Using N-body simulations of the Galactic disks, we qualitatively study how
the metallicity distributions of the thick and thin disk stars are modified by
radial mixing induced by the bar and spiral arms. We show that radial mixing
drives a positive vertical metallicity gradient in the mono-age disk population
whose initial scale-height is constant and initial radial metallicity gradient
is tight and negative. On the other hand, if the initial disk is flaring, with
scale-height increasing with galactocentric radius, radial mixing leads to a
negative vertical metallicity gradient, which is consistent with the current
observed trend. We also discuss impacts of radial mixing on the metallicity
distribution of the thick disk stars. By matching the metallicity distribution
of N-body models to the SDSS/APOGEE data, we argue that the progenitor of the
Milky Way's thick disk should not have a steep negative metallicity gradient.Comment: 4 pages, 1 figure, to appear in the proceedings of the IAU Symposium
  334 "Rediscovering our Galaxy", Potsdam, 10-14 July 2017, eds. C. Chiappini,
  I. Minchev, E. Starkenburg, M. Valentin

Kawata, Daisuke

English

arXiv

Using N-body simulations of the Galactic disks, we qualitatively study how the metallicity distributions of the thick and thin disk stars are modified by radial mixing induced by the bar and spiral arms. We show that radial mixing drives a positive vertical metallicity gradient in the mono-age disk population whose initial scale-height is constant and initial radial metallicity gradient is tight and negative. On the other hand, if the initial disk is flaring, with scale-height increasing with galactocentric radius, radial mixing leads to a negative vertical metallicity gradient, which is consistent with the current observed trend. We also discuss impacts of radial mixing on the metallicity distribution of the thick disk stars. By matching the metallicity distribution of N-body models to the SDSS/APOGEE data, we argue that the progenitor of the Milky Way's thick disk should not have a steep negative metallicity gradient

Kawata, D

UCL Discovery

arXiv:1708.03374v1  [astro-ph.GA]  10 Aug 2017Rediscovering our GalaxyProceedings IAU Symposium No. 334, 2017C. Chiappini, I. Minchev, E. Starkenburg & M. Valentini, eds.c© 2017 International Astronomical UnionDOI: 00.0000/X000000000000000XImpacts of Radial Mixing on the GalacticThick and Thin DisksDaisuke Kawata11Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking,Surrey, RH5 6NT, UKemail:d.kawata@ucl.ac.ukAbstract. Using N-body simulations of the Galactic disks, we qualitatively study how themetallicity distributions of the thick and thin disk stars are modified by radial mixing inducedby the bar and spiral arms. We show that radial mixing drives a positive vertical metallicitygradient in the mono-age disk population whose initial scale-height is constant and initial ra-dial metallicity gradient is tight and negative. On the other hand, if the initial disk is flaring,with scale-height increasing with galactocentric radius, radial mixing leads to a negative ver-tical metallicity gradient, which is consistent with the current observed trend. We also discussimpacts of radial mixing on the metallicity distribution of the thick disk stars. By matchingthe metallicity distribution of N-body models to the SDSS/APOGEE data, we argue that theprogenitor of the Milky Way’s thick disk should not have a steep negative metallicity gradient.Keywords.methods: n-body simulations, Galaxy: abundances, Galaxy: disk, Galaxy: evolution,Galaxy: kinematics and dynamics1. IntroductionThe evolution of radial metallicity gradients should provide strong constraints on diskformation scenarios (e.g. Gibson et al. 2013), and hence it is important to compare gra-dients of different age populations of the Milky Way with Milky Way-like disk galaxiesat different redshifts. However, it is not straightforward to infer initial metallicity dis-tribution for mono-age populations at the time they formed, from the current Galacticmetallicity distribution as a function of age, because radial mixing can alter the distribu-tions (e.g. Schönrich & Binney 2009; Minchev et al. 2014; Grand et al. 2015). We referto “radial mixing” to describe the overall radial re-distribution due to both “churning”and “blurring” (Schönrich & Binney 2009). Churning indicates the change of angularmomentum of stars, and blurring describes the radial re-distribution of stars due to theirepicyclic motion. Churning can be split into two mechanisms, “radial scattering” and“co-rotation radial migration”. Radial scattering describes the change of angular mo-mentum with kinematic heating, i.e. the increase in random energy of the orbit. On theother hand, co-rotation radial migration indicates a gain or loss of angular momentumof stars at the co-rotation resonance of the spiral arms (Sellwood & Binney 2002) or bar,and does not involve significant kinematic heating. Here, we discuss the effect of radialmixing, without distinguishing these mechanisms.Using simple numerical experiments based on N-body simulations of an idealised iso-lated galactic disk, we qualitatively study the impact of the radial mixing on the metal-licity distributions of the thin and thick disk populations. Here, we consider chemicallydefined thick (high-[α/Fe]) and thin (high-[α/Fe]) disk, and also consider that thick diskpopulation is generally older than thin disk population.12 Daisuke KawataFigure 1. Vertical metallicity distributions of the thin disk component for constant scale-height,zd, model (left two panels) and flaring model (right two panels) in the radial ranges of6 < R < 10 kpc at t = 0 and 8 Gyr. The white dots and the error bars at t = 8 show themean and dispersion of [Fe/H] at different height, |z|, and the solid line shows the best fitstraight line. The dotted line shows the vertical metallicity gradient assumed at R = 8 kpc att = 0.2. Vertical Metallicity Gradient and Flaring DiskCombining Gaia DR1 TGAS data (Gaia Collaboration et al. 2016; Lindegren et al.2016) and RAVE DR5 (Kunder et al. 2017), Ciucă et al. (2017) analysed the verti-cal metallicity gradient of solar neighbourhood dwarf stars, and found that the oldermono-age population shows a steeper negative vertical metallicity gradient (see alsoXiang et al. 2015). On the other hand, the thin disk population stars are expected toform within very thin high density molecular gas. It is a natural expectation that thestar forming gas disk has almost no vertical metallicity gradient, because metal mixing invertical direction should be quite efficient. Then, how was the observed negative verticalmetallicity gradient of mono-age thin disk populations built up?We ran an N-body simulation of the evolution of a barred disk galaxy similar in size tothe Milky Way. We initially set up an isolated disk galaxy which consists of stellar disks,with no bulge component, in a static dark matter halo potential (Rahimi & Kawata 2012;Grand et al. 2012), using our original Tree N-body code, GCD+ (Kawata & Gibson 2003;Kawata et al. 2013). In the initial condition, we set a smaller thick disk particles and alarger thin disk particles. We first assumed the thin disk has a constant scale-height, zd,independent of the radii, ”constant zd model”. We then assigned the metallicity of thethin disk particles to follow the radial metallicity gradient of [Fe/H] = 0.5−0.08× R witha dispersion of 0.05 dex with no vertical metallicity gradient at t = 0. Left two panelsof Fig. 1 show the initial (at t = 0) and final (t = 8) vertical metallicity distribution forthe thin disk component of this model (constant zd model). Interestingly, after 8 Gyr ofevolution, the vertical metallicity gradient becomes positive, which is inconsistent withthe negative vertical metallicity gradients observed in the mono-age population of the thindisk as mentioned above. However, this is a natural outcome of radial mixing, becausewhen the stars in the inner region with higher metallicity migrate outwards, they tendto end up at a higher height in the outer region of the disk, due to their higher initialvertical action.In Kawata et al. (2017b) we presented that a flaring thin disk is one possibility toremedy this issue. In our N-body simulation we include a 2nd thin disk componentwhose vertical scale height increases with radius, ”flaring model”. This flaring thin diskcomponent is representative of a mono-age population that is born in a flaring star-forming region. We assigned the metallicity following the same radial metallicity gradientas our constant zd model to the flaring disk particles. Right two panels of Fig. 1 showthe initial (at t = 0) and final (t = 8) vertical metallicity distribution for the flaringthin disk component of this model. In this case, the metal poor stars formed in theRadial mixing and Galactic thick and thin disks 3outer disk become dominant at high vertical height at every radii, which can drive anegative vertical metallicity gradient. Therefore, if mono-age populations of the MilkyWay thin disk stars are formed within a flaring star forming disk, each mono-age thin diskpopulation can have a negative vertical metallicity gradient. Then, older population has asteeper negative vertical metallicity gradient, because they have more time to experiencemore radial mixing. This can explain the steeper negative vertical metallicity gradientobserved in the older population of the thin disk (Ciucă et al. 2017).The flaring younger thin disk population helps to explain the observed abundancedistribution of thin and thick disk populations. Analysing a cosmological simulationresult, Rahimi et al. (2014) found that the old compact thick disk population and theflaring younger thinner disk population leads to a negative radial metallicity gradientat the disk plane, and a positive radial metallicity gradient at the high vertical height,2 < |z| < 3 kpc, which is consistent with the observed radial metallicity gradientsat different vertical heights in the Milky Way (e.g. Carrell et al. 2012). Rahimi et al.(2014) predicted that if this is true, we should see a negative radial [α/Fe] gradientand a negative radial age gradient at a high vertical height (see also Minchev et al.2015; Miranda et al. 2016). This prediction has been confirmed by several observationalstudies (e.g. Anders et al. 2014; Martig et al. 2016).3. Metallicity Gradients of the Thick disk ProgenitorSpectroscopic surveys of the Galactic disk stars found that the chemically-defined thickdisk shows no radial metallicity gradient, but a clear negative vertical metallicity gradient(e.g. Mikolaitis et al. 2014). This indicates that the chemical properties of the thick diskare well mixed radially, but maintain a negative vertical gradient. Combining an idealisedN-body disk model with a MCMC chemical painting technique, in Kawata et al. (2017a)we explored what metallicity distribution for the thick disk progenitor was needed, toexplain the current thick disk metallicity distribution observed by the APOGEE survey(Hayden et al. 2015).Similar to Sec. 2, we ran an N-body simulation with thin and thick disks for 8 Gyr.The main assumptions in our study is that thick disk formation was completed a longtime (8 Gyr) ago and the thick disk stars experienced effective radial mixing for a longtime since then (e.g. Brook et al. 2012). The simulation mimics the evolution history ofthe Galactic disk after the thick disk formed. At this time, we set two components for thethick disks, a thicker, smaller one (thick1) and a thinner, larger one (thick2), to mimicthe inside-out and upside-down formation of the thick disk (e.g. Brook et al. 2006). Westudy what radial and vertical metallicity gradients these two thick disk componentsshould originally have had by comparing with the APOGEE observations of metallicitydistribution function (MDF) at different Galactocentric radii and height. We run MCMCusing emcee (Foreman-Mackey et al. 2013) with 8 parameters, i.e. two different sets ofthe initial central metallicity, [Fe/H]0, radial metallicity gradient, (d[Fe/H]/dR)0, ver-tical metallicity gradient, (d[Fe/H]/dz)0, and metallicity dispersion, σ[Fe/H],0, at t = 0for thick1 and thick2 disks, to explore what parameter set would best match with theAPOGEE thick disk MDFs at t = 8 Gyr snapshot.We found that thick1 disk prefers to be high metallicity and positive radial metallicitygradient. On the other hand, thick2 prefers to be metal rich and a negative vertical metal-licity gradient. Because we set thick1 is more massive, overall the thick disk is required tohave a positive radial metallicity gradient. An overall negative radial metallicity gradientfor the thick disk progenitor is rejected. This is because radial mixing in a disk with aninitially negative radial metallicity gradient leads to a positive vertical metallicity gradi-4 Daisuke Kawataent as demonstrated in Sec. 2, unless they have a strong flaring disk initially. It should bedifficult to have a thick disk flaring strong enough to cause a negative vertical metallicitygradient with a negative radial metallicity, because the thick disk progenitor is likelyalready quite kinematically hot even in the inner region, when they born (Brook et al.2004). However, this could be an interesting question to be explored.Our result of metal poor thick1 and metal rich thick2 components support a scenarioin which the thick disk formed in an inside-out and upside-down fashion, and a younger,thinner and larger disk (like thick2) is more metal rich. Then, inside-out formation andage-metallicity relation produced an overall positive metallicity gradient when their for-mation was completed (see also Schönrich & McMillan 2017; Minchev et al. 2014). If wecould measure the age of the old stars accurately enough, we would expect that the olderthick disk would be smaller and more metal poor, and each generation of the thick diskwould exhibit a more negative radial metallicity gradient than the overall gradient of thethick disk. It would be challenging to divide the sample of thick disk stars into age binsfine enough to test this scenario. Hence, this would be a key challenge for future workon Galactic archaeology (e.g. Miglio et al. 2017).ReferencesAnders, F et al. 2014, A&A, 564, A115Brook, C. B., Kawata, D., Gibson, B. K., & Freeman, K. C. 2004, ApJ, 612, 894Brook, C. B. et al. 2006, ApJ, 639, 126Brook, C. 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Impacts of Radial Mixing on the Galactic Thick and Thin Disks

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