Breathing FIRE: How Stellar Feedback Drives Radial Migration, Rapid Size Fluctuations, and Population Gradients in Low-Mass Galaxies
Kareem El-Badry, Andrew R. Wetzel, Marla Geha, Philip F. Hopkins, Dušan Kereš, T. K. Chan, Claude-André Faucher-Giguère
DDraft version September 14, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
BREATHING FIRE: HOW STELLAR FEEDBACK DRIVES RADIAL MIGRATION, RAPID SIZEFLUCTUATIONS, AND POPULATION GRADIENTS IN LOW-MASS GALAXIES
Kareem El-Badry , Andrew Wetzel , Marla Geha , Philip F. Hopkins , Dusan Kereˇs ,T. K. Chan , Claude-Andr´e Faucher-Gigu`ere Draft version September 14, 2018
AbstractWe examine the effects of stellar feedback and bursty star formation on low-mass galaxies ( M star =2 × − × M (cid:12) ) using the FIRE (Feedback in Realistic Environments) simulations. Whileprevious studies emphasized the impact of feedback on dark matter profiles, we investigate the im-pact on the stellar component: kinematics, radial migration, size evolution, and population gradients.Feedback-driven outflows/inflows drive significant radial stellar migration over both short and longtimescales via two processes: (1) outflowing/infalling gas can remain star-forming, producing youngstars that migrate ∼ > ∼
200 Myr, andthese rapid size fluctuations can account for much of the observed scatter in radius at fixed M star .Second, the cumulative effects of many outflow/infall episodes steadily heat stellar orbits, causingold stars to migrate outward most strongly. This age-dependent radial migration mixes—and eveninverts—intrinsic age and metallicity gradients. Thus, the galactic-archaeology approach of calculatingradial star-formation histories from stellar populations at z = 0 can be severely biased. These effectsare strongest at M star ≈ − . M (cid:12) , the same regime where feedback most efficiently cores galax-ies. Thus, detailed measurements of stellar kinematics in low-mass galaxies can strongly constrainfeedback models and test baryonic solutions to small-scale problems in ΛCDM. Subject headings: galaxies: dwarf – galaxies: evolution – galaxies: star formation – galaxies: kinematicsand dynamics INTRODUCTIONLow-mass “dwarf” ( M star (cid:46) M (cid:12) ) galaxies provideprobes of structure formation on the smallest cosmologi-cal scales and thus represent compelling laboratories fortesting the ΛCDM (cold dark matter plus a cosmologi-cal constant) framework. In addition, because low-massgalaxies reside in low-mass halos with shallow gravita-tional potential wells and low escape velocities, they arehighly sensitive to stellar feedback as compared to moremassive galaxies.During episodes of star formation, radiation pressure,photoionization and photoelectric heating, stellar winds,and supernovae inject both energy and momentum intothe interstellar medium (ISM). Especially in low-massgalaxies, these processes can fuel powerful galactic windsthat drive significant ISM mass into the halo (Larson1974; Dekel & Silk 1986; van Eymeren et al. 2007) andcause the star formation rate (SFR) to decline until gascools and reaccretes back into the galaxy. As a result,low-mass galaxies are thought to have highly stochas-tic and bursty SFRs (for example, Gerola et al. 1980; Department of Astronomy, Yale University, New Haven, CT,USA. [email protected] TAPIR, California Institute of Technology, Pasadena, CAUSA Carnegie Observatories, Pasadena, CA, USA Department of Physics, Center for Astrophysics and SpaceSciences, University of California at San Diego, La Jolla, USA Department of Physics and Astronomy and CIERA, North-western University, Evanston, IL, USA Moore Prize Fellow Carnegie Fellow in Theoretical Astrophysics
Stinson et al. 2007; McQuinn et al. 2010; Weisz et al.2011; Gonz´alez-Samaniego et al. 2014), which in turncan have significant effects on these galaxies’ dynamicaland morphological evolution. For instance, bursty starformation may explain the lack of coherent, rotationally-supported disks in galaxies with M star (cid:46) . M (cid:12) (Kauf-mann et al. 2007; Muratov et al. 2015; Simons et al. 2015)and the fact that star-forming galaxies are more likely tobe dispersion-supported at low mass than at high mass(S´anchez-Janssen et al. 2010; Roychowdhury et al. 2010;Teyssier et al. 2013; Wheeler et al. 2015).Many studies have shown that stellar feedback-drivengas outflows can displace a significant fraction of agalaxy’s total gas mass (for example, Mathews & Baker1971; Haehnelt 1995; Muratov et al. 2015; Christensenet al. 2015), and several recent works have investigatedhow the resulting time-varying potential can transferorbital energy to dark matter. Baryon-driven poten-tial fluctuations have been invoked as a possible solu-tion to several of the discrepancies between the pre-dictions of the ΛCDM framework and observation, in-cluding the “core-cusp” problem (for example, Navarroet al. 1996; Mashchenko et al. 2008; Pontzen & Governato2012; O˜norbe et al. 2015; Chan et al. 2015; Tollet et al.2015) and the related “too-big-to-fail” problem (Boylan-Kolchin et al. 2011; Zolotov et al. 2012; Garrison-Kimmelet al. 2013; Chan et al. 2015; Dutton et al. 2015), demon-strating that baryonic physics can have significant andlasting effects on the distribution of (collisionless) darkmatter.Stars are also (effectively) collisionless and thus feel a r X i v : . [ a s t r o - ph . GA ] M a r El-Badry et al.the same fluctuations in the gravitational potential thattransfer energy to dark matter. Therefore, one mightexpect the kinematics of stars to respond to feedback-driven outflows in much the same way as dark mat-ter. Some theoretical works have shown that gas out-flows/inflows can drive kinematic fluctuations of all mat-ter in the central regions of bursty gas-rich dwarf galax-ies, particularly at high redshifts (Stinson et al. 2009;Maxwell et al. 2012; Teyssier et al. 2013; Governato et al.2015; Chan et al. 2015). However, few works have stud-ied in detail the effects of outflows on stellar kinematics,especially at late cosmic times.Stellar migration has been studied extensively inother contexts, though mostly in massive ( ∼ L ∗ ), disk-dominated galaxies. Here, non-axisymmetric gas andstellar structures within the disk have been shown todrive radial migration without appreciably heating thestellar population (Sellwood & Binney 2002; Roˇskar et al.2008a; Di Matteo et al. 2013; Loebman et al. 2015).However, fewer works have investigated radial migra-tion in low-mass galaxies. Because low-mass galaxiesgenerally lack strong disks, bars, or spiral arms, radialmigration often is assumed to be less important in thisregime. Some previous studies of low-mass galaxies havefound that their stellar orbits are perturbed primarily bygentle dynamical heating (Stinson et al. 2009; Schroyenet al. 2013; Teyssier et al. 2013), which becomes im-portant only on cosmological timescales (if at all) anddoes not appreciably change radial population gradients.In general, most studies of stellar kinematics and ra-dial migration assume that the global galactic poten-tial is smooth and varies gradually over time. However,the many recent studies of dark-matter coring, as citedabove, demonstrate that this assumption is not necessar-ily valid in the low-mass regime.In this work, we investigate in detail the effects of stel-lar feedback-driven gas outflows/inflows on stellar kine-matics in isolated low-mass galaxies using cosmologicalzoom-in hydrodynamic simulations. We examine howfeedback drives rapid radial migration of stars over shorttimescales and demonstrate that the cumulative effectsof many starburst episodes drive systematic outward mi-gration over cosmological timescales. We organize ourpaper as follows. In Section 2, we describe our simula-tions and the properties of our galaxy sample at z = 0.In Section 3, we examine in detail one of our galaxies asa case study, highlighting its bursty star formation andthe effects of gas outflows/inflows on stellar kinematics,radial migration, and population gradients. In Section 4,we explore this behavior across our entire galaxy sample.In Section 5, we discuss the relation between stellar mi-gration and dark matter coring and compare with pre-vious theoretical and observational results. Finally, inSection 6, we summarize our results and discuss possibleobservational tests. METHODS2.1.
FIRE Simulations
We use cosmological zoom-in hydrodynamic simula-tions of isolated galaxies from the FIRE (Feedback in Re-alistic Environments) project (Hopkins et al. 2014). All http://fire.northwestern.edu simulations were run using the GIZMO code (Hopkins2015) with pressure-entropy based smoothed particle hy-drodynamics (P-SPH; Hopkins 2013) and an updatedversion of the PM+TREE gravity solver from GADGET-3 (Springel 2005). For more details and tests of
GIZMO ,see Hopkins (2015). All of our runs use a ΛCDM cosmol-ogy with (Ω M , Ω Λ , Ω b , h ) = (0 . , . , . , . CLOUDY (Ferland et al. 2013) across 10–10 K, whichinclude cooling from atoms, metals (using 11 species),and molecules. We include ionization and heating froma redshift-dependent ultraviolet background computed inFaucher-Gigu`ere et al. (2009) and estimate self-shieldingin dense gas via an on-the-fly local Jeans-length approx-imation.As the simulation evolves, stars form as individual gasparticles turn into star particles if three conditions aremet:1. The local gas density must be n > n SF , where n SF = 100 h cm − ≈
50 cm − .2. Star-forming gas must be locally self-gravitating.3. Star-forming gas must be molecular, as determinedby the molecular fraction calculated from the lo-cal column density and metallicity according toKrumholz & Gnedin (2011).If these conditions are met, star particles form with aninstantaneous efficiency of 100% per local free-fall time,though stellar feedback quickly regulates this efficiencywithin a gas cloud. Each star particle that forms rep-resents a single stellar population with single age andmetallicity, assuming a Kroupa (2002) initial mass func-tion.Some previous papers using FIRE simulations cited n > n SF = 100 cm − , inadvertently omitting the h term. We cite the correct value here. Regardless of theexact threshold, we emphasize that the most importantcriterion in the FIRE model is that star-forming gas mustbe locally self-gravitating: we have tested thresholds of n SF = 5 −
500 cm − and find no significant differences ingalaxy-wide properties.As star particles evolve, they deposit energy, momen-tum, mass, and metals into nearby gas particles. Weincorporate a comprehensive set of stellar feedback pro-cesses, as detailed in Hopkins et al. (2014): radiationpressure from massive stars, local photoionization andphotoelectric heating, core-collapse and type Ia super-novae with appropriate momentum and thermal energyinjection, and stellar winds. We use energy, momentum,mass, and metal return computed directly from STAR-BURST99 (Leitherer et al. 1999); we never turn off cool-ing of supernova-heated gas. This feedback is injectedinto the ≈
32 gas particles nearest to a given star particle,with each gas particle receiving a fraction proportionalto h j , where h j is the gas particle’s kernel length.We simulate each galaxy individually using the cos-mological “zoom-in” technique (Porter 1985), followingthe method outlined in O˜norbe et al. (2014). We firstadial Migration in Low-Mass Galaxies 3run several lower-resolution dark-matter-only cosmologi-cal simulations at uniform resolution to identify isolatedhalos of interest. We then trace the particles aroundeach halo at z = 0 back to their initial conditions at z = 100 and reinitialize this Lagrangian volume at higherresolution with dark matter and gas particles using the MUSIC code (Hahn & Abel 2011). We then run thesezoom-in initial conditions to z = 0. For further details,see Hopkins et al. (2014) and Chan et al. (2015).2.2. Galaxy Sample
Table 1 summarizes the properties of our simulatedgalaxies at z = 0. We study 8 galaxies across M star ( z =0) = 2 × M star to 5 × M star . Our analysis fo-cuses primarily on the 7 low-mass “dwarf” galaxies with M star ( z = 0) < × M star . We include a MilkyWay-like galaxy (m12i) as a comparison for the low-mass regime. All of these galaxies are isolated at z ∼ R , where R is the spherical radius enclosing 200 × the averagematter density of the Universe.All our galaxies have been presented in previous pa-pers. Specifically, Hopkins et al. (2014) first pre-sented m10, m11, m11v, and m12i, showing that thesegalaxies reproduce the observationally-inferred M star − M halo relation at all redshifts where observational con-straints are available. Chan et al. (2015) first presentedm10.1, m10.2, m10.6, and m11.2 and showed that thephysically-motivated FIRE feedback prescription pro-duces realistic dark matter density profiles for all thegalaxies in our sample. Furthermore, Ma et al. (2015)studied the enrichment histories of m10, m11, m11v, andm12i and showed that these galaxies reproduce the ob-served redshift-evolution of the mass-metallicity relation;Muratov et al. (2015) studied m10, m11, and m12i andshowed that mass-loss from feedback-driven gas outflowscan explain the suppressed star-formation efficiencies oflow-mass galaxies; Faucher-Gigu`ere et al. (2015) studiedm10, m11, and m12i at redshifts z = 2 − M star (cid:46) . M (cid:12) .2.3. Calculating Centers and Sizes of Galaxies
We define the center of a galaxy (which also defines thecenter of its host halo) via an iterative zoom-in methodusing only star particles. We first calculate the center of(stellar) mass using the entire zoom-in region. We thenrecalculate this iteratively by reducing the search radiusby 50% at each iteration until we identify the positionthat encompasses only 32 particles. This iterative zoom-in method ensures that we always center on the density Because m11v is undergoing a major merger at z = 0, we citeits values and carry out our analysis at z = 0 .
2, before the mergerbegins, not at z = 0. Chan et al. (2015) refer to simulations m10.1, m10.2, m10.6,and m11.2 as m10h1297, m10h1146, m10h573, and m11h383, re-spectively. For m10.2, we study the halo within the zoom-in regionthat has the largest stellar mass, while they studied the halo withthe largest total mass. peak closest to the center of mass. We also experimentedwith centering on dark matter rather than stars, findingonly modest ( < R , the spherical radius that encloses 90%of the total M star . We also compute R e , the effectiveradius that encloses half of the (observable) light.We calculated R e as follows. First, we construct a gridof 6150 r -band luminosity functions calculated from themost recent Padova isochrones (Bressan et al. 2012) as-suming a Kroupa (2002) initial mass function. These arelogarithmically spaced in stellar age and linearly spacein metallicity to span the full range of stellar propertiesin the simulations. We integrate over each luminosityfunction to obtain a grid of stellar luminosities per unitinitial mass as a function of age and metallicity. We as-sign each star particle a luminosity by interpolating itsage and metallicity from the grid and weighting the re-sult by its initial mass. Finally, we mock observe eachgalaxy along a given line of sight to calculate the surfacebrightness in elliptical radius bins that are aligned withthe galaxy’s major axis. Our measurements of R e do notattempt to account for scattering or dust attenuation.We define R e as the semi-major axis of the ellipse thatcontains 50% of the light above an r -band surface bright-ness threshold of 26 mag arcsec − (similar to the SDSSobservations against which we compare). We quantifiedthe line-of-sight scatter in these measurements via mockobservations along randomly chosen lines of sight. Noneof our galaxies with M star < M (cid:12) have axis ratios < .
5, and the R e calculated along different lines of sightdiffer by only ∼ Effects of Resolution
To test whether our results depend significantly on res-olution, we analyzed two of our galaxies (m11 and m11.2)simulated at 8 times lower resolution in mass. In bothsimulations, the instantaneous SFR is more bursty in thelower-resolution runs, but the burstiness of the SFR av-eraged over 100 Myr is unchanged. For both galaxies, wefind that the fractional radial migration, population gra-dients, and size fluctuations agree to within a few percentat both resolutions. We thus conclude that, althoughstar formation in the FIRE simulations depends some-what on resolution (see Hopkins et al. 2014; Sparre et al.2015), the specific processes that we study—radial mi-gration, size fluctuation, and the effect on populationgradients—do not depend significantly on resolution. CASE STUDY: EVOLUTION OF A SINGLEGALAXYWe present our results in two parts. First, in thissection, we examine in detail the SFH, stellar and gaskinematics, size evolution, and population gradients of asingle galaxy, m10.6, with M star ( z = 0) ≈ × M (cid:12) (see Table 1). We use this galaxy, which is represen-tative of the mass regime in which radial migration is El-Badry et al. Table 1
Parameters of the simulations at z = 0.Name log( M m )[M (cid:12) ] R m [kpc] log( M star )[M (cid:12) ] R e [kpc] R [kpc] f gas α log( N star ) t dyn [Myr] m dm [M (cid:12) ] m b [M (cid:12) ] (cid:15) dm [pc] (cid:15) star [pc] (cid:15) gas [pc]m10 9.92 64 6.35 0.17 1.40 0.77 -1.63 4.04 78 1.3e3 2.6e2 29 7 3m10.1 10.16 77 7.22 0.65 3.97 0.88 -0.65 3.98 194 1.0e4 2.1e3 43 7 4m10.2 9.84 61 8.08 0.47 2.62 0.41 -0.76 4.81 160 1.0e4 2.1e3 43 7 4m10.6 10.60 110 8.47 1.94 9.02 0.81 -0.43 5.23 263 1.0e4 2.1e3 100 21 10m11 11.17 170 9.32 5.26 15.45 0.48 -0.37 5.47 296 3.5e4 7.1e3 71 14 7m11v 11.28 150 9.36 4.39 14.05 0.46 -0.34 4.73 282 2.8e5 5.7e4 142 14 7m11.2 11.23 180 9.59 3.99 14.87 0.50 -0.36 5.43 263 8.3e4 1.7e4 100 21 10m12i 12.09 340 10.74 5.35 12.50 0.33 -1.32 5.99 88 2.8e5 5.7e4 142 50 20 R m is the radius at which ρ ( < R m ) = 200 ρ matter , where ρ ( < R m ) is the average matter density over a sphere of radius R m . M m and M star are the total mass and stellar mass inside R m and 0 . R m , respectively. R e is the effective radius enclosing 50%of the stellar light above a surface-brightness threshold of 26 mag arcsec − in the r -band; R is the radius enclosing 90% of thestellar mass. f gas = M gas / ( M star + M gas ) is the gas fraction inside 0 . R m . α is central slope of the dark matter density profile( ρ DM ∝ r α ) in the interval r = (1 − R m . N star is the number of star particles inside R . t dyn = (cid:112) π/ G ¯ ρ is the dynamicaltime within R , using the average density of all matter, ¯ ρ . m dm and m b are the average particle masses for dark matter andbaryons; (cid:15) dm , (cid:15) star , and (cid:15) gas are the minimum gravitational softening lengths, in physical units. most significant, as a case study to explore in detail bothshort-timescale behavior across a single gas inflow- out-flow episode and long-term trends across cosmic time.Then, in Section 4, we present results for all 8 galaxiesto highlight trends with M star from 2 × to 5 × M (cid:12) .3.1. Bursty Star Formation Histories
The SFHs of our low-mass galaxies are highly stochas-tic, even at late cosmic times. Figure 1 shows the specificstar formation rate (sSFR = SFR / M (cid:63) ) of m10.6 from z = 1 to 0. We focus on late-time evolution to high-light behavior at redshifts where such low-mass galaxiescurrently are observable.Bursty star formation (even at late times) is typical ofour simulated galaxies near this mass (Sparre et al. 2015).This burstiness is driven by stellar feedback, which drivesgas outflows and regulates the central gas density onshort timescales. Following a burst of star formation,young stars and supernovae inject energy and momentuminto the ISM to drive gas out into the halo, temporar-ily disrupting star formation. However, because mostoutflowing gas is not accelerated past the escape veloc-ity at late times (Muratov et al. 2015), it rapidly coolsand re-accretes into the center of the galaxy, where theSFR rises again. Figure 1 illustrates this cycle in m10.6;the SFR falls each time the sSFR approaches 10 − yr − .These fluctuations in SFR are semi-periodic, with a typ-ical spacing of a few 100 Myr, which is comparable tothe galaxy’s dynamical time (Table 1).As Figure 1 shows, m10.6 goes through ∼
10 periods ofstrongly increased, then decreased, sSFR between z = 1and 0. Even averaged over 10 and 100 Myr, the typicaltimescales over which observable H α and UV emissionare enhanced, these reduced sSFRs briefly fall below thetypical threshold of sSFR < − yr − , where galaxiesare classified as quiescent.For the rest of this section, we focus in particular onevolution within the 400-Myr burst episode at z ≈ . Kinematics and Morphology of Gas and Stars
Age [Gyr] -12 -11 -10 -9 -8 s S F R [ y r − ] Instantaneous sSFR10 Myr Average100 Myr Average redshift z M ( z =0) =10 . M fl Figure 1.
Specific star formation rate (sSFR) in m10.6 from z =1 to z = 0. Different colored curves show sSFR smoothed overdifferent timescales: 10 (100) Myr approximates the timescale forsignificant H α (UV) emission. Horizontal black line shows sSFR= 10 − yr − , a common threshold used to define a galaxy asquiescent. The sSFR fluctuates by several orders of magnitudeover <
100 Myr. Major starburst episodes, which blow much ofthe cold gas out into the halo and cause the sSFR to temporarilyquench (fall below the quiescence threshold), occur several timesafter z = 1. Vertical dashed lines at ≈
12 Gyr ( z ≈ .
13) enclose asingle starburst episode, which we examine in detail below.
We first examine the influence of stellar feedback andbursty star formation on the kinematics and morphologyof cold gas, and its consequent influence on the kine-matics and morphology of stars, during the single star-burst/quenching episode highlighted in Figure 1.Figure 2 shows the surface density of neutral atomichydrogen (top), all stars (middle), and young stars (age <
50 Myr) across 8 snapshots spaced by ≈
60 Myr. (Notethe change in spatial scale between the top and mid-dle/bottom panels.) In the first snapshot, the SFR ishigh and concentrated within the inner ≈ .
03 Gyr 12 .
08 Gyr 12 .
14 Gyr 12 .
20 Gyr
16 8 0 8 161680816 .
26 Gyr
16 8 0 8 16 .
32 Gyr
16 8 0 8 16 .
38 Gyr
16 8 0 8 16 .
44 Gyr n e u t r a l h y d r og e n m a ss [ M fl ] .
03 Gyr 12 .
08 Gyr 12 .
14 Gyr 12 .
20 Gyr .
26 Gyr .
32 Gyr .
38 Gyr .
44 Gyr r − b a nd l u m i n o s i t y [ L fl ] .
03 Gyr 12 .
08 Gyr 12 .
14 Gyr 12 .
20 Gyr .
26 Gyr .
32 Gyr .
38 Gyr .
44 Gyr r − b a nd l u m i n o s i t y [ L fl ] HIAll StarsYoung Starsx [kpc]x [kpc]x [kpc] y [ k p c ] y [ k p c ] y [ k p c ] Figure 2.
Evolution of neutral gas (top), all stars (middle), and young stars (bottom) in m10.6 across a single 400-Myr starburst episode(vertical lines in Figure 1). Panels show snapshots spaced by ≈
60 Myr; sSFR in each snapshot is shown by blue points in Figure 3. Notethe difference in spatial scale between the top and bottom two panels.
Top : Distribution of neutral atomic hydrogen. The SFR is highestin the first panel, when the gas is densest. The SFR reaches its lowest value at t = 12 .
26 Gyr, when nearly all the gas is blown beyondthe stellar distribution. Once the gas cools back into the center, the SFR rises quickly again, nearly returning to its pre-outflow value by t = 12 .
44 Gyr.
Middle : Projected distribution of stellar light (in the r -band). Black ellipses enclose show R e , the radius enclosing 50%of the light. The stellar distribution expands and contracts similar to the gas, with R e varying by a factor of ≈ .
5, across this timescale.
Bottom : Projected distribution of stellar light for stars younger than 50 Myr (smaller than the time spacing between panels). Blackcontours show logarithmically spaced luminosity of all stars (from middle panel). Some stars continue to form during the beginning of theoutflow phase, but almost no stars form after this, when gas is diffuse, ionized, and not self-bound.
El-Badry et al. ≈ r -band luminositysurface density for all stars. Critically, the stellar distri-bution expands and contracts in the same way and overthe same timescale as the gas. This expansion is presentboth at the center, where the surface density drops sig-nificantly, and in the outskirts, where the stars expandto even larger radii. The black ellipses show the 2-Dfit to R e at each snapshot, highlighting that within just ≈
200 Myr, R e increases by more than a factor 2. Similarfluctuations occur for dark matter (Chan et al. 2015).Figure 2 (bottom) shows the r -band luminosity sur-face density of only stars younger than 50 Myr, slightlyless than the time spacing between these snapshots. Thishighlights the effect of stellar feedback on star-formingregions. Initally, star formation occurs primarily justwithin the inner ≈ v r = v · r | r | ) as afunction of time over 1 Gyr spanning the same 400-Myrperiod as Figure 2. In all the following plots, averages areweighted by particle mass. The top panel shows the sSFRto highlight its correlation with gas and stellar kinemat-ics. The middle panel shows the radial velocity of all gas(red) and instantaneously star-forming gas (blue) within25 kpc. Finally, the bottom panel shows the radial veloc-ity of extremely young stars (age <
10 Myr, blue) and oldstars (age > t ≈
12 Gyr, just aftergas has (re)accreted into the center. Then, just ∼ −
40 km s − (on av-erage), at which point sSFR declines most rapidly. Asthe gas approaches turn-around ( v r = 0) and is mostrarefied, the sSFR reaches its minimum. Finally, as thegas starts to cool back into the galaxy, the sSFR startsto increase, and the cycle continues. During this outflowperiod, less than 2% of all gas is accelerated beyond theescape velocity ( v esc ≈
160 km s − in the center of thisgalaxy), and none of the galaxies in our sample expe-rience significant mass loss after z = 1 (Muratov et al.2015).Figure 3 (middle) shows that even star-forming gasclouds participate in this inflow-outflow cycle. That is,some outflowing/infalling gas remains in dense ( n H >
50 cm − ), cool ( T (cid:46) K), self-bound clumps withongoing star formation. Figure 3 (bottom) shows thatthe radial velocity of young stars closely traces that of star-forming gas. Thus, young stars inherit the complexinflow-outflow kinematics of the gas clouds in which theyform . Furthermore, the majority of all stars in our sim-ulated galaxies with M star (cid:46) M (cid:12) form during burstepisodes (Sparre et al. 2015); thus, a majority of starscan experience non-trivial radial migration within theirfirst ∼
100 Myr.Figure 3 (bottom) shows a systematic time offset be-tween the radial velocities of young and old stars. Youngstars (almost by definition) are strongly coupled to thegas clouds in which they form. Stars with intermediateages of a few 100 Myr (not shown) start to separate kine-matically from their progenitor gas clouds. Importantly, old stars still fluctuate kinematically , though their fluc-tuations are not as strong as those of young stars or gas.The delayed response of old stars demonstrates that theydo not respond directly to the kinematics of gas, but in-stead, respond to the change in the galactic potentialwhen feedback drives significant gas mass beyond thestellar component.It is important to note that although gas and starsmove in and out on average during the burst cycle,some particles on radial orbits do move inward dur-ing outflow periods and vice-versa. At the peak of theoutflow shown in figure 3, approximately 87% of gasand 73% of stars have positive radial velocities, with( σ r, gas , σ r, star ) ≈ (39 ,
26) km s − . We have verified thatthe average velocities shown in Figure 3 are not drivenprimarily by high-velocity outliers; the mean and medianradial velocities typically agree within a few percent.All together, we summarize the following two-stagephysical picture for the cause of strong radial migra-tion of stars in low-mass galaxies, where stellar feedbackdrives strong outflow-inflow cycles of gas: • (1) Outflowing/infalling gas clouds can remainstar-forming, producing young stars that inheritthe radial kinematics of their progenitor gas cloudsand thus migrate significantly within their first ∼
100 Myr. • (2) Gas outflows/inflows in low-mass galaxies withhigh gas fractions drive strong fluctuations in thegalaxies’ overall potentials, which in turn drivestrong kinematic fluctuations in stars of all ages.These processes are fundamentally different from theprocesses thought to cause radial migration in massivedisk galaxies, where stellar orbits are scattered via inter-actions with massive non-axisymmetric structures (forexample, Wielen 1977; Binney & Lacey 1988), or arestirred by spiral waves and/or bars (for example, Sell-wood & Binney 2002; Minchev et al. 2011). In our low-mass galaxies, the entire stellar distribution “breathes”(expands and contracts) due to global processes resultingfrom stellar feedback and bursty star formation. This,together with radial kinematics inherited from outflow-ing/infalling gas, is the primary driver of radial migrationin our simulations. Unlike the well-studied spiral wave-driven migration processes that are important in cooldisks, the processes driving migration in our simulationsalso kinematically heat the stellar population and placesome stars on highly radial orbits.3.3. Radial Migration of Stars adial Migration in Low-Mass Galaxies 7 -11 -10 -9 s S F R [ y r − ]
10 Myr Average100 Myr Average star forming gasall gas
Age [Gyr] young starsold stars r a d i a l v e l o c i t y [ k m s − ] gasstars Figure 3.
Short-timescale effects of stellar feedback on the kine-matics of gas and stars across a single starburst episode (verticallines in Figure 1) in m10.6.
Top : Specific star formation rate(sSFR) averaged over timescales of 10 (cyan) and 100 (black) Myr.Blue points show time-spacing of the 8 snapshots shown in Fig-ure 2.
Middle : Average radial velocity of gas within 25 kpc, forstar-forming (blue; ee Section 2.1) and all (red) gas. The radial ve-locity of gas closely traces the evolution of the SFR.
Bottom : Av-erage radial velocity of stars, both young (age <
10 Myr, blue) andold (age > We next explore how the above complex radial kine-matics drive radial migration of stars over both short andlong timescales.3.3.1.
Measuring Radial Migration
We define radial migration as any change in the galac-tocentric radius of a star particle since its formation. Tomeasure radial migration since formation, we identify thefirst simulation snapshot that occurs immediately afterthe formation time of each star particle, at which pointwe record the particle’s radius with respect to the centerof the main galaxy. We then compute the radial migra-tion as ∆ r = r current − r form , the difference between theparticle’s current radius in a given snapshot and its ra-dius in the snapshot immediately following its formation.Our typical time spacing between snapshots is ≈
50 Myr. This finite time separation means that the ra-dius that we measure after formation does not exactlyequal the radius at which the particle formed, so ourvalues are subject to some extremely short-timescale mi-gration. We tested this by examining only star particlesthat formed <
10 Myr before the snapshot at which wemeasure r form . We find no systematic difference in any of our results when examining only these particles.To avoid ambiguity from stars that formed in dif-ferent (satellite) galaxies that then merged with themain galaxy, we ignore star particles that formed at r > R ( z ), where R ( z ) is the radius enclosing90% of M star of the main galaxy at a given z . For sev-eral of our galaxies, this means that we exclude ≈
50% ofthe stars that formed before z ∼ (cid:104) ∆ r (cid:105) , the average of the net (vector) radial migration distance across all parti-cles, and (cid:104)| ∆ r |(cid:105) , the average of the absolute radial mi-gration distance. The former measures systematic in-ward/outward migration, while the latter measures thescatter induced by simultaneous inward and outward mi-gration.3.3.2. Radial Migration over Short Timescales
Figure 4 compares the time-evolution of the sSFR, themean stellar radial migration, and the slope of the cen-tral dark-matter density profile over the same starburstepisode shown in Figure 3. The middle panel shows theaverage migration distance for all stars. Like radial ve-locity, radial migration distance is closely related to thesSFR: stars migrate outwards when the sSFR falls dur-ing periods of net outflow and migrate inward once gasfalls back into the galactic center and the sSFR rises.This has a dramatic effect on the radial distribution ofstars: during the main outflow episode, the overall stellarpopulation migrates coherently ≈ . (cid:104) ∆ r (cid:105) is always positive becausewe measure radial migration since formation , and as wewill show in Section 3.3.3, stars experience coherent andlasting outward migration over long timescales.The bottom panel shows the time-evolution of thecentral slope α of the dark matter density profile( ρ DM ∝ r α ) . We define α as the power law which bestfits ρ DM in the r = (1 − R m interval; see Chanet al. (2015) for further discussion of α. Here, α ∼ α (cid:46) − α evolves similarly to the meanstellar migration and sSFR, changing from a cuspy pro-file at peak sSFR to a core at peak outflow.3.3.3. Radial Migration over Long Timescales
We next examine stellar radial migration in m10.6 overlong (cosmological) timescales. Figure 5 shows the dis-tribution of radial migration distances since formation, (cid:104) ∆ r (cid:105) and (cid:104)| ∆ r |(cid:105) , as a function of stellar age. Here westack results across all snapshots, measuring each par-ticle’s migration distance in each snapshot and binningthe simulation in stellar age. Thus, young ages includea combination of stars measured at z ∼ z ,while old ages necessarily come from stars measured onlyat z ∼ (cid:104)| ∆ r |(cid:105) in Figure 5 (bottom), stars un-dergo a significant fraction of their absolute migrationwithin (cid:46)
200 Myr, consistent with Figure 4. The insetzooms in on young ages, showing an early peak of ≈ -11 -10 -9 -8 s S F R [ y r − ]
10 Myr Average100 Myr Average m i g r a t i o n [ k p c ] › ∆ r fi › | ∆ r | fi Age [Gyr] α starsdark matter Figure 4.
Changes in the distribution of stars and dark matter inm10.6 across the same starburst episode shown in Figure 3.
Top :Specific star formation rate (sSFR) averaged over timescales of10 (cyan) and 100 (black) Myr.
Middle : Mean radial migrationof stars relative to their formation radius. (cid:104) ∆ r (cid:105) (purple) showsthe net radial migration, while (cid:104)| ∆ r |(cid:105) shows the absolute radialdistance. Migration correlates strongly and inversely with sSFR.During this outflow episode, the half-mass radius increases from2.5 to > ≈
200 Myr.
Bottom : Central slope α of thedark matter density profile ( ρ DM ∝ r α ) . α correlates with meanstellar migration, since star and dark matter particles feel the sametime-varying gravitational potential. Most importantly, the oldest stars, which have undergonethe largest number of burst episodes, have migrated themost .Second, examining (cid:104) ∆ r (cid:105) (top), young stars ( (cid:46)
200 Myr) show a strong scatter in their net radial migra-tion distance, consistent with the bottom panel, but theydo not show systematic net inward/outward migrationover such short times. That is, short-timescale migra-tion is limited to temporary outward/inward burst cycles .However, over sufficiently long ( (cid:38) > ∼ R e ( z = 0), from theradius where they formed.3.4. Impact of Radial Migration on PopulationsGradients time since formation [Gyr] ∆ r [ k p c ] mean1 σ σ time since formation [Gyr] | ∆ r | [ k p c ] Figure 5.
Distribution of radial migration distances of stars sincetheir formation as a function of their stellar age in m10.6.
Top :∆ r , the difference between a star particle’s radius when it is ata given age and its radius when it formed. Positive (negative)values correspond to stars that have migrated outward (inward)since formation. Bottom : Same, but for | ∆ r | , the absolute ra-dial migration distance. Inset shows stars younger than 1 Gyr,highlighting short timescales. After (cid:46)
200 Myr, stars move an av-erage absolute radial distance of 1 kpc. As the top panel shows,the average coherent (net) migration is weak over this timescale,but over longer timescales ( (cid:38)
Our simulated galaxies develop significant radial popu-lation gradients by z = 0, with the youngest, most metal-rich stars concentrated near the galactic center and theoutskirts dominated by old, metal-poor stars. These gra-dients are similar to those observed in low-mass galaxiesin the local Universe (for example, Mateo 1998; Kirbyet al. 2012; Vargas et al. 2014). Galactic archeologystudies, which attempt to infer the formation-history of agalaxy base on its properties at z ∼
0, commonly assumethat one can translate population gradients observed at z ∼ z = 0 accurately reflects the distributionof stars at the time of their formation. However, dynam-ical heating can can mix different stellar populations andthus alter radial population gradients, and radial migra-tion can preferentially affect old stars (Governato et al.2015; Brooks & Teyssier 2015; Gonzalez-Samaniego et al.2015). The significant radial migration which we presentabove suggests that, in low-mass galaxies, SFHs that areadial Migration in Low-Mass Galaxies 9calculated from population gradients at z = 0 may becontaminated significantly by migration. We now inves-tigate this possibility in m10.6.Figure 6 shows the SFH of m10.6 as a joint functionof both lookback time and radius. In both versions, theright projection shows SFR versus time, while the leftprojection shows the azimuthally integrated SFR (den-sity) versus radius.The left panel shows the SFH if we use the radial dis-tribution of stellar ages at z = 0 to infer the SFH, asobservational studies do. The radial SFH calculated at z = 0 appears to show that early star formation occurredat all radii and in fact was distributed almost uniformlywith radius out to 9 kpc; by contrast, the youngest starsappear to have formed within the central regions. At facevalue, this appears to support an “outside-in” quenchingscenario (for example, Hidalgo et al. 2003; Zhang et al.2012), wherein star formation becomes increasingly cen-trally concentrated as a galaxy evolves.However, the right panel of Figure 6 shows the trueunderlying SFH, which we measure by tracing the starsback to the radii at which they formed. Thus, this SFHremoves any effects of post-formation migration. In re-ality, star formation has been concentrated in the coresince early times: the oldest stars preferentially formed atsmaller radii, while the youngest stars formed at system-atically larger radii. Thus, the significant effects of radialmigration, over both short and long timescales, qualita-tively have changed the inferred radial SFH in m10.6.This represents a critical systematic in any galactic-archeaology approaches.Figure 7 demonstrates these effects more quantita-tively. The black curves show stars measured at theirradius at z = 0, while the red curves show stars measuredat their formation radius. The top panel shows the cumu-lative stellar mass profile: the black curve shows the massprofile at z = 0, while the red curve shows the mass pro-file if stars stayed at their formation radius. Even thoughall stars form in a centrally concentrated manner, with90% having formed within 3 . R ( z = 0) > Z (cid:12) = 0 .
02. The old-est stars, which were the most metal-poor, formed atsmall radii but experienced more outward radial migra-tion, while the younger more metal-rich stars formed atlarger radii, on average, but experienced less outward migration. Again, radial migration has inverted the truemetallicity gradient.Thus, we conclude that stellar radial migration, in-duced by feedback-driven outflows, not only can diluteintrinsic population radial gradients, but also can invertthem entirely . DEPENDENCE ON GALAXY MASSHaving explored stellar kinematics, radial migration,and population gradients in detail for a single galaxy,m10.6, we now explore these trends for all 8 galaxies inour sample, which span M star ( z = 0) = 10 . − . M (cid:12) (or halo M = 10 − M (cid:12) ).Figure 8 shows the late-time evolution (over the last ∼ z ∼ .
45) of three galaxies that span therange of masses in our sample. This shows, as a func-tion of time, the same quantities that we explored above:sSFR (top row), average radial velocity of stars (secondrow), average radial migration distance of stars (thirdrow), and stellar half-light radius, R e , as well as 90%- M star radius, R (bottom row).The sSFRs of the low-mass m10 and m11 are highlybursty and stochastic, with fluctuations similar to m10.6.By contrast, m12i shows much smoother sSFR because(1) it has a much deeper and more stable potential, and(2) being a more massive galaxy, its sSFR is averagedover many more star-forming regions. See Sparre et al.(2015) for the dependence of star-formation burstinesson mass in our simulations.The evolution of stellar radial velocity, radial migra-tion, and size evolution in m11 are all similar to m10.6,with radial velocity fluctuations of ±
10 km s − , typicalradial migration since formation of ≈ ≈ R e that fluctu-ates by a factor of 2 over a similar timescale.In m12i, stellar feedback does drive gas out of thedisk, but the galaxy’s potential well is deeper, with amuch smaller contribution from gas in the central re-gions. Thus, coherent fluctuations in the average radialvelocity of stars are limited to a few km s − . Similarly,the amount of radial migration is much less, though it isnon-zero at 1 − R e evolves significantly be-cause of changes in the distribution of young stars, whichcontribute most of the light, R remains nearly con-stant, showing no late-time fluctuations in the distribu-tion of stars. This is because, despite also having shal-low potential wells and high gas fractions, galaxies at thismass form too few stars, in part from significant baryonicmass loss early in their evolution from cosmic reioniza-tion and stellar feedback (Munshi et al. 2013; Muratovet al. 2015; Christensen et al. 2015). Thus, such galaxiesexperience insufficient stellar feedback to drive significantgas mass into the halo and significantly change the galac-tic potential. Bursty star formation alone does not nec-essarily imply strong stellar kinematic fluctuations andradial migration in galaxies of all masses.Overall, stellar migration and size evolution are mostextreme in galaxies with M star ∼ M (cid:12) (halo M ∼ Figure 6.
Star formation history (SFH) of m10.6 as a joint function of both time and galactocentric radius. In both versions, the rightprojection shows the normalized star formation rate (SFR) versus time, while the left projection shows the integral of SFR (mass density)versus radius.
Left : SFH as calculated from the radial distribution of stars at z = 0: we bin star particles by their radius at z = 0 andcompute the SFH in each radius bin, similar to observational approaches for nearby galaxies. Right : Intrinsic SFH of stars at formation:we bin star particles by their radius at formation (rather than at z = 0) and show the true radial SFH, without the post-formation effects ofradial migration. The differences between these panels, especially for the oldest stars, demonstrate that radial migration can significantlybias the inferred radial SFHs of low-mass galaxies, a critical systematic for galactic-archaeology studies. M (cid:12) ). This is the same mass scale where feedbackmost efficiently produces dark matter cores via the samemechanism (for example, Pontzen & Governato 2012;Tollet et al. 2015; Chan et al. 2015; Read et al. 2015).4.1. Dependence of Radial Migration on Mass
We next quantify the amount of stellar radial migrationacross our mass range, using the procedure described inSection 3.3.1. Again, we compute both (cid:104) ∆ r (cid:105) , the average net radial migration, and (cid:104)| ∆ r |(cid:105) , the average absolute radial migration.Figure 9 shows the average radial migration as a func-tion of M star ( z = 0). Points show the average migrationfor each galaxy averaged over the 40 snapshots between z ∼ . M star radius, R .First, the net radial migration, (cid:104) ∆ r (cid:105) (black points),in either physical units or scaled to R , is largestin galaxies with M star ≈ − . M (cid:12) . This confirms themass scaling apparent in Figure 8: galaxies with signif-icantly higher or lower mass than this have more stablekinematics (little variability) and little systematic out-ward migration. Note, however, that a larger sample ofsimulated galaxies is needed to determine precisely themass at which migration becomes unimportant.Importantly, the galaxies at M star ∼ M (cid:12) with thestrongest net radial migration also show the strongestshort-time variability (scatter). This is because suchshort-time variability is required to drive coherent long-term migration: the net migration at late times reflectsthe permanent dynamical heating of stellar orbits causedby many outflow/inflow episodes that slowly transfer en-ergy to collisionless particles over many Gyr. This is the same phenomenon that is expected to drive dark-mattercoring, as we discuss in Section 5.1.Although m12i has undergone little net migration(black points), it does show non-trivial absolute radialmigration (red points) of ≈ z = 0.That is, many stars in m12i have migrated away fromtheir formation radius, but approximately equal num-bers of stars have migrated inward and outward. Qual-itatively, this agrees with previous studies of radial mi-gration in massive disk galaxies, which found that sig-nificant radial migration occurs as stars scatter off ofmassive non-axisymmetric structures such as spiral armsand bars. For example, in a simulation of a disk galaxywith mass similar to m12i, Roˇskar et al. (2008b) foundthat over the course of 10 Gyr, stars migrated an rmsdistance of 2 . Dependence of Population Gradients on Mass
We next examine how the above mass dependence ofradial migration affects radial gradients in stellar popu-lations. For each galaxy, we measure the average prop-erty (age, total metallicity) of the stellar population at R and at the galactic center, and we compute thedifference across the galaxy such that, for property P ,∆ P = P ( r = R ) − P ( r = 0). We compute thisboth using stellar radii at z = 0 and using each star par-ticle’s radius when it formed (also recomputing R based on formation radii).Figure 10 shows the gradients in stellar age (top) andtotal metallicity (bottom). Considering first age, we findstrong positive age gradients at z = 0 in lower-massgalaxies, with younger stars nearer the galactic center, inqualitative agreement with observations (Schroyen et al.2013, and references therein). However, at all masses,outward migration since formation has driven these gra-dients to be more positive (less negative). This effect isadial Migration in Low-Mass Galaxies 11 n o r m a li ze d M ( < r ) z = 0formation m e a n ag e [ G y r ] radius [kpc] m e a n l og ( Z / Z fl ) Figure 7.
Radial distribution of stellar properties in m10.6. Blackcurves show stars measured at their radius at z = 0, while redcurves show stars measured at their formation radius. Top : Cumu-lative stellar mass within the given radius. Black curve shows themass profile at z = 0, while red curve shows the mass profile if starsstayed at their formation radius. While ∼
90% of all stars formedwithin ∼ . R ( z = 0) > Middle : Mean stellar age as a function of ra-dius at z = 0 (black) and at formation (red). Age-dependent radialmigration has inverted the true age gradient: while the age gradi-ent measured at z = 0 naively implies that younger stars formedpreferentially at smaller radii, in reality, the oldest stars formedpreferentially at small radii but experienced stronger outward mi-gration. (See also Figure 6.) Bottom : Mean total metallicity asa function of radius at z = 0 (black) and at formation (red). Aswith the age gradient, the stronger outward migration of older starshas inverted the metallicity gradient. In reality, older metal-poorstars formed only at small radii but then migrated outward, whileyounger metal-rich stars formed at all radii and experienced lessmigration. weakest in m10 and m12i, which undergo the least netoutward migration. m10 is the only galaxy in our sam-ple whose positive age gradient at z = 0 is not primarilydriven by migration. In this galaxy, star formation be-comes increasingly centrally concentrated over time; thefew star particles which do form at large radius form be-fore z = 2.The most dramatic effect occurs in galaxies with M star ≈ − . M (cid:12) . Most of these formed with intrin-sically negative age gradients (inside-out growth), butsubsequent radial migration has inverted this underlyingtrend to appear to be positive (appearance of outside-ingrowth) at z = 0.Figure 10 shows similar trends for metallicity gradi- ents. All of our galaxies have negative metallicity gra-dients at z = 0, with more metal-rich stars near thecore. For m12i and m10, these gradients are close to theunderlying gradients at formation, with modest changesdue to subsequent radial migration. However, most ofour galaxies with M star ≈ − . M (cid:12) formed with in-trinsically positive (though nearly flat) gradients, suchthat more metal-rich stars formed at slightly larger radii;migration inverted the true population gradient.There is significant variation in the extent to whichradial migration alters galaxies’ z = 0 population gradi-ents, since this depends both on the total amount of mi-gration and on the radial star formation history. Galax-ies with extended radial star formation at early times(for example, m11) have positive intrinsic age gradients,which are altered less by migration.In summary, radial migration can significantly and sys-tematically bias and even invert intrinsic stellar popu-lation gradients within galaxies in the critical range of M star ≈ − . M (cid:12) . This means that intrinsic popula-tion gradients observed at z = 0 do not necessarily reflectthe true gradients at formation, thus raising significantconcerns for galactic-archaeology studies that aim to in-fer radial SFHs from stellar populations at z = 0.4.3. Rapid Size Evolution
Finally, we examine size evolution. We have shownthat galaxies with M star ≈ − . M (cid:12) undergo rapidfluctuations that drive significant stellar migration ontimescales of a few 100 Myr, which in turn leads to rapidfluctuations of the stellar effective radii by factors of 2 − M star .This comparison serves two purposes. First, compar-ing against observations tests whether our simulationsproduce realistic galaxy sizes, and in particular, whetherthe dramatic size evolution overestimates the observedscatter in galaxy sizes. Second, the comparison can shedlight onto the physical origin of the observed scatter ingalaxy sizes at fixed mass.Figure 11 shows the SDSS r -band half-light radius, R e ,as a function of M star for galaxies at z ∼
0. We com-pare the radii measured in our simulations to the effectiveradii of galaxies observed in the SDSS, as measured in theNASA-Sloan Atlas (NSA; Blanton et al. 2011). We com-pare only to galaxies in isolated environments, using theisolated sample described in Bradford et al. (2015). Forreference, in the lowest M star bin in Figure 11, the NSAcontains 20 isolated galaxies; all the bins above 10 M (cid:12) contain at least 100 isolated galaxies. We do not compareagainst m10 because of the small number of galaxies at M star < M (cid:12) in the NSA.The different colored/shaped points show each sim-ulated galaxy sampled across the 40 snapshots from z = 0 . R e by a factor of 2 − light radius, whose fluctuations arestronger than the half- M star radius (not shown). This isbecause younger stellar populations are brighter and thusdisproportionately affect R e , and as we showed in Sec-tion 3.2, the kinematic fluctuations and radial migrationof young stars are stronger than those of older (fainter)stellar populations.2 El-Badry et al. -14 -13 -12 -11 -10 -9 s S F R [ y r − ]
100 Myr Average v r [ k m s − ] stars m i g r a t i o n / R m a ss › ∆ r fi › | ∆ r | fi
10 11 12 13
Age [Gyr] R / R z = R e R
10 11 12 13
Age [Gyr]
10 11 12 13
Age [Gyr]m10 (M = 10 . M fl ) m11 (M = 10 . M fl ) m12i (M = 10 . M fl ) Figure 8.
Late-time evolution since z ≈ .
45 of galaxies in three mass regimes, as labeled.
Row 1 : Specific star formation rate (sSFR)averaged over 100 Myr.
Row 2 : Average radial velocity of all stars.
Row 3 : Average of the net (purple) and absolute (red) radial migrationdistance of stars since their formation, scaled to R . Row 4 : Effective radius, R e , which encloses 50% of the stellar light, and R ,which encloses 90% of M star , both scaled to their values at z = 0. Star formation is burstier in lower-mass galaxies. However, the effecton stellar kinematics is strongest at M star ∼ M (cid:12) . Significantly lower-mass galaxies, such as m10, have more stable kinematics becausetheir overall star-formation efficiency, and thus total feedback, is much lower. This, combined with their lower total baryon fractions, leadsto weaker potential fluctuations. However, R e still fluctuates significantly due to changes in the distribution of the youngest stars, whichcontribute most of the light. More massive galaxies, such as m12i, also show weaker kinematic fluctuations; their deeper potential wellsand lower gas fractions stabilize the potential and inhibit any significant systematic (outward) migration. However, non-trivial absolute(combination of both inward and outward) radial migration still occurs. Figure 11 highlights several key results in compar-ing our simulations with observations. First, the time-averaged R e of all of these galaxies are consistent withthe average R e of observed galaxies at the same M star .Thus, even for these highly bursty galaxies, our simula-tions produce correct sizes. Second, the significant short-timescale fluctuations in R e for our simulated galaxies re-mains within the observed scatter. Thus, as dramatic astheir size variations are, our simulations do not overpre-dict the amount of scatter in R e . Finally, and most inter-estingly, the short-timescale (within just a few 100 Myr)variation in R e that galaxies with M star ≈ − . M (cid:12) experience is sufficient to account for a large fraction ofthe observed scatter in R e at fixed M star . This impliesthat, at least for isolated galaxies at this critical rangeof M star ≈ − . M (cid:12) , the observed scatter in radius atfixed M star does not simply reflect systematic differencesin long-term evolutionary histories, but it also reflects thesize fluctuations that individual galaxies undergo withinjust a few 100 Myr .In the critical mass range, the scatter in the radii ofobserved galaxies is consistent with being driven primar-ily by short-timescale fluctuations. These are smallerin m12i, suggesting that the observed scatter at highermasses may be driven primarily by a diversity of long-term evolutionary histories. Given our limited sample,we are unable to determine robustly whether more var- ied long-term evolutionary histories contribute signifi-cant scatter at lower masses. COMPARISONS WITH PREVIOUS WORK5.1.
Relation to Dark Matter Core-Creation
The transfer of energy from gas outflows/inflows tocollisionless particles is well-studied in the context of the“core-cusp” (Moore 1994; Oh et al. 2015) and related“too-big-to-fail” (Boylan-Kolchin et al. 2011; Jiang & vanden Bosch 2015) problems, which express the discrepancybetween the steep central density profiles (“cusps”) pre-dicted by ΛCDM models and and the flatter density pro-files (“cores”) observed in many nearby low-mass galax-ies. Recently, a number of studies (for example, Read& Gilmore 2005; Pontzen & Governato 2012; Governatoet al. 2012; Di Cintio et al. 2014; O˜norbe et al. 2015;Chan et al. 2015) have shown that including stellar feed-back in simulations can significantly alter dwarf galax-ies’ density profiles, removing dark matter from the cen-tral regions and potentially reconciling the predictionsof ΛCDM models with observations, at least for galaxieswith M star = 10 − . M (cid:12) ( M halo ≈ − . M (cid:12) ).We find similar dynamics for the stellar population,which is not surprising given that both stars and darkmatter behave as (effectively) collisionless fluids, so thata time-varying gravitational potential will transfer en-adial Migration in Low-Mass Galaxies 13 m i g r a t i o n [ k p c ] › ∆ r fi › | ∆ r | fi log M / M fl m i g r a t i o n / R m a ss Figure 9.
Average radial migration of stars since their formationfor all galaxies in our sample. Top panel shows migration in phys-ical kpc, while bottom shows migration scaled by each galaxy’s90%- M star radius, R , at z = 0. Black and red points showaverage of the net and absolute radial distance, respectively, with asmall horizontal offset for clarity. For each galaxy, the point showsthe average across the 40 snapshots from z = 0 . M star ≈ − . M (cid:12) . Our highest- andlowest-mass galaxies shows weaker systematic outward migrationbut do show non-trival absolute radial migration (combination ofinward and outward migration), especially as scaled to R .This significant absolute migration of our lowest-mass galaxy islikely the combined result of scattering and stars on radial but sta-ble orbits, since the stellar distribution of these galaxies does notchange on short timescales at late times. ergy to both species, regardless of particle mass (Lynden-Bell 1967; Henriksen & Widrow 1997; Levin et al. 2008).Across a wide range of galaxy M star , the scale lengthsof observed and simulated stellar density profiles are ap-proximately equal to the characteristic sizes of galaxies’dark matter cores (Gentile et al. 2009; Governato et al.2010; Brooks et al. 2011). This relation also holds truein our simulations: the effective radii R e of all of ourgalaxies with M star < M (cid:12) are equal to the galaxies’core radii r core to within a factor of < if stellar feedback creates dark-matter coresin low-mass galaxies, it also should significantly changethe kinematics and spatial distribution of stars . Thisconnection can be seen clearly in Figure 4: the time-evolution of the mean stellar migration is very similar tothat of α, the central slope of the dark matter densityprofile.The mass-scaling of radial migration shown in Figure 9supports this picture, though larger simulated samplesare needed to delineate the mass dependence in detail. log M / M fl ∆ ag e [ G y r ] log M / M fl ∆ l og ( Z / Z fl ) [ d e x ] formationz = 0 Figure 10.
Radial gradients in stellar populations for all galaxiesin our sample, for average stellar age (top) and total metallicity(bottom). Black points show the difference between the averageage/metallicity of stars at R and at the galactic center, suchthat ∆ P = P ( r = R ) − P ( r = 0), with radii measured at z = 0. Red points show the same but using stars’ radius at for-mation , that is, if stars did not migrate from where they formed.For our lowest- and highest-mass galaxies, where radial migrationis weakest, the age gradients remain positive and negative, respec-tively, such that the gradients at z = 0 largely reflect the true un-derlying gradients at formation. However, at intermediate masses,the significant outward migration typically inverts the intrinsicallynegative age gradients at formation, such that they appear posi-tive at z = 0. Metallicity gradients show similar trends: while allgalaxies have negative metallicity gradients (more metal-poor starsat larger radii) at z = 0, this reflects an inversion of the underlyinggradient at formation for most galaxies with M star ≈ − . M (cid:12) . Both the time-averaged migration and the correspondingscatter are most significant at M star ≈ − . M (cid:12) (halo M ∼ − . M (cid:12) ), with the effect weaker at bothhigher and lower masses. This scaling is similar to that ofdark matter core sizes found by Chan et al. (2015), whostudied the same simulated galaxies, and both Di Cintioet al. (2014) and Tollet et al. (2015), who studied largersamples of simulated galaxies in the same mass range.Galaxies with M star ≈ − . M (cid:12) have the optimalbalance between shallow gravitational potentials, highgas fractions, sufficiently high star-formation efficiency,and bursty SFRs to allow for significant transfer of en-ergy between gas and collisionless particles. Althoughhigher-mass galaxies have more efficient star formation,their deep gravitational potentials retain most of theirgas during periods of high star formation (Muratov et al.2015; Christensen et al. 2015; Tollet et al. 2015), sothey have fewer coherent outflows and more stable SFRsat late cosmic times. Conversely, while galaxies with M star (cid:46) M (cid:12) have bursty SFRs, they have low star-formation efficiency as a result of gas expulsion via cos-mic reionization and stellar feedback, so they do not formenough stars to generate the feedback energy needed tosignificantly change their gravitational potentials at late4 El-Badry et al. log M / M fl R e [ k p c ] observed medianobserved middle 68%observed middle 95%FIRE snapshots Figure 11.
Half-light radius, R e , versus stellar mass, M star .Black curve and shaded regions show the median, 1 σ , and 2 σ scatter for observed isolated galaxies, which we obtain from theNASA-Sloan Atlas (NSA). Different colored points show 7 of oursimulated galaxies (m10.1, m10.2, m10.6, m11, m11v, m11.2 andm12i), sampled across the 40 snapshots from z = 0 . ≈ . M star ≈ − . M (cid:12) ,feedback-driven outflows cause the radius of an individual galaxy tofluctuate by more than a factor of 2 over just a few 100 Myr. Thus,the short-timescale evolution of individual galaxies can account formuch of the observed scatter in radius at fixed M star . times. Consistent with this explanation, Chan et al.(2015) showed that the total energy injected by super-novae alone is sufficient to create dark-matter cores ingalaxies with M star (cid:38) M (cid:12) , while at significantlylower masses, only small cores can be created even if100% of feedback energy is transferred to dark matter.Radial migration of both stars and dark matterare driven by different dynamics on short and longtimescales. On short timescales, migration is semi-periodic and nearly reversible: though stars migrate out-ward during outflow periods, they migrate back towardthe galactic center as gas cools and the potential con-tracts (see Figures 3 and 4). Pontzen & Governato (2012)showed that such expansion is exactly reversible in theadiabatic limit, when changes in the potential occur ontimescales which are long compared to the dynamicaltime. On the other hand, when outflows change the po-tential rapidly relative to the dynamical time, energy canbe added permanently to the orbits of collisionless par-ticles, be they dark matter or stars. Several studies (forexample, Pontzen & Governato 2012; Ogiya & Mori 2014;O˜norbe et al. 2015; Chan et al. 2015; Tollet et al. 2015)found that, while individual outflow episodes temporarilycan move dark matter outward on short timescales, manyrepeated, semi-periodic oscillations are required to exca-vate lasting cores. Radial migration is strongest for theoldest stars, which have undergone the largest number ofinflow-outflow cycles; this generates positive populationgradients rather than simply mixing stars of all ages.We do, however, note one key difference between thekinematics of stars and dark matter: the migration ofyoung stars can be even stronger on short timescales, be-cause outflowing/inflowing gas can remain star-forming,producing young stars that directly inherit the strongkinematic fluctuations of the feedback-driven gas.Overall, the similarities between the physical drivers of core creation and stellar migration imply that stel-lar kinematics and morphologies should provide strongobservational tests for baryonic solutions to the “core-cusp” and “too-big-to-fail” problems, as we will discussin Section 6.2.5.2. Comparison with Theoretical Work
Bursty SFHs in low-mass galaxies are characteristicof our FIRE simulations and other simulations that useexplicit treatments of stellar feedback at high resolu-tion with a high density threshold for star formation, n SF (cid:38)
10 cm − (for example, Shen et al. 2014; Madauet al. 2014; Kawata et al. 2014; Hu et al. 2015; Sparreet al. 2015; Hayward & Hopkins 2015). Schroyen et al.(2013) investigated the relation between n SF and theSFHs of low-mass galaxies in idealized simulations in-cluding supernova feedback, finding that a high densitythreshold results in clumpier gas and more clustered starformation as well as increased scattering of stars off gasclumps, leading to moderate stellar migration. Our sig-nificant radial migration is consistent with this interpre-tation, though we find that migration in our simulationsis primarily the result of global fluctuations in the po-tential rather than isolated scattering events.Using an idealized simulation of a dwarf galaxy,Teyssier et al. (2013) found that strong supernova feed-back leads to the creation of a dark matter core, andthis also creates a thick stellar disk that is kinematicallyhot ( v star /σ star ∼ ∼
70% of the observed isolated star-forming dwarfgalaxies in the Local Group have dispersion-supported( not rotation-supported) stellar populations.Thus, the stellar kinematics of low-mass galaxies inFIRE simulations largely agree with observations in theLocal Group. A larger sample of simulations is neededto determine whether the FIRE simulations can also re-produce small fraction of observed rotation-supportedlow-mass galaxies. It is possible that the FIRE simu-lations somewhat overpredict the burstiness of star for-mation at late times, as Sparre et al. (2015) found thatthe fraction of temporarily quenched isolated galaxiesat M star < M (cid:12) in the FIRE simulations is higher(roughly 30%) than the nearly 0% observed in nearbyisolated galaxies (Geha et al. 2012; Karachentsev et al.2013).Radial migration in low-mass galaxies also has beenstudied in the context of the formation of stellar halos.Maxwell et al. (2012) studied a simulated galaxies with M star ( z = 0) ∼ × M (cid:12) and found that, between z = 8and z = 5, highly localized and episodic stellar feedbackdrove rapid gas flows that in turn drove stellar kinematicsin the central ∼
100 pc. This caused stars that formedin the central regions to migrate outward significantly.However, they found that migration became significantlyless efficient by z = 5 and predicted that it would becomenegligible at late times. Similarly, Stinson et al. (2009)found significant radial migration in the oldest stellarpopulations of simulated galaxies with M star ( z = 0) =10 − M (cid:12) , suggesting that radial migration, rather thanaccretion events, might be responsible for the creationadial Migration in Low-Mass Galaxies 15of the stellar halo. Consistent with this result, Figure 5showed that the oldest stars ( > ∼ R e ( z = 0),from the radius where they formed; many of these starslikely would be classified as part of the stellar halo.Finally, Ben´ıtez-Llambay et al. (2015) recently studiedthe origin of observed population gradients in simulateddwarf galaxies using the CLUES cosmological zoom-insimulation of a Local Group analogue. They found thatthe observed positive gradients of stellar age with radiusin dwarf galaxies can be generated via major mergers,which heat old stellar populations and trigger new burstsof centrally concentrated star formation. Our results areconsistent with this possibility; however, the low-massgalaxies that we study have relatively calm merger his-tories, and despite this, almost all of them form posi-tive age gradients. Thus, our results imply that positivegradients in stellar age can form even in the absence oflate-time mergers, via stellar feedback and bursty starformation. 5.3. Comparison with Observations
Low-mass galaxies in the local Universe exhibit signif-icant scatter in their SFRs, consistent with high vari-ability on short timescales, and many show evidence formultiple episodes of star formation separated by periodsof quiescence ranging from a few 10’s of Myr to severalGyr (for example, Dolphin et al. 2003; Rizzi et al. 2004;Skillman 2005; Lianou & Cole 2013; de Boer et al. 2014;Weisz et al. 2014; VandenBerg et al. 2015; Geha et al.2015). Most of these star-forming galaxies are relativelyisolated at z = 0, indicating that starbursts are triggerednot just by interactions. Lee et al. (2009) found that 6 +4 − percent of L (cid:46) . L (cid:63) galaxies in the local volume are cur-rently undergoing a starburst. Weisz et al. (2012) usedH α -to- U V flux ratios to constrain bursty star formationin 185 galaxies, finding that low-mass galaxies are bestdescribed by SFHs with burst amplitudes of ∼
30 and in-terburst spacings of ∼ . Sparre et al. (2015)compared galaxies from the FIRE simulations to obser-vations using the same H α -to- U V ratios and found thatburst spacings and amplitudes from the simulations werebroadly consistent with observationally-inferred values,though the FIRE simulations may somewhat overpredictburst amplitudes at lower masses.Almost all low-mass galaxies in the local Universe havenegative metallicity gradients. Several studies (for exam-ple, Mehlert et al. 2003; Spolaor et al. 2009; Kirby et al.2011; Schroyen et al. 2013; Vargas et al. 2014; Pilyu-gin et al. 2015) find an average metallicity gradient of∆[Fe / H] ∼ − . ∼ . M star ≈ − . M (cid:12) would be nearly0. SUMMARY AND DISCUSSION6.1.
Summary
Using the FIRE suite of cosmological zoom-in hydro-dynamic simulations of isolated low-mass galaxies across M star ( z = 0) = 2 × − × M (cid:12) , we have exploredthe effects of stellar feedback and bursty star formationon stellar kinematics, radial migration, size evolution,and population gradients at late cosmic times, wheresuch low-mass galaxies are observable. In galaxies with M star ≈ − . M (cid:12) , stellar feedback frequently drivesoutflows of significant gas mass well beyond the stellarradius; these cool and fall back into the galaxy centeron timescales of a few 100 Myr. These outflow/infall cy-cles occur semi-periodically many times throughout thesegalaxies’ evolutionary histories and drive strong fluctua-tions in the galactic potential, leading to dramatic effectson the stellar population. We summarize our main re-sults as follows.1. Physical origin of stellar migration : Stars in low-massgalaxies experience significant radial migration viatwo related processes. First, outflowing/inflowing gasclouds can remain star-forming, producing young starsthat inherit the outflowing/infalling kinematics of gas.Second, gas outflows/inflows drive strong fluctuationsin the overall galactic potential, and in response, theorbits of stars of all ages expand and contract overshort timescales and gradually are heated over longtimescales. These physical processes are fundamen-tally different from the scattering processes known tocause radial migration in massive disk galaxies.2.
Timescales of stellar migration : Stellar radial migra-tion occurs over both short (a few 100 Myr) and long(a few Gyr) timescales. Short-timescale fluctuationsin the potential result in rapid changes in kinemat-ics and radial migration for all stars within a few100 Myr, comparable to the galaxy’s dynamical time.Young stars experience the strongest short-timescalemigration, typically (cid:38) cumu-lative effects of many repeated semi-periodic fluctu-ations gradually heat stellar orbits, driving perma-nent and coherent outward migration of stars overGyr timescales. Thus, the amount of stellar migrationdepends on stellar age: the oldest stars, having ex-perienced the most outflow/inflow cycles, exhibit thestrongest systematic outward migration since forma-tion.3.
Impact on radial gradients of stellar populations : Stel-lar migration can systematically change radial gradi-ents of stellar age and metallicity because the amountof outward migration depends on stellar age. For al-most all of our galaxies at M star ≈ − . M (cid:12) , stellarmigration inverts true underlying age gradients fromnegative to positive, or metallicity gradients from posi-tive to negative, by z = 0. This means that populationgradients observed at z = 0 do not necessarily reflectthe intrinsic gradients at formation, and that radialSFHs inferred from present-day populations gradients,as common in galactic-archaeology studies, may besignificantly biased.6 El-Badry et al.4. Fluctuations of galaxy sizes : Our simulations produceconsistent half-light radii ( R e ) of galaxies as comparedwith observations. Short-term stellar migration leadsto fluctuations in effective radius by factors of 2 − R e at fixed M star ,which suggests that the observed scatter does not justreflect systematic differences in long-term evolution-ary histories, but it also reflects the size fluctuationsthat individual galaxies undergo within just a few 100Myr.5. Dependence on galaxy mass : All of these effects arestrongest in galaxies with M star ( z = 0) ≈ − . M (cid:12) (halo M halo ∼ − . M (cid:12) ). This is the same massrange where stellar feedback has been shown to mostefficiently produce dark matter cores. Since migra-tion and coring are driven by the same physical pro-cesses, galaxies with significant feedback-driven coresalso should have experienced significant stellar migra-tion. Although galaxies with lower mass also experi-ence similarly bursty SFHs, their higher dark-matterfractions and lower overall SFRs (in particular, lowSFR /M halo ) lead to weaker fluctuations in the galacticpotential, with weak effects on stellar kinematics andradial migration. More massive galaxies have deeperpotential wells and lower gas fractions within R e , sothey do not experience strong coherent fluctuations instellar kinematics.6. Stellar kinematics provide a strong test to constrainfeedback models : Our stellar feedback models predictstrong effects on stellar kinematics and sizes of low-mass galaxies. If stellar feedback drives dark-mattercoring, galaxies with large cores also should have expe-rienced significant stellar migration. Detailed studiesof nearby dwarf galaxies, with resolved spectroscopyand/or proper motions of individual stars, thereforecan provide strong tests of our model predictions, aswe outline below.6.2.
Discussion: Implications for Observational Testsof Stellar Feedback
We have shown that stellar feedback can cause dra-matic changes in the radial kinematics and distributionof stars in isolated galaxies with M star ≈ − . M (cid:12) .These effects are analogous to feedback-driven coring ofsuch galaxies’ dark-matter profiles, as explored in previ-ous works. Because the distribution and kinematics ofstars (and gas) are more directly observable than (in-ferred) dark-matter mass profiles, our results imply thatdetailed observations of resolved stellar populations andkinematics, which are obtainable for nearby galaxies, canprovide strong tests of stellar feedback models. We out-line a few possible observational tests, which we will in-vestigate in more detail in future work. Biased stellar kinematics : Figure 3 (bottom) showedthat because young stars inherit the kinematics of out-flowing/infalling gas from which they form, young starscan have biased kinematics as compared with older stars.In addition, Figure 3 suggested that the observed ra-dial velocity (or line-of-sight velocity dispersion) shouldbe higher in actively star-forming galaxies than in post-starburst galaxies with extended outflows. Indeed, we find that the velocity dispersion falls by ∼
40% duringoutflow periods, when stars are more weakly bound. Fi-nally, at any stage of evolution, our results suggest thatthe orbits of stars in low-mass galaxies may be stronglyanisotropic, in particular, strongly radially biased.
Gas outflows : Figure 2 showed that significant neutralgas is blown beyond the outskirts of the stellar distribu-tion following starburst episodes. First, these outflowsshould be observable directly in nearby post-starburstgalaxies. Several of the late-time outflows in m10.6, m11,m11v, and m11.2 carry more than 10 M (cid:12) of neutral hy-drogen beyond R , which is at least 10 × more thanthe lower limits of resolved HI interferometric observa-tions of nearby galaxies (Hunter et al. 2012). Second,one could compare the short-timescale fluctuations in HImass in our simulated galaxies over a single starburst cy-cle to the scatter in observed HI mass at fixed M star (see,for example, Bradford et al. 2015). Relation between population gradients and cores : Fig-ure 10 showed that stellar feedback dramatically can af-fect and even invert age and metallicity radial gradientsin low-mass galaxies. Although our simulated galaxiesexperience inside-out growth, radial migration erases orinverts these population gradients because old stars mi-grate outward more than young stars. Because the phys-ical processes responsible for stellar migration are thesame processes that produce dark matter cores, our re-sults appear to imply that, at fixed M star , galaxies withstronger cores will have more positive age gradients andmore negative metallicity gradients than those with cuspsor weaker cores. However, a larger suite of simulations,with a greater diversity of late-time population gradients,is needed to make this prediction concrete, since all thelow-mass galaxies we study here develop both positiveage gradients and strong dark matter cores. Stellar halos of low-mass galaxies : Figure 5 showedthat the oldest stars ( > ∼ R e ( z = 0),from where they formed, and Figure 7 showed that theoldest stars (on average) are at the largest radii at z =0. Many of these oldest stars migrated sufficiently farthat they likely would be classified as part of the stellarhalo. Thus, our results suggest that the stellar halos ofsuch galaxies may provide observational probes of theearliest stars that formed near the core, as has also beensuggested by studies that find radial migration at highredshift (Stinson et al. 2009; Maxwell et al. 2012).Our analysis represents an early examination into stel-lar kinematics and radial migration in low-mass galaxies.These results motivate more comprehensive theoreticalstudies, with larger simulation samples, to delineate fur-ther the dependence on mass and formation history, aswell as the scatter across populations.We thank Jeremy Bradford for sharing observationaldata and Coral Wheeler and Frank van den Bosch foruseful discussions and comments. We also thank thereviewer for helpful comments. KE acknowledges sup-port from the Caltech SURF program. ARW grate-fully acknowledges support from the Moore Center forTheoretical Cosmology and Physics at Caltech via aMoore Prize Fellowship, and from Carnegie Observa-tories via a Carnegie Fellowship in Theoretical Astro-adial Migration in Low-Mass Galaxies 17physics. MG acknowledges a fellowship from the JohnS. Guggenheim Memorial Foundation. Support for PFHwas provided by an Alfred P. Sloan Research Fellowship,NASA ATP Grant NNX14AH35G, and NSF Collabo-rative Research Grant REFERENCESBen´ıtez-Llambay, A., Navarro, J. F., Abadi, M. G., et al. 2015,ArXiv e-prints, arXiv:1511.06188Binney, J., & Lacey, C. 1988, MNRAS, 230, 597Blanton, M. R., Kazin, E., Muna, D., Weaver, B. A., &Price-Whelan, A. 2011, AJ, 142, 31Boylan-Kolchin, M., Bullock, J. S., & Kaplinghat, M. 2011,MNRAS, 415, L40Bradford, J. D., Geha, M. C., & Blanton, M. 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