Metallicity gradients through disk Instability: A simple model for the Milky Way's boxy bulge
aa r X i v : . [ a s t r o - ph . GA ] F e b Draft version February 5, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
METALLICITY GRADIENTS THROUGH DISK INSTABILITY: A SIMPLE MODELFOR THE MILKY WAY’S BOXY BULGE
Inma Martinez-Valpuesta and Ortwin Gerhard Max-Planck-Institut f¨ur Extraterrestrische Physik, Giessenbachstrasse, 85748 Garching, Germany
Draft version February 5, 2018
ABSTRACTObservations show a clear vertical metallicity gradient in the Galactic bulge, which is often takenas a signature of dissipative processes in the formation of a classical bulge. Various evidence shows,however, that the Milky Way is a barred galaxy with a boxy bulge representing the inner three-dimensional part of the bar. Here we show with a secular evolution N-body model that a boxybulge formed through bar and buckling instabilities can show vertical metallicity gradients similar tothe observed gradient, if the initial axisymmetric disk had a comparable radial metallicity gradient.In this framework the range of metallicities in bulge fields constrains the chemical structure of theGalactic disk at early times, before bar formation. Our secular evolution model was previously shownto reproduce inner Galaxy star counts and we show here that it also has cylindrical rotation. We useit to predict a full mean metallicity map across the Galactic bulge from a simple metallicity modelfor the initial disk. This map shows a general outward gradient on the sky as well as longitudinalperspective asymmetries. We also briefly comment on interpreting metallicity gradient observationsin external boxy bulges.
Subject headings:
Galaxy: structure — Galaxy: bulge — Galaxy: abundances — Galaxy: kinematicsand dynamics — galaxies: evolution — methods: numerical INTRODUCTION
About half of edge-on disk galaxies contain boxyor peanut-shaped bulges (BPBs, L¨utticke et al. 2000).Their photometric and kinematic properties are con-sistent with predictions from disk galaxy simulationsin which a BPB formed through bar and bucklinginstabilities (Bureau & Freeman 1999; Debattista et al.2004; Bureau & Athanassoula 2005). The Galacticbulge shows many characteristics of a BPB formed inthis way: a boxy shape in projection (Dwek et al. 1995;Skrutskie et al. 2006); a triaxial density distribution(Binney et al. 1997; L´opez-Corredoira et al. 2005) witha dense inner, rounder component (Gonzalez et al.2012; Gerhard & Martinez-Valpuesta 2012, hereafterGMV12); an X-shaped structure (McWilliam & Zoccali2010; Nataf et al. 2010; Ness et al. 2012a; Li & Shen2012); cylindrical rotation (Howard et al. 2009;Shen et al. 2010); and a transition to an outer pla-nar bar (Martinez-Valpuesta & Gerhard 2011, hereafterMVG11), seen in star count observations as ’long bar’(Benjamin et al. 2005; Cabrera-Lavers et al. 2007).The Galactic bulge is also known to consist of pre-dominantly old stars (Zoccali et al. 2003; Clarkson et al.2008) with a broad, asymmetric metallicity distribu-tion function (MDF) (Rich 1990; Ibata & Gilmore 1995;Zoccali et al. 2003). The data clearly show a verticalmetallicity gradient, such that the more metal-rich partof the MDF thins out towards high latitudes ( b < − ◦ ,Minniti et al. 1995; Zoccali et al. 2008; Gonzalez et al.2011). At latitudes lower than Baade’s window ( − ◦
The simulation used in this work is that already an-alyzed in MVG11 and GMV12, with similar character-istics as described in Martinez-Valpuesta et al. (2006).The model evolved from an exponential disk, with Q =1 .
5, initial radial scale length of h = 1 .
29 kpc and verti-cal scale height of h z = 0 .
225 kpc, embedded in a darkmatter halo. Following bar and buckling instabilities itdeveloped a prominent boxy bulge which is already re-laxed at ∼ . T b ≃ . l ∼ ◦ (MVG11),and in the inner boxy bulge for − ◦ ≤ l ≤ ◦ and b = ± ◦ (GMV12) as well as for b = − ◦ , where the Inma Martinez-Valpuesta & Ortwin Gerhard Fig. 1.—
Mean radial velocity and velocity dispersion versus lon-gitude for the model’s boxy bulge, as seen from the Sun for differentlatitudes | b | = 4 ◦ , ◦ , ◦ . Note how the dispersion decreases withlatitude, and that in this projection the rotation is only approx-imately cylindrical; i.e., the slope of the velocity curve increasesslightly towards the plane, as also seen in the Galactic bulge data. predictions of the model were subsequently confirmed byGonzalez et al. (2012). Here we show that the model’sboxy bulge at that time also shows approximate cylin-drical rotation, with the slope of the mean velocity curvealong l increasing slightly towards lower latitudes; seeFig. 1. This is similar to the BRAVA kinematic data(Howard et al. 2009) and the simulation by Shen et al.(2010). The cylindrical rotation in boxy bulges is clearestin edge-on view, as shown in previous simulations (e.g.,Combes et al. 1990; Athanassoula & Misiriotis 2002); itis weakened by the nearly end-on orientation of the MilkyWay bar and the perspective effects. As in our previouswork (MVG11, GMV12), we here take the solar galac-tocentric distance D ⊙ = 8 kpc, scale the bar length to4 . α = 25 ◦ with respectto the Sun-Galactic center line.We study the formation of bulge metallicity gradientsin the unstable disk – boxy bulge scenario with a simpleillustrative model. We assume that the initial exponen-tial disk follows a specified radial metallicity gradient,which we imagine is set up during disk build-up priorto bar formation. We assign to each particle a metal-licity depending on its initial radius (e.g., Friedli et al.1994), according to [ M/H ]( R ) = [ M/H ] + α R × R/ kpc.After some exploration we choose [ M/H ] = 0 . α R = − .
4. Unlike Bekki & Tsujimoto (2011), we donot link these metallicities to the present-day Galacticdisk near the Sun, because the buckling instability inthe Milky Way must have happened long ago when theouter disk may have been only incompletely assembled. RESULTS
Vertical metallicity gradient in the Milky Way bulge
The bar and buckling instabilities leading to the for-mation of the boxy bulge strongly change the particle or-bits. Thereby the initial disk metallicity distribution ismapped into the bulge accordingly. Fig. 2 shows longitu-dinal and vertical metallicity profiles for the bulge at T b .The vertical gradient for 3 ◦ < | b | < ◦ along the minoraxis is α b = − .
064 dex/deg, compared to the observedslope in the Milky Way bulge α MW = − .
075 dex/deg
Fig. 2.—
Longitudinal and vertical metallicity profiles of themodel as seen from the Sun. Left: with l for | b | = 2 ◦ , ◦ , ◦ ;the gradient along l decreases towards larger distances from theGalactic plane. Right: with | b | for l = 0 ◦ , ◦ , ◦ ; the verticalgradient decreases with distance from the minor axis. from Zoccali et al. (2008) and α b = − .
06 dex/degfrom Gonzalez et al. (2011). Near the Galactic plane, | b | < ◦ , the vertical gradient becomes flatter and evenpositive. The positive gradient is due to the contami-nation from foreground/background disk particles. Theflat part comes from the mixing during the buckling in-stability in the inner regions that evolve into the cen-tral near-spheroidal component (GMV12), and also fromthe greater fraction of low-latitude outer bar particles.The absence of a clear vertical gradient near the Galac-tic plane is consistent with recent results from Rich et al.(2007, 2012). However, their measured mean metallici-ties for M-giants ([Fe/H] ≃ − .
2) are slightly lower inBaade’s window than those for K-giants (Zoccali et al.2008) and for our simple model.Fig. 3 shows the resulting MDFs in several minor axisfields in the boxy bulge at T b = 1 . ≃ .
6, the central value in the initial disk,and the lowest value is ≃ − .
2. 2 Gyr later, at T b = 4Gyr, the model metallicity gradient is nearly identical,while the mean metallicities in the minor axis fields haveslightly decreased, due to the capture of lower-metallicitydisk stars by the slowly growing bar. Had we assumed ashallower radial gradient in the initial disk, also the finalvertical gradient in the bulge would be smaller. Full metallicity map for the boxy bulge
So far we have shown that a radial metallicity gra-dient in the unstable initial disk can survive throughthe bar and buckling instabilities, and generate, for suit-able parameters, a vertical metallicity gradient similarto that observed in the Milky Way bulge. For compari-son with upcoming survey results (e.g., VVV, ARGOS,Gaia-ESO), we now provide a full metallicity map, whichgives a different view of the predicted metallicities forthis scenario. Differently from Fig. 3, we exclude fore-ground/background disk stars with a distance cut, usingonly particles with 4 < D <
12 kpc from the position ofthe Sun. The assumed initial disk metallicity distribu-tion and simulated galaxy snapshot are as before. Fig. 4shows the resulting average bulge metallicity map overthe area on the sky extended by the Galactic bulge. Itertical metallicity gradients 3
Fig. 3.—
Metallicity histograms (MDFs) for model particles in 4 fields along the minor axis of the boxy bulge ( left panels ). The meanvalue for each MDF is given by the red arrow pointing up from the bottom. The corresponding mean value for the data of Zoccali et al.(2008) is indicated by the blue arrow from the top. The histograms in the right panels are based on data from Zoccali et al. (2008) for b = − ◦ , − ◦ , − ◦ , and from Johnson et al. (2011) for b = − ◦ . has several noteworthy properties:(i) The approximate outline of the boxy bulge canbe seen together with low-metallicity indentations inthe Galactic plane. The latter are due to fore-groud/background stars in the planar bar, which in thesepositions dominate the bulge stars.(ii) A metallicity gradient is present in all directionson the sky, both vertically and radially. This is expectedfrom the binding energy argument of Sect. 3.3. How-ever, in the central few degrees the gradients becomeshallower.(iii) Iso-metallicity contours are more elongated verti-cally than horizontally, whereas the surface density con-tours are flattened to the plane (MVG11).(iv) The asymmetry between l > l < | l | on the l > | b | ≃ ◦ , but for | b | ≃ ◦ they extend to larger | l | on the l < b = 2 ◦ is α l = − .
05 dex/deg (see Fig. 2). Minniti et al. (1995)found mean metallicities [Fe/H]= − . l, b ) = (8 ◦ , − ◦ ) and (10 ◦ , − ◦ ) for bulge stars selectedwith [Fe/H] > −
1. The model values in these fields are-0.30 and -0.28.
Origin of the vertical gradient
Clearly, while the bar and buckling instabilities scram-ble the orbits of disk stars, they do not do so enoughto completely erase the preexisting metallicity gradient.High-metallicity stars tightly bound to the Galactic cen-ter initially remain more tightly bound in the final bulge,and initially more loosely bound stars with lower metal-licities end up at larger final radii, on average. This can
Fig. 4.—
Metallicity map of the model bulge and bar in galacticcoordinates. Foreground and background disk particles with dis-tances < >
12 kpc from the solar position are excluded.The colour in each square corresponds to the average metallicityin a cone with radius 0 . ◦ centered at this position. be quantified by considering the change in Jacobi energy E J = 12 v + Φ( R, φ, z ) −
12 Ω p R (1)in the rotating frame of the boxy bulge and bar duringthe evolution. Here we use standard cylindrical coor-dinates, v is total velocity, Φ is the gravitational po-tential, and Ω p is the pattern speed at T b = 1 . Fig. 5.—
Change of Jacobi energy between different times duringthe evolution of the model, evaluated in a rotating frame for patternspeed Ω p ( T b ) = 40 km/s/kpc. For each bin in initial Jacobi energy E J0 , the mean value of Jacobi energy at time t is plotted with errorbars denoting the standard deviation of the distribution of E J ( t )in the bin. Black points: E J ( t = 0) versus E J (initial scatterin each bin). Blue points: E J final ( t = T b ) versus E J (final boxybulge compared to initial disk). Red open circles (slightly displacedhorizontally for clarity): E J bar ( t = T bar ) versus E J (after full bargrowth but prior to buckling instability, compared to initial disk). Fig. 5 shows that particles are scattered in Jacobi en-ergy by the two instabilities, but only over a fractionof the available total range in E J . I.e., they retainsome memory of their initial values. It has also beenshown that most bar particles inside the vertical in-ner Lindblad resonance (VILR) mix during the buck-ling instability, but stay in the inner bar regions, whilemost bar particles around VILR are scattered to orbitswhich can visit larger heights (Pfenniger & Friedli 1991;Martinez-Valpuesta & Shlosman 2004).From these arguments follows that the number of high-metallicity particles in the final boxy bulge will decreasewith height above the plane where E J becomes less neg-ative. In the histograms of Fig. 3, therefore, the numberof stars on the metal-rich part of the distribution de-creases with latitude. The maximum metallicity in allhistograms, but that at b = − ◦ , is still given by theassumed maximum metallicity at the center of the initialdisk, here +0 .
6, because a small fraction of the tightlybound particles is scattered up even to b = 8 ◦ .The low-metallicity tail, on the other hand, is moreprominent at high latitudes, because of the larger frac-tion of particles coming from the outer parts of the bar.Note that within the assumed model, a lower limit to themetallicity in the bulge fields is expected, which is set bythe outer boundary of the part of the disk which partic-ipates in the instability. From the histograms in Fig. 3,this is ≃ − .
2, which is due to particles in the initial diskat R = 4 . . Boxy bulges in other galaxies
Vertical gradients have so far been publishedonly for a small number of galaxies with boxybulges. Falc´on-Barroso et al. (2004); Jablonka et al.(2007) found a vertical metallicity gradient in NGC 7332comparable to that in the Milky Way. Williams et al.(2011) determined vertical gradients in two other boxybulges, NGC 1381 and NGC 3390. They integrated alongslits parallel to the major axis to increase signal-to-noise,and obtained a single bulge measurement at several z .A similar averaging over l ∈ [ − ◦ , ◦ ] in our model re-duces the measured gradient from α z = − .
46 dex/kpcto α z = − .
33 dex/kpc, because radial and verticalgradients are comparable. Still, in NGC 1381 the ob-servations show a strong gradient of averaged α z = − .
27 dex/kpc, while only a weak gradient is seen inNGC 3390, α z = − . z ∈ [5 ,
10] arcsec).P´erez & S´anchez-Bl´azquez (2011) found negative metal-licity gradients along the major axis for the majority ofbulges in barred galaxies, while Williams et al. (2012)found a range of major axis metallicity gradients in boxybulges, from negative to positive, with shallower sam-ple average than for unbarred early-type galaxies. Insummary, the limited data suggest a range of metallicitygradients in boxy bulges, with the metallicity gradientin the Milky Way on the steep side. In the frameworkdiscussed here, this suggests a range of initial disk metal-licity gradients before buckling in these galaxies, perhapsdepending on the time of bulge formation.
Comparison with previous simulations
The results presented in the previous subsections areconsistent with early N-body simulation work by Friedli(1998). He found that pre-existing vertical abundancegradients in the disk were quickly flattened both in thebar and disk regions but not entirely erased. Theirmodels also included a shallow, outward radial gradient,which became much flatter in the disk region due to themixing induced by the bar, but was approximately pre-served in the bar region. Friedli (1998) also stated thatwhen no initial vertical gradient was present, a negativevertical gradient appeared at R = 0. However, in hismodel the initial gradient was α R = − . α R = − . α R = − .
26 dex/kpc and the final vertical gra-dient is α z = − .
46 dex/kpc (for b ∈ [ − ◦ , − ◦ ]). Con-sistent with Friedli (1998) we also find that at larger l the vertical gradient is shallower (Fig 2, right ).Recent N-body numerical simulations byBekki & Tsujimoto (2011) for a pure exponentialdisk initial model (PDS in their nomenclature) showedonly a very shallow vertical gradient in the final boxybulge. The difference to our results can be traced tothe different initial disk metallicity profile. While theirinner disk parameters are similar to ours, due to linkingthe profile to the present metallicity near the Sun, theirprofile becomes quite shallow beyond ≃ .
25 times theeventual final bar length. Thus the stars in the upperbulge which come from the outer parts of the bar arequite metal-rich. The difference, and the reason for thesteep vertical gradient in the bulge of our model is itssteep initial radial gradient in the disk.Finally we note that if the secular evolution proceedsslowly, a radial gradient in the disk before the instabilitymay be (partially) erased by migration processes. Thusa steep final bulge gradient is favoured by rapid secularevolution such as in the model investigated here. CONCLUSIONS
We can summarize our conclusions as follows:(i) The vertical metallicity gradient observed in theGalactic bulge can be reproduced with a secularlyevolved barred galaxy model in which a boxy bulgeformed after a buckling instability. In itself, a verticalgradient is therefore not a strong argument for the exis-tence of a classical bulge in the Milky Way.(ii) Mixing during the bar and buckling instabilities isincomplete, and therefore radial metallicity gradients in the initial disk can transform into gradients in the boxybulge.(iii) In this framework, the range of bulge star metal-licities at various latitudes constrains the radial gradientin the precursor disk.(iv) The full bulge metallicity map shows an overall ra-dial gradient on the sky as well as longitudinal perspec-tive asymmetries. Iso-metallicity contours are elongatedvertically.(v) Depending on when the bulge formed and on theproperties of the precursor disk at that time, boxy bulgesmay or may not show metallicity gradients.The success of our simple model in explaining MilkyWay observations suggests that its underlying idea hassome merit and should be pursued further. Future workalso needs to consider chemical evolution and possiblevertical metallicity gradients in the initial disk, star for-mation induced by the bar, the possible late build-up of ametal rich inner disk, and the contribution of halo starsand other components (Ness et al. 2012b) to the bulgeMDFs.Another important next step for understanding the ori-gin of the Milky Way bulge is to investigate the correla-tions between metallicities and kinematics in this modeland in generalisations of it. Comparison with similarobservations (Babusiaux et al. 2010; Ness et al. 2012b)is likely to shed light on the possible multi-componentnature of the Galactic bulge. The results will be impor-tant also for interpreting the data for bulges in externalgalaxies.We thank Ken Freeman and Mike Williams for dis-cussions on metallicity gradients and Oscar Gonzalez forshowing us the VVV metallicity map before publication.
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