Mem. S.A.It. Vol. 85, 422c© SAIt 2014 Memorie della

The in uence of radial stellar migration on thechemical evolution of the Milky Way

Yue Wang1,2 and Gang Zhao1

1 Key Laboratory of Optical Astronomy, National Astronomical Observatories, ChineseAcademy of Science, Beijing 100012, China, e-mail: ywang@nao.cas.cn

2 University of Chinese Academy of Sciences, Beijing 100049, China

Abstract. The existence of stellar migration in Galactic disk has been demonstrated byseveral works in recent years. Here we use an analytical method to model radial stellarmigration in the Galactic disk, then add it to detailed Galactic chemical evolution model tostudy its influence on the chemical evolution of the Milky Way, especially for the abundancegradients. We found that the radial stellar migration in the Galactic disk can scatter the age-metallicity relation, but cannot change essentially the abundance distributions along theGalactic radius. However, it can flatten the radial gradients of the mean chemical abundanceof stars, and older stars possess flatter abundance gradients than younger stars. Besides, themigration can also scatter the abundance of stars at a place from a relatively concentratedvalue to a range.

Key words. Galaxy: abundances – Galaxy: evolution – Galaxy: disk – Galaxy: kinematicsand dynamics

1. Introduction

The existence of stellar migration in theGalactic disk has been demonstrated by sev-eral works in recent years. Observationally,the age-metallicity relation of stars in the so-lar neighborhood is shown to be flat togetherwith large scatter (Edvardsson et al. 1993;Nordstrom et al. 2004), and the scatter in-creases with age increasing (Haywood 2008;Casagrande et al. 2011). Besides, the metal-licity distribution function (MDF) in the so-lar neighborhood obtained by Casagrande et al.(2011) shows that old stars have a consid-erably broader distribution than young starswhile the peak always remains around the solarvalue. All these phenomena suggest that stars

in the solar neighbour could have been bornat various Galactocentric radii with differentmetallicities and migrated to the current po-sition over different timescales. Theoretically,Schonrich & Binney (2009) has distinguishedtwo drivers of radial migration: by scatter-ing at an orbital resonance or by non-resonantscattering by a molecular cloud. Minchev &Famaey (2010) identified another radial mi-gration mechanism in barred galaxies that theresonance overlap of the bar and spiral struc-ture can induce a nonlinear response leading toa strong redistribution of angular momentumin the disk. As a consequence, the radial stel-lar migration is an important component thatshould be considered in the Galactic chemicalevolution model.

Wang: Influence of radial stellar migration on the Milky Way 423

Abundance gradients are very importantconstraints for the Galactic chemical evolutionmodel. As suggested by Sellwood & Binney(2002) and Schonrich & Binney (2009), sincethe migration of stars makes it possible totransport materials to any place along the diskno matter where they originally located, themixture of chemical elements over large rangeof radius would reduce the differences of abun-dances between different regions along the diskand flatten the abundance gradients. Here, westudy the influence of radial stellar migration inthe disk on the chemical evolution of the MilkyWay, especially for the abundance gradients.

2. Galactic chemical evolution modeland radial stellar migration

The model adopted here is based on the modelof Portinari & Chiosi (2000), in which the diskforms gradually by accretion of protogalacticgas and radial gas flow exists. We consideran inside-out disk formation scenario in whichthe disk formation time scale increases withGalactic radius. The main parameters of mod-els are listed in Table 1.

We describe the radial stellar migrationwith normal and Gama distribution functionsrespectively, modeling the probability thatstars, born at a given radius, appear at differ-ent radii after migrating for a period of time.For the normal distribution,

fSM = fN(r) =1

σ√

2πexp

[−1

2

( r − µσ

)2]

(1)

We make its center at the birth radii of starsand σ increase with the stellar age exponen-tially so that stars would stay around their birthradii with the highest probability and migratefurther with time elapsing. The normal distri-butions at all radii are adopted to be same.

Following the hint of Figure 13 ofSellwood & Binney (2002), we also use Gamadistribution Γ(α, β) which is an asymmetricaldistribution. The basic form of Γ(α, β) is

fSM = fG(r) =1

βα Γ(α)r α−1 exp

(− rβ

), r > 0

(2)

Γ(α) =

∞∫

0

t α−1e−tdt (3)

We make α radius-dependent indicating starsborn at different radii have different migra-tion tendencies or preferences, and β increaseswith stellar age exponentially. The peaks ofthe Gama distributions are also made to cor-respond to the birth radii of stars.

For both the normal and Gama distribu-tions, we adopt two scenarios for the variationof their profiles with stellar age: standard con-dition and extreme condition. In the extremecondition, stars migrate much faster than inthe standard condition, to test what the effectswould be if stars migrate under an extreme sce-nario.

3. Results and conclusions

In the top panel of Figure 1 we show thedistributions of birth radii of stars that areat present in the solar neighbourhood. Whilemost stars come from the local area, a largeproportion come from inner disk, as a con-sequence of the higher stellar density there,which is more obvious for the models adoptingGama-distribution stellar migration. For ourbest model GCM2G, we show this distributionfor stars in different ages in the bottom panel.With the age increasing, the birth radii of starscover larger range of the disk, and more starscome from inner disk, which is consistent withthe stellar migration theory.

The stellar age-metallicity relation (AMR)in the solar neighbourhood is an important fac-tor when consider stellar migration. As a con-sequence of radial stellar migration, the so-lar neighbourhood consists of stars of differentages and metallicities coming from differentradii, and they scatter the classic AMR to anage-metallicity distribution (AMD), as roughlyshown in Figure 2, while a slope is preservedin the AMD and stars from the same birthradius still follow a classic local AMR. Thisphenomenon is also found by Minchev et al.(2012).

Figure 3 shows the comparison among theabundance distributions from models and ob-servation. It can be seen that our models can

424 Wang: Influence of radial stellar migration on the Milky Way

Table 1. Main parameters of the models. ‘(e)’ represents the model adopting extreme conditionfor stellar migration, eg. GCM2Ne. τD is the disk formation time scale, vg f (r) is the velocity ofradial gas flow.

Models Stellar migration τD vg f (r)(Gyr) (km s−1)

GCM2 No 0.88r − 0.9 −0.16r + 0.6, r < 10 kpcGCM2N(e) Normal 0.88r − 0.9 −0.2r + 1.0, 10 kpc ≤ r < 15 kpcGCM2G(e) Gama 0.88r − 0.9 −1/3r + 3.0, r ≥ 15 kpc

Fig. 1. Top panel shows the distributions ofbirth radii of the stars that are at present inthe solar neighbourhood. Bottom panel showsthe same distribution by model GCM2G but forstars in different ages.

reproduce the observational [Fe/H] (top panel)and oxygen abundance (bottom panel) distri-butions on the whole. In each panel, differentlines representing the distributions producedby different models coincide with each other.Being inconsistent with previous predictions,looking from the whole radius range, the radialdistributions of chemical element abundanceshave not flattened after radial stellar migra-tion, even in the extreme condition the abun-dance gradients also have not changed much.So we may infer that the radial stellar migra-tion cannot lead to significant flattening of ra-dial chemical abundance gradients. It can beunderstood as the important chemical contrib-utors are massive stars which only have shortlifetime and contribute mostly around their

Fig. 2. Age-metallicity distribution in the solarneighbourhood. In each panel the lines fromtop to bottom represent the stars migrated tothe solar neighbourhood from their birth radiiof r = 4 kpc to 18 kpc, respectively, and therelative proportion are shown by the colors in-creasing from blue to red.

birth regions, so few stars can migrate far toa region and contribute to change significantlythe chemical composition there. However, asthe migration is a motion of stars, it can flattenthe radial gradient of the mean chemical abun-dance of stars. Since older stars have migratedfor more time, their chemical abundances arehigher with flatter abundance gradients com-pared with young stars, which is consistentwith the findings of Minchev et al. (2012).Besides, the abundance of stars at a place canbe scattered by the radial migration from a rela-tively concentrated value to a range, which canalready been inferred from the age-metallicitydistribution.

Wang: Influence of radial stellar migration on the Milky Way 425

Fig. 3. [Fe/H] (top) and oxygen abundance(bottom) along the disk obtained from mod-els and observation. The black rhombuses,triangles and squares represent the observa-tional abundances of Cepheids, HII regionsand OB stars, respectively. The iron abundanceare from: Andrievsky et al. (2002c,a,b, 2004),Luck et al. (2003, 2006), Luck & Lambert(2011), and Lemasle et al. (2007, 2008). Theoxygen abundance are from: Andrievsky et al.(2002c,a,b, 2004), Lemasle et al. (2007), Lucket al. (2003, 2006), Shaver et al. (1983),Esteban et al. (2005), Vilchez & Esteban(1996), Rudolph et al. (1997), and Rudolphet al. (2006), Smartt & Rolleston (1997),Gummersbach et al. (1998), and Daflon &Cunha (2004). The yellow line with filled cir-cles shows the mean value of the observationaldata.

Acknowledgements. We thank the organizers of theworkshop ”Metal Production and Distribution in aHierarchical Universe”. We also thank F. Matteucciand Y. Liang for their advice for the constructionof the model, and R. Chang and X. Fan for manyuseful discussions. This work is supported by theNational Natural Science Foundation of China un-der grant No. 11233004.

References

Andrievsky, S. M., Bersier, D., Kovtyukh,

V. V., et al. 2002a, A&A, 384, 140Andrievsky, S. M., Kovtyukh, V. V., Luck,

R. E., et al. 2002b, A&A, 392, 491Andrievsky, S. M., Kovtyukh, V. V., Luck,

R. E., et al. 2002c, A&A, 381, 32Andrievsky, S. M., et al. 2004, A&A, 413, 159Casagrande, L., Schonrich, R., Asplund, M.,

et al. 2011, A&A, 530, A138Daflon, S., & Cunha, K. 2004, ApJ, 617, 1115Edvardsson, B., Andersen, J., Gustafsson, B.,

et al. 1993, A&A, 275, 101Esteban, C., Garcıa-Rojas, J., Peimbert, M.,

et al. 2005, ApJ, 618, L95Gummersbach, C. A., et al. 1998, A&A, 338,

881Haywood, M. 2008, MNRAS, 388, 1175Lemasle, B., Francois, P., Bono, G., et al. 2007,

A&A, 467, 283Lemasle, B., Francois, P., Piersimoni, A., et al.

2008, A&A, 490, 613Luck, R. E., Gieren, W. P., Andrievsky, S. M.,

et al. 2003, A&A, 401, 939Luck, R. E., Kovtyukh, V. V., & Andrievsky,

S. M. 2006, AJ, 132, 902Luck, R. E., & Lambert, D. L. 2011, AJ, 142,

136Minchev, I., Chiappini, C., & Martig, M. 2012,

ArXiv e-printsMinchev, I., & Famaey, B. 2010, ApJ, 722, 112Nordstrom, B., Mayor, M., Andersen, J., et al.

2004, A&A, 418, 989Portinari, L., & Chiosi, C. 2000, A&A, 355,

929Rudolph, A. L., et al. 1997, ApJ, 489, 94Rudolph, A. L., Fich, M., Bell, G. R., et al.

2006, ApJS, 162, 346Schonrich, R., & Binney, J. 2009, MNRAS,

396, 203Sellwood, J. A., & Binney, J. J. 2002, MNRAS,

336, 785Shaver, P. A., et al. 1983, MNRAS, 204, 53Smartt, S. J., & Rolleston, W. R. J. 1997, ApJ,

481, L47Vilchez, J. M., & Esteban, C. 1996, MNRAS,

280, 720