dex with respect to most stars of the same age and Galactocentric position (Holmberg, Nordström & Andersen 2009) and the presence of a radial metallicity gradient in the Milky Way. Other studies also support the idea that the Sun has migrated from its birth place. Based on chemo-dynamical simulations of Galactic discs, Minchev, Chiappini & Martig (2013) found that the most likely region in which the Sun was born is between 4.4 and 7.7 kpc from the Galactic Centre. However, if the metallicity of the Sun is not unusual with respect to the surrounding stars of the same age, it would no longer be valid  C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society The determination of the birth radius of the Sun is important to understand the evolution and consequent disruption of the Sun’s birth cluster in the Galaxy. Motivated by this fact, we study the motion of the Sun in the Milky Way during the last 4.6 Gyr in order to find its birth radius. We carried out orbit integrations backward in time using an analytical model of the Galaxy which includes the contribution of spiral arms and a central bar. We took into account the uncertainty in the parameters of the Milky Way potential as well as the uncertainty in the present-day position and velocity of the Sun. We find that in general, the Sun has not migrated from its birth place to its current position in the Galaxy (R ). However, significant radial migration of the Sun is possible (1) when the 2: 1 outer Lindblad resonance of the bar is separated from the corotation resonance of spiral arms by a distance ∼1 kpc, and (2) when these two resonances are at the same Galactocentric position and further than the solar radius. In both cases, the migration of the Sun is from outer regions of the Galactic disc to R , placing the Sun’s birth radius at around 11 kpc. We find that in general, it is unlikely that the Sun has migrated significantly from the inner regions of the Galactic disc to R . 824 C. A. Martı́nez-Barbosa, A. G. A. Brown and S. Portegies Zwart 2 G A L AC T I C M O D E L Since the past history of the structure of the Milky Way is unknown, we simply assume that the values of the Galactic parameters have been the same during the last 4.6 Gyr, i.e. during the lifetime of the Sun (Bonanno, Schlattl & Paternò 2002). We model the Milky Way as a fully analytical potential that contains an axisymmetric component together with a rotating central bar and spiral arms. We use the potentials and parameters of Allen & Santillán (1991) to model the axisymmetric part of the Galaxy, which consist of a central bulge, a disc and a dark matter halo. The values of the MNRAS 446, 823–841 (2015) Table 1. Parameters of the Milky Way model potential. Axisymmetric component 1.41 × 1010 M 0.3873 kpc 8.56 × 1010 M 5.31 kpc 0.25 kpc 1.07 × 1011 M 12 kpc Mass of the bulge (Mb ) Scalelength bulge (b1 ) disc mass (Md ) Scalelength disc 1 (a2 ) Scalelength disc 2 (b2 ) Halo mass (Mh ) Scalelength halo (a3 ) Central bar 40–70 km s−1 kpc−1 3.12 kpc 0.37 9.8 × 109 –1.4 × 1010 M 20◦ Pattern speed (bar ) Semimajor axis (a) Axis ratio (b/a) Mass (Mbar ) Orientation Spiral arms Pattern speed (sp ) Locus beginning (Rsp ) Number of spiral arms (m) Spiral amplitude (Asp ) Strength of the spiral arms () Pitch angle (i) Scalelength (R ) Orientation 15–30 km s−1 kpc−1 3.12 kpc 2, 4 650–1300 km2 s−2 kpc−1 0.02– 0.06 12.◦ 8 2.5 kpc 20◦ parameters of these Galactic components are shown in Table 1. For the central bar and spiral arms, we use the models presented in Romero-Gómez et al. (2011) and Antoja et al. (2011) as detailed below. 2.1 Central bar The central bar of the Milky Way is modelled as a Ferrers bar (Ferrers 1877) which is described by a density distribution of the form   k ρ0 1 − n2 n<1 , (1) ρbar = 0 n≥1 where n2 = x2 /a2 + y2 /b2 determines the shape of the bar potential, where a and b are the semimajor and semiminor axes of the ba (...truncated)