The imprint of radial migration on the vertical structure of galaxy disks
DDraft version November 6, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE IMPRINT OF RADIAL MIGRATION ON THE VERTICAL STRUCTURE OF GALAXY DISKS
Carlos Vera-Ciro , Elena D’Onghia , Julio F. Navarro Department of Astronomy, University of Wisconsin, 475 N. Charter Street, Madison, WI 53076, USA Departamento de Ciencias B´asicas, Universidad de Medell´ın, Cra 87 N 30-65, Medell´ın, Colombia and Department of Physics and Astronomy, University of Victoria, Victoria, BC, V8P 5C2, Canada
Draft version November 6, 2018
ABSTRACTWe use numerical simulations to examine the effects of radial migration on the vertical structureof galaxy disks. The simulations follow three exponential disks of different mass but similar circularvelocity, radial scalelength, and (constant) scale height. The disks develop different non-axisymmetricpatterns, ranging from feeble, long-lived multiple arms to strong, rapidly-evolving few-armed spirals.These fluctuations induce radial migration through secular changes in the angular momentum of diskparticles, mixing the disk radially and blurring pre-existing gradients. Migration affects primarily starswith small vertical excursions, regardless of spiral pattern. This “provenance bias” largely determinesthe vertical structure of migrating stars: inward migrators thin down as they move in, whereas outwardmigrators do not thicken up but rather preserve the disk scale height at destination. Migrators ofequal birth radius thus develop a strong scale-height gradient, not by flaring out as commonly assumed,but by thinning down as they spread inward. Similar gradients have been observed for low-[ α /Fe]mono-abundance populations (MAPs) in the Galaxy but our results argue against interpreting themas a consequence of radial migration. This is because outward migration does not lead to thickening,implying that the maximum scale height of any population should reflect its value at birth. In contrast,Galactic MAPs have scale heights that increase monotonically outwards, reaching values that greatlyexceed those at their presumed birth radii. Given the strong vertical bias affecting migration, a properassessment of the importance of radial migration in the Galaxy should take carefully into account thestrong radial dependence of the scale heights of the various stellar populations. Subject headings:
Galaxy: disk - Galaxy: evolution - galaxies: kinematics and dynamics - stars:kinematics and dynamics INTRODUCTIONNon-axisymmetric patterns in disk galaxies have longbeen known to drive secular changes in the energy andangular momentum of disk stars (e.g., Lynden-Bell &Kalnajs 1972). Angular momentum changes are gener-ally accompanied by radial shifts in the average galacto-centric distance of a star. Although such changes usuallylead to increased orbital eccentricities and a gradual in-crease in the velocity dispersion of the disk, Sellwood &Binney (2002) demonstrated, in an influential paper, thatstars can also migrate while preserving their circularitiesif they are near corotation of fluctuating spiral patterns,a process usually referred to as “radial migration”.This realization has led to new insights into the inter-pretation of a number of properties of galaxy disks, in-cluding (i) the (weak) correlation between age and metal-licity in the solar neighborhood (Edvardsson et al. 1993;Haywood 2008; Bergemann et al. 2014); (ii) the upturnof the mean age in the outer parts of disks (Roˇskar et al.2008; Bakos et al. 2008); (iii) the formation of the Galac-tic thick disk (Sch¨onrich & Binney 2009; Loebman et al.2011); and (iv) the radial dependence of the metallicitydistribution function in the Galactic disk (Hayden et al.2015; Loebman et al. 2016; Martinez-Medina et al. 2016).Although there is consensus that migration should some-how contribute to those trends, its actual importance in e-mail:[email protected] Alfred P. Sloan Fellow Senior CIfAR Fellow each particular case is still a matter of debate.One example concerns the effect of migration on thevertical structure of the Galactic disk. Earlier work sug-gested that migration can thicken a galaxy disk by push-ing stars from the inner regions (where the velocity dis-persion is high) to the outskirts of the disk, where thesurface density—and hence the vertical restoring force—is lower (e.g. Sch¨onrich & Binney 2009). Minchev et al.(2012), on the other hand, argued that migration haslittle effect on disk thickness, since outward migratorsshould conserve their vertical action and cool down, aconclusion that has been debated further by Solway et al.(2012), Roˇskar et al. (2013) and Vera-Ciro & D’Onghia(2015).The vertical structure of migrators was also studied byVera-Ciro et al. (2014), who noted that migrators are aheavily biased subset of stars with preferentially low ver-tical velocity dispersions. This “provenance bias” arisesbecause stars with small vertical velocities spend moretime near the disk plane, and thus couple more readily tonon-axisymmetric perturbations. The resulting verticalstructure of migrators is further complicated by the factthat the velocity dispersion of outward migrators gen-erally decreases, whereas the opposite applies to inwardmigrators.A potential application of these ideas to the Galac-tic disk is provided by recent results from the APOGEEsurvey. By dissecting the Milky Way stellar disk intodistinct populations according to their α and Fe con-tent, Bovy et al. (2015, hereafter B15) were able to a r X i v : . [ a s t r o - ph . GA ] M a y Vera-Ciro, D’Onghia & Navarroconfirm the presence of two chemically-distinct popu-lations differing in their [ α/ Fe] ratio. This distinctionprovides an improved characterization of the traditional“thick” and “thin” disks of the Galaxy that does not relyon kinematics. Such purely chemical characterization ishighly preferable, since, unlike kinematics, chemistry isa durable and stable property of a star that should faith-fully reflect its local conditions at birth (see, e.g., Navarroet al. 2011).An interesting property of low-[ α/ Fe] stars (i.e., thetraditional “thin disk”) is that their spatial distributionvaries smoothly and systematically with iron abundance.In particular, the surface density of stars of a mono-abundance population (MAP) of fixed [Fe/H] peaks atsome radius and decreases both inside and outside thatradius. The “peak radius” increases with decreasing[Fe/H], in a manner that defines the overall metallicitygradient of the disk.More importantly for our current discussion, there areclear radial trends in the thickness of each MAP: theyflare outward, a result that has been interpreted by B15as an “essential test of the predictions of radial mi-gration”. This conclusion relies on a simple scenariowhere, broadly speaking, stars in each MAP share a sim-ilar birth radius—i.e., the “peak radius” of their radialdistribution—and disperse through the Galaxy by thesecular changes induced by spiral patterns, flaring out-ward in the process.However, given the uncertainties in our understandingof the effects of radial migration cited earlier, this sce-nario seems premature. Here, we report on results of aset of numerical simulations of isolated stellar disks de-signed to test the role of radial migration in establishingradial gradients in scale height. The simulations weredesigned so that disks develop different spiral patterns,allowing us to assess the robustness of our conclusions re-garding the specific nature of the spiral, such as numberof arms and the overall strength of the pattern.This paper is organized as follows: Section 2 describesthe numerical simulations while our main results are pre-sented in Section 3. We end with a brief discussion anda summary of our main conclusions in Section 4. NUMERICAL SIMULATIONS2.1.
Galaxy models
The stellar disk in all of our simulations is describedby an exponential surface density profile: Σ( R ) = M d / (2 πR ) exp ( − R/R d ) , with M d the total disk mass and R d the disk scale-length. The vertical distribution of diskstars follows an isothermal sheet with a radially constantscale height, z d . The 3D stellar density in the disk isthen: ρ d ( R, z ) = Σ( R ) ζ ( z )= M d πz d R sech ( z/z d ) exp ( − R/R d ) (1)The disk mass is sampled with N = 5 × particlesand is evolved in a dark matter halo modeled as a staticHernquist profile (Hernquist 1990). One of the simula-tions also includes a bulge modeled as a second Hernquistprofile. Table 1
Galaxy Model ParametersParameters
LD HD HD-MW M d [10 M (cid:12) ] a R d [kpc] b z d /R d c M halo [10 M (cid:12) ] d R halo [kpc] e M bulge [10 M (cid:12) ] f ... ... 1.40 R bulge [kpc] g ... ... 0.35 f disk (2 . R d ) h t [Gyr] i t [Gyr] j t [Gyr] k a ; disk scale length b ; disk scale height c ; halo mass d ;halo scale length e ; bulge mass f ; bulge scale length g ; disk massfraction h within 2 . R d ; initial time i ; times j,k when radialvelocity dispersion has increased by 10-30% respectively. We consider three different galaxy models, labeled LD (“light disk”), HD (“heavy disk”) and HD-MW (“MilkyWay-like”). The structural parameters of each galaxymodel are listed in Table 1.The LD galaxy is the same model as presented byD’Onghia et al. (2013) and analyzed in detail by Vera-Ciro et al. (2014). It corresponds to a low-mass diskwhere the spiral patterns are recurrent and relativelyweak, but long-lived and characterized by multiple arms.The HD model is a heavier-disk version of the LD galaxywhere the disk mass has been increased by a factor of twowhile keeping the halo parameters basically unchanged.Finally, the model labeled as HD-MW is designed to havea disk mass and radial scalelength consistent with theMilky Way. The addition of a bulge and the adjustmentof the halo parameters yields a flat circular velocity curvein good agreement with that of the Galaxy; i.e., V circ ∼
220 km s − roughly constant in the range 0 . < R < ≈
70% of the totalcircular speed at 2.2 scale lengths (Bovy et al. 2012).The radial component of the disk stellar velocity dis-persion, σ R = σ θ , is assumed to scale proportionally tothe vertical component, σ z : σ R = f R σ z , where σ z isspecified by the chosen scaleheight, z d (Hernquist 1993).The ratio z d /R d is chosen to be in the range 0 . .
15 forall disks. The factor f R is chosen so as to set a minimumvalue of the Toomre parameter ( Q = σ R κ/ (3 . G Σ)) ofunity at two disk scale lengths.2.2.
The runs
The simulations were carried out with the parallelTreePM code GADGET-3. We only employ the tree-based gravity solver coupled to a static external poten-tial to solve for the evolution of collisionless particles.Pairwise particle interactions are softened with a splinekernel (Hernquist & Katz 1989) on scales h s , so thatforces are strictly Newtonian for particles separated bymore than 2 h s . The resulting force is roughly equiva-lent to traditional Plummer-softening with scale length ≈ h s /2.8. For our simulations the gravitational softeninglength was set to 50 pc.2.3. Disk evolution adial migration and the vertical structure of galaxy disks 3
Figure 1.
Face-on disk projected stellar density for the three simulated galaxies: the low-mass disk case LD (top panels), and the twoheavy-disk models HD (middle panels) and HD-MW (bottom panels). Note the different spiral patterns in each case. The two heavy diskseventually develop a strong central bar. The structural parameters of the disks and characteristic times are listed in Table 1.
Because of their different mass and circular velocityprofiles, each disk develops different spiral patterns overtime, as shown in Fig. 1. The LD model may be describedas a flocculent spiral with multiple arms, whereas the twoheavy disks show stronger patterns with fewer arms thatevolve relatively quickly into a central bar. The non-axisymmetric perturbations gradually heat the disk inall cases, but at a much faster rate for the case of theheavier disks than for the LD model.In an attempt to compare the three models at com-parable stages of evolution we select three characteris-tic times for analysis; (i) an initial time, t , before thespiral patterns develop and defined so that the rms po-tential fluctuations on the disk plane in the radial range3 < R/ kpc < σ Φ ∼ . × − ); (ii) anintermediate time, t , when the radial velocity dispersionin that same radial range has increased by 10%; and (iii) a final time, t , when σ R has increased by 30% since t .We list these times (in Gyr) in Table 1. Note that ittakes many more half-mass disk rotations to heat up the LD model (24/87) than the other two (10/26 and 13/30for HD and HD-MW , respectively).Fig. 2 shows the surface density profiles, as well as thecircular velocity and velocity dispersion profiles at thosethree times for all disks. Aside from the development ofa central ( ∼ t to t is in the radial ve-locity dispersion, which, by construction, grows by 30%in all cases. Note that despite the large and varied spiralpatterns present, neither the disks thicken noticeably northey evolve substantially in terms of their mass profiles. RESULTS Vera-Ciro, D’Onghia & Navarro
Figure 2.
Left to right columns : Radial profiles of stellar surface density, circular velocity, radial velocity dispersion and vertical velocitydispersion, shown at the initial time, t , an intermediate time, t , and the final time, t . Intermediate and final times are defined by theradial velocity dispersion, which increases by 10 and 30% since t . All times are listed in Table 1. The provenance bias of radial migration
The non-axisymmetric patterns shown in Fig. 1 leadto large exchanges of angular momentum and energybetween disk particles. Since the mass profiles remainbasically unchanged, a change in specific angular mo-mentum, L z , translates directly into a change in guidingcenter radius, R g , defined by L z = R g V circ ( R g ), where V = ∂ Φ /∂ ln R and Φ is the gravitational potential onthe disk plane. The larger the change in R g the farthera star migrates from its original (“birth”) radius.As discussed by Vera-Ciro et al. (2014), migrating starsare expected to exhibit a heavy vertical bias: the mostextreme migrators are almost invariably those whose ini-tial orbits do not take them far from the disk plane.This provenance bias of migrators is not surprising:kinematically-cold stars with modest vertical excursionsspend more time near the midplane and at the samegalactocentric distance, and are thus able to couple moreeffectively to non-axisymmetric perturbations in the disk.We illustrate this in Fig. 3, where we have tracked theevolution in cylindrical radius (left panels) and heightfrom the plane (right panels) of three particles in eachsimulation, chosen so that they share a common birthradius (i.e., R g ( t ) = 5 kpc) but which either migrate in-ward (green curves) or outward (blue) by roughly 50%,or stay put at their original radius (red). This figureillustrates clearly that migrating particles are preferen- tially those initially close to circular orbits and with smallvertical excursions. Interestingly, we find the same qual-itative result for all three simulated disks, despite thelarge differences in their spiral patterns.The same conclusion is illustrated in Fig. 4, where theleft panels show, for all disk stars, the fractional changein guiding center radius, δR g = ln R g ( t ) /R g ( t ), as afunction of birth radius, R g ( t ). The colors encode the initial vertical velocity dispersion of migrators, in unitsof the average at the birth radius; i.e., σ z ( R g ( t )). Bluecolors denote kinematically-cool stars whose vertical ve-locity dispersion are ∼
20% below the mean; red corre-spond to stars ∼
15% hotter than the average.The left panels of Fig. 4 demonstrate that the efficiencyof migration is a sensitive function of the initial σ z : ex-treme migrators are primarily those with small verticalmotions at birth, a conclusion that applies equally well toall three simulations. Grand et al. (2015) reach the sameconclusion in their study of a number of cosmological hy-drodynamical simulations of Milky Way-sized galaxies,so this finding seems robust: the provenance bias afect-ing stellar migration holds regardless of the morphologyof spiral structure and strength of the non-axisymmetricperturbations.3.2. The vertical structure of radial migrators
What is the vertical motion of migrators at their des-tination radii? This is shown in the right-hand panelsadial migration and the vertical structure of galaxy disks 5
Figure 3.
Orbits of three particles with similar guiding center ra-dius at the initial time, R g ( t ) = 5 kpc, but which migrate outwardor inward by roughly ∼
50% (blue/green curves, respectively.) Thethird (shown in red) does not show any substantial secular changein R g . Left : Cylindrical radius, R , as a function of time Right :Vertical displacement, z , (scale on right) as a function of time.Note the “provenance bias” of radial migrations, where extrememigrators are primarily particles initially on nearly circular orbitsconfined to the plane. of Fig. 4, which are analogous to those on the left, butas a function of the final (“destination”) guiding cen-ter radius, R g ( t ), and colored by the velocity disper-sion in units of the average at the destination radius, σ z ( R g ( t )). A distinction appears here between inwardand outward migrators, where inward migrators settleinto orbits much more closely confined to the plane thanthe average star at at their new radii, whereas outwardmigrators end up with vertical velocity dispersions closeto or, in some cases, even slightly higher than the averagethere.The asymmetry between inward and outward migra-tors may be traced to the strong decline with radius of σ z (see right-hand panels of Fig. 2) coupled with thevertical bias discussed above. The strong radial gradi-ent implies that particles that move out arrive at radiiwhere the velocity dispersion is much lower than at theirbirth radius. Although they are initially biased and evencool down a little as they move out (Vera-Ciro et al.2014), the gradient is so strong that their final velocitydispersions are much closer to the average in their newneighborhood than those that migrate inward. For thelatter, the effects of the vertical bias are amplified by thelarger velocity dispersion and higher surface densities of Figure 4.
Left : Fractional changes in guiding center radius( δR g = ln R g ( t ) /R g ( t )) as a function of the initial “birth ra-dius”, R g ( t ), colored by initial vertical velocity dispersion, σ z ( t ),expressed in units of the average value at the birth radius. Blueindicates stars with initial vertical excursions smaller than the av-erage, red the opposite. Right : Same as left, but as a function ofthe final guiding center “destination” radius, R g ( t ), and coloredby the final vertical velocity dispersion, scaled to the average atthe destination radius. the inner regions: the vertical distribution of inward mi-grators becomes thinner and thinner the further in theydrift.We should note that, although outward migrators ingeneral do not “heat” the disk vertically, there are someradii where they do end up with higher-than-average ve-locity dispersion. An example is provided by the “redband” at R g ( t ) ∼ HD . Thisfeature is thus caused by a bar resonance, and is actuallynot present at t , before the bar develops. (Similar pat-terns develop in the case of HD-MW , which also developsa bar at late times.) Indeed, no “red band” of verticallyhot material is seen in the case of LD , where no bar de-velops at all. We should also note that these extrememigrators make up only a small fraction of all stars attheir destination radius, and their effect on the averagekinematics there is negligible, as shown by the invarianceof the σ z profiles shown in the right-hand panels of Fig. 2.3.3. Migration and radial gradients
We explore now the effects of radial migration on pre-existing radial gradients in the disks. Migration-led mix-ing is expected to blur initial trends, increasing the localdispersion and perhaps changing the shape of the localdistribution of any stellar property tightly linked with Vera-Ciro, D’Onghia & Navarro
Figure 5.
Left : Metallicity gradient for the three simulated disks at t (in grey), assumed to be (cid:104) [Fe / H] (cid:105) = 0 .
12 [8 kpc − R g ( t )], withintrinsic width of σ ([Fe / H]) = 0 .
04. This is chosen to match the [Fe/H] dependence of the “peak” radius of mono-abundance populationsin the α -poor Galactic disk. The peak radius of five MAPs with [Fe/H] = -0.2, -0.1, 0.0, 0.1, 0.2, respectively, are shown by the coloredsymbols. Middle:
Same as left, but at t . A dashed line traces the initial gradient; the solid line tracks the median [Fe/H] as a function ofradius at t . Colored symbols are unchanged from the left panels. Right:
Exponential scale heights, h z , as a function of [Fe/H]. Blue andred curves correspond to the initial and final scale height of the simulated disks, respectively. The initial scale height was assumed constantin our models, and remains basically unchanged, despite substantial radial migration. The Galactic disk, on the other hand, shows a strongtrend of increasing thickness with decreasing metallicity, shown here at the “peak” radius of each MAP by the colored symbols with errorbars. Data in all panels from B15. its birth radius. One example of this is provided by themetallicity distribution function in the Galactic plane,which changes skewness inside/outside the solar circle,a feature probably caused by migration (Hayden et al.2015).In order to address such issues, we tag stars, at theinitial time, t = t , according to the following relation: (cid:104) [Fe / H] (cid:105) = 0 .
12 [8 kpc − R g ( t )] , (2)with a Gaussian dispersion of σ ([Fe / H]) = 0 . α -poor disk. We show this inthe left panels of Fig. 5, which display the initial metal-licity gradient of each disk according to Eq. (2), com-pared with the “peak radii” of five mono-abundance pop-ulations ([Fe/H]= − . , − . , . , . , .
2, respectively).By construction, our initial disks have metallicities thatmatch, at their birth radii, those of MAPs in the α -poor(“thin”) disk of the Galaxy.How would the metallicity gradient evolve as a conse-quence of radial migration? This is shown in the middle panels of Fig. 5, where we show the final gradient, com-puted at t . Although migration significantly blurs theinitial trend, increasing the dispersion at given radius, itdoes not affect the slope of the overall gradient much.Interestingly, it does not change the scale-height profileof the disk either, as may be seen in the right-hand pan-els of Fig. 5. Here the solid blue and red curves run-ning vertically indicate the exponential scale-height ofstars at t and t , respectively, as a function of [Fe/H].Clearly, migration has had little effect on the overall diskscale height, measured either at fixed radius, or at fixedmetallicity.3.4. Vertical structure of radial migrators
The right-hand panels of Fig. 5 also illustrate one ofthe main differences between our models and the Galacticdisk. Our models assume a constant initial scale height,which is basically unchanged by migration, and cannottherefore match, through the simple tagging proposed byEq. (2), the marked increase in thickness with decreasingmetallicity observed in the Galaxy (colored symbols witherror bars). The inability of radial migration to thickenthe disk strongly suggests that the observed increase inadial migration and the vertical structure of galaxy disks 7Galactic disk thickness with decreasing metallicity (andincreasing radius) is probably an intrinsic feature of thedisk, and not a consequence of radial migration.As mentioned in Sec. 1, one interesting property ofGalactic mono-abundance populations is the presence ofradial gradients in their vertical structure. These affectprimarily MAPs in the low-[ α /Fe] (“thin”) disk, whosescale heights increase monotonically with radius (B15).The gradients are such that, at fixed [Fe/H], thin-diskstars are thinner inside their “peak radius”, and thickeroutside. For example, Sun-like stars ([Fe/H]= 0) “peak”at ∼ h z ∼
300 pc: their scale height is a factor of ∼ . R ∼ ∼ . R ∼
14 kpc.Could this be the result of radial migration?We address this question in Fig. 6, where the thicksolid curves display the radial profile of the scale height, h z ( R ), for 5 MAPs with metallicities selected between − . < [Fe/H] < . . not thickenup as they move outward. As a result, although thevertical trend of a given MAP inside the peak radiusagrees relatively well with the observed trend, outside that radius the simulated scale heights are systematicallybelow those observed.We emphasize that our results do not rule out thatmigration might play some role in the vertical trend, but,if it did, it would be responsible for the “thinning down”of a population inside its peak radius, rather than for itsflaring outside of it, as is usually envisioned in scenarioswhere the trend is driven by migration (Sec. 1). A furtherdifficulty of such scenario concerns the strong sensitivityof radial migration to the initial height of the population,and the fact that it would take longer for stars born inthe outskirts of the Galaxy to move inward, given theirlong orbital times.The latter is a strong constraint, given the strongdependence of migration efficiency with radius seen inFig. 4: whereas changes in radius of 100% are not un-usual at ∼ R ∼ ∼ − . R ∼
12 kpc with a thickness of nearly 1 kpc (B15)—would be able to spread efficiently around the Galaxythrough radial migration, given their long orbital timesand large thickness.We end by noting that our models do not match thevertical structure of the Galaxy as a function of radius,neither at the beginning nor at the end of the simula-tions, so our conclusions are probably not the final wordon this topic. Nevertheless, our discussion should serveto emphasize the critical role of provenance bias on ra-dial migration, and the importance of carefully modeling
Figure 6.
Radial dependence of the scale height of mono-abundance populations with [Fe/H] = -0.2, -0.1, 0.0, 0.1, 0.2, re-spectively. Black curves indicate results for the simulated disksat t , colored bands show the results for the α -poor Galactic diskfrom B15. Results for each MAP have been shifted vertically forclarity. The height of each simulated MAP has also been rescaledto match the observed value of the corresponding Galactic MAPat its “peak” radius. The latter are indicated by heavy symbols.Note that migrating stars thin down as they spread inward, but do not thicken up as they move outwards. The observed radial trendis therefore unlikely to be caused by radial migration, particularlythe outer “flaring” of each MAP. the radial and vertical structure of the various Galacticpopulations when assessing the effects of migration. CONCLUSIONSWe have used N -body models of isolated disk galax-ies with realistic mass and circular velocity profiles tostudy the effects of radial migration. We focus on thevertical bias (which we term “provenance bias”) favoringthe migration of kinematically-cold stars on nearly cir-cular orbits confined to the disk (Vera-Ciro et al. 2014).The models contrast the effects of migration in a low- Vera-Ciro, D’Onghia & Navarromass disk with weak, slowly-evolving multi-armed spi-rals with those in heavy disks where the spiral patternsare stronger and with fewer arms, evolving quickly intoa central bar.Our main conclusions may be summarized as follows: • Provenance bias is present in all of our simulations,regardless of the nature of the spiral pattern. Thisbias implies that the efficiency of migration willdepend sensitively on the thickness of a particularstellar population, a feature that must be takencarefully into account when modeling the effects ofradial migration. • Provenance bias has a strong effect on the verticalstructure of stars that have migrated away fromtheir initial “birth” radius. Migrators are generallya kinematically colder subset whose vertical veloc-ity dispersion typically drops as they move out orincrease as they move in. Their final structure istherefore heavily dependent on the radial gradientof the vertical structure of the disk. • In our models, which feature a constant scale heightand a strong radial gradient in σ z , inward migratorsbecome more and more heavily biased relative tothe average population at their destination radius.Outward migrators, on the other hand, move toregions of lower σ z and become a closer match tothe average population at their final radii. • In general, radial migrators thin down as they movein, but do not substantially thicken up as they moveout, at least in disks like the ones we consider here.Radial migration alone thus does not provide a nat-ural explanation for the monotonic increase withradius of the scale height of mono-abundance pop-ulations in the α -poor Galactic disk reported bythe APOGEE survey (B15).Our results demonstrate that “provenance bias” playsa crucial role in the final vertical structure of stars thathave migrated as a consequence of internal processes suchas internally-driven spiral patterns. Such migration doesnot lead, in general, to thicker disks, suggesting that thestrong and monotonic increase of scale height seen in the α -poor Galactic disk has a different origin. Either thetrend is inherent to the disk, or it was driven by exter-nal perturbations, such as accretion events and collisionswith dark matter substructures.A more definitive assessment of the importance of ra-dial migration in the Galaxy will likely require cosmo-logical models that are able to reproduce in detail theobserved trends in the radial and vertical distributions ofthe various mono-abundance populations that make upthe disk. Encouraging first steps have already been taken (see, e.g., Grand et al. 2015, and references therein), buta full understanding of the relative importance of inter-nal and external mechanisms in shaping the Galactic diskseems still beyond reach.This research has been partially funded by ATP NASAGrant No NNX144AP53 and by the National ScienceFoundation under grants NSF AST-1211258 and NSFPHY11-25915. CVC and JFN acknowledge the hospi-tality of the Kavli Institute for Theoretical Physics atthe University of California, Santa Barbara. ED grate-fully acknowledges the support of the Alfred P. SloanFoundation. Simulations have been run on the High Per-formance Computing cluster provided by the AdvancedComputing Infrastructure (ACI) and Center for HighThroughput Computing (CHTC) at the University ofWisconsin. We are grateful to Rob Grand for his veryconstructive comments and to Jo Bovy for kindly grant-ing us access to his results.-poor Galactic disk has a different origin. Either thetrend is inherent to the disk, or it was driven by exter-nal perturbations, such as accretion events and collisionswith dark matter substructures.A more definitive assessment of the importance of ra-dial migration in the Galaxy will likely require cosmo-logical models that are able to reproduce in detail theobserved trends in the radial and vertical distributions ofthe various mono-abundance populations that make upthe disk. Encouraging first steps have already been taken (see, e.g., Grand et al. 2015, and references therein), buta full understanding of the relative importance of inter-nal and external mechanisms in shaping the Galactic diskseems still beyond reach.This research has been partially funded by ATP NASAGrant No NNX144AP53 and by the National ScienceFoundation under grants NSF AST-1211258 and NSFPHY11-25915. CVC and JFN acknowledge the hospi-tality of the Kavli Institute for Theoretical Physics atthe University of California, Santa Barbara. ED grate-fully acknowledges the support of the Alfred P. SloanFoundation. Simulations have been run on the High Per-formance Computing cluster provided by the AdvancedComputing Infrastructure (ACI) and Center for HighThroughput Computing (CHTC) at the University ofWisconsin. We are grateful to Rob Grand for his veryconstructive comments and to Jo Bovy for kindly grant-ing us access to his results.