Origin of chemical and dynamical properties of the Galactic thick disk
aa r X i v : . [ a s t r o - ph . GA ] M a y Draft version August 21, 2018
Preprint typeset using L A TEX style emulateapj v. 8/13/10
ORIGIN OF CHEMICAL AND DYNAMICAL PROPERTIES OF THE GALACTIC THICK DISK
Kenji Bekki
ICRAR, M468, The University of Western Australia 35 Stirling Highway, Crawley Western Australia, 6009, Australia
Takuji Tsujimoto
National Astronomical Observatory, Mitaka-shi, Tokyo 181-8588, Japan
Draft version August 21, 2018
ABSTRACTWe adopt a scenario in which the Galactic thick disk was formed by minor merging between thefirst generation of the Galactic thin disk (FGTD) and a dwarf galaxy about ∼ R > V φ ) can correlate with metallicities ([Fe/H]) for the simulated thick disks depends on theinitial metallicity gradients of the FGTDs. The simulated orbital eccentricity distributions in thethick disk for models with higher mass-ratios ( ∼ .
2) and lower orbital eccentricities ( ∼ .
5) of minormergers are in good agreement with the corresponding observations. The simulated V φ - | z | relationof the thick disk in models with low orbital inclination angles of mergers are also in good agreementwith the latest observational results. The vertical metallicity gradient of the simulated thick diskis rather flat or very weakly negative at the solar neighborhood. Our Galactic chemical evolutionmodels show that if we choose two distinctive timescales for star formation in the thin and thickdisks, then the models can explain both the observed metallicity distribution functions (MDFs) andcorrelations between [Mg/Fe] and [Fe/H] for the two disks in a self-consistent manner. We discuss howthe early star formation history and chemical evolution of the Galactic thin disk can be influenced bythe pre-existing thick disk. Subject headings:
Galaxy: stellar content – Galaxy: structure – Galaxy solar neighborhood – stars:abundances – galaxies: evolution INTRODUCTION
The thick disk of the Galaxy is a fundamental Galacticcomponent containing fossil records of the early chemi-cal and dynamical evolution of the Galaxy (e.g., Free-man 1987; Majewski 1993; Freeman & Bland-Hawthorn2002). Since Yoshii (1982) and Gilmore & Reid (1983)first revealed the presence of the thick disk with scaleheight ∼ α /Fe] (e.g.,Fuhrmann 1998), larger scale-height (e.g., Ojha 2001,Larsen & Humphresy 2003; Juri´c et al. 2008), and largerradial, azimuthal, and vertical velocity dispersions (e.g.,Soubiran et al. 2003; Dinescu et al. 2011) of the thickdisk in comparison with the thin disk have long been con-sidered to provide constraints on the formation modelsof the thick disk. Theoretical models for the formation ofthe Galaxy based on a cold dark matter cosmology have started to explore the origin of the observed complicatednature of the thick disk (e.g., Abadi et al. 2003; Brooket al. 2004).Previous numerical simulations showed that accretionof a small satellite galaxy on the pre-existing thin stellardisk of a disk galaxy can dynamically heat up the diskto form the thick disk (e.g., Quinn et al. 1993; Walkeret al. 1996; Huang & Carlberg 1997; Velazquez & White1999 Villalobos & Helmi 2008): this formation process isreferred to as the “minor merger” scenario. Using cosmo-logical simulations with self-consistent chemical evolu-tion models, Brook et al. (2004) demonstrated that thickdisks of galaxies can be formed by accretion/mergingof gas-rich dwarfs at high redshifts (this is referred toas the “gas-rich merger” scenario). Radial migration ofstars due to internal stellar dynamics of disk galaxies(Sellwood & Binney 2002) has been demonstrated to beimportant for the formation of the Galactic thick disk(e.g., Sch¨onrich & Binney 2009; Loebman et al. 2010).Noguchi (1998) first showed that massive clumps devel-oped in the early dynamical evolution of galactic disks The Galaxy formationcan heat up the original disks to form thick disks.The predicted properties of the Galactic thick diskfrom these formation scenarios have recently been com-pared with the present-day properties of the thick disk:the orbital eccentricity distribution (e.g., Sales et al.2009; Dierickx et al. 2010; Dinescu et al. 2011), radialand vertical metallicity gradients (e.g., Allende Prietoet al. 2006; Ivezi´c et al. 2008), [ α /Fe]-[Fe/H] relationdifferent from that of the thin disk (e.g., Reddy & Lam-bert 2009; Reddy 2010), and rotational velocities of thickdisk stars dependent on vertical distances (e.g., AllendePrieto et al. 2006) and on metallicities (Spagna et al.2010). These comparisons between theoretical and obser-vational results have pointed out strength and weaknessof the above mentioned scenarios in explaining chemicaland dynamical properties of the Galactic thick disk. Forexample, the observed orbital eccentricity distribution ofthe thick disk stars is consistent either with the gas-richmerger scenario or the minor merger scenario (e.g., Di-erickx et al. 2010; Di Matteo et al. 2011 Dinescu etal. 2011; Wilson et al. 2011). These comparisons how-ever are not yet extensive enough to decide which of theproposed scenarios is the most self-consistent and con-vincing.Although previous numerical studies based on the mi-nor merger scenario provided some key predictions onstructural and kinematical properties of the Galacticthick disk (Quinn et al. 1993; Walker et al. 1996; Huang& Carlberg 1997; Villalobos & Helmi 2008), they did notdiscuss chemical properties nor their correlation with thedynamical properties observed in the Galactic thick disk.Given that the thick disk is composed largely of ratherold stars with ages larger than ∼ ∼ ∼ live thin disk influence the dynam- ical evolution of a thick disk in a galaxy. The presentstudy therefore adopts a new two-component disk modelin which a live thin disk can dynamically influence a thickdisk through the growth of non-axisymmetric structuresover a long timescale. We then use the model to dis-cuss structural and kinematical properties of the presentGalactic thick disk surrounding the thin disk.We also construct a new self-consistent chemical evolu-tion model in which the early star formation history andchemical evolution of the thin disk is influenced by (i) theremaining gas of the thick disk, (ii) later gas accretiononto the thin disk, and (iii) dynamical properties of thethick disk. Since the present chemical evolution model isthe first one that is based on the minor merger scenario,the predicted properties of the model enable us to discussstrength and weakness of the minor merger scenario inexplaining the observed properties of the thick disk (e.g.,Chen et al. 2000; Gratton et al. 2000; Prochaska et al.2000; Mashonkina & Grhren 2001; Tautvaisiein˙e et al.2001; Bensby et al. 2003, 2005; Reddy et al. 2003; 2006;Casagrande et al. 2011). Based on our chemical and dy-namical models, we particularly discuss the radial metal-licity gradient of the thick disk, dynamical interactionbetween the thin and thick disks after the formation ofthe thick disk, the metallicity distribution function, andthe [ α /Fe]-[Fe/H] relation of the thick disk. The presentmodel is novel, because these thick disk properties havenot been discussed in previous theoretical studies basedon the minor merger scenario.The structure of the paper is as follows. In the nextsection, we describe our new two-component dynamicalmodels of the Galactic disk and our chemical evolutionmodels for the Galactic thin and thick disks. In §
3, wepresent the results of the present chemical and dynamicalmodels for the Galactic disks. In §
4, we discuss a num-ber of key observational results in the context of differentformation scenarios for the thick disk and we summarizeour conclusions in §
5. Although our previous chemody-namical models of the formation of the Galaxy discussedphysical correlations between [Fe/H] and kinematic ofthe Galactic disk and stellar halo (Bekki & Chiba 2000,2001), the present study, which is not based on a fullyself-consistent chemodynamical model, does not allow usto do so. Because of this limitation, we only brieflydiscuss the observed correlations between chemical andkinematical properties of the thick disk in the present pa-per, and will extensively discuss these in our future stud-ies based on fully self-consistent chemodynamical simu-lations. Because we focus exclusively on the Galacticthick disk in the present paper, we will discuss the ori-gin of thick disks observed in other disk galaxies (e.g.,Yoachim & Dalcanton 2008) in the context of the minormerger scenario in forthcoming papers. MODELS
We discuss chemical and dynamical properties of theGalactic thick disk by using both N-body simulations andone-zone chemical evolution models. We first describethe models for the ancient minor mergers, the growth ofthe thin disk, and the dynamical evolution of the stel-lar disk composed of thin and thick disks ( § TABLE 1Model parameters for N-body simulations.
Model M d a f dm b m r p d e p e Θ f f thick g M d , n h a d , n i M1 4.0 157 0.2 1.0 0.5 30 0.12 4.0 0.2M2 4.0 157 0.05 1.0 0.5 30 0.105 4.0 0.2M3 4.0 157 0.1 1.0 0.5 30 0.11 4.0 0.2M4 4.0 157 0.3 1.0 0.5 30 0.13 4.0 0.2M5 4.0 157 0.2 0.5 0.8 30 0.12 4.0 0.2M6 4.0 157 0.1 1.0 0.5 60 0.12 4.0 0.2M7 4.0 157 0.2 1.0 0.5 30 0.12 4.0 0.14M8 8.0 79 0.2 1.0 0.5 30 0.24 4.0 0.2M9 4.0 99 0.2 1.0 0.5 30 0.12 4.0 0.2M10 4.0 99 0.05 1.0 0.5 30 0.105 4.0 0.2M11 4.0 99 0.2 1.0 0.5 30 0.12 4.0 0.14M12 4.0 157 0.2 1.0 0.5 30 0.24 2.0 0.2M13 4.0 157 0.2 1.0 0.5 30 0.40 1.2 0.2M14 4.0 157 0.05 1.0 0.8 30 0.105 4.0 0.2M15 4.0 157 0.1 1.0 0.5 0 0.11 4.0 0.2M16 4.0 157 0.2 1.0 0.5 0 0.12 4.0 0.2 a The total mass of the stellar disk in the FGTD in units of 10 M ⊙ . b The mass ratio of the dark matter halo to the stellar disk in the FGTD. c The mass ratio of the dwarf disk to the FGTD in a minor merger. d The pericenter distance of the orbit in a minor merger model in units of R d , where R d is the disk size of the FGTD. e The orbital pericenter distance in a minor merger model. f The inclination angle between the orbital plane of the dwarf disk and the x - y plane (corresponding to the disk plane of the FGTD). g The mass ratio of the thick disk to the thin disk in a two-component disk model. h The total mass of the stellar disk in the thin disk in units of 10 M ⊙ . i The scale-length of the thin disk in units of the disk size ( R d , n ). thick disk. We then describe one-zone chemical evolutionmodels that are used for deriving the MDFs and cor-relations between different chemical abundances of thethin and thick disks ( § Dynamical models
FGTD
The FGTD is modeled as a bulge-less disk galaxy withtotal mass M d and size R d embedded in a massive darkmatter halo. The total mass and the virial radius ofthe dark matter halo of the FGTD are denoted as M dm and r vir , respectively. We adopt an NFW halo densitydistribution (Navarro, Frenk & White 1996) suggestedfrom CDM simulations: ρ ( r ) = ρ ( r/r s )(1 + r/r s ) , (1)where r , ρ , and r s are the spherical radius, the char-acteristic density of a dark halo, and the scale length ofthe halo, respectively. We adopted c = 12 (= r vir /r s ) and r vir = 12 R d for the dark matter halo, and the mass ratioof halo to disk ( f dm ) is regarded as a free parameter thatcan control the mass-ratio of the simulated thick diskto the thin disk. In the present scenario, minor merg-ing occurred when the FGTD was still rapidly growingand thus a much less massive disk embedded in a mas-sive dark matter halo. We therefore consider that f dm should be rather large and investigate models with f dm ranging from 79 to 157. We mainly describe the resultsof the models with f dm = 157 in which the final stellardisk has a thick disk component with the mass ∼
10% ofits thin disk component and a maximum circular velocity( V c ) ∼
240 km s − , which is reasonable for the Galaxy(e.g., Binney & Tremaine 2007).The stellar component of the FGTD is assumed tohave an exponential profile with radial and vertical scalelengths of 0 . R d and 0 . R d , respectively. In additionto the rotational velocity made by the gravitational fieldof the disk and halo components, the initial radial andazimuthal velocity dispersion are given to the disk com-ponent according to the epicyclic theory with Toomre’sparameter (Binney & Tremaine 1987) Q = 1.5. The ver-tical velocity dispersion at a given radius is set to be 0.5times as large as the radial velocity dispersion at thatpoint. The initial disk plane of the FGTD is set to bethe x - y plane in the present study (i.e., the z -axis isthe polar direction of the disk). Figure 1 shows the ra-dial profile of the circular velocity V c for the FGTD in amodel with M d = 4 × M ⊙ and R d = 17 . V c that is significantly smaller than the present one in theGalaxy.Recent photometric and spectroscopic observations ofthe Galactic stellar and gaseous components have demon-strated that the present thin disk has metallicities thatdepend on location within the disk, i.e., metallicity gra-dients (e.g., Friel 1995). In the present minor merger sce-nario, stars within the present Galactic bulge had beenalready formed before the minor merger occurred andthey initially consisted of the inner part of the FGTD.The inner part of the thick disk became the part of theGalactic bulge in response to the bar formation in theinner part of the two-component Galactic disk. We thusneed to assume that the inner disk of the FGTD has The Galaxy formationa metallicity gradient that is different from that of theouter part and similar to that of the bulge. In the presentstudy, we consider that the metallicity gradient is differ-ent between the inner ( R < R th ) and outer ( R ≥ R th )regions of the FGTD, where R < R th is set to be 2 kpc,corresponding to the size of the bulge.We allocate metallicity to each disk star in the outerdisk ( R ≥ R th ) according to its initial position: at r = R , where r ( R ) is the projected distance (in units of kpc)from the center of the disk, the metallicity of the star isgiven as: [m / H] r=R = [m / H] d , r=0 + α d × R . (2)We consider that (i) the slope α d is a free parameter and(ii) [m / H] d , r=0 is determined such that the metallicity atthe solar radius ( R = R ⊙ corresponding to 8.5 kpc) is − . α d . We adopt the observed value of α d ∼ − .
04 (e.g., Andrievsky et al. 2004). Guided by theobservational results on the radial metallicity gradient ofthe Galactic bulge (e.g., McWilliam & Rich 1994; Wyseet al. 1997; Frogel et al. 2000), we assign the metallicityof a star at r = R in the inner disk ( R < R th ), where r ( R ) is the projected distance (in units of kpc) of the starfrom the center of the disk, to be:[m / H] b , r=R = [m / H] b , r=0 + α b × R . (3)We allow the slope of the metallicity gradient to be a freeparameter and investigate different models with different α b . The central metallicity of the disk is determined suchthat the metallicity at R = R ⊙ is consistent with thevalue derived from the equation (2) for the outer disk.If we adopt the metallicity gradient from Frogel et al.(2000) in which the slope α b = − .
4, then [m / H] b , r=0 =0 .
36 for α d = − .
04 and [m / H] d , r=0 = − . / H] r=R = [m / H] dw , r=0 + α dw × R . (4)The slope of the metallicity gradient α dw is assumed tobe a free parameter that can control the final metallicitygradients of merger remnants (i.e., thick disks). Sincethere is an observed relation between luminosity ( L ) andmetallicity ( Z ) for galaxies ( Z ∝ L . ; Mould 1984), weallocate a smaller metallicity of [m / H] dw , r=0 for the dwarfdisk according to the mass of the stellar disk in the dwarf( M d , dw ). The dwarfs disks in the present study are as-sumed to have total masses being 5 −
20% of the FGTDand thus cannot be similar to low-mass dwarfs with lower[ α /Fe] observed in the local group: they are not literallydwarfs. The adopted massive dwarf disks can experi-ence rapid star formation in their early histories (thushave higher [ α /Fe]) and correspond to the Large Mag-ellanic Cloud which shows higher [ α /Fe] in its old stel-lar populations. Thus the simulated thick disks in thepresent study, which can have stars from disrupted dwarfdisks, can show higher [ α /Fe], which is consistent withrecent observations by Ruchti et al. (2011) and Lee etal. (2011). Fig. 1.—
The radial profile of the circular velocity ( V c ; reddashed) for the FGTD with M d = 4 × M ⊙ , R d = 17 . f dm = 157: contributions from the dark matter halo and the stellardisk are shown by blue solid and green dotted lines, respectively.The maximum circular velocity of a dwarf disk that merges withthe FGTD is shown by a dotted line for m = 0 .
05, 0.1, 0.2, and0.3, where m is the mass ratio of the dwarf to the FGTD. In order to show more clearly how minor galaxy merg-ing can influence radial metallicity gradients of mergerremnants, we allocate metallicities to stars at each radiusaccording to their positions R alone. We do not intro-duce initial vertical metallicity gradients in the FGTDin the present study, because we need to assume a fewadditional unknown parameters, which can make the in-terpretation of the simulation results much less straight-forward. It would be possible for different stars at thesame R in the FGTD to have different metallicities owingto chemical and dynamical evolution, but we do not con-sider this possibility. Ignoring such a dispersion in theinitial metallicity at each radius allow us to avoid intro-ducing additional free parameters for clarity. The finalmean metallicity in the central region ( R < − .
3, owing to radial mixingof stellar populations in the present study. The centralmetallicity can be higher if we adopt higher metallicitiesin the inner regions of the FGTD. Since the purpose ofthis paper is not to discuss the origin of the bulge, we donot consider its chemical properties.The total numbers of particles used for the dark mat-ter halo ( N dm ) and the stellar disk ( N disk ) of the FGTDin each simulation are 800000 and 100000, respectively.The total number of particles used for the dark mat-ter halo and the stellar disk in a dwarf are m N dm and m N disk , respectively, where m is the mass ratio of thedwarf to the FGTD. As demonstrated by Waker et al.(1996), the total particle number of more than 5 × isenough to properly investigate the formation processes ofthick disks from thin ones through minor galaxy merg-ing. Therefore, the present simulations with N ∼ enable us to derive physical properties of galactic thickdisks in a convincing way. In all of the present mod-els, the adopted gravitational softening length is fixed at0 . R d , which corresponds to 252pc for R d = 17 . Minor mergers
We consider minor galaxy mergers with mass ratios( m ) of merger progenitor galaxies ranging from 0.05to 0.3, so that we can investigate the physical proper-ties of thick disks. The FGTD and the satellite galaxythat finally merges with the FGTD are assumed toekki 5 Fig. 2.—
The final stellar distribution projected onto the x - y plane (left) and the x - z plane (right) for the minor merger modelwith m = 0 . r p = R d , e p = 0 .
5, and Θ = 30.
Fig. 3.—
The initial stellar distribution projected onto the x - z plane for the thick disk component (left) and thin one (right) inthe two component disk model constructed from the remnant ofthe minor merger model with m = 0 . r p = R d , e p = 0 .
5, andΘ = 30. have self-similar structures and kinematics in dark mat-ter halos and stellar disks: they both have NFW ha-los with R vir /R d = 12 and exponential disks with scalelengths and vertical scale heights of 0 . R d and 0 . R d ,respectively. We investigate only galaxy mergers be-tween bulge-less stellar disks in the present study, thoughthere can be some differences in dynamical properties ofmerger remnants between disk-disk merger models anddisk-spheroidal ones (e.g., Villalobos et al. 2008). Sinceour main focus is not the detailed properties of minormerger remnants, we do not discuss the results of disk-spheroidal merger models in the present study. The disksize of the dwarf ( R d , dw ) is assumed to depend on themass of the disk ( M d , dw ) such as R d , dw ∝ M . , dw , whichcorresponds to Freeman’s law (Freeman 1970). There-fore, m can determine the size of the stellar disk for thedwarf and thus the structural and kinematical propertiesof the dark matter halo and the stellar disk.In the present simulation of a minor merger, the orbitof the two disks is set to be initially in the x - y plane, andthe orbital plane of the satellite disk is assumed to be in-clined by Θ degrees with respect to the orbital plane.The initial distance between the two spirals ( r i ) is setto be either 3 R d or 4 R d in the present study. The peri-center distance ( r p ) and the orbital eccentricity ( e p ) areassumed to be free parameters which control the orbitalangular momentum and the energy of the merging galax-ies. For most merger models, r p and e p are set to be 1.0(in our units) and 1.0, respectively. The spin of the satel-lite dwarf galaxy is specified by two angles θ and φ (inunits of degrees). Here, θ is the angle between the z -axisand the vector of the angular momentum of the disk, and φ is the azimuthal angle measured from the x axis to theprojection of the angular momentum vector of the disk onto the x - y plane. We show the results of the modelswith θ = 45 and φ = 30 in the present study. We in-vestigate the dynamical evolution of a minor merger for[32 − × t dyn in each model (depending on m andorbital configurations), where t dyn is the dynamical timescale of the FGTD. We adopt t dyn = 1 . × yr in thepresent study.Figure 2 shows an example of the final stellar distri-butions in the stellar remnants of minor galaxy mergers.The initial thin disk in this merger model has m = 0 . r p = R d , and e p = 0 . M d = 4 × M ⊙ , R d = 17 . f dm = 157. The thin disk can bedynamically heated up by the sinking dwarf disk so thatthe disk can be transformed into a thick disk with outerdisturbed stellar substructures. The vertical stellar ve-locity dispersion and the rotational velocity in the thickdisk are ∼
30 km s − and ∼
120 km s − at R = R ⊙ (=8.5 kpc), respectively. The stellar velocity dispersionsand rotational velocity of the thick disk can increase sig-nificantly during the growth of a thin disk surroundedby the thick disk. As described later, the final rota-tional velocity of the thick disk (formed in this minormerger model) after the growth of the thin disk is notaltogether consistent with observations. In the presentstudy, merger remnants with larger m ( ∼ .
2) can beregarded as better models for the thick disk formation.
Slow growth of thin disks for two-component diskmodels
A thin stellar disk is placed within the thick disk sothat the dynamical response of the thick disk to theslowly growing thin disk can be investigated. The thickdisk formed in a minor merger model is inclined signif-icantly with respect to the x - y plane with the inclina-tion angle depending on Θ. Accordingly a coordinatetransformation is performed for the thick disk, so thatthe final disk plane can be again coincident with the x - y plane and thus with the disk plane of the thin disk. Thenthe stellar particles that finally consist of the new thindisk are slowly added to the thick disk until the thin diskfinally has a mass of M d , n and a size of R d , n . This addi-tion of stellar particles can mimic the slow growth of thethin disk by gas accretion from the Galactic halo regionand the subsequent star formation from the gas. Theaccretion/formation timescale of the thin disk is set tobe 20 t dyn for all models in the present study. The valuesof M d , n and R d , n are fixed at 4 × M ⊙ and 17 . . R d , n or 0 . R d , n and the vertical scale height being 0 . R d , n . Stellar par-ticles with the total particle number n acc are randomlyallocated their initial locations at each time step dur-ing the growth of the thin disk. We assume that thedisk growth rate is constant, n acc at each time step is N d , n /N step in the present study, where N d , n is the to-tal number of stellar particles used in the thin disk and N step is the total number of time steps in a numerical The Galaxy formationsimulation for the growth of the thin disk. After thecompletion of the thin disk formation, we then allocatethe three dimensional (3D) velocities to each thin diskstellar particle according to the final mass profiles of thedark matter, thick disk, and thin disk in the same waythat we did for the FGTD. In addition to the rotationalvelocity made by the gravitational field of halo and diskcomponents, the initial radial and azimuthal velocity dis-persion are given to the disk component according to theepicyclic theory with Toomre’s parameter Q = 1.5. Thetotal number of stellar particles in the thin disk is set tobe 100000 for all models in the present study. Thus thetwo-component disk consists of collisionless particle withthe same softening length for thin and thick disks andthe total particle number of 900000 × (1 + m ) + 100000in the simulation.Figure 3 shows the final stellar distributions of thethick and thin disk components in the two-componentdisk constructed from the remnant of the minor mergershown in Figure 2. The mass ratio of the thick diskto the thin one ( f thick ) is 0.105 and a d , n = 0 . R d , n inthis model. Clearly, the thick disk has a larger scale-height and still shows a diffuse flattened halo-like struc-ture ( R >
10 kpc). The original thick disk is dynamicallycompressed and stellar substructures formed in minormerging cannot be clearly seen in this two-componentdisk. The vertical velocity dispersion and rotational ve-locity of the thick disk finally becomes 39 km s − and 187km s − at R = R ⊙ , respectively, both of which are signif-icantly higher than the original values in the thick diskbefore the slow growth of the thin disk. The final verticalvelocity of the thick disk is larger by a factor of 2.8 thanthat of the thin disk in this two-component disk model.Although we mainly investigate dynamical evolution oftwo-component disk models with a d , n = 0 . R d , n , we com-pare the results between models with a d , n = 0 . R d and0 . R d , n . A parameter study
We investigate the dynamical evolution of the thin andthick disks for 40 t dyn by using the two-component stellardisks constructed above. We particularly investigate ro-tational velocities ( V φ ), radial ( σ r ), azimuthal ( σ φ ), andvertical ( σ z ) velocity dispersions in the thin and thickstellar disks when the central stellar bar (=boxy bulge)is formed for each model. Although we have run modelswith different model parameters, we mainly describe theresults of the “standard model” with M d = 4 × M ⊙ , R d = 17 . f dm = 157, m = 0 . r p = R d , e p = 0 . M d , n = 4 × M ⊙ , and R d , n = 17 . V c and V φ in the thinand the thick disk for the two-component disk model.The standard model shows larger differences in V φ ( ∼ − ), which is more consistent with observations (e.g.,Soubiran et al. 2003) in comparison with other models.The mass-ratio of the thick disk to the thin one ( f thick ) is0.12, which is consistent with the observed range of themass-ratio.We consider that the models with higher m ( ∼ . m ( ∼ . V φ in the simulated thin and thickdisks in the models with larger m are more similar to the observed one (e.g., Soubiran et al. 2003). Thetwo-component disk model shown in Figure 3 shows arather small difference in V φ at R = R ⊙ (at most ∼ − ) so that the model cannot be the best model.Two-component disk models constructed from stellarremnants of more energetic mergers with m = 0 . r p = 0 . R d , and large e p (e.g., 0.8) however show largerdifferences in V φ between the thin and thick disks. Weinvestigate the following four kinematical properties at R = R ⊙ in each model: (i) the circular velocity V c , (ii)the difference in V φ between the thin and thick disks, (iii) σ z , and (iv) σ r /σ z , σ φ /σ z , and σ r /σ φ . Since the entirestructure and kinematics of the thick disk are currentlyunknown, we compare the above kinematical propertiesat R = R ⊙ with the corresponding observational ones(e.g., Dinescu et al. 2011) for the diagnosis of the bettermodels.Most of the present models show higher σ z (40 − − ) at R = R ⊙ in the thick disk component, whichis slightly larger than the observed value. The presentminor merger simulations are purely collisionless onesso that they can overpredict stellar velocity dispersionsof merger remnants (=thick disks) owing to the lack ofgaseous dissipation and cooling. We therefore considerthat models with σ z ∼
50 km s − that is appreciablylarger than the observed one (40 ±
10 km s − ; Freeman1986; 39 ± − Soubiran et al. 2003) can be regardedas reasonable. The present minor models are less realisticin some points (e.g., non-inclusion of gas dynamical andstar formation), and we have explored a limited rangeof model parameters. Therefore, it should be stressedthat the the present standard model does not explainall of the observed properties of the thick disk in a fullyself-consistent manner.The Table 1 summarizes the parameters values for therepresentative models investigated in the present study.The standard model is labeled as M1. For each of thesemodels, we investigate the radial metallicity gradient andthe MDF of the simulated thick disk and their depen-dences on the model parameters for the initial metallic-ity gradient of the FGTD (e.g., α d ). Numerical com-putations were carried out both on (i) the latest ver-sion of GRAPE (GRavity PipE, GRAPE-DR) – which isthe special-purpose computer for gravitational dynamics(Sugimoto et al. 1990) and (ii) one IBM system iData-Plex with two GPU cards (NVIDIA Tesla M2050) andthe CUDA G5/G6 software package installed for calcula-tions of gravitational dynamics at University of WesternAustralia. It took about 9 CPU hours, 6 CPU hours,and 14 CPU hours for one GRAPE-DR machine to sim-ulate one minor merger model, slow growth of a thindisk surrounded by a thick disk, and dynamical interac-tion between the thin and thick disks, respectively (thusabout 29 CPU hours for ∼ t dyn dynamical evolutionof one sequential dynamical simulation). The time T represents the elapsed time for each simulation of thetwo-component disk evolution. Chemical evolution models
Since the present one-zone chemical evolution modelsfor the Galaxy are essentially the same as those adoptedin our previous paper (Tsujimoto et al. 2010), we herebriefly describe the models. The basic picture is that theekki 7
Fig. 4.—
The radial profiles of the rotational velocity of the thindisk (blue), that of the thick disk (red), and the circular velocity(green) in the two-component disk for the standard model.
Fig. 5.—
The radial distribution of stellar metallicities in thethick disk formed in the minor merger model with m = 0 . r p = R d , e p = 0 .
5, and Θ = 30, which is used for constructing thetwo-component disk in the standard model. Each small black dotrepresent the location of a star in the thick disk. The red, blue,and green line represent the initial metallicity gradients for thestellar disk of the FGTD, the dwarf, and the bulge component ofthe FGTD, respectively. Each magenta filled circle represents themean [Fe/H] for each radial bin.
Galactic thin and thick disks were formed by gas infallfrom outside the disk region. For the infall rate, we applyan exponential form with a timescale τ in . Taking intoaccount the relatively rapid formation of the thick diskand the presence of the G-dwarf problem for the thindisk, we assume a rather short timescale of τ in =0.3 Gyrfor the thick disk, and a much longer timescale of τ in =4Gyr for the thin disk. The metallicity Z in of infalling gasis set up as follows. The MDF of the thick disk shows asharp increase from [Fe/H] ∼ − . ∼ − .
7. This feature was first reported by Wyse &Gilmore (1995) with a small number of complete samples,and the location of its peak is confirmed by the hugeSDSS database of stars within the thick disk (Allendeet al. 2006). These observational results suggest thatmaterial for the proto-thick disk was pre-enriched up to[Fe/H] ∼ − .
3. The mechanism of pre-enrichment may beattributable to wind enrichment triggered by an initialstarburst in the Galactic bulge (Tsujimoto et al. 2010;Tsujimoto 2011). Accordingly, [Fe/H]= − . Z in of the thin disk (i.e., metallicityof the gas accreted from the Galactic halo) is determinedby an implication from the cosmic evolution of dampedLy α systems (Wolfe et al. 2005). Its metallicity at the epoch of thin disk formation, i.e., ∼ − . α /Fe] ratioin the gas accreted onto the thin disk is fixed at a highvalue (e.g., [Mg/Fe]=+0.4) as expected from chemicalenrichment dominated by SNe II. As shown later in § Z in and the[ α /Fe] ratios for gas accreted onto the disks.The star formation rate (SFR) is assumed to be pro-portional to the gas fraction with a constant coefficient ν for the duration ∆ SF . The higher value of ν =2 Gyr − for∆ SF = 1.5 Gyr is adopted for the thick disk, comparedwith ν =0.7 Gyr − and ∆ SF =12 Gyr for the thin disk.Here, the duration of thin disk formation is set so thatthe sum of timescales for two disk formation is broadlyequivalent to the age of the Universe (=13.7 Gyr). Forthe initial mass function (IMF), we assume a power-lawmass spectrum with a slope of − .
35, which is combinedwith the nucleosynthesis yields of SNe Ia and II takenfrom Tsujimoto et al. (1995). In our model, the productsof SNe II are ejected with the short lifetime ∼ − yr ofmassive stars depending on their masses, while those ofSNe Ia are released with a delay of a considerably longerlifetime spanning over 0.5 - 3 Gyr (Yoshii et al. 1996).The fraction of stars that eventually produce SNe Ia for3-8 M ⊙ is assumed to be 0.05.In the present scenario of thick disk formation, starformation within the thin disk can occur after the termi-nation of star formation in the thick disk. Accordingly,the present chemical evolution models are different fromthose previously adopted (e.g., Chiappini et al. 1997).We consider the three models for the star formation his-tory of the thin disk after the formation of the thick diskby minor merging described below. The first scenario isthe “continuous star formation model” in which the thindisk stars start to form from the thick disk’s remaininggas (corresponding to only ∼
10% of the original gas)mixed with the gas accreted onto the disk immediatelyafter the thick disk formation . In this model, chemicalabundances of the first stars in the thin disk are similarto those of the most metal-rich stars in the thick disk.The second scenario is the “temporal truncationmodel” in which star formation in the thin disk cannotstart until some amount of gas is accreted onto the disk.Therefore, the first stars in the thin disk will have chem-ical abundances different from those of the final stars inthe thick disk. Here the timing to initiate the formationof thin disk stars is set at the time when the metallicity ofgas is diluted to [Fe/H]= − . -1 -0.8 -0.6 -0.4 -0.2 0 0.200.20.40.60.81 Fig. 6.—
The MDFs for R ≤ ≤ R ≤ R ≥
12 kpc (outer disk,green) in the thick disk shown in Figure 5. The number distributionof stars is normalized by the maximum number of stars in themetallicity bins for each of the three regions. -1-0.500.5 0 5 10 15-1-0.500.5 0 5 10 15
Fig. 7.—
The same as Figure 5 but for four different mod-els: (a) shallower metallicity gradient in the bulge ( α b = − . α d = − . α d = − . α dw = 0). Fig. 8.—
The same as Figure 6 but for four different modelsshown in Figure 7. and gas accretion, do not allow us to determine the mostprobable model among the above-mentioned three, weinvestigate all three scenarios and compare them withone another in § RESULTS
Metallicity gradients and MDFs in thick disks
Figure 5 shows the radial distribution of stellar metal-licities in the thick disk formed from minor merging with m = 0 . r p = R d , e p = 0 .
5, and Θ = 30 (i.e., thestandard model M1) for α d = − .
04 , α b = − .
4, and α dw = − .
04. During minor merging, stellar populations with different metallicities can be radially mixed so thatthe original radial metallicity gradient changes signifi-cantly. As shown clearly in Figure 5, the initial steeperradial metallicity gradient of the FGTD can become sig-nificantly flattened after minor merging. More metal-richstars initially in the inner disk region can be finally lo-cated at
R >
R >
R <
R >
R <
10 kpc) can be transferred to the outer region.The radial mixing of the stellar population in minormerging can transfer metal-rich stars with [Fe/H] ∼ − . − − . R = R ⊙ corresponding to 8.5 kpc). Thisresult implies that some fraction of metal-rich stars cur-rently at R = R ⊙ in the thick disk can originate fromthe inner disk of the FGTD. It should be stressed thatthe radial transfer of the inner metal-rich stars into thesolar neighborhood depends strongly on m and that theradial transfer can be less effective in minor mergingwith smaller m . As a result of radial mixing of stel-lar populations with different metallicities, the MDF ofthe thick disk is different between different regions. Fig-ure 6 shows that the MDF in the solar neighborhood (8kpc ≤ R ≤ ∼ − . R ≤ ∼ − . > . R ≥
12 kpc shows a lowerpeak metallicity at [Fe/H] ∼ − . < − . m . Figure 7 shows thatthe radial metallicity gradient of the thick disk is notinfluenced so much by that of the bugle, because onlya minor fraction of the bulge stars can be transferredto the disk region during minor merging. As shown inFigure 7, the flattening of the radial metallicity gradientcan be more clearly seen in the model with the steeperinitial metallicity gradient of the FGTD. There is no sig-nificant difference in the final metallicity gradient of thethick disk between the standard model and the one withno initial metallicity gradient in the dwarf disk, whichmeans the transfer of of metal-poor stellar populationsfrom a dwarf disk to the thick disk is not an importantfactor for determining the radial metallicity gradient ofthe thick disk. Figure 8 shows that the shapes of theMDFs for the three different regions of the thick diskdepend on the adopted initial metallicity gradient of theFGTD, which suggests that the MDFs can have somefossil information on the original metallicity gradient ofthe FGTD before ancient minor merging transformed itekki 9 Fig. 9.—
The time evolution of stellar distributions for thethin disk component (upper six) and for the thick one (lower six)projected onto the x - y plane in the two-component disk for thestandard model. The time T in units of Gyr is shown in the upperleft corner of each panel. Fig. 10.—
The same as Figure 9 but for the x - z plane. into the thick disk. Dynamical properties of two-component disks
Figures 9 and 10 show the long-term dynamical evo-lution of the two-component stellar disk in the standardmodel (M1) in which the final mass fraction of the thickdisk versus the thin disk is 0.12. A stellar bar can formspontaneously from global bar instability in the thin diskwithin ∼ T = 2 . T = 5 . T = 6 . Fig. 11.—
The radial (upper) and vertical (lower) stellar surfacedensity (Σ s ) profiles for the thin (blue) and thick (red) disks at T = 0 Gyr (solid) and T = 2 . s (49.6 M ⊙ pc − ) at R = R ⊙ . ties of the thick disk can be significantly changed. Oneof the remarkable effects of the barred thin disk is thatthe initially non-barred thick disk can be transformedinto a barred one with the position angle and patternspeed of the bar being similar to those of the bar in thethin disk. As shown in Figure 9, a slightly shorter stellarbar is formed in the thick disk at T = 2 . s ) of the thin and thick disks at T = 0Gyr (initial) and T = 2 . ≤ R ≤ R <
R >
12 kpc) parts ofthe thin disk show slight increases in the radial surfacestellar density profile (Σ s ( R )) whereas the inner part at R ∼ s ( R ). The thick diskat 5 ≤ R ≤ Fig. 12.—
The radial profiles of V φ (top), σ φ (the second fromthe top), σ r (the second from the the bottom), and σ z (bottom)for the thin disk (blue) and the thick disk (red). of the thin disk can be more strongly influenced by thestellar bar in comparison with those of the thick disk.Figure 12 shows that the thin and thick disks havedifferent kinematical properties just after the formationof the inner stellar bar at T = 2 . V φ difference in the thin and thick disk at R = R ⊙ becomes smaller ( ∼
16 km s − ). The vertical velocitydispersion of the thick disk also become slightly larger( σ z ∼
53 km s − ) after the stellar bar formation. Thethick disk has σ r = 70 km s − (i.e., σ r /σ z ∼ .
3) and σ φ = 55 km s − ( σ φ /σ z ∼ . σ φ and σ z at R = R ⊙ can become slightly larger at T = 6 . σ z means that the stellar bar in the thindisk can continue to change the kinematics of the thickdisk within ∼ Fig. 13.—
The same as Figure 12 but for four different models:(a) m = 0 .
05 (model M2), (b) m = 0 . m = 0 . m = 0 . r p = 0 . R d , and e p = 0 . -1-0.50 DiskDwarfBulgeT=2.8 (Gyr)0 5 10 15-1-0.50 T=6.9 Fig. 14.—
The same as Figure 5 but for the two-component diskat T = 2 . T = 6 . Figure 13 shows that the kinematical properties of thesimulated two-component disks depend largely on themodel parameters of minor mergers ( m , r p , and e p ) inthe models, M2 − M5. The two-component disks con-structed from merger remnants with m = 0 .
05 (M2)and 0.1 (M3) have smaller V φ differences in the thin andthick disks and smaller σ z . In these models with smaller m , the differences in the radial profiles of V φ , σ r , and σ φ between the thin and the thick disks at R <
10 kpcare small and thus are less consistent with observations,which means that minor merging with lower m is un-likely to be responsible for the formation of the Galacticthick disk. The model M4 with larger m (=0.3) showsekki 11a higher degree of kinematical differences in the thin andthick disks, which can be still consistent with observa-tions. The stellar bar developed in the thick disk forthis model is a shorter (or fatter) and weaker one. Thethick disk in the model M5 with m = 0 . r p = 0 . R d ,and e p = 0 . V φ difference in the thin and thick disk is quite large,even after the slow growth of the thin disk. This modelcannot be regarded as reasonable for the Galactic disk.Although we confirm that stellar bars can be formedin thick disks for most models (i.e., M1-M12 exceptM5), the morphological properties of the simulated barsare different between different models. For example,the model M12 with a smaller mass of the thin disk( M d , n = 2 × M ⊙ ) shows the formation of a shorterand weaker bar in the thin disk so that the thick disk can-not clearly show a strongly barred structure (but showa fat, elliptic morphology) owing to the weaker dynam-ical effect of the bar of the thin disk on the thick disk.The models with smaller M d , n (e.g., M d , n ≤ M ⊙ ) donot show the formation of bars in the thin (thus thick)disk. These results suggest that the thick disk can beinfluenced by the barred structure of the thin disk onlyin the later stage of the disk evolution (i.e., when thedisk has a larger mass). These models with smaller M d , n show lower velocity dispersion within the thick disk (e.g., σ z ∼
40 km s − ), which is more consistent with observa-tions. The present results on the kinematical differencesbetween thin and thick disks do not depend so stronglyon M d , f dm , and a d , n , but they depend more strongly on m and Θ. The dynamical properties of the model M6with large Θ (=60) are less consistent with observationsthan than other models with lower Θ ( ≤ T = 2 . R < m (=0.05 and 0.1): the radial metallicity gradients of thethick disks at R > R = 2 kpc to the outer diskregions at R > R ⊙ . However the number fractions ofstars that are located initially at R ≤ S F R T(Gyr) thick thin N [Fe/H] [Fe/H] [ M g / F e ] [Fe/H] Fig. 15.—
Chemical features predicted by the continuous starformation model for the thick and thin disks in the solar neighbor-hood.
Upper panel : The star formation rate as a function of timefor the thick disk (red curve) and the thin disk (blue curve). EachSFR is normalized so that each total stellar mass is unity.
Middlepanel : Predicted MDFs of the thick disk (left) and the thin diskstars (right) compared with the observations. The calculated dis-tributions are convolved using a Gaussian with a dispersion of 0.1dex considering a measurement error expected in the data. Filledcircles represent data taken from Wyse and Gilmore (1995), andopen circles are from Edvardsson et al. (1993).
Bottom panel : Ob-served and predicted correlations of [Mg/Fe] with [Fe/H] for thethick and thin disks, compared with those for the Galaxy. The ob-served data of the thick disk are denoted by filled circles (Bensbyet al. 2005), and those for the thin disk are denoted by crosses(Edvardsson et al. 1993; Bensby et al. 2005). at R ≥ − for the present models,even if the central bars become long and strong. There-fore, the radial transfer of bulge stars with high [Fe/H]to the solar-neighborhood is much less efficient in thepresent models. It should be stressed here that somefraction of metal-rich stars in the inner disk regions canbe transferred to the solar neighborhood. On the otherhand, the slow growth of the thin disk can contract thethick disk so that the number fractions of more metal-rich stars ([Fe/H] > − .
5) at
R > § R = R ⊙ inthe Galactic thick disk.2 The Galaxy formation N [ M g / F e ] [Fe/H] Fig. 16.—
Predicted features by the temporal truncation model(solid curve) and the expulsion model (dashed curve) for the thindisk. The symbols are the same as in Figure15. For reference, theresult for the thick disk is shown as a red curve in the lower panel.
Chemical evolution of the thin and thick disks
Figure 15 shows the star formation histories, MDFs,and [Mg/Fe]-[Fe/H] relations for the thin and thick disksin the continuous star formation model. The upper panelof Figure 15 shows the predicted star formation historyof the Galactic disk, where the thick disk is first formedrapidly, followed by a gradual formation of the thin diskover a prolonged timescale. Here, each SFR is normal-ized so that each total stellar mass is unity. The resul-tant MDFs for thick disk and thin disk, and the corre-lations of [Mg/Fe] with [Fe/H] are shown in this figure.In this model, the thick disk formation terminates whenthe metallicity reaches [Fe/H] ∼ > > ∼
10% (e.g., Bensby et al. 2007), this ap-parent inconsistency implies that such metal-rich starscannot form in situ at the solar-neighborhood. Thus,we need to consider that (i) this apparent inconsistencyis due largely to the limitation of the adopted one-zonechemical evolution model which does not consider mix-ing of stellar populations between different disk regionsand thus (ii) these metal-rich stars with [Fe/H] > ∼ . § ∼ ∼ ∼ +0.4). This reverse evolution comes to an end whenthe chemical enrichment by star formation exceeds theeffect of gas dilution, and subsequently an usual evolu-tionary path appears. In the end, the overall behaviorexplains, in part, a large dispersion in stellar ages as wellas in [Mg/Fe] among the thin disk stars. In addition, itmay be possible to claim that the remaining metal-richgas after the thick disk formation results in the presenceof no metal-poor thin disk stars.The results of the temporal truncation model do notdiffer significantly from those of the continuous star for-mation model in terms of the MDF of the thin disk stars.Figure 16 shows that the temporal truncation model canreproduce the observed MDF of the thin disk stars aswell as the continuous one. The remarkable differencebetween the two is that there are no old thin disk starswith [Fe/H] ∼ ∼ . ∼ − . < −
1) and high [Mg/Fe] ( ∼ . DISCUSSION
The possible presence of the barred thick disk
The present study has first demonstrated that theGalactic thick disk can have a barred structure if it wasformed prior to the formation of the Galactic thin diskand thus has long been influenced dynamically by thethin disk with a stellar bar. Given that most modelshave shown the formation of the barred thick disk in thetwo-component stellar disks, the present prediction onthe presence of the barred thick disk in the Galaxy mightwell be regarded as robust. Recent theoretical studies onthe formation of the thick disk through radial mixing ofekki 13
Fig. 17.—
The two-dimensional (2D) distribution of V φ for thickdisk stars at T = 2 . V φ distribution is clearly asymmetric, in particular, in the central5kpc of the thick disk. Fig. 18.—
The same as Figure 5 but for the model M2 with m = 0 .
05. It is clear that radial mixing of stellar populations byminor merging in this model is less efficient in comparison with thestandard model M1 shown in Figure 5. stars did not show the formation of the barred thick diskin their models (e.g., Sch¨onrich & Binney 2009; Loebmanet al. 2010). Previous cosmological simulations on thethick disk formation via accretion (Abadi et al. 2003)and gas-rich mergers (Brook et al. 2004) did not showthe formation of the barred thick disk either. It is thuspossible that the presence or absence of the global barredstructure of the thick disk can be a clue as to how thethick disk was formed. However, it should be stressedhere that the present study could overestimate the dy-namical influence of the stellar bar on the thick disk, be-cause the simulated bars are stronger and longer than thereal Galactic bar owing to the adopted model in whichthe entire disk has a smaller Q (1 .
5) when it is fully de-veloped: a stronger and longer stellar bar can form fromsuch a massive disk with a smaller Q parameter.Larsen & Humphreys (1996) first revealed an excessof faint blue stars with B - V bluer than by 0.6 mag in Quadrant 1 (Q1) in comparison with Quadrant 4 (Q4)and thus suggested that the observed excess can resulteither from the elliptic thick disk or heating of the diskby the bar. Parker et al. (2004) later confirmed the pres-ence of the asymmetric thick disk in Q1 and also revealedkinematical asymmetry between the thick disk stars inQ1 and Q4 (i.e., differences in V φ ). Humphreys et al.(2011) confirmed the kinematical differences of the thickdisk stars in Q1 and Q4 and suggested that the dynami-cal interaction between the stellar bar and the thick diskcan be responsible for the observed kinematical differ-ences. Given that these observations did not map theentire region of the thick disk, it remains observationallyunclear whether or not the thick disk stars have a globalbarred structure, in particular, in the inner disk ( R < V φ in the thick disk can bedifferent in different regions of the Galaxy. Fig. 17 showsthe 2D distribution of V φ for thick disk stars projectedonto the x - y plane at T = 2 . ×
50 local regions within 12 kpc fromthe center of the disk and the mean V φ at each regionis estimated. The derived 2D V φ distribution clearlyshows an elongated and asymmetric (bar-like) feature,in particular, for the inner region ( R < V φ distribution in the thick disk, thereis kinematical evidence which supports the presence of abarred thick disk in the Galaxy. There is no clear signof a past minor merger event in the 2D V φ distribution,which implies that kinematical evidence for past minormerger events would be hard to find in observations onthe 2D V φ distribution of the Galactic thick disk.If the Galactic thick disk really has a barred structurein its inner part, then the observed 2D structure andkinematics can give strong constraints on the formationprocesses of the thick disk. A discovery of a barred struc-ture with the position angle and pattern speed of the barbeing almost identical to those of the Galactic bar wouldsupport the minor merger scenario. If such a bar is notfound in the inner region of the Galaxy, then the minormerger scenario would need to clarify why the formationof a bar in the thick disk is suppressed in spite of thepresence of ongoing interaction between the realistic barand the thick disk. Given that there is no paper that ex-tensively investigated dynamical interaction between therealistic Galactic bar and the thick disk, it is doubtlesslyworthwhile for future studies to investigate their dynam-ical interaction in a comprehensive way, and compare thesimulated 2D radial and azimuthal velocity dispersions inthe thick disk with the corresponding observations (e.g.,Humphreys et al. 2011). The radial metallicity gradient in the thick disk
Allende Prieto et al. (2006) revealed that G-dwarfstars in the Galactic thick disk have a very flat radialmetallicity gradient for 4 < R <
14 kpc and 1 < | z | < < R <
14 kpc is about [Fe/H] ∼ − . R ). Although the presence of more metal-rich stars in4 The Galaxy formationthe outer part ( R >
10 kpc) of the thick disk is consistentwith the present merger scenario, the observed no/littleradial metallicity gradient appears to be less consistentwith the predictions of the present minor merger mod-els. The above mentioned problem of the present mi-nor merger scenario is due to the larger mean metallicity([Fe/H] > − .
7) of the thick disk stars at 4 < R < < R <
11 kpc,though the thick disk stars appears to have higher [Fe/H]ranging from − . − . R < R = R ⊙ , 8.5kpc) and thus provide a clue to the origin ofthe observed presence of metal-rich stars with [Fe/H] > α /Fe] ( ∼ .
1) in the thick disk (e.g., Bensbyet al. 2003; Casagrande et al. 2011). In the presentstudy, the final number fractions ( F mr ) of metal-rich starswith [Fe/H] > R > − (even after the formation of bars).This number F mr can increase significantly if we adopta more realistic model in which the initial MDF at eachradius in the FGTD has a dispersion: the metallicity ateach radius in the FGTD is fixed at a certain value (withno dispersion) according to the adopted metallicity gra-dient in the present study. It should also be stressedhere that minor merging with m ≤ .
05 does not showsuch efficient radial mixing as seen in other models with m ≥ . R > m = 0 .
05 and (ii) the trans-fer of the metal-rich stars initially within
R <
Fig. 19.—
Dependence of V φ for thick disk stars at thesolar-neighborhood on [Fe/H] in the standard model with differ-ent metallicity gradients for the FGTD: (a) α d = − .
04, (b) α d = − .
06, (c) α d = − .
08, and (d) α d = − .
04 and the cen-tral metallicity of the FGTD 0.1 dex lower than that in the model(a). Each filled circle and error bar represent the mean V φ andits dispersion at each [Fe/H] bin. The observed positive V φ -[Fe/H]correlation from Lee et al. (2011) is shown by a solid line in eachframe. Here stars with 8 ≤ R ≤ ≤ | z | ≤ Fig. 20.—
Dependence of V φ on R (upper) and | z | (lower) in themodel M15 which can reproduce well the observations by Lee et al.(2011). The mean V φ and dispersion in V φ at each bin are shownby filled circles and error bars, respectively. The small dots showthe results of individual thick disk particles in the model. Theobserved correlations from Lee et al. (2011) are shown by solidlines. The observed V φ -[Fe/H] relation of the thick disk Chiba & Beers (2000) investigated space motions andmetal-abundances of 1203 solar-neighborhood stars with[Fe/H] < − . V φ of the more metal-richstars are larger for | z | < < | z | < V φ and sug-gested that this correlation can give a constraint on theformation models of the thick disk. Lee et al. (2011)have recently confirmed a positive correlation between V φ and [Fe/H] in the thick disk and derived a relation ofekki 15∆ V φ / ∆[Fe/H]=49.0 ± . − dex − ). If future ob-servations (e.g., GAIA and HERMES) can select thickdisk stars based both on their locations and kinematicsand thereby investigate the V φ -[Fe/H] relation, then wewill be able to make a more robust conclusion on theviability of the minor merger scenario based on the com-parison between the observed and simulated V φ -[Fe/H]relations. However, it is worthwhile for the present studyto investigate whether there is a positive correlation be-tween [Fe/H] and V φ in the simulated thick disks.Figure 19 shows the V φ -[Fe/H] relation for 1789 starsof the thick disk at 8 ≤ R ≤ ≤ | z | ≤ T = 2 . ∼
50 km s − ), there is no clear V φ -[Fe/H]correlation for α d = − .
04 in the standard model. Inthe present minor merger scenario, more metal-rich starsare initially located in the inner regions of the FGTD(owing to the adopted negative metallicity gradient ofthe FGTD), where V φ is smaller, so that they can havesmaller V φ . Therefore, it is not so straightforward forthe minor merger scenario to explain the higher V φ inmore metal-rich stars at R = R ⊙ . It is found that for asteeper metallicity gradient ( α d = − . V φ − [Fe/H] relation becomes similar to the observed oneby Lee et al. (2011), which shows a weak positive correla-tion between V φ and [Fe/H]. There would be a possibilitythat the thin disk stars with higher [Fe/H] and larger V φ are included in the observed thick disk sample. If thiscontamination of the thin disk stars is real, then the ob-served V φ − [Fe/H] becomes even weaker so that it canbe more consistent with the simulated one in the presentstudy. We confirm that models with α d = − .
04 and dif-ferent central metallicities in the disk (e.g., (d) in Figure19) cannot reproduce the observation very well. Theseresults imply that the observed correlation between V φ and [Fe/H] can give some constraints on the initial metal-licity gradient of the FGTD in the Galaxy. V φ and orbital eccentricities of the thick disk starsdependent on | z | Recent observational studies have revealed that V φ depends on | z | such that V φ is smaller for larger | z | (∆ V φ / ∆ | z | = − . ± . − kpc − ) for the Galacticthick disk at the solar neighborhood (Lee et al. 2011).Although Villalobos & Helmi (2008) have already shownthat thick disks which formed from minor merging withlower Θ (0 and 30 in their Figure 20) can clearly show V φ − | z | correlations, they did not directly compare theirresults with the corresponding observations. Accord-ingly, it is worthwhile for the present study to comparethe results with the observational result by Lee et al.(2011). We have investigated which model in the presentstudy can reproduce the observed V φ − | z | and V φ − R re-lations best among the representative models and foundthat model M15 can show these relations similar to theobserved ones better than other models (including M16with m = 0 . m = 0 . V φ − | z | correlation can be betterreproduced in models with low Θ ( ≤
30) in the present
Fig. 21.—
Distributions of orbital eccentricities ( f ( e ), top), de-pendence of mean orbital eccentricities ( e m ) on R (middle), andthose on | z | (bottom), for five different models: the standard M1(blue), M2 (red), M3 (green), M14 (magenta), and M15 (cyan).The observed correlations from Lee et al. (2011) are shown bysolid lines in the middle and bottom panels. Fig. 22.—
Vertical metallicity gradients at different radii inthe standard model: at 0 < R ≤ < R ≤ . . < R ≤ . . < R ≤
14 kpc (cyan),and 14 . < R ≤ . R = 8 . V φ and R whereas observa-tions (Lee et al. 2011) show a rather weak correlation(∆ V φ / ∆ R = − . ± . − kpc − ).Lee et al. (2011) furthermore have revealed that theorbital eccentricities of thick disk stars at the solar neigh-borhood show a correlation between e and | z | (and R ).If the thick disk formed before the formation of the thindisk in the Galaxy, then orbital eccentricities of the thickdisk stars could be influenced by the formation processesof the thin disk. Previous simulations on the eccentricitydistribution ( f ( e )) of the thick disk stars however did notconsider the evolution of f ( e ) during the formation of thethin disk. We accordingly have investigated f ( e ) basedon the first ∼ ≤ R ≤
10 kpc and 0 ≤ | z | ≤ . f ( e ) and mean orbital eccentricity ( e m ) at a given R and | z | in each model.Observations on e m at different radial and vertical binsby Lee et al. (2011) show positive correlations of e m with R and | z | (i.e., larger e m for larger R and | z | ). Figure21 shows f ( e ) and e m dependent on | z | (and R ) derivedin the five representative models and accordingly can becompared with observational results shown in Figures 9and 10 by Lee et al. (2011). The standard model M1with e p = 0 . m (0.05 and 0.1) and e p = 0 . e . Themodel M14 with m = 0 .
05 and e p = 0 . e ( > . e m on | z | in this model M14 is qualitatively inconsistent with theobserved one. The model M15 with m = 0 . e p = 0 . V φ −| z | relation (in Figure 20), shows a peak around e ∼ . e ∼ .
2. These results imply that the models with larger m ( ∼ .
2) and lower e p ( ∼ .
5) can better reproducethe observed f ( e ) in the Galactic thick disk.The standard model M1 shows a very weak positivecorrelation between e m and R (i.e., larger e m at larger R ) whereas models with lower m show rather flat e m − R relations. The observations by Lee et al. (2011) show aweak positive flat e m − R relation (i.e., larger e m for larger R ), which appears to be more consistent with modelswith higher m . These results imply that the observed e m − R relation can give some constraints on m of minormergers that formed the thick disk. Only the model M15(lower Θ) clearly shows a positive correlation between e m and | z | (i.e., larger e m for larger | z | ), which appears to bemore consistent with the observation by Lee et al. (2011),though other models do not show such a correlation. Thisresult for model M15 is consistent with those in Figure20 which show that V φ is lower at lower | z | : stars withlower | z | have lower e (i.e., more circular orbits) and thushigher V φ . The observed e m − | z | relation combined with the V φ − | z | relation imply that if the thick disk wasformed by minor merging, then the orbital inclinationangle (Θ) of merging dwarf disks should be low. Thusthe observed f ( e ), e m − | R | correlation, and e m − | z | cangive some constraints on the present formation model ofthe Galactic thick disk. Vertical metallicity gradient in the thick disk
Recently Allende Prieto et al. (2006) have revealedthat there is no vertical metallicity gradient discerniblein the thick disk between 1 < z < r = R and a vertical distance( | z | ) from the x - y (equatorial) plane of the FGTD de-pends also on | z | and it is assigned as follows:[m / H] r=R , | z | = [m / H] | z | =0 + α v × | z | , (5)where [m / H] r=R , | z | =0 is a metallicity at r = R and | z | = 0. We adopted the slope α v ≈ − . R and | z | . Itshould be stressed here that equation (5) is used only forinvestigating the vertical gradient shown in Figure 22:other results shown in Figures 1-21 are not based on theequation (5). During minor merging and evolution ofthe two-component disk, the initial vertical metallicitygradient of the FGTD can change owing to dynamicalinfluences of minor mergers and the stellar bar.Figure 22 shows vertical metallicity gradients of thethick disk at different radii ( R ) at T = 2 . R , theoriginal steep gradients can be significantly flattened.This is mainly because minor merging can cause ver-tical heating of the initially thin disk (the FGTD) andthus mixing of stellar populations with initially differentmetallicities. The vertical metallicity gradient at the so-lar neighborhood (7 < R ≤ . | z | > R <
R > CONCLUSIONS
We have investigated chemical and dynamical proper-ties of the Galactic thick disk formed by ancient minormerging based on the results of N-body numerical sim-ulations and chemical evolution models. In the presentminor merger scenario, dynamical evolution of the thickdisk can be influenced by the mass growth and non-axisymmetric structures of the thin disk whereas theearly star formation history and chemical evolution ofthe thin disk can be influenced both by gas left behindfrom the thick disk formation (i.e., the FGTD) and bydynamical properties of the thick disk. The main resultsare summarized as follows:(1) Minor merging can cause radial mixing of starswith different metallicities so that more metal-rich starsinitially in the inner part of the FGTD can be trans-ported into the outer region. As a result of this, thethick disk formed by minor merging can have stars with[Fe/H] ∼ − . R = 0 . R d (corresponding roughly to R = R ⊙ ) and those with [Fe/H] ≈ − . R = R d justafter merging, even if such metal-rich stars do not ex-ist there initially. Therefore the mean metallicities inthe outer regions ( R > . R d ) of the disk can increasesignificantly owing to this mixing. This radial mixingof different stellar populations during minor merging ismore effective in mergers with larger m . Thus the pres-ence of more metal-rich stars in the outer part of theGalactic thick disk can be possible evidence for ancientminor mergers occurring in the early dynamical historyof the Galaxy.(2) As a result of radial mixing of stars during minormerging, the original metallicity gradient of the FGTDcan become significantly flattened in the final thick disk.Although the final radial metallicity gradients of the sim-ulated thick disks depend on model parameters of theoriginal metallicity gradients, the present models do notshow the very flat radial metallicity gradient that wasderived in some previous observations. The simulatedmetallicity gradients are more flattened in the outer part( R > . R d ) for most models in the present study. Ra-dial mixing can also cause the differences in MDFs be-tween different regions of the thick disks.(3) The pre-existing thick disk can be strongly influ-enced by the growth processes of the thin disk, in particu-lar, by the formation of a stellar bar in the thin disk. Thethick disk can be transformed into a “barred thick disk”with position angle and bar length similar to those of thestellar bar in the thin disk. Given that the formation ofthe barred thick disk can be seen in most models of thepresent study, we suggest that the bar formation in thethick disk is highly likely if the thick disk was formedprior to the thin disk formation. In some models, theinner part of the thick disk can be vertically expandeddue to the dynamical interaction with the thin disk. Thebarred thick disk cannot be formed in models with lowermasses of the thin disks ( M d , n ≈ M ⊙ ) owing to theabsence of the strong stellar bars in the thin disks.(4) The final structural and kinematical properties ofthe thick disk after the formation of the thin disk dependlargely on m . Although minor mergers with m = 0 . V φ , σ r , σ φ , and σ z between the thin and thick disks at least qual-itatively, the simulated σ z at R = R ⊙ can be slightlylarger than the observed one. Most models with smaller m (= 0 .
05) are difficult to explain so well the observeddifference in V φ at R = R ⊙ between the thin and thickdisks. The observed kinematical differences between thethin and thick disks can give some constraints on phys-ical parameters of minor merging, if the thick disk wasindeed formed by minor merging.(5) The final thick disks in most models do not clearlyshow positive correlations between V φ and [Fe/H] at8 ≤ R ≤ R ∼ R ⊙ ) and 1 ≤ | z | ≤ α d ∼ − .
08 for the FGTD can however show a weak yetpositive V φ -[Fe/H] correlation. Some observations clearlyshow a positive V φ -[Fe/H] correlation (i.e., higher V φ formore metal-rich stars), which suggests that the observed V φ -[Fe/H] correlation can give strong constraints on thepresent minor merger model, in particular, the radialmetallicity gradient of the FGTD. However, it would bepossible that the stars used for observational derivationof the V φ -[Fe/H] relation include thin disk stars whichformed later in the Galactic disk.(6) The present numerical studies have confirmed thatonly models with lower Θ ( ≤
30) can reproduce the ob-served V φ −| z | correlation in the Galactic thick disk. Thesimulated V φ − R relations in most models are rather flatwhereas the latest observations show a very weakly neg-ative correlation between V φ and R (smaller V φ for larger R ) for the thick disk. This implies that the present minormerger model needs to improve in terms of reproducingthe observed V φ − R correlation. Accordingly the ob-served V φ − | z | and V φ − R correlations can be used fordetermining model parameters that are the most reason-able for the thick disk formation.(7) The simulated orbital eccentricity distribution( f ( e )) of the thick disk stars in the solar neighborhoodis in good agreement with the observations for the mod-els with higher m ( ∼ .
2) and lower e p ( ∼ . e p show bumps at higher e ( > . f ( e ), which is inconsistent with obser-vations. The observed mean orbital eccentricities ( e m ) ofthe thick disk stars dependent on R can be reproducedby some models in the present study. Although the latestobservations have revealed a positive e m − | z | correlation(larger e m for higher | z | ) in the Galactic thick disk, onlysome models with low Θ can clearly show such a positivecorrelation in the present study.(8) The star formation timescale of the FGTD needsto be ∼ . > > R = R ⊙ owing to the themodel assumption that no radial mixing can occur. Assuggested by the present N-body simulations, the ob-served metal-rich stars in the thick disks at R = R ⊙ can be transferred from the inner regions of the FGTDwith the higher metallicity owing to radial mixing duringminor merging.(9) The chemical evolution of the thin disk depends onhow star formation proceeds from the infalling halo gasmixed with the remaining gas left behind from the for-mation of the thick disk. If the remaining gas of the thick8 The Galaxy formationdisk can be used for star formation in the thin disk at theearly stage of the thin disk evolution, then the new starscan have high [Fe/H] ( ∼
0) and low [ α /Fe] ( ∼ . V φ , R , | z | and [Fe/H] of the thick disk stars cangive strong constraints on model parameters in the for-mation scenarios of the thick disk. The present study didnot extensively discuss the physical properties of the thindisk and the bulge of the Galaxy. We therefore plan toexplore a theoretical model that can reproduce physicalproperties of the thin and thick disks and the bulge fullyself-consistently in our forthcoming papers.We are grateful to the referee Timothy Beers for hisconstructive and useful comments that improved this pa-per. We are grateful also to Jonathan Diaz, who reviewedthis paper and gave us scientific comments and Englishcorrections of the paper. KB acknowledges the financialsupport of the Australian Research Council throughoutthe course of this work. APPENDIX
POSSIBLE SUPPRESSION OF STAR FORMATION IN THE EARLY EVOLUTION PHASE OF THE THIN DISK BY THETHICK DISK ?
Although the temporal truncation model for the chemical evolution of the Galactic thin disk has provided someexplanations for the origin of the observed [Mg/Fe]-[Fe/H] relation of the thin disk,it did not show how the early star formation of the thin disk can be truncated until the gas metallicity of the thindisk becomes as low as [Fe/H] ∼ − .
7. Accordingly the temporal truncation model needs to explain why such severesuppression of star formation could occur in the early formation history of the thin disk. One of possible physicalreasons for the suppression of star formation in the thin disk is a higher Toomre’s Q parameter of the thin disk due tothe higher stellar velocity dispersion of the thick disk. Wang & Silk (1994) proposed that one of important parametersfor galactic star formation in the two-component disk composed of gas and stars is the effective Q parameter ( Q e ),which is defined as Q − = Q − + Q − , where Q − and Q − are the stellar and gaseous Q parameters, respectively.Given that the radial velocity dispersion of the thick disk can be a factor of ∼ m (thus Q s becomes larger than ∼ Q e .If we adopt Q s = 3 and if we assume that star formation in the thin disk can happen for Q e <
1, then Q g needs to beless than 1.5. Therefore, it is possible that star formation in the thin disk cannot efficiently occur until Q g becomes aslow as 1.5 owing to the increase of the surface gas density (and/or the decrease of the gaseous velocity dispersion). Thepossible higher Q e in the early stage of the thin disk formation therefore would be responsible for severe suppressionof star formation in the thick disk for the minor merger scenario. If all of the remaining gas were expelled from thethick disk after the minor merger owing to energetic stellar winds associated with a triggered starburst, then new starsin the thin disk can be formed purely from gas accreted onto the disk from the Galactic halo. If this is the case, thenthere is no chemical connection between the thin and thick disks, and the above severe suppression of star formationin the thin disk does not need to be considered in the minor merger scenario. REFERENCESAbadi, M. G., Navarro, J. F., Steinmetz, M., & Eke, V. R. 2003,ApJ, 597, 21Allende P. C., Beers, T. C., Wilhelm, R., Newberg, H. J.,Rockosi, C. M., Yanny, B., & Lee, Y. S. 2006, ApJ, 636, 804Andrievsky, S. M., Luck, R. E., Martin, P., & L´epine, J. R. D.2004, A&A, 413, 159Bekki, K. 2009, in The Magellanic System: Stars, Gas, andGalaxies, Proceedings of IAU Symposium, Vol 256, p105Bekki, K., Chiba, M. 2000, ApJ, 534, L89Bekki, K., Chiba, M. 2001, ApJ, 558, 666Bensby, T., Feltzing, S., & Lundstr¨om, I. 2003, A&A, 410, 527Bensby, T., Feltzing, S., & Lundstr¨om, I. 2004, A&A, 421, 969Benby, T., Feltzing, S., Lundstr¨om, I., & Ilyin, I. 2005, A&A, 433,185Benby, T., Zenn, A. R., Oey, M. S., & Feltzing, S. 2007, ApJ, 663,L13Binney, J., & Tremaine, S. 1987 in Galactic Dynamics, Princeton;Princeton Univ. Press. Binney, J., & Tremaine, S. 2007 in Galactic Dynamics, Secondedition, Princeton; Princeton Univ. Press.Brook, C. B., Kawata, D., Gibson, B. K., & Freeman, K. C. 2004,ApJ, 612, 894Carollo, D., et al. 2010, ApJ, 712, 692Casagrande, L., et al. 2011, in preprint (arXiv1103.4651)Chen, Y. Q., Nissen, P. E., Zhao, G., Zhang, H. W., & Benoni, T.2000, A&AS, 141, 491Chiappini, C.; Matteucci, F., & Gratton, R. 1997, ApJ, 477, 765Chiba, M., & Beers, T. C. 2000, AJ, 119, 2843Di Matteo, P., Lehnert, M. D., Qu, Y., & van Driel, W. 2011,A&A, 525, L3Dinescu, D. I., Girard, T. M., Korchagin, V. I., & van Altena, W.F. 2011, ApJ, 728, 7Dierickx, M., Klement, R., Rix, H-W., & Liu, C. 2010, ApJ, 725,L186Edvardsson, B., Andersen, J., Gustaffson, B., Lambert, D. L.,Nissen, P. E., & Tomkin, J. 1993, A&A, 275, 101 ekki 19ekki 19