Stellar Haloes As a Sensitive Probe of Supernova Feedback

MNRAS 000, 000–000 (0000) Preprint 19 March 2021 Compiled using MNRAS LATEX style ﬁle v3.0

Is There a Missing Outskirts Problem? Stellar Haloes as a Sensitive Probe of Supernova Feedback

B. W. Keller? Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchofstraße 12-14, D-69120 Heidelberg, Germany

19 March 2021

ABSTRACT Recent comparisons between the stellar haloes of simulated Milky Way-mass galaxies and observations of similar objects have identified a significant tension between the masses of simulated and observed stellar haloes. Simulated stellar haloes appear to have both total masses and surface density profiles 1 2 dex higher than observed galaxies. In this paper, we compare two suites of 15 simulated− Milky Way-like galaxies, each drawn from the same initial conditions and simulated with the same hydrodynamical code, but with two different models for feedback from supernovae. We find that the MUGS simulations, which use an older “delayed-cooling” model for feedback, suffer from the same problems as other simulations examined in the literature, with median surface densities well above observational constraints. The MUGS2 simulations, which instead use a new, physically-motivated superbubble model for stellar feedback, have significantly reduced stellar halo masses and surface densities ( 25 times lower on average compared to MUGS stellar haloes), and generally match both the∼ median surface density as well as the diversity of structure seen in observed stellar haloes. We examine how feedback produces differences in the assembly of the stellar halo, both through in-situ stars scattered out of the disc by high-redshift mergers and in ex-situ stars stripped from accreted haloes. We conclude that there is no “missing outskirts” problem in cosmological simulations, so long as supernova feedback is modelled in a way that allows it to efficiently regulate star formation in the progenitor environments of stellar haloes. Key words: – galaxies: haloes – galaxies: formation – galaxies: star formation – galaxies: structure – galaxies: evolution – methods: numerical

1 INTRODUCTION Many solutions to these problems have been proposed, from reion- ization regulating star formation in low-mass dwarfs (Bullock et al. The stellar haloes of galaxies provide an interesting laboratory for 2000; Gnedin 2000) to enhanced tidal disruption by the stellar disc testing theories of cosmological galaxy formation. The long dy- (Kelley et al. 2019). The advent of higher-resolution cosmological namical times (e.g. Bullock & Johnston 2005) and high stellar ex- simulations, using better models for “strong” stellar feedback (e.g. situ fractions (e.g. Font et al. 2011) outside of the stellar disc can Okamoto et al. 2010; Nickerson et al. 2013; Sawala et al. 2016; allow the structures formed by the accretion and tidal disruption Akins et al. 2020) has produced a growing consensus that the issues (Bullock & Johnston 2005) of progenitors to persist for a signiﬁcant of satellite abundances around MW-like galaxies is largely solved fraction of a Hubble time, preserving a relic of the accretion history

arXiv:2103.09833v1 [astro-ph.GA] 17 Mar 2021 when the full range of baryonic processes (star formation and feed- of the galaxy. However, the low stellar mass (relative to the disc) back primarily) are accounted for. Recently, a comparison between of stellar haloes (Merritt et al. 2016) makes them difficult to re- a new survey of stellar haloes around MW mass galaxies and the solve in cosmological simulations, and their extremely low surface Illustris-TNG100 cosmological simulations (Merritt et al. 2020) brightness makes them exceptionally difficult to observe. Some of has pointed towards a tension between observed stellar haloes and the most heavily studied issues in galaxy formation over the past simulated stellar haloes. Merritt et al.(2020) has found that the decades have related to the abundance and luminosity of satellites stellar haloes in Illustris-TNG100 simulated galaxies have signifi- within the halo of Milky Way (MW)-like galaxies. The “missing cantly higher surface densities than observations from Merritt et al. satellites” problem (Klypin et al. 1999) and the “Too-Big-To-Fail” (2016), a problem they dub “missing outskirts”. problem (Boylan-Kolchin et al. 2011) both relate to an overabun- dance of dwarf satellites in simulations compared to observations. The most precise observations of stellar haloes are those of our own galaxy and of Andromeda (M31). For these two L* galaxies, we have detailed censuses of the positions (e.g. Searle & Zinn ? Email: benjamin.keller ‘at’ uni-heidelberg.de 1978), ages (Helmi et al. 1999, e.g.), metallicities (e.g. Ibata et al.

2001), and kinematics (e.g. Yanny et al. 2003) for thousands of in- resolution and physical fidelity of large, cosmological galaxy sim- dividual stars within the stellar halo (now tens of thousands with ulations has allowed the study of stellar haloes from self-consistent the advent of Gaia). However, surveys of other galaxies have sug- models of galaxy formation, including both hydrodynamic effects gested that both the MW and M31 have relatively extremal stellar and radiative processes, as well as star formation and stellar feed- haloes, with M31 having an unusually massive stellar halo com- back (e.g. Font et al. 2011; Pillepich et al. 2014; Sanderson et al. pared to the MW’s unusually light stellar halo (Deason et al. 2013; 2018; Monachesi et al. 2019; Obreja et al. 2019; Font et al. 2020). D’Souza et al. 2014; Harmsen et al. 2017). Surveys of extragalactic Different simulation studies of stellar haloes have all relied on dif- stellar haloes have been primarily limited by the low surface bright- ferent models for star formation and stellar feedback, a wide range ness of stellar haloes, typically 8-10 mag/arcsec2 lower than the of numerical resolutions, and different simulation volumes. Thus, stellar disc. Studies of stellar haloes around other galaxies have typ- comparing different models to observations can allow us to tease ically relied on either stacking (D’Souza et al. 2014, for example, out the impact these various choices and assumptions have on the stacked ∼ 45, 000 SDSS galaxies to study their average stellar halo assembly of different stellar populations within the galaxy. In gen- properties) or on deep, “pencil-beam” studies that observe only a eral, there has been a growing concern that simulated stellar haloes small fraction of the covering area of a galaxy’s halo (Harmsen are too massive (Merritt et al. 2016; Sanderson et al. 2018; Monach- et al. 2017, for example, used the Hubble Space Telescope (HST)’s esi et al. 2019; Font et al. 2020), a problem that Merritt et al.(2020) Advanced Camera for Surveys (ACS) to examine the haloes along names the “missing outskirts” problem in their comparison to the the major and minor axis of six nearby disc galaxies). The advent Illustris-TNG simulations. of telephoto array telescopes, such as Dragonfly (Abraham & van In this paper, we reproduce the key results of Merritt et al. Dokkum 2014) and Huntsman (Horton et al. 2020) provide two (2020) using a set of paired simulations of 15 MW-like galaxies, critical features that make them ideal instruments for observing with each pair simulated using two different models for stellar feed- stellar haloes. The first, a feature of the advanced anti-reflection back from core-collapse supernovae (SNe). We demonstrate that coatings available in modern high-end photography lenses, is ex- the surface density and total mass of stellar haloes are highly sen- tremely low imaging noise, giving them the ability to probe surface sitive to the model of SN feedback used to simulate the galaxy. In brightnesses below ∼ 30 mag/arcsec2. The second, owing to their particular, we demonstrate that the impact of feedback on stellar construction from consumer/off-the-shelf photography equipment, haloes is much stronger than the impact on the total stellar mass, is a large field of view (∼ 10 deg2), which allows them to cover the which owes to the different assembly history of halo stars versus entire halo out to nearly a virial radius for most nearby L* galaxies. the stars that make up the majority of the stellar mass in the disc of These new telescope systems have lead to a revolution in low sur- the galaxy. face brightness observations, and have discovered new classes of unusual, low surface brightness galaxies (van Dokkum et al. 2015, 2018). The Dragonfly Nearby Galaxy Survey (DNGS) (Merritt et al. 2 METHODS 2016) imaged 8 nearby, MW-like galaxies down to a surface bright- 2.1 Simulations ness of 31 mag/arcsec2, measuring the stellar halo profiles and halo mass fractions. In their results, they found that the stellar In this paper, we compare matched pairs of cosmological zoom- halo fractions beyond 5 half-mass radii Rh were detectably lower in simulations of 15 MW-like L* galaxies with observations of than in a number of simulations. Measuring stellar halo fractions 8 galaxies from the DNGS. Each of the 15 pairs of galaxies is is a somewhat tricky matter, however, as Sanderson et al.(2018) simulated from the same initial conditions (ICs), derived from the demonstrated using simulations from the FIRE-2 and ELVIS suite. McMaster Unbiased Galaxy Simulations (MUGS) project (Stinson Because of the steep power-law density profile of stellar haloes et al. 2006). These simulations use a WMAP3 ΛCDM cosmol- −1 −1 (with density slopes of −2 to −4, Font et al. 2011), the choice ogy with H0 = 73 km s Mpc , Ωm = 0.24, ΩΛ = 0.76, of inner cut for integrated mass measurements of the stellar halo Ωb = 0.04, and σ8 = 0.76 (Spergel et al. 2007). The DM reso- 6 can have a significant impact on the integrated stellar halo mass lution of the simulations is 1.1 × 10 M per particle, while the 5 and halo mass fractions. Merritt et al.(2020) sidesteps this issue by baryonic resolution is 2.2 × 10 M . All particles use a uniform comparing the radial profiles of stellar surface brightness and mass softening length of 312.5 pc. surface density to simulated galaxies from the Illustris-TNG project The pairs of simulations we compare were run as part of (Pillepich et al. 2018). These results show that the stellar haloes of the MUGS and MUGS2 simulation projects (Stinson et al. 2010 simulated galaxies, beyond radii of ∼ 30 kpc, are systematically and Keller et al. 2016 respectively). They share identical initial higher in the entire population of simulated galaxies, despite care- conditions and parameters used in the gravity solution, but fea- ful a “apples-to-apples” comparison of mock observations to the ture a number of differences in the hydrodynamic solver and the actual DNGS data. sub-grid prescription for star formation and feedback. The orig- While sparse, observational data for stellar haloes in MW- inal MUGS galaxies used a “traditional” pressure-density pre- mass galaxies has still been a useful tool for comparison to both scription for Smoothed-Particle Hydrodynamics (SPH) in the code semi-analytic models and numerical simulations. These compar- GASOLINE, which has subsequently been found to artificially sup- isons have sought to test our predictions on the assembly of stel- press mixing in shearing and turbulent flows (Agertz et al. 2007). lar haloes in the ΛCDM framework. Many early models use an- MUGS2 is the first set of cosmological simulations produced using alytic or semi-analytic models, combined with “particle tagging” the new GASOLINE2 code (Wadsley et al. 2017). GASOLINE2 in- approaches applied to collisionless N-body simulations (e.g. Bul- cludes a treatment for turbulent diffusion (Wadsley et al. 2008), lock & Johnston 2005; Cooper et al. 2010, 2017). In these ap- improved time-step calculation (Saitoh & Makino 2009), and a proaches, dark matter (DM) particles are tagged as carrying stel- new treatment for the calculation of P dV forces (Wadsley et al. lar mass into the galaxy halo, based on their kinematic and host 2017). While the hydrodynamics improvements in MUGS2 result halo properties (e.g. Cooper et al. 2010). Recently, the improving in a more accurate treatment of the interstellar medium (ISM) and

MNRAS 000, 000–000 (0000) Probing Feedback with Stellar Haloes 3

circumgalactic medium (CGM), the primary differences arise due MUGS MUGS2 MUGS MUGS2 GalaxyID M200 M M R R to the difference in sub-grid feedback models between MUGS and ∗ ∗ 1/2 1/2 MUGS2. g7124 36.6 4.98 0.5 1.37 4.72 In the original MUGS sample, SN feedback is modelled using g5664 47.7 4.83 0.9 1.57 3.81 a delayed-cooling “blastwave” mechanism (Stinson et al. 2006). g8893 58.0 6.21 0.7 1.82 8.18 This model is designed to prevent numerical overcooling by dis- g1536 64.9 8.28 1.9 1.74 6.53 abling radiative cooling in feedback-heated gas until the end of g21647 74.4 7.84 1.2 4.25 3.02 the momentum-conserving snowplow phase. Alternatively, in the g422 76.2 7.55 1.5 2.94 7.10 MUGS2 simulations, SN feedback is modelled using the Keller g22437 85.2 7.35 9.0 1.76 0.68 et al.(2014) “superbubble” model. In this model, radiative cool- g22795 85.2 6.54 10.6 1.52 0.94 g3021 97.8 10.44 3.6 3.60 4.11 ing is included self-consistently for SN-heated gas by temporarily g28547 98.5 12.36 1.6 53.75 6.57 including a two-phase component within recently heated gas parti- g24334 102.2 10.95 2.6 6.35 5.89 cles. The two isobaric phases each calculate their cooling rates us- g4145 119.5 9.51 15.0 2.25 1.19 ing a separate density and temperature, and mass is evaporated from g25271 125.5 10.49 15.6 1.73 1.21 the cold “shell” phase into the hot “bubble” phase using the clas- g15784 203.2 11.40 13.0 2.83 1.53 sical evaporation rates derived in Cowie & McKee(1977). Once g15807 214.7 17.57 21.4 4.00 1.03 the entirety of a two-phase particle’s cold shell is evaporated, it can continue evaporating neighbours using a stochastic evaporation Table 1. Basic properties of the MUGS and MUGS2 galaxies compared method described in Keller et al.(2014). The difference in strat- in this study. The halo masses M200 shown are the MUGS2 halo masses, egy between these two models can be summarized as: “blastwave” while the stellar masses and half-mass radii are shown separately for each galaxy. As can be seen, below a halo mass of M ∼ 1012 M , the feedback seeks to prevent numerical overcooling by disabling cool- 200 MUGS2 galaxies produce significantly less stellar mass than the MUGS ing for some appropriate time, while “superbubble” feedback pre- galaxies. These galaxies also tend to be less compact, with stellar half-mass vents it by heating only the correct amount of gas. In Keller et al. radii typically more than twice as large as the MUGS equivalent. The large (2014) and Keller et al.(2015), we demonstrated that superbubble outlier in stellar radii for the MUGS example of g28547 is due to a variation feedback drives significantly more mass-loaded galactic outflows in the timing of a major merger that occurs slightly earlier in MUGS2 than 10 than the blastwave model, and can reduce the overall star forma- in MUGS. All mass units are given in 10 M , and all length units are tion rate and bulge fraction in both isolated and cosmological sim- given in kpc. ulations of MW-like galaxies. As can be seen in table1 and figure1, the MUGS galaxies with “blastwave” feedback produce more stars 12 than their MUGS2 pairs below 10 M , while both models produce comparable stellar masses above this critical threshold (Keller et al. 2016). The range of stellar masses covered by MUGS and 11 MUGS2 also covers the range of galaxies observed in the DNGS. 10

In all instances here, we deﬁne the virial radius R200 (and the en- ) closed virial mass M ) as the radius around the halo such that the

200 M ( enclosed density is 200 times the critical density (ρ = 200ρcrit). ∗ In both the MUGS and MUGS2 simulations, haloes were found in M each of the simulations using the Amiga Halo Finder (AHF; Knoll- 10 mann & Knebe 2009). 10 Stellar Mass

2.2 Stellar Surface Density Maps MUGS Merritt et al.(2020) considers a number of potential observa- MUGS2 tional and numerical effects in comparing observations to mock Behroozi+ 2013 SMHMR 109 stellar maps from the Illustris-TNG simulations (Pillepich et al. 1012 2018). Simply radially binning star particles will of course not Halo Mass M200(M ) allow a comparison to 2D image maps, and will suffer from discreteness noise in the lower-density regions. Discreteness noise is somewhat less important for the higher baryonic mass resolution Figure 1. Stellar mass to halo mass relation in the MUGS, MUGS2, and 6 MUGS simulations we analyze here (1.4×10 M in TNG100 vs. DNGS galaxies. DNGS does not measure halo masses, but the stellar 5 2.2 × 10 M in MUGS/MUGS2), but for purposes of comparison masses are shown with the green dashes along the left side of the panel. we will follow the strategy of Merritt et al.(2020). Using the built- The abundance-matched SMHMR from Behroozi et al.(2013) is shown as in analysis features of PYNBODY (Pontzen et al. 2013), we generate the dashed black curve, with one-sigma uncertainties in the grey region. smoothed 2D column density maps of stellar mass, using a cubic As can be seen, the MUGS galaxies consistently overproduce stars, while MUGS2 galaxies regulate star formation below a characteristic halo mass spline kernel, with an adaptive smoothing length set by the dis- 12 tance to the 64th neighbour particle. These methods are designed of 10 M , beyond which SN feedback becomes inefﬁcient. to mimic the SPH smoothing operations, and produce smoothed maps of quantities comparable to those analyzed in Merritt et al. (2020). We use smoothed maps with pixel dimensions of 0.5 kpc, as is used in Merritt et al.(2020). To further follow Merritt et al. (2020), we centre our galaxies at the deepest point in each halo’s potential well, but do not rotate the galaxies to orient the disc either

MNRAS 000, 000–000 (0000) 4 B.W. Keller edge or face on, giving each galaxy an effectively random orien- in the left panel of figure3, and g28547 in the centre panel of the tation. For a brief discussion of the (non-) importance of galaxy same figure). Interestingly, the MUGS2 version of g28547 appears orientation to our results, see appendixA. to have completed this merger, while in the MUGS case that merger will occur soon after z = 0. We leave a detailed examination of the individual assembly histories of these galaxies for a future study. 3 RESULTS The total mass within the stellar halo is difficult to measure in a self-consistent way for both observations and theory (see Sander- The galaxies in the MUGS/MUGS2 sample span the range of stel- son et al. 2018 for a thorough discussion of this issue). The criti- lar masses probed by DNGS, as is shown in figure1. As we pre- cal issue in this is that the strong negative slope of the stellar sur- viously demonstrated in Keller et al.(2015, 2016), superbubble face density means the choice of inner radius for the stellar halo feedback drives outflows much more effectively from galaxies be- will have significant impact on the stellar halo mass and the halo 12 low a characteristic 10 M halo mass, allowing them to better fraction. It is especially important to ensure that the volume that is match the stellar mass to halo mass relation (SMHMR) derived us- examined to measure the stellar halo mass is large enough that it ing abundance matching (Behroozi et al. 2013) and weak lensing excludes the outskirts of the disc. As the gas disc can extend much (Hudson et al. 2015) observations. For the most massive DM haloes further than the stellar half-light radius Rh (or even 5Rh), small in our sample, the stellar masses of both the MUGS and MUGS2 amounts of star formation in the outskirts of the disc can contam- galaxies are comparable, and lie above this relation, likely owing to inate the population of halo stars with rotationally-supported disc the absence of active galactic nucleus (AGN) feedback in MUGS stars. In order to sidestep this issue, we examine the masses of the and MUGS2 (Keller et al. 2016). outer stellar haloes in figure4, in a relatively distant spherical shell from 40 − 140 kpc. This is well beyond the edge of the gaseous disc, and is significantly further out than the edge of the stellar disc, 3.1 The Distinct Impact of Feedback in Diverse Stellar and is larger in every galaxy than the typical 5Rh used in Merritt Haloes et al.(2016), for example. While this makes comparing directly to The stellar surface density as a function of radius for the DNGS observations difficult (only one of the DNGS observations extends sample, as well as MUGS and MUGS2 is shown in Figure2. As can beyond 60 kpc), it allows us to make a clear comparison of exclu- be seen, in all three samples of observed/simulated galaxies there is sively halo stars in the simulations we examine. As both panels of significant galaxy-to-galaxy variance in the surface density of the figure4 show, the outer stellar haloes in the MUGS galaxies are stellar halo beyond ∼ 20 kpc. However, the median stellar halo in ∼ 1.5 dex more massive than in the MUGS2 case (the mean ratio the MUGS galaxies is ∼ 1 − 2 dex more dense beyond the inner of MUGS to MUGS2 outer stellar halo masses is 27 ± 14). De- halo ∼ 40 kpc. As is clear, the median trend in MUGS2 is much spite choosing a highly conservative radial cut for our outer halo closer to the observed stellar haloes from DNGS. Comparing these measurements, most MUGS outer haloes have masses much larger results to Figure 6 of Merritt et al.(2020), the stellar haloes of the than the DNGS constraints (the most halo-dominated of which has MUGS galaxies are qualitatively similar to those of the TNG100 fhalo = 0.049±0.023). The upper panel also shows that the lower sample. outer halo masses occur in both the MUGS2 galaxies with low 11 11 Figure3 shows the stellar halo each of the 15 pairs of galax- (< 10 M ) and high (> 10 M ) stellar masses. The MUGS2 ies from MUGS and MUGS2. Peaks in these profiles correspond to galaxies with high stellar masses have overproduced stars by a fac- satellites, and as is clear, the stellar haloes contain many more mas- tor of 2-3 compared to the expected values from the SMHMR (see sive satellites in the MUGS simulations compared to the MUGS2 also figure1 and the discussion in Keller et al. 2016). Despite this, simulations. However, the diffuse halo between these satellites also they still have outer stellar halo masses comparable to those which shows, in every galaxy, a markedly lower density in the MUGS2 match the SMHMR, indicating that the mechanism by which the simulations. This is evidence that the satellites we see in MUGS disc and bulge “run away” in the absence of AGN feedback does have not simply accreted with equal mass and then stripped in the not have any appreciable impact on the stellar halo. In the lower MUGS2 haloes, but have accreted with a much lower stellar con- panel, we show the relationship between the galaxy virial mass tent than their MUGS counterparts. The diversity of stellar haloes M200. Interestingly, in this case the slope of the relations appear we see in each of these galaxies is a relic of the diverse assem- to be comparable, with the outer halo masses linearly proportional bly histories of these simulated L* galaxies. Notably, as we show to the halo mass. As this figure shows, despite having a similar re- in Keller et al.(2015) and Keller et al.(2016), superbubble feed- lationship to halo mass, the normalization is much higher in MUGS back preferentially supresses star formation at high redshift, which (∼ 1%) than in MUGS2 (∼ 0.05%). we also examine later here in section 3.2. Only one of the pairs of MUGS/MUGS2 galaxies, g24334, has comparable halo surface 3.2 How Feedback Shapes Stellar Haloes density in both MUGS and MUGS2 (aside from the large dwarf satellite visible at r ∼ 80 kpc in the central panel of figure3). This The results we have shown thus far demonstrate that the “superbub- galaxy has a highly deformed morphology, as is visible in figure 1 ble” feedback in MUGS2 produces significantly less massive stel- of Keller et al. 2016. It is also one of the latest assemblers in the lar haloes compared to the “blastwave” feedback in their equivalent MUGS2 sample, only forming half of its stellar mass by z ∼ 0.5, MUGS simulations. This effect appears to be robust to the diverse later than all but 2 galaxies of the MUGS2 sample. These point assembly histories of the galaxies, and is even robust in the cases towards recent merger activity that has spread a large fraction of where the total stellar mass of the MUGS and MUGS2 galaxies are in-situ stars out into the stellar halo, which may still be out of dy- comparable. This suggests that the stellar halo is a more sensitive namical equilibrium. The other two late assemblers in the MUGS2 probe of stellar feedback than the stellar content of the disc (which sample are g28547 and g21647. Both are in the process of undergo- dominates the overall stellar mass). In Figure5, we show how the ing a major merger in both MUGS and MUGS2 (as is evidenced by different models for SN feedback impact the age and ex-situ/in- the large infalling satellite visible in the surface density of g21647 situ stellar components of the two samples of simulated galaxies.

MNRAS 000, 000–000 (0000) Probing Feedback with Stellar Haloes 5

109 DNGS Observations MUGS Simulations (Blastwave Feedback) MUGS2 Simulations (Superbubble Feedback) 108

) 7

2 10 kpc /

∗ 6

Σ 10

105

104 10 20 30 40 50 60 70 80 Radius (kpc)

Figure 2. Stellar surface density proﬁles for the MUGS, MUGS2, and DNGS galaxies (blue, orange, and black curves). The individual MUGS and MUGS2 galaxies are shown as the thin, semi-transparent lines, while the median trend is shown by the thick solid line. As is clear, despite having comparable stellar surface densities near the disc (< 20 kpc), the MUGS2 galaxies have stellar haloes roughly 2 dex less dense beyond ∼ 50 kpc compared to the MUGS sample.

) 10 2 − kpc 108 Σ (M

106

g1536 g22795 g4145 g15784 g24334 g422 104 g15807 g25271 g5664 g21647 g28547 g7124 g22437 g3021 g8893 Stellar Surside Density 102 20 40 60 80 20 40 60 80 20 40 60 80 Radius (kpc) Radius (kpc) Radius (kpc)

Figure 3. Comparison of stellar surface density in stellar haloes of each pair of MUGS/MUGS2 galaxies. The solid curves show the surface density of stars in MUGS2, while the dotted curves show the same for the original MUGS simulations. As can be seen, there is a signiﬁcant diversity of the stellar halo surface densities in the MUGS/MUGS2 population, with >1 dex galaxy-to-galaxy variation in the outer halo. However, as is also clear, for essentially all galaxy pairs, the MUGS2 stellar haloes are much less massive than their MUGS twin.

Previous models (both analytic, e.g. Bullock & Johnston 2005 and fraction in all MUGS and MUGS2 galaxies increases with galac- numerical, e.g. Font et al. 2011) have suggested that anywhere from tocentric radii, reaching a median of ∼ 0.8 in both MUGS and the majority to the totality of the stellar halo is composed of tidal MUGS2 galaxies beyond ∼ 60 kpc. Especially for the outer stel- debris from accreted satellites (an ex-situ formation scenario). lar halo, both MUGS and MUGS2 are dominated by ex-situ stars (but still contain a non-trivial fraction of in-situ stars in most cases). In the top panel of Figure5, we show the radial profile and Inside 30 kpc, the picture becomes very different for the two pop- ±1σ variance of the ex-situ fraction of stars in the MUGS and ulations, with MUGS2 ex-situ fractions dropping to nearly zero at MUGS2 galaxies as a function of galactocentric radius. We define r = 0, while nearly 20% of the stellar mass in the MUGS belongs ex-situ stars as those stars which are first identified in a halo other to ex-situ stars. This suggests that much of the difference we see is than the primary progenitor of the galaxy, and are subsequently ac- due to a reduction in overall contribution of ex-situ stars, as even creted by each galaxy. As can be seen in the top panel, the ex-situ

MNRAS 000, 000–000 (0000) 6 B.W. Keller

1.0 MUGS

) MUGS2

0.8 1010 1% M M ∗ ( 10% M ∗ 0.6 109 0.4 Ex-Situ Fraction 8 Outer Halo Mass 10 0.2 MUGS MUGS2 10 11 10 10 0.0 Galaxy Stellar Mass (M ) 0 10 20 30 40 50 60 70 80

) 102 1010 M ( 2

1 9 10 10 MUGS ∗ MUGS Σ / MUGS2 Outer Halo Mass

1% M200 MUGS ∗ 8 0 10 Σ 10 0.05% M200 All Stars Ex-Situ Stars Only 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 In-Situ Stars Only 11 Galaxy Virial Mass M200 (10 M ) 1 10− 0 10 20 30 40 50 60 70 80 Radius (kpc) Figure 4. Outer halo masses in a 100 kpc thick shell (40 − 140 kpc) for the MUGS and MUGS2 galaxies as a function of stellar mass (upper plot) and halo mass (lower plot). As the upper plot shows, the outer halo masses Figure 5. The origins of the stellar haloes in MUGS and MUGS2. In the in MUGS2 are relatively constant compared to their stellar masses, with top panel, we show the median ex-situ fraction in the sample of MUGS the most massive galaxies seeing a reduction in the outer halo masses by and MUGS2 galaxies (blue and orange curves respectively). In the bottom ∼ 1.5 dex relative to the equivalent galaxy in MUGS. The lower plot shows panel, we show the surface density ratios between MUGS and MUGS2 for that the outer halo masses scale relatively linearly with the total virial mass all stars, ex-situ stars, and in-situ stars (Brown, green, and purple curves re- of the galaxy in both cases, with the MUGS galaxies having outer halo spectively). Both MUGS and MUGS2 show outer stellar haloes dominated ∝ −1 masses ∼ 10 M200, while the MUGS2 galaxies have outer halo masses by ex-situ stars, while the inner regions of the MUGS2 galaxies become ∝ −4 ∼ 5 × 10 M200. much more in-situ dominated than their MUGS counterparts. The reduction of the ex-situ stellar population in MUGS2 is constant as a function of radius, while the in-situ population in the disc is relatively unchanged (or a complete elimination of in-situ stars could only reduce the outer even enhanced) from 5 − 15 kpc. The standard deviation of each quantity stellar halo mass by at most a factor 25%, rather than the > 1 dex is shown by the transparent areas. reduction we see. Of course, this also means that a complete reduction of ex-situ stars also cannot explain the differences we see. Indeed, as we show in the bottom panel of Figure5, the surface formed at high redshift, when the merger rate was more frequent density of both in-situ and ex-situ stars in the MUGS2 galaxies are and the disc potential was lower. We can see this in the dashed reduced by > 1 dex beyond a galactocentric radius of ∼ 30 kpc. line of Figure6, where the in-situ stars in the MUGS2 galaxies are As we would expect from the top panel, the contribution of ex- much older (∼ 8Gyr vs. ∼ 5Gyr in the outer halo, > 40kpc, com- situ stars in the disc and bulge are reduced within 30 kpc, and we pared to in the disc). Interestingly, in both the MUGS and MUGS2 can also see the reduced bulge fraction already demonstrated in galaxies the ex-situ stellar population is the oldest, with ages of MUGS2 (Keller et al. 2016) by the upturn in the surface density 10 − 12 Gyr. Along with the higher ex-situ fraction in the halo, ratio within ∼ 5 kpc. This clearly shows that the lower stellar halo this is why we see the increasing stellar age as we move to larger surface densities in the MUGS2 galaxies arise from a reduction in galactocentric radii. both in-situ and ex-situ halo stars. Figure6 shows how the trends we see in the upper panels relate to the median stellar age profiles of the MUGS and MUGS2 4 DISCUSSION & CONCLUSION galaxies. In general, we see that a similar flattening to the ex-situ fraction shown in the top panel of Figure5 towards low galactocen- We have shown here how the modelling of SN feedback can have tric radius in MUGS relative to MUGS2 also appears in the median dramatic effect on the diffuse stellar haloes of MW-mass galax- stellar ages. The stellar ages of MUGS and MUGS2 stellar haloes ies. We are only able to match the observed stellar surface den- are nearly equal in the outer regions (> 40 kpc), with both having sity profiles from the DNGS when SN feedback is simulated with a median stellar ages of ∼ 9 − 10 Gyr (though the median stellar physically-motivated superbubble model (Keller et al. 2014), which age in MUGS2 is somewhat lower). The population of in-situ stars takes into account thermal conduction and evaporation and drives most easily scattered into the outer halo by mergers are those which much more efficient, buoyant galactic winds (Keller et al. 2020a).

MNRAS 000, 000–000 (0000) Probing Feedback with Stellar Haloes 7

10 11 12 of 1656 central galaxies with mass stellar mass 10 − 10 M , selecting 50 galaxies chosen to match the distribution of stellar 11 mass in DNGS (compared to the 15 galaxy pairs we compare here). In addition to the larger sample size, TNG100 has somewhat 5 10 lower baryonic resolution than MUGS/MUGS2 (2.2 × 10 M in 6 MUGS/MUGS2, 1.4 × 10 M in TNG100), as well as a signiﬁ- 9 cantly different model for gas cooling, star formation, and feedback from both stars and AGN (see Pillepich et al. 2018 for details of the 8 models in TNG100, Stinson et al. 2010 for the models in MUGS, and Keller et al. 2014, 2015 for the models used in MUGS2). The 7 results we present here strongly suggest the differences between

Median Stellar Age (Gyr) the stellar haloes in MUGS2 and TNG100 are primarily a result of 6 these different feedback models, rather than the numerical resolu- All Stars MUGS tion or sample size. 5 In-Situ Stars MUGS2 Ex-Situ Stars Of course, Merritt et al.(2020) is not the first study to examine stellar haloes through numerical simulation. Both hydrody- 0 10 20 30 40 50 60 70 80 namic and collisionless N-body studies have attempted to trace the Radius (kpc) origin of the stellar halo in the MW and other galaxies. The earliest attempts to study stellar haloes through simulation relied on collisionless N-body simulations (e.g. Bullock & Johnston 2005; Figure 6. Median stellar age profiles for stars in the MUGS/MUGS2 sim- Abadi et al. 2006; Cooper et al. 2010). While N-body simulations ulations (blue/orange curves). The median ages of all stars are shown by are inexpensive compared to full hydrodynamic runs, they must use the solid curve, while in-situ stars are shown in the dashed line and ex-situ stars are shown in the dotted line. As can be seen, the median age of ex-situ particle tagging and semi-analytic models to translate the assembly stars are higher than in-situ stars, and are relatively constant as a function history of DM subhaloes into a star formation history and stellar of galactocentric radius. The in-situ stars (which dominate the total stellar morphology. The additional uncertainties introduced by this pro- mass) are older in MUGS compared to MUGS2, and are relatively constant cess have been studied in Bailin et al.(2014), which suggests they as a function of radius in MUGS. For the MUGS2 galaxies, the ages of the may introduce significant systematics (though Cooper et al. 2017 in-situ stars in the disc and bulge (< 30 kpc) are significantly lower, with argue that this effect can be mostly mitigated through more careful typical in-situ star ages in the disc of ∼ 5 Gyr. selection techniques for particle tagging). Hydrodynamic simulations of stellar halo formation have used both cosmological zooms, as we have used here, as well as stud- The MUGS2 galaxies, which include this new model, have stellar ies of large volumes (as is done in Merritt et al. 2020). One of haloes with significantly reduced mass and surface density com- the earliest studies, Zolotov et al.(2009), used five high-resolution pared to the older MUGS simulations, even when the galaxy mass SPH zoom-in simulations of MW-mass galaxies using the same becomes large enough that AGN feedback is required to regulate blastwave feedback model as MUGS. Like in the MUGS/MUGS2 the total stellar mass of the galaxy (Keller et al. 2016). As the dif- galaxies we have studied, Zolotov et al.(2009) found that the in- fuse stellar halo is primarily composed of smaller dwarf progeni- situ component of the stellar halo was concentrated towards the tors, their properties track the early history of star formation in the inner halo, and that the ex-situ fraction of the total stellar halo was lowest mass progenitors of the final galaxy. between 32−87% (in contrast to the some of the assumptions made Despite the significantly higher masses in the MUGS stellar in semi-analytic models such as Bullock & Johnston 2005). Tissera haloes compared to MUGS2 (typically a factor of ∼ 25), we find et al.(2013) used six simulated MW zooms from the Aquarius suite a number of trends are robust in both simulation samples. In the to study the chemical properties of halo stars based on their binding outer stellar halo > 10 kpc, the stellar populations are old (∼ 9 − energy, connecting this to their formation history. More recently, 10Gyr) and dominated by the debris of satellite accretion, with ex- the latest generation of sub-grid modelling for star formation and situ fractions of ∼ 0.8. The largest changes in the ex-situ fraction feedback has produced zoom-in simulations of MW galaxies with and stellar ages occur in the inner halo and stellar disc/bulge. Here exceptional resolution and agreement with observational scaling re- we find that MUGS2 significantly reduces the ex-situ fraction and lations. Simulations from FIRE (Hopkins et al. 2014; Sanderson median age of stars within the inner 30kpc of the galaxy, producing et al. 2018), the EAGLE-derived ARTEMIS (Font et al. 2020) and an inner halo and disc that is ∼ 3 − 4 Gyr younger and dominated E-MOSAICS projects (Pfeffer et al. 2018; Kruijssen et al. 2019; by in-situ star formation. Hughes et al. 2019; Reina-Campos et al. 2020; Keller et al. 2020b), and the Illustris-derived AURIGA project (Monachesi et al. 2019) have studied the formation history, mass, and metallicity proper- 4.1 Comparison to Other Simulations ties of stellar haloes. All of these studies have found that accreted The main study we have compared our results with is Merritt et al. stars dominate the stellar halo, especially at larger radii, and those (2020), which is the first study to comprehensively compare the which examine larger populations (Monachesi et al. 2019; Hughes stellar halo profiles observed in Merritt et al.(2016) with simu- et al. 2019; Sanderson et al. 2018) also find a large diversity in the lations. The large discrepancy they found in the Illustris-TNG100 population of stellar haloes of different MW-mass galaxies. The E- galaxies (Pillepich et al. 2018) (the “missing outskirts” problem), MOSAICS results (Hughes et al. 2019; Reina-Campos et al. 2020; along with their observationally-motivated analysis, has been the Keller et al. 2020b) also include a model for globular cluster (GC) primary motivator of this study. The major difference between the formation and evolution, and use these simulated GCs to study the simulations we examine here and those of TNG100 are the larger GC population in stellar haloes, and compare them to the popu- population in TNG100. Merritt et al.(2020) samples from a total lations of field stars in the galactic halo. Future simulations that

MNRAS 000, 000–000 (0000) 8 B.W. Keller compare different feedback models will allow us to study the co- the stellar halo being composed of stripped or evaporated GC stars. evolution of stellar haloes and halo GCs in a similar fashion to the Future studies, covering a large range of halo masses through large- comparison we have presented here for the overall stellar haloes volume and zoom simulations, may be able to reveal if this trend in MUGS and MUGS2. Large-volume simulations have also been is a robust relationship or simply an artifact of the small range we used to study the stellar haloes of galaxies spanning a mass range have probed here. much wider than the narrow MW-mass region we have studied here (Font et al. 2011; Pillepich et al. 2014; Cañas et al. 2020). While the sample size and mass ranges probed by these larger-volume simu- 4.3 Summary lations exceed what we have shown here, they all are limited by The results we have presented in this paper lead to a number of substantially lower resolution than what is capable in the highest- clear conclusions on stellar haloes and the impact of SN feedback resolution zoom-in simulations. Studies adopting both approaches and galaxy assembly on them: will be essential to understand the full diversity of stellar haloes and the impact of feedback upon them. • The surface density of stellar haloes is a sensitive probe of stellar feedback physics. Galaxies simulated with different feedback models, even if they produce similar stellar masses, may still 4.2 Limitations & Future Work show significant differences in the masses and surface densities of The primary limitations of this study are in numerical resolu- their stellar haloes. tion and sample size. The MUGS and MUGS2 galaxies are cos- • The low virial mass of the ex-situ progenitors allows us to mological zoom-in simulations with baryonic mass resolution of probe a regime where SN feedback dominates even in systems as 5 massive as the Milky Way, where AGN feedback can contaminate 2.2 × 10 M . While this is better than what is achievable in the largest cosmological volumes, the highest-resolution MW-mass the picture of feedback regulation. This makes the diffuse stellar 4 halo a useful tool, along with field and dwarf galaxies, to probe the zoom simulations are now achieving resolutions of ∼ 10 M (e.g. Hopkins et al. 2018). In the stellar halo, this resolution effect can SN feedback-dominated regime of galaxy regulation. be significant. At the lower surface density limits of surveys like • The “missing outskirts problem” appears to be a result of par- 4 −2 ticular models used for stellar feedback which fail to regulate high- DNGS, ∼ 10 M kpc , our simulated stellar haloes are relatively poorly sampled, with a single star particle sampling a pro- redshift star formation in the progenitors of Milky Way-like galax- jected area of 10 kpc2. Probing low-density areas will always be ies. We also find an over-massive stellar halo in simulations gen- challenging for both observations and simulations, but higher res- erated using a delayed-cooling “blastwave” feedback model, while olution will help to better sample the lowest density outskirts of haloes simulated using “superbubble” feedback are in much better the stellar halo and reduce the sampling noise that may occur in agreement with the DNGS galaxies. lower resolution studies. The sample of galaxies we study here is • Superbubble feedback works to reduce contributions to stellar also relatively small, especially compared to the population from haloes from both in-situ and ex-situ stars, and is especially effective Illustris-TNG100 studied in Merritt et al.(2020). Unfortunately, the at reducing the ex-situ fraction of the inner halo and disc. This both observational samples are even more limited, and so larger samples changes the morphology of galaxy discs and bulges (Keller et al. of simulated galaxies will not allow us to make full statistical com- 2016), and produces a much sharper gradient in the age profile of parisons to observations for many years. stars in MW-mass galaxies. Our results have shown that, as has been seen in observations • Despite the greatly reduced surface density in the MUGS2 (Merritt et al. 2016; Harmsen et al. 2017) and simulations (Merritt stellar haloes, both MUGS and MUGS2 MW-like galaxies show et al. 2020), the stellar haloes of MW-mass galaxies exhibit tremen- an outer halo that is old (∼ 9 − 10 Gyr median stellar age) and dous diversity in their masses and profiles. We have limited our accretion dominated (with ex-situ fractions of ∼ 0.8). analysis to the impact of SN feedback models, but there remains a With growing observational capabilities, along with the increasing great deal of information to be studied in the assembly history of sophistication of numerical simulations, stellar haloes are a promis- the individual MUGS/MUGS2 galaxies, as well as the metallicity ing new frontier for exploring the impact of galaxy assembly, star and kinematics of the stellar halo. In an upcoming paper (Keller formation, and stellar feedback in a cosmological environment. et al. in prep), we will examine how the different merger trees and star formation histories of galaxies produce diverse structures in both the metallicity and phase space of stellar haloes, and how SN ACKNOWLEDGEMENTS feedback can change and reshape these structures. We also have found an interesting relationship between the BWK would like to thank Allison Merritt for useful discussions galaxy virial mass M200 and the mass of the outer stellar halo. and for providing data from DNGS. BWK would also like to thank While we only probe a small range of virial masses here, there is a James Wadsley, Sebastian Trujillo-Gomez, Diederik Kruijssen, and hint that there may be a linear relationship between the halo mass Sümeyye Suri for interest and encouragement, and Tessa Klettl for and the outer stellar halo. The outer stellar halo contains a popu- help editing and proofreading this manuscript. BWK gratefully ac- knowledges funding from the European Research Council (ERC) lation of stars that is both old and primarily ex-situ, similar to the under the European Union’s Horizon 2020 research and innovation properties of halo GCs (Zinn 1985; Helmi et al. 2018; Keller et al. programme via the ERC Starting Grant MUSTANG (grant agree- 2020b). Our results suggest that the outer stellar halo may follow ment number 714907). a similar linear relation to halo mass that is observed in globular cluster populations (Kruijssen 2014, 2015; Choksi & Gnedin 2019; Bastian et al. 2020). Recent studies (Reina-Campos et al. 2020) have suggested that the GC population in the halo is unlikely to REFERENCES contribute more than a small (∼ 2%) fraction of the stellar halo, Abadi M. G., Navarro J. F., Steinmetz M., 2006, MNRAS, 365, 747 so the linear relationship we see is unlikely to be simply a result of Abraham R. G., van Dokkum P. G., 2014, PASP, 126, 55

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3.0 Arbitrary Rotation Face On )

2 2.5 Side On 2.0 MUGS ∗ Σ / 1.5

MUGS ∗ 1.0 (Σ

10 0.5

log 0.0

0.5 − 0 20 40 60 80 100 120 140 Radius (kpc)

Figure A1. Relative surface densities of the MUGS and MUGS2 in random, face-on, and edge-on orientation. Each curve is the ratio of the median surface density for each galaxy in MUGS and MUGS2. As can clearly be seen, there is little impact in the relative surface density of the MUGS and MUGS2 galaxies whether they are in a random, face-on, or edge-on orientation.

MNRAS 000, 000–000 (0000)