Planes of satellites around Milky Way/M31-mass galaxies in the FIRE simulations and comparisons with the Local Group
Jenna Samuel, Andrew Wetzel, Sierra Chapman, Erik Tollerud, Philip F. Hopkins, Michael Boylan-Kolchin, Jeremy Bailin, Claude-André Faucher-Giguère
MMNRAS , 1–16 (2020) Preprint 20 October 2020 Compiled using MNRAS L A TEX style file v3.0
Planes of satellites around Milky Way/M31-mass galaxies in theFIRE simulations and comparisons with the Local Group
Jenna Samuel ★ , Andrew Wetzel , Sierra Chapman , Erik Tollerud ,Philip F. Hopkins , Michael Boylan-Kolchin , Jeremy Bailin ,Claude-André Faucher-Giguère Department of Physics and Astronomy, University of California, Davis, CA 95616, USA Space Telescope Science Institute, 3700 San Martin Dr, Baltimore, MD 21218, USA TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA Department of Astronomy, The University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA Department of Physics and Astronomy, University of Alabama, Box 870324, Tuscaloosa, AL 35487-0324, USA Department of Physics and Astronomy and CIERA, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA
20 October 2020
ABSTRACT
We examine the prevalence, longevity, and causes of planes of satellite dwarf galaxies,as observed in the Local Group. We use 14 Milky Way/Andromeda-(MW/M31) mass hostgalaxies from the FIRE-2 simulations. We select the 14 most massive satellites by stellarmass within 𝑑 host ≤
300 kpc of each host and correct for incompleteness from the foregroundgalactic disk when comparing to the MW. We find that MW-like planes as spatially thinand/or kinematically coherent as observed are uncommon, but they do exist in our simulations.Spatially thin planes occur in 1–2 per cent of snapshots during 𝑧 = − .
2, and kinematicallycoherent planes occur in 5 per cent of snapshots. These planes are generally short-lived,surviving for <
500 Myr. However, if we select hosts with an LMC-like satellite near firstpericenter, the fraction of snapshots with MW-like planes increases dramatically to 7 −
16 percent, with lifetimes of 0 . − ∼ 𝜎 ofthe simulation median for every plane metric we consider. We find no significant difference inaverage satellite planarity for isolated hosts versus hosts in LG-like pairs. Baryonic and darkmatter-only simulations exhibit similar levels of planarity, even though baryonic subhalos areless centrally concentrated within their host halos. We conclude that planes of satellites arenot a strong challenge to Λ CDM cosmology.
Key words: galaxies: dwarf – galaxies: Local Group – galaxies: formation – methods:numerical
Astrometric measurements have revealed that a subset of the MilkyWay (MW) satellite galaxies coherently orbit their host galaxywithin a spatially thin plane (‘thin’ describes systems with minor-to-major axis ratios of 𝑐 / 𝑎 (cid:46) .
3, and ‘coherent’ indicates that amajority of satellites share the same orbital direction) (e.g., Lynden-Bell 1976; Kroupa et al. 2005; Pawlowski et al. 2012a). Recently,precise proper motions from
Gaia
Data Release 2 have affirmedan even tighter orbital alignment of MW satellites than previouslymeasured (Fritz et al. 2018; Pawlowski & Kroupa 2020). Similar ★ E-mail: [email protected] structures have also been observed around Andromeda (M31) (Ibataet al. 2013; Conn et al. 2013) and Centaurus A (Müller et al. 2018).However, the spatial and kinematic coherence of satellite planesbeyond the Local Group (LG) is less certain because of projec-tion effects, distance uncertainties, and the inaccessibility of propermotions. Even at the relatively close distance of M31, currentlyonly two of its satellites have measured proper motions (Sohn et al.2020), making it difficult to determine true 3D orbital alignment ofthe entire satellite population.The cosmological significance of these satellite planes remainsa topic of ongoing investigation, largely because of a lack of consen-sus on the incidence of planarity in both simulations and observa-tions. Studies using dark matter-only (DMO) simulations have often © a r X i v : . [ a s t r o - ph . GA ] O c t J. Samuel et al. yielded conflicting interpretations of how rare satellite planes arein the standard cosmological model of cold dark matter with a cos-mological constant ( Λ CDM). Most analyses of DMO simulationsfind such configurations to be rare, highly significant, and thereforepossibly in conflict with Λ CDM (e.g. Metz et al. 2008; Pawlowski& McGaugh 2014; Buck et al. 2016). However, DMO simulationscombined with semi-analytic models of galaxy formation suggestthat planes might be more common (Libeskind et al. 2009; Cautunet al. 2015), but this is not a universal result (Pawlowski et al. 2014;Ibata et al. 2014b). Results from baryonic simulations have variedtoo, often relying on a much smaller sample of host-satellite sys-tems compared to what is available from DMO simulations. Somebaryonic simulations show evidence for a more natural presence ofsatellite planes in the universe (e.g. Libeskind et al. 2007; Sawalaet al. 2016). While other baryonic results show that satellite planescan be uncommon, but find conflicting evidence for whether planescan be explained by anisotropic satellite accretion along filamentarystructures (Ahmed et al. 2017; Shao et al. 2018, 2019).Beyond just checking for the presence and significance of satel-lite planes in simulations, several authors have also explored whatmay cause planes to form, with mixed results. Though one might ex-pect the host halo to affect satellite planes, Pawlowski & McGaugh2014 found no connection between planes and host halo proper-ties. Some authors have argued either for (Libeskind et al. 2011) oragainst (Pawlowski et al. 2012b) the preferential infall of satellitesalong cosmic filaments as a causal factor in the formation of satel-lite planes. Li & Helmi 2008 proposed the accretion of satellites insmall groups as an explanation of correlated orbits, and Wetzel et al.2015a showed that 25 −
50 per cent of satellite dwarf galaxies inMW-mass hosts today previously were part of a group. Metz et al.2007 has even speculated that satellite planes arise naturally fromthe creation of tidal dwarf galaxies in fly-bys or mergers of largergalaxies.Several authors have investigated the orbital stability of LGsatellite planes. Recently, Riley & Strigari 2020 showed that glob-ular clusters and stellar streams around the MW do not seem tobe members of the satellite plane, suggesting that plane membersmay be recently accreted or in a particularly stable orbital config-uration. Pawlowski et al. 2017 noted that integrating present-daysatellite orbits either forward or backward in time typically leadsto the disintegration of the plane, especially when sampling mea-surement uncertainties on satellite galaxy positions and velocities.Shaya & Tully 2013 took a different approach and, by searching thedynamical parameter space of Local Volume satellites, found pasttrajectories that could possibly lead to the observed satellite planes.Many previous attempts to investigate satellite planes have re-lied on simulations that may not resolve the dynamical evolutionof “classical” ( 𝑀 ∗ ≥ M (cid:12) ) dwarf galaxies, or that do not in-clude baryonic physics. Insufficient resolution can lead to artificialsatellite destruction (e.g. Carlberg 1994; van Kampen 1995; Mooreet al. 1996; Klypin et al. 1999; van Kampen 2000; Diemand et al.2007; Wetzel & White 2010; van den Bosch & Ogiya 2018). Thismay introduce a bias in satellite plane metrics if the destruction isspatially varying (such as near the host disk), and because earlierinfalling satellites are preferentially destroyed, leading to an agebias that correlates with satellite orbit today (Wetzel et al. 2015a).If baryonic effects act to create or destroy planes of satellites,then dark matter-only simulations may not be able to wholly cap-ture the theoretical picture of satellite plane formation. The centraldisk in baryonic simulations tidally destroys satellites, altering theirradial profile at small distances from the host (e.g., D’Onghia et al.2010; Sawala et al. 2017; Garrison-Kimmel et al. 2017; Nadler et al. 2018; Kelley et al. 2018; Rodriguez Wimberly et al. 2019; Samuelet al. 2020). This leads the surviving satellites to have more tangen-tially biased orbits (Garrison-Kimmel et al. 2017, 2019a), but theseeffects do not necessarily imply an effect on planarity. In addition,Ahmed et al. 2017 found that the members of satellite planes inbaryonic versus DMO simulations of the same host halo can be dif-ferent, suggesting that baryonic effects may alter halo occupation inunexpected ways and hence affect satellite planes. Garrison-Kimmelet al. 2019a also noted that satellites in baryonic simulations of LG-like pairs do not necessarily trace the most massive subhalos inDMO runs of the same systems.Outside of the MW, the satellite plane around M31 is somewhatmore ambiguous. Taken as a whole, M31’s satellites do not appearto be particularly planar, but a subset of 15 satellites lie within asignificantly spatially thin plane and most of those are kinematicallyaligned, based on line-of-sight velocities (Conn et al. 2013; Ibataet al. 2013). Many works have focused in on this particular subset,but it is important to understand the overall satellite distribution,because there are no clear evolutionary differences between M31plane members and non-members (Collins et al. 2015).Satellite planes outside of the LG are more difficult to ro-bustly characterize because of projection effects and larger distanceuncertainties. Studies using the Sloan Digital Sky Survey (SDSS)database have revealed that while there is evidence for spatial flat-tening of satellites (e.g., Brainerd 2005), their kinematic distributionis unlikely to indicate a coherently orbiting satellite plane (Phillipset al. 2015). Furthermore, the Satellites Around Galactic analogues(SAGA) survey (Geha et al. 2017), which aims to study satellitesof ∼
100 MW analogues in the nearby Universe, has found littleevidence for coherently orbiting satellite planes (Mao et al. 2020).In this paper, we seek to understand if the FIRE-2 simulationscontain satellite planes similar to those found in the Local Group,whether those satellite planes are long-lived or transient, and if thepresence of satellite planes correlates with host or satellite proper-ties. We leave comparisons to systems outside of the LG for futurework. We organize this paper as follows: in Section 2 we describeour simulations and satellite selection criteria, in Section 3 we de-scribe the 3D positions and velocities of Local Group satellites used,in Section 4 we describe the plane metrics we apply to simulationsand observations, in Section 5 we present our results of planarity insimulations compared to observations, and in Section 6 we discussour conclusions and their implications for observed satellite planes.
The zoom-in simulations we use in this work reproduce the massfunctions, radial distributions, and star formation histories of clas-sical ( 𝑀 ∗ ≥ M (cid:12) ) dwarf galaxies around MW/M31-like hosts(Wetzel et al. 2016; Garrison-Kimmel et al. 2019a,b; Samuel et al.2020).We use two suites of cosmological zoom-in hydrodynamicsimulations from the Feedback In Realistic Environments (FIRE)project . Latte is currently a suite of 7 isolated MW/M31-massgalaxies with halo masses M = − × M (cid:12) introducedin Wetzel et al. 2016. We selected the Latte halos for zoom-in re-simulation from a periodic volume dark matter simulation box ofside length 85.5 Mpc. We selected two of the Latte halos (m12r and https://fire.northwestern.edu/ ‘200m’ indicates a measurement relative to 200 times the mean matterdensity of the Universe MNRAS , 1–16 (2020) atellite planes in FIRE m12w) to host an LMC-mass subhalo at 𝑧 = (cid:12) , but at 𝑧 = ≈ (cid:12) because of stellar mass loss. Dark matter particleshave a mass resolution of m dm = . × M (cid:12) . The gravitationalsoftenings (comoving at 𝑧 > 𝑧 <
9) of dark matterand stars particles are fixed: 𝜖 dm =
40 pc and 𝜖 star = ≈ baryon , ini = (cid:12) ).The second suite of simulations we use is “ELVIS on FIRE”.This suite consists of three simulations, containing two MW/M31-mass galaxies each, wherein the main halos were selected to mimicthe relative separation and velocity of the MW-M31 pair in the LG(Garrison-Kimmel et al. 2014, 2019a,b). ELVIS on FIRE has ≈ × better mass resolution than Latte: the Romeo & Juliet and Romulus& Remus simulations have m baryon , ini = (cid:12) and the Thelma& Louise simulation has m baryon , ini = (cid:12) .We ran all simulations with the upgraded FIRE-2 implementa-tions of fluid dynamics, star formation, and stellar feedback (Hop-kins et al. 2018). FIRE uses a Lagrangian meshless finite-mass(MFM) hydrodynamics code, GIZMO (Hopkins 2015). GIZMOenables adaptive hydrodynamic gas particle smoothing dependingon the density of particles while still conserving mass, energy, andmomentum to machine accuracy. Gravitational forces are solved us-ing an upgraded version of the 𝑁 -body GADGET-3 Tree-PM solver(Springel 2005).The FIRE-2 methodology includes detailed subgrid modelsfor gas physics, star formation, and stellar feedback. Gas modelsused include: a metallicity-dependent treatment of radiative heat-ing and cooling over 10 − K (Hopkins et al. 2018), a cos-mic ultraviolet background with early HI reionization ( 𝑧 reion ∼ < K), dense ( 𝑛 > − ), and molecular (following Krumholz & Gnedin 2011) to formstars. Star particles represent individual stellar populations underthe assumption of a Kroupa stellar initial mass function (Kroupa2001). Once formed, star particles evolve according to stellar pop-ulation models from STARBURST99 v7.0 (Leitherer et al. 1999).We model several stellar feedback processes including core-collapseand Type Ia supernovae, continuous stellar mass loss, photoioniza-tion, photoelectric heating, and radiation pressure.For all simulations, we generate cosmological zoom-in initialconditions at 𝑧 =
99 using the MUSIC code (Hahn & Abel 2011),and we save 600 snapshots from 𝑧 =
99 to 0, with typical spacingof (cid:46)
25 Myr. All simulations assume flat Λ CDM cosmologies, withslightly different parameters across the full suite: ℎ = . − . Ω Λ = . − . Ω 𝑚 = . − . Ω 𝑏 = . − . 𝜎 = . − .
82, and 𝑛 s = . − .
97, broadly consistent withPlanck Collaboration et al. 2018.
We use the ROCKSTAR 6D halo finder (Behroozi et al. 2013a)to identify dark matter halos and subhalos in our simulations. Weinclude a halo in the catalog if its bound mass fraction is > . . We generatea halo catalog for each of the 600 snapshots of each simulation,using only dark matter particles. The subhalos that we use in thiswork (within 300 kpc of their host) are uncontaminated by low-resolution dark matter particles. We then construct merger treesusing CONSISTENT-TREES (Behroozi et al. 2013b).We describe our post-processing method for assigning star par-ticles to (sub)halos further in Samuel et al. 2020. First, we identifyall star particles within 0.8 R halo (out to a maximum 30 kpc) ofa halo as members of that halo. Then, we further clean the mem-ber star particle sample by selecting those (1) that are within 1.5times the radius enclosing 90 per cent of the mass of memberstar particles (R ) from both the center-of-mass position of mem-ber stars and the dark matter halo center, and (2) with velocitiesless than twice the velocity dispersion of member star particles( 𝜎 vel ) with respect to the center-of-mass velocity of member stars.We iterate through steps (1) and (2) until the total mass of mem-ber star particles (M ∗ ) converges to within 1 per cent. Finally, wesave halos for analysis that contain at least 6 star particles and thathave an average stellar density >
300 M (cid:12) kpc − . We performedthis post-processing and the remainder of our analysis using the GizmoAnalysis and
HaloAnalysis software packages (Wetzel &Garrison-Kimmel 2020a,b).
Throughout this paper we refer to the central MW/M31-mass galax-ies in our simulations as hosts, and their surrounding population ofdwarf galaxies within 300 kpc as satellites. Our host galaxies havestellar masses in the range M ∗ ∼ − M (cid:12) and dark matter ha-los in the mass range M = . − . × M (cid:12) . The eightLatte+m12z simulations contain a single isolated host per simula-tion. Each of the three ELVIS on FIRE simulations contains twohosts in a LG-like pair, surrounded by their own distinct satellitepopulations. Thus, we use a total of 14 host-satellite systems tostudy satellite planes in this work. Our fiducial redshift range is 𝑧 = − . ∼ . 𝑧 = − .
5, 219 snapshots, ∼ . 𝑀 ∗ ≥ M (cid:12) .We also choose the 15 most massive satellites around hosts for ourcomparison to M31 (see Section 5.1.2 for more details). Satelliteswith 𝑀 ∗ ≥ M (cid:12) contain ≥
20 star particles and have peak halomasses of 𝑀 peak ≥ × M (cid:12) ( (cid:38) . × dark matter particlesprior to infall). Satellite galaxies with 𝑀 ∗ ≥ M (cid:12) are also nearlycomplete in observations (e.g. Koposov et al. 2007; Tollerud et al.2008; Walsh et al. 2009; Tollerud et al. 2014; Martin et al. 2016), sowe choose this as our nominal stellar mass limit to select satellites MNRAS000
20 star particles and have peak halomasses of 𝑀 peak ≥ × M (cid:12) ( (cid:38) . × dark matter particlesprior to infall). Satellite galaxies with 𝑀 ∗ ≥ M (cid:12) are also nearlycomplete in observations (e.g. Koposov et al. 2007; Tollerud et al.2008; Walsh et al. 2009; Tollerud et al. 2014; Martin et al. 2016), sowe choose this as our nominal stellar mass limit to select satellites MNRAS000 , 1–16 (2020)
J. Samuel et al. around the MW and M31. As an example, at 𝑧 =
0, the satellitewith the lowest stellar mass in our fixed-number satellite selectioncriteria has M ∗ = . × M (cid:12) (11 star particles), which is enoughto at least indicate the presence of a true satellite, given that it alsosatisfies the criteria outlined in Section 2.1.We also consider a stellar mass threshold selection method inSection 5.3.2 whereby we require satellites to have 𝑀 ∗ ≥ M (cid:12) and maintain the same distance cutoff ( 𝑑 host ≤
300 kpc). This selec-tion means that the number of satellites considered around all hostsvaries from 10 to 31 in the redshift range 𝑧 = − .
2. See Samuelet al. 2020 for more details on the radial distributions and resolu-tion of simulated satellites meeting our criteria, and completenessestimates in the Local Group. See Garrison-Kimmel et al. 2019a,bfor how the stellar mass, velocity dispersion, dynamical mass, andstar-formation histories of satellite dwarf galaxies in our simula-tions all broadly agree with MW and M31 observations, makingthese simulations compelling to use to examine planarity.
We consider all known MW satellite galaxies with 𝑀 ∗ ≥ M (cid:12) and 𝑑 host ≤
300 kpc, based on the satellite stellar masses and galac-tocentric distances listed in Table A1 of Garrison-Kimmel et al.2019a. While we are not confident that our halo finder is able to cor-rectly identify analogues of the Sagittarius dwarf spheroidal (SgrI)galaxy, given its significant tidal interactions, we include it in ourobservational sample, because it is a historical member of the MW’ssatellite plane. Excluding SgrI from the MW satellite galaxy sam-ple does not significantly change the resulting spread in the MW’splane metrics, and therefore we achieve essentially the same resultsin our comparisons to simulations regardless of this choice. For eachobserved satellite, we take the sky coordinates and heliocentric dis-tances with uncertainties from McConnachie 2012. Furthermore,we include Crater 2 and Antlia 2, which meet our stellar mass anddistance criteria as described in Samuel et al. 2020, and use thepositions and uncertainties from their discovery papers (Torrealbaet al. 2016, 2018). This brings the total number of MW satellites thatwe consider in this study to 14. We consider effects of observationalincompleteness from the Galactic disk in Section 5.3.1.We use proper motions from
Gaia
Data Release 2 as presentedin Fritz et al. 2018. We use the larger of the statistical or systematicuncertainties on
Gaia proper motions, which typically is the sys-tematic uncertainties. We take line-of-sight heliocentric velocities( 𝑣 los ) for MW satellites and their uncertainties from Pawlowski &Kroupa 2020 and Fritz et al. 2018, where available. To supplementthis, we use the proper motions and 𝑣 los for the Magellanic Cloudspresented in Kallivayalil et al. 2013, and Antlia 2’s kinematics comefrom its discovery paper (Torrealba et al. 2018).In our analysis of the MW satellite plane, we first samplethe heliocentric distances and velocities (and proper motions) 1000times assuming Gaussian distributions on the uncertainties. Wethen convert these values to a Cartesian galactocentric coordinatesystem using Astropy (Astropy Collaboration et al. 2013, 2018). Wemeasure planarity on the resulting satellite phase space coordinatesin the same way we describe for simulated satellites in Section 4.We take a different approach to sample M31’s satellites. Weimpose the same stellar mass limit of 𝑀 ∗ ≥ M (cid:12) and 3D dis-tance limit of 𝑑 host ≤
300 kpc, but we additionally require thatthe projected distance from M31 listed in McConnachie 2012 ad-here to 𝑑 host , proj ≤
150 kpc, because M31’s satellite populationis most complete within this range from the Pan-Andromeda Ar- chaeological Survey (PAndAS, McConnachie et al. 2009) coverage.We sample 1000 line-of-sight distances for each satellite, using theposterior distributions published in Conn et al. 2012 where avail-able, and elsewhere assuming Gaussian distributions on distanceuncertainties (McConnachie 2012; Martin et al. 2013). We assumethat M32 and NGC205 have the same posterior distance distribu-tion as M31 itself because they are too close to M31 to reliablydetermine their line-of-sight distances. The double-peaked posteri-ors of AndIX and AndXXVII cause the actual number of satelliteswithin 𝑑 host ≤
300 kpc of M31 in each sample to range from 14to 16, but this is unlikely to cause significant differences in ouranalysis. We take the line-of-sight velocities for M31 satellites fromMcConnachie 2012; Tollerud et al. 2012; Collins et al. 2013, andwe use them for the 2D kinematic coherence metric described inSection 4.
Figure 1 is a visual demonstration of how we measure planarityusing two spatial metrics and one kinematic metric. We show thesemetrics as measured on the MW’s 14 satellites with 𝑀 ∗ ≥ M (cid:12) and 𝑑 host ≤
300 kpc. For clarity we do not show the effects ofobservational uncertainties here, which have the largest effect onkinematic coherence, but we do include them in our analysis. Ourplanarity metric definitions are based on and consistent with thosefrom e.g., Cautun et al. 2015; Pawlowski et al. 2015; Pawlowski &Kroupa 2020. We require all planes to pass through the center ofthe host galaxy. Below, we describe in detail each metric and howwe calculated it at each simulation snapshot.
We measure the spatial coherence of satellite galaxies in two ways:root-mean-square (RMS) height ( Δ h ) and minor-to-major axis ratio( 𝑐 / 𝑎 ). The RMS height of a satellite distribution characterizes thevertical spread of satellites above and below a plane using the RMScomponent of satellites’ 3D positions along the direction normalto a plane according to Equation 1. This can be thought of as thethickness or height of the plane. We randomly generate 10 planescentered on the host galaxy and quote the minimum value amongstthese iterations. Δ h = √︄ (cid:205) N sat i = ( ˆn ⊥ · (cid:174) 𝑥 i ) N sat (1)We also use the minor-to-major axis ratio ( 𝑐 / 𝑎 ) of the satellitespatial distribution to characterize satellite planes with a dimension-less metric. This is the ratio of the square root of the eigenvaluesof the inertia tensor corresponding to the minor ( 𝑐 ) and major ( 𝑎 )axes. We define a modified moment of inertia tensor treating satel-lites as unit point masses, weighting each one equally regardlessof its stellar or halo mass, so it is a purely geometrical measure ofthe satellite distribution. The elements of the 3D inertia tensor aregiven by Equation 2. 𝐼 𝑖 𝑗 = N sat ∑︁ 𝑘 = ∑︁ 𝛼 = 𝛿 𝑖 𝑗 𝑟 𝛼,𝑘 − 𝑟 𝛼𝑖,𝑘 𝑟 𝛼 𝑗,𝑘 (2)We explored a third metric of spatial planarity, enclosing angle,motivated by the desire to mitigate effects of radially concentrated MNRAS , 1–16 (2020) atellite planes in FIRE Figure 1.
Diagram showing each plane metric that we use, as measured on the 3D positions and velocities of 14 MW satellites ( 𝑀 ∗ ≥ M (cid:12) and 𝑑 host ≤
300 kpc), shown in order of decreasing stellar mass. All planes are centered on the MW and observational uncertainties are neglected here for visualclarity. RMS height ( Δ h , left) is the root-mean-square distance of satellites from the satellite midplane. Axis ratio (middle) is the ratio of the minor-to-majoraxes ( 𝑐 / 𝑎 ) from the moment of inertia tensor of satellite positions. The ellipse shown has the same minor-to-major axis ratio as the MW’s satellites. Orbitalpole dispersion ( Δ orb , right) is the root-mean-square angle in the range [ ◦ , ◦ ] of the angular momentum unit vectors of satellites around their averagedirection. We show each metric in the same projection, to illustrate that the MW’s satellite plane is kinematically coherent within a spatially thin plane. satellite distributions on planarity measurements. We define enclos-ing angle as the smallest angle that encompasses the population ofsatellites, as measured off of the ‘midplane’ of the satellite plane.Similar to the galactocentric latitude ( 𝑏 𝑐 ) used in Section 5.3.2,the coordinate origin is placed at the center of the host galaxy. En-closing angle ranges from 0 to 180 degrees by definition, where ameasured angle of near 180 degrees indicates an isotropic distri-bution of satellites. Similar to the method used for RMS height,in practice we randomly orient planes centered on the host galaxyfrom which to measure enclosing angle, and find the minimum an-gle from these iterations. We found that this metric was significantlynoisier over time compared to the other spatial metrics, and oftenselected a different plane orientation from RMS height and axisratio, so we do not use it in our final analysis. We consider both 3D and 2D measures of orbital kinematic co-herence of satellite populations to compare against observed 3Dvelocities of satellites in the MW, and line-of-sight velocities ( 𝑣 los )of satellites around M31. The 3D metric we use is orbital poledispersion ( Δ orb ), which describes the alignment of satellite orbitalangular momenta relative to the average satellite orbital angular mo-mentum for the entire satellite population. We are not taking intoaccount the magnitude of satellite orbital velocities, so orbital poledispersion is a measure of purely directional coherence in satelliteorbits. The orbital pole dispersion is defined as the RMS angulardistance of the satellites’ orbital angular momentum vectors withrespect to the population’s average orbital angular momentum direc-tion, given by Equation 3. A system with all satellite orbital angularmomenta aligned will have Δ orb = ◦ , while a random, isotropicdistribution of satellite velocities has Δ orb ∼ ◦ Δ orb = √︄ (cid:205) N sat 𝑖 = [ arccos ( ˆn orb , avg · ˆn orb , i )] N sat (3)To investigate 2D orbital kinematic coherence around M31 we examine whether satellites share the same ‘sense of orbital direction’around their host galaxy. We measure this by computing the max-imum fraction ( 𝑓 max 𝑣 los ) of satellites with opposing (approaching orreceding) 𝑣 los on the left and right ‘sides’ of a satellite distribution.A fraction close to unity indicates a highly coherent system, anda fraction of 0.5 represents a purely isotropic system. We computethis fraction along 10 randomly generated lines of sight. To compare the ‘true’ satellite planes (as measured at each snapshot)across different simulations, we quantify the likelihood of measur-ing thinner or more kinematically coherent planes in a statisticallyisotropic distribution of satellites. This is a more general charac-terization of planarity, independent of the actual values measuredfor observed systems, that can also address whether satellite planesare statistically significant. We generate isotropic realizations ofsatellite positions by randomly generating 10 polar and azimuthalangles for each satellite, keeping their radial distance from the hostfixed, following Cautun et al. 2015. For isotropic kinematic distri-butions, we generate random unit velocities (using a similar pre-scription as for the randomization of angular coordinates) whilealso randomizing the angular spatial coordinates of each satellite.We then take measurements of each plane metric for each of the10 realizations. We quantify the significance of a planar align-ment by quoting the fraction ( 𝑓 iso ) of isotropic realizations withsmaller values of plane metrics than the true value at each snapshot.In effect this is the conditional probability of finding a more planardistribution of satellites among the isotropic realizations. A fraction 𝑓 iso ≤ . 𝑓 iso ≤ .
05 to mean the true satellite distribution is significantlyplanar.
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Figure 2.
Planarity of simulated satellite galaxies (N sat =
14 and 𝑑 host ≤
300 kpc) around MW/M31-mass hosts compared to the MW’s satellite plane. Wemodel incompleteness in the simulations by excluding any satellites that lie within ± ◦ of the plane of the host galaxy’s stellar disk. We generate KDEs(purple) using 114 snapshots over 𝑧 = − . − As we showed in Samuel et al. 2020, the simulations are a rea-sonable match to the radial distribution of satellites in the LG as afunction of both distance from the host and stellar mass of the satel-lite. This provided an important first benchmark of just the 1D radialpositions of satellites in our simulation. We now seek to leveragethe full 3D positions and velocities of satellites in our simulations(and around the MW) to characterize satellite planes. We compareour simulations to observations of LG satellites, leaving compar-isons to systems such as other MW/M31 analogues and CentaurusA for future work. In this section, we make physically rigorous com-parisons using mock observations that include disk completenesscorrections. In subsequent sections we further explore selection ef-fects on measured satellite planes and possible physical origins ofsatellite planes.
We select the 14 most massive satellites in M ∗ within 𝑑 host ≤
300 kpc to compare planarity in simulations and the 14 MW satel-lites in our observational sample. Furthermore, we apply a simplecompleteness correction for seeing through the MW’s disk by firstexcluding all satellites that lie within a galactocentric latitude of | 𝑏 𝑐 | ≤ ◦ from the host’s galactic disk (Pawlowski 2018), andthen choosing the 14 most massive satellites from the remainingpopulation. See Section 5.3.2 for an investigation of how disk in-completeness affects planarity metrics.Figure 2 shows plane metrics for simulated satellites stackingover 114 snapshots spanning 𝑧 = − .
2, compared to the MW satel-lite plane. Spatial plane metrics for the MW are tightly constrainedby well-measured 3D positions of MW satellites. The MW’s satel-lite plane is thinner and more kinematically coherent than mostof our simulated satellite systems. We define MW-like planes asthose with plane metrics at or below the one sigma upper limit onthe MW’s corresponding distribution. Notably, the MW’s plane issignificantly spatially flattened compared to the average simulationwhen measured by RMS height and axis ratio. While MW-like spatial planes are rare in our simulations, wedo identify satellite populations that are as thin as the MW’s planein 1 − − 𝑧 = − . ≈ . 𝑧 = − . ≈ . 𝑧 = − .
2. The fractionof the full sample containing these planes actually increases to 8per cent when measured over 𝑧 = − .
5, likely from the correlatedinfall of satellites in groups or along filaments at earlier times. Thespread in the MW’s orbital pole dispersion is large compared to thespatial metrics, so we also provide the fraction of the simulationsample lying at or below the median MW value, 0.3 per cent. Thereare even a few (5) snapshots that extend below the MW distribution.The MW’s satellite kinematics, while rare, do not appear to beextreme outliers compared to our simulations. This broadly agreeswith Pawlowski & Kroupa 2020, who found that ∼ − 𝑧 = sat = −
11) in both simulations and observations in order toaccount for the “look elsewhere” effect (the spurious detection ofhigh significance events from searching a large parameter space),but they find that their conclusions do not vary for any number ofplane members greater than three. The IllustrisTNG simulationsthey use allow them to analyze a larger number of hosts, in partbecause they choose to include dark subhalos as satellites in orderto maximize their sample size of hosts with at least 11 satellites. The
MNRAS , 1–16 (2020) atellite planes in FIRE Figure 3.
Planarity of the 15 simulated satellite galaxies with the highest stellar mass within 𝑑 host , proj ≤
150 kpc of each MW/M31-mass host (consistent withcompleteness in PAndAS). We generate KDEs (green) using 114 snapshots over 𝑧 = − . ∼ 𝜎 of the simulation peak. Typical simulation axis ratios (center) are even more similar to M31’s satellites.In the right panel, more planar snapshots are shown to the right of the M31 value. LOS velocity uncertainties are too small to broaden the M31 velocitycoherence measurement M31’s satellites are slightly more kinematically coherent than most simulations, but only by ∼ 𝜎 , consistent with the spatial planaritycomparisons. larger host sample size comes at the cost of resolution though, with 𝑚 DM = . × M (cid:12) , 𝑚 baryon = . × M (cid:12) , and 𝜖 DM , ∗ = . sat =
14) and we only have14 hosts. Instead, we leverage our time resolution to increase oursample size given that our planes are often transient features (seeSection 5.2.2). Our simulations also have order-of-magnitude higherresolution, which may allow planes of satellites to survive that wouldbe disrupted in lower resolution simulations. This is evidenced bytheir broad agreement with the MW and M31 in their radial distri-butions down to ∼
50 kpc (Samuel et al. 2020). Our measured planemetrics should be considered upper limits on absolute planarity ateach snapshot. If we instead varied N sat = −
14, to test for thelook-elsewhere effect, we might find even thinner or more coherentplanes. Likewise, our quoted fractions of MW-like planes are upperlimits on the incidence of MW-like planarity, as this can only bediminished by accounting for the look-elsewhere effect. Because weare always choosing a larger number of plane members (N sat = 𝑧 = − . 𝑧 = .
5, we find 10 snapshotsthat are simultaneously as thin and kinematically coherent as theMW are today. This amounts to 0.3 per cent of the total sampleof snapshots over 𝑧 = − .
5. This level of simultaneous spatialand kinematic planarity agrees with Pawlowski & Kroupa 2020,who find that thin and coherent MW-like planes occur in < . ∗ ≥ M (cid:12) )satellite galaxy. The massive satellite that passes near m12b meetsour criteria for being an LMC analog. We explore the influence ofLMC-like companions further in Section 5.4.1.We do not see a significant difference in planarity betweensatellites of isolated hosts and satellites of hosts in LG-like pairs.Both the medians and ranges of plane metrics for each host type areessentially the same, so we do not further separate our results by hosttype. In Section 4.3, when we compare true satellites distributionsto statistically isotropic distributions, the paired and isolated hostsdo not appear systematically different from each other either. Thisis consistent with results from Pawlowski et al. 2019, who reportedno significant differences in planarity between dark matter-onlysimulations of isolated MW-mass halos and paired LG-like halos inthe ELVIS simulations (Garrison-Kimmel et al. 2014). For comparison to M31’s satellites, we mimic the completeness ofPAndAS in our simulations. We first select all simulated satelliteswithin 𝑑 host ≤
300 kpc. Then, we randomly choose a line of sightfrom which to observe the simulation, and we select only the satel-lites that then fall within a (2D) projected radius of 150 kpc fromthe host galaxy. We choose the 15 satellites with greatest stellarmass that fall within our mock PAndAS-like projection, to matchthe number of M31 satellites in our observational sample. We repeatthis process along 10 random lines of sight.In order to meet the 15 satellite criteria, we do not impose alower limit on the stellar mass of satellites. At 𝑧 =
0, the lowestmass satellite included in this sample has M ∗ ≈ . × M (cid:12) .While most simulations easily meet the 15 satellite criteria, thereare a few hosts that have fewer than 15 luminous satellites withinthe mock survey area. At 𝑧 =
0, four of the isolated hosts have fewerthan 15 satellites selected (as few as 9 satellites) for some linesof sight, so we exclude those snapshots. All simulations meet thesatellite quota along most lines of sight, and in particular the hosts
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J. Samuel et al. in LG-like pairs never suffer from this issue. The results that weachieve with this satellite number selection method are essentiallythe same as for a stellar mass selection method ( 𝑀 ∗ ≥ M (cid:12) ).We use the full 3D phase space coordinates of these satellites tocalculate spatial plane metrics, because the 3D spatial coordinatesof each satellite within the coverage of PAndAS are well known.We calculate planarity metrics along each of 10 lines of sight ateach snapshot over 𝑧 = − . ∼ 𝜎 of the simulation median. Furthermore, throughout 𝑧 = − . 𝑓 max 𝑣 los , where a larger fraction indicates greater kine-matic coherence (see Section 4.2 for details). As Figure 3 shows, 14per cent of simulations are more kinematically coherent than M31’ssatellites, though this is still within about 1 𝜎 of the simulation me-dian. None of our simulations have all satellites sharing the samesense of orbital direction. Buck et al. 2016 have pointed out thata 2D metric like 𝑓 max 𝑣 los likely overestimates the true 3D kinematiccoherence, so we may be overestimating the kinematic coherence inboth our simulated and observed samples. The velocity coherenceplot (right panel) is shown as a histogram because the underlyingdistribution is essentially discretely binned. Because each satellitepopulation contains 15 satellites, the fraction of satellites sharingcoherent velocities varies from 0.53 to 1.0 in steps of ∼ .
07 (seeSection 4 for calculation details).We find that the M31 satellite population as a whole is notsignificantly more planar than our simulations. This agrees withConn et al. 2013 who found that M31’s overall satellite populationis consistent with a statistically isotropic distribution of satellites,though the 15 most-planar of its satellites lie within an exceptionallythin (12 kpc) plane. While Buck et al. 2015 use a different planefitting method different from ours (a fixed-height plane), they alsorecover many instances of satellite planes as thin as the most-planarsubset of M31 satellites.We stress that our comparison to observations is not predicatedon selecting the most planar subset of satellites in either simulationsor observations. This is because we prioritize a wholistic view of theplanarity of the satellite population as a whole, rather than highlyplanar subsets of those satellites. Other than having coherent LOSvelocities, which do not unambiguously indicate orbital coherence,the member satellites of M31’s plane are not significantly differentfrom non-members, suggesting that they do not have different for-mation mechanisms or evolutionary histories (Collins et al. 2015).In addition, sampling the satellite distributions to calculate planemetrics is computationally expensive (see Section 3), and this ismade more difficult by finding optimal planes for all satellite com-binations. We defer such an investigation to future work.For the rest of this work, we do not investigate M31-like planesfurther. Instead, we examine MW-like planes, given that complete-ness is more certain out to the virial radius, and precise 3D velocitiesof MW satellites are available. The availability of 3D velocities of MW satellites provides a more realistic metric of kinematic coher-ence.
We now move from absolute metrics of planarity to a more generalinvestigation of planarity, that is not predicated on MW or M31observations. We characterize the statistical significance of satelliteplanes in our simulations by randomizing the positions and veloci-ties of satellites in order to form a statistically isotropic distributionas a control sample (see Section 4.3 for how we set this up). By gen-erating 10 isotropic iterations and acquiring plane metrics fromthem, we create a bank of plane metrics that one might expect tomeasure if the distribution is statistically isotropic. This isotropicbank is used to compute plane significance by calculating the frac-tion ( 𝑓 iso ) of isotropic iterations that are more planar than the truemeasured value at each snapshot. In effect, this provides an esti-mate of the probability of finding a thinner or more coherent planein a random distribution of satellites. Small fractions ( 𝑓 iso < . 𝑓 iso ≥ .
5) show that the measured plane is consistent with anisotropic distribution of satellites.We distinguish between two different measures of plane statis-tical significance: conditional probability and marginalized proba-bility (following Cautun et al. 2015). Marginalized probability refersto the significance of a system’s planarity relative to an ensembleof planarity measurements on that system where the number ofsatellites considered is allowed to vary from the minimum num-ber of points needed to define a plane (3) to some maximum.Weconcentrate our analysis on conditional probability, because it rep-resents the significance of a system’s planarity given a certain set ofconstraints (such as completeness or total number of satellites). Wecalculate the significance of planes on simulations across 𝑧 = − . | 𝑏 𝑐 | ≤ ◦ . This is the same selection that we used inFigure 2.By these simple metrics, and without correcting for selectionor the look-elsewhere effect, the MW’s plane is highly significantrelative to a statistically isotropic distribution. Less than one percent of the MW’s isotropic realizations of its satellites have a thin-ner plane ( 𝑓 iso = .
003 for RMS height or axis ratio), or a morekinematically coherent plane ( 𝑓 iso = .
005 for orbital pole dis-persion). In comparison, many of our simulation snapshots havemedian 𝑓 iso (cid:38) .
5, indicating that they are broadly consistent withand have no meaningful degree of planarity relative to a statisticallyisotropic distribution of satellites. See Appendix A for a visual rep-resentation of 𝑓 iso for each host during 𝑧 = − .
2. About halfof both the isolated and paired hosts have median 𝑓 iso < .
5, andthis similarity indicates that the paired host environment does notsignificantly enhance the statistical significance of satellite planes.About half of the hosts have ∼ −
10 per cent of their snapshots with 𝑓 iso < .
05, indicating significant spatial planes for these particularsnapshots.Only 3 out of the 14 hosts have significant kinematic coherencerelative to a statistically isotropic distribution of satellite velocities,consistent with previous studies (e.g. Metz et al. 2008; Pawlowski& McGaugh 2014; Ahmed et al. 2017; Pawlowski & Kroupa 2020).Notably, none of the hosts have satellites that are simultaneouslyhighly spatially significant ( 𝑓 iso < .
05) and highly kinematically
MNRAS , 1–16 (2020) atellite planes in FIRE Figure 4.
Satellite plane lifetimes measured over 𝑧 = − . ∼
25 Myr spacing) for the 14 satellites with the greatest M ∗ within 𝑑 host ≤
300 kpc. We define lifetimes independently for each plane metric.
Left:
MW-like planes are those that have plane metrics at or below the MW upperone sigma limits. We have applied the same completeness correction for seeing through the disk as in Section 5.1.1. Such planes are rare and short-lived, withmost lasting < . ∼ >
500 Myr occur in hosts thatexperience a pericenter passage of an LMC-like satellite.
Right:
Generic planes are any flattened or kinematically coherent systems whose plane metrics fallbelow the lower 68 percent limits of our simulations shown in red in Figure 6. Generic planes are also typically short-lived and many last for only a singlesnapshot. Half of the hosts have an instance of a generic plane that last > significant relative to a statistically isotropic distribution at anysnapshot during 𝑧 = − .
2. In general, hosts that with small ( < . 𝑓 iso for spatial planarity metrics do not have correspondinglysmall 𝑓 iso for kinematic coherence (orbital pole dispersion), andvice versa. While our simulations contain instances of planes thatare simultaneously as spatially thin and kinematically coherent atthe MW in an absolute sense (by directly comparing plane metrics),the planes found in our simulations are not as significant relative toa statistically isotropic distribution. Thus far we have focused our analysis on the spatial and kinematiccoherence of satellite galaxies in our simulations over 𝑧 = − . ∼ 𝑧 = − . ∼ . ∼ ≥ < <
500 Myr to be “transient” alignments thatdo not indicate coherence amongst satellite orbits because they areso short.We examine the distribution of plane lifetimes over 𝑧 = − . ≤
28 kpc, axis ratio ≤ .
24, or orbital pole dispersion ≤ ◦ . “Generically” flattened means having plane metric values:RMS height ≤ . ≤ .
45, or orbital pole dispersion ≤ ◦ , defined by the lower 68 per cent limit on simulation planemetrics during 𝑧 = − . Δ 𝑡 plane )as the amount of time that a system spends consecutively at orbelow these plane metric thresholds. Whether a satellite system isplanar for only a single snapshot ( ∼
25 Myr) or many consecutivesnapshots, we count it as a single instance of planarity.Figure 4 shows that for both MW-like and generic planes, mostplanar instances are transient alignments and many last for just onesnapshot ( Δ 𝑡 plane <
25 Myr). There are 348 snapshots with MW-like planes in our simulations across all hosts over 𝑧 = − . (cid:38) < <
10 per cent) of separate instances extending upto 3 Gyr. One host, m12f, has a generic kinematic plane lasting 3Gyr and also experiences an LMC-like passage during this time. Weconclude that satellite planes in our simulations, regardless of exactplane metric, are typically transient alignments that do not indicate along-lived orbiting satellite structure, though the presence of LMC-like satellites can lead to longer-lived planes.We also examine our simulations for instances of satellite con-figurations that are simultaneously spatially thin and kinematicallycoherent. We use the same plane metric thresholds as above to lookat how often a satellite system meets the kinematic threshold andat least one of the spatial thresholds at the same snapshot. We donot find any instances of simultaneously thin and coherent MW-likeplanes over 𝑧 = − . sat =
14 and 𝑑 host ≤
300 kpc) or combining that with a com-pleteness correction due to seeing through the host’s galactic disk.However, there are several instances of coincident thinness and co-
MNRAS000
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5, especially when we apply a completenesscorrection for seeing through the host disk. In particular, m12b andm12r have up to 13 snapshots ( ∼
325 Myr) of simultaneous spatialand kinematic planarity over 𝑧 = − .
5. We also consider thecoincidence of generic planes, and find that m12b, m12r, and m12fall have snapshots with simultaneous spatial and kinematic planeseven without implementing a completeness correction for the hostdisk. Both m12f and m12b have LMC satellite analogues duringthis time, as we discuss in Section 5.4.1. Interestingly, none of ourhosts in LG-like pairs exhibit simultaneous planarity, reinforcingthe result that LG-like host environments are not more likely tohave satellite planes.Shao et al. 2019 looked at plane lifetimes in the EAGLE sim-ulations. They considered both a different sample size (N sat = 𝑧 ≈ − ≈ . < In our analysis of MW-like planarity thus far, we have applied a fixedobscuration correction for seeing through the host disk, maskingout everything that lies within | 𝑏 𝑐 | ≤ ◦ (where 𝑐 indicates agalactocentric coordinate system). We now analyze how the relativeincidence of MW-like planes changes as a function of how much ofthe sky is obscured by the host’s disk. We vary the region obscuredby the galactic disks of simulated hosts from 𝑏 𝑐 = ◦ (completelyunobscured) to | 𝑏 𝑐 | ≤ ◦ (majority obscured) in increments of Δ | 𝑏 𝑐 | = ◦ . For each obscured region we select the 14 most massivesatellites in M ∗ within 𝑑 host ≤
300 kpc of a host to use in the planesample. We define the relative incidence of MW-like planes asfollows: we compute the fraction of snapshots with MW-like planesfor each obscured region, and normalize it to the ‘true’ (unobscured, | 𝑏 𝑐 | = ◦ ) fraction of snapshots with MW-like planes. We repeatthis process for each plane metric individually. However, for | 𝑏 𝑐 | ≥ ◦ there are typically fewer than 14 luminous satellites in theunobscured region and near | 𝑏 𝑐 | ∼ ◦ there are only about 10satellites available on average, so we cannot draw strong conclusionsabout completeness effects in those limits.Figure 5 shows the incidence of MW-like planes, measuredindependently for each metric, as a function of disk obscuration an-gle. We find that such incompleteness artificially boosts the fractionof snapshots with MW-like spatial planes for any value of | 𝑏 𝑐 | > | 𝑏 𝑐 | = ◦ ), the incidence of MW-likeplanes is increased by about an order of magnitude. For | 𝑏 𝑐 | (cid:46) ◦ ,disk obscuration has a much smaller and opposite effect on kine-matic planarity compared to spatial planarity; MW-like kinematicplanes tend to be somewhat washed out by incompleteness. Nearour fiducial obscuration for the MW, the relative incidence of MWkinematic planes is about 0.77. As expected, disk obscuration hasthe largest effect on planarity when | 𝑏 𝑐 | ∼ ◦ , where so much of Figure 5.
Effects of disk incompleteness on measured planarity. We definethe relative incidence of MW planes as the fraction of snapshots during 𝑧 = − . | 𝑏 𝑐 | = ◦ ). We select the 14 most massive satellites in M ∗ within 𝑑 host ≤
300 kpc of each host, but for | 𝑏 𝑐 | ≥ ◦ there are usually fewer than14 luminous satellites available. The horizontal line represents consistencywith the unobscured fraction. The arrow shows the fiducial obscuration thatwe adopt for MW-like planes, | 𝑏 𝑐 | = ◦ . Spatial planarity ( 𝑐 / 𝑎 ≤ . Δ h ≤
28 kpc) is much more affected by host disk obscuration than kinematicplanarity. Spatial planarity jumps an order of magnitude between | 𝑏 𝑐 | = ◦ and | 𝑏 𝑐 | ∼ ◦ . Kinematic planarity ( Δ orb ≤ ◦ ) is slightly diminishedby host disk obscuration. At | 𝑏 𝑐 | = ◦ , we are 8 . − . × more likely tomeasure a MW-like spatial plane and 1 . × less likely to measure a MW-likekinematic plane. As expected, when nearly half of the sky is obscured spatialplanarity is highly likely to be measured. the sky is obscured that any detected satellites would appear to bein a plane purely due to incompleteness.Our results show that observational incompleteness from thehost disk can have a strong effect on measured spatial planarity. Ifthe MW’s satellite population is incomplete from seeing throughthe Galactic disk at our fiducial level, then MW observations maybe overestimating the spatial planarity of MW satellites by a fac-tor of ∼ −
20. To a much lesser degree, MW observations mayunderestimate the kinematic coherence of satellites by a factor of ∼ −
2. Because this incompleteness may bias our analysis of theunderlying causes of satellite planes, we only use a host disk correc-tion when comparing directly to MW observations in Sections 5.1.1– 5.2.2. For the remainder of this paper, we do not include a hostdisk correction.
We also explore how using a fixed number selection for satellitescompared to using a stellar mass threshold affects planarity mea-surements. Our primary method of satellite selection throughout thiswork is to choose the 14 most massive satellites by rank-orderingthem in stellar mass, because the number of satellites in a sam-ple strongly correlates with the measured planarity (e.g. Pawlowskiet al. 2019). In terms of observational completeness and resolutionin simulations, another way to select satellites may be to impose asimple stellar mass threshold. So we test our fixed number selec-tion against a stellar mass threshold method: 𝑀 ∗ ≥ M (cid:12) and MNRAS , 1–16 (2020) atellite planes in FIRE Figure 6.
Planarity of simulated satellite galaxies ( 𝑑 host ≤
300 kpc) selected using a fixed number method versus a stellar mass threshold. Note that we do notinclude a correction for completeness due to seeing through the host galactic disk here. We generate KDEs using 114 snapshots over 𝑧 = − . 𝑀 ∗ ≥ M (cid:12) . Thin and coherent planes are rare in the simulations using these particular selections and timebaseline, but using the number selection for satellites yields lower (more planar) metrics because the stellar mass selection allows for many more satellites tobe included (N sat = − 𝑑 host ≤
300 kpc. However, this leads to a range of numbers of satel-lites selected around each host, which makes it difficult to compareplane metrics across simulations and observations. The total num-ber of satellites with 𝑀 ∗ ≥ M (cid:12) and 𝑑 host ≤
300 kpc per hostvaries from 10-31 during 𝑧 = − . sat =
14 tend to be boththinner and more kinematically coherent than planes with 𝑀 ∗ ≥ M (cid:12) , because while some 𝑀 ∗ ≥ M (cid:12) satellite populationshave N sat <
14, more actually have N sat >
14. One consequenceis that when using the M ∗ selection the simulations never reachthe MW’s RMS height (27 kpc) during 𝑧 = − .
2, but the fixednumber selection does. The small bump in the N sat =
14 orbitalpole dispersion distribution is from a single host, m12f, duringthe snapshots following a close passage of an LMC-like satellite.We discuss effects of such an LMC-like companion further in thefollowing section.This selection exercise highlights an important aspect of thesatellite plane problem: many of the conclusions drawn about thenature of satellite planes are sensitive to satellite selection method,likely because of underlying sensitivity to the number of satellitesin the sample. Had we used the stellar mass threshold as our fidu-cial selection method in previous sections, we would have foundmore evidence for tension between simulations and observations,but deciding whether that tension is cosmologically significant ishampered by the sensitivity of plane metrics to both incompletenessand sample selection.
The presence of a massive satellite galaxy near pericenter, like theLarge Magellanic Cloud (LMC), has been suggested as a possibleexplanation for the dynamical origin of the MW’s satellite plane(Li & Helmi 2008; D’Onghia & Lake 2008), from the accretionof multiple satellites in a group with the LMC (e.g., Wetzel et al.2015b; Deason et al. 2015; Jethwa et al. 2016; Sales et al. 2017; Jahnet al. 2019). We seek to determine whether or not the presence of anLMC-like companion has an effect on the planarity in simulations. We compare planarity metrics measured on systems experiencingan LMC-like passage to those without an LMC-like passage. Weidentify pericentric passages of four LMC-mass analogues in oursimulations based on the following selection criteria:(i) 𝑡 peri > . 𝑧 < . sub , peak > × M (cid:12) and M ∗ > M (cid:12) (iii) 𝑑 peri <
50 kpc(iv) The satellite is at its first pericentric passage.This broad time window allows us to capture a larger numberLMC-like passages, which tend to be rare as we have defined them.The minimum mass is consistent with measurements of the LMC’smass (Saha et al. 2010), and the maximum pericenter distance re-flects the measured distance and orbit of the LMC (Freedman et al.2001; Besla et al. 2007; Kallivayalil et al. 2013). Table 1 lists thefour hosts in our simulations with LMC satellite analogues thatmeet these criteria, all of which are from simulations of isolatedMW-like hosts rather than paired/LG-like hosts. We emphasize thatthese satellites are not the only sufficiently massive satellites in thesimulations, but that they are the only instances that satisfy all ourLMC analogue criteria simultaneously.To compare planarity during LMC-like passages and other-wise, we first select all snapshots within ± ∼
250 Myr) of the LMC-like pericenter passage in each ofthe four simulations containing an LMC analogue. This gives usa total of 44 snapshots that we classify as occurring close enoughto an LMC analogue pericenter to exhibit any dynamical effects ofgroup infall. We compare plane metrics from those snapshots toplane metrics measured on all other simulations (excluding the fourhosts with LMC analogues) up to the earliest snapshot included inthe LMC sample ( 𝑧 ∼ − .
7, 247 snapshots per host). We applyour fiducial disk obscuration correction, masking out all satelliteswithin | 𝑏 𝑐 | ≤ ◦ of the hosts’ galactic disks in our simulations.To calculate plane metrics we select N sat =
14 of the most massivesatellites ranked by stellar mass.Figure 7 summarizes our results for the planarity of satellitesduring an LMC analogue pericenter passage compared to all othersatellite systems during 𝑧 ∼ − .
7. In general, the presence ofan LMC analogue leads to thinner and more kinematically coher-
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Table 1.
Properties of the LMC satellite analogues at their first pericentric passage about their MW/M31-mass host in our FIRE-2 simulations. We selectsatellites with M sub , peak > × M (cid:12) and M ∗ > M (cid:12) that have their first pericenter after 7.5 Gyr ( 𝑧 < .
7) and within 50 kpc of their host.Host M sub , bound [10 M (cid:12) ] M sub , peak [10 M (cid:12) ] M ∗ [10 M (cid:12) ] 𝑡 peri [Gyr] 𝑧 peri 𝑑 peri [kpc]m12b 12.0 2.1 7.1 8.8 0.49 38m12c 5.1 1.6 1.2 12.9 0.07 18m12f 6.0 1.5 2.6 10.8 0.26 36m12w 4.9 0.8 1.3 8.0 0.59 8 Figure 7.
Planarity of satellites of hosts experiencing a first pericenter passage of an LMC satellite analogue (red) compared to all other hosts without anLMC-like passage (blue). We rank order satellites by stellar mass and choose the 14 most massive around each host within 𝑑 host ≤
300 kpc. We select snapshotswithin ±
125 Myr of LMC-like passages that occur during 𝑧 = − .
7. Only 4 hosts have such LMC-like passages (see Table 1). Vertical colored lines are themedians of the simulation distributions. MW planarity values are the vertical black lines and shaded regions. We apply a disk obscuration correction and omitsatellites within | 𝑏 𝑐 | ≤ ◦ . LMC passages push towards ∼
20 per cent lower plane metric medians and smaller ranges of spatial planarity metrics. MW-likeplanes are ∼ − ent satellite planes on average. The presence of an LMC analogueshrinks the range of spatial plane metric values and slightly shiftsthem towards smaller (thinner) values. In particular, the range ofaxis ratios is much smaller in the presence of an LMC analogue.The right panel of Figure 7 also shows that the presence of an LMCanalogue is correlated with more of the simulation distribution hav-ing tighter orbital alignment of satellites. For all three metrics, weare ∼ − − 𝑀 ∗ ≥ M (cid:12) , consistent with the results pre-sented in Jahn et al. 2019 for both likely satellites of the LMC andFIRE-2 simulation predictions for satellites of LMC-mass hosts.Of the 2 − − sat =
14 satellites in the plane sample. The host withthe most planar configuration that we find (m12b), which also hasinstances of simultaneous spatial and kinematic planarity, bringsin four satellites with 𝑀 ∗ ≥ M (cid:12) and three of these (plus theLMC analogue itself) are counted in the plane calculations. Thismeans that the LMC analogue and its satellites account for ∼ . − ∼ − We also ran all of our simulations without baryonic physics, exceptfor one of the isolated hosts, m12z. We compare planarity of thesedark matter-only (DMO) simulations to our baryonic simulationsin order to investigate potential baryonic effects on satellite planes,given that many previous studies of planes have used DMO simula-tions. We ran the DMO simulations with the same number of DMparticles and the same gravitational force softening. We compare
MNRAS , 1–16 (2020) atellite planes in FIRE Figure 8.
Planarity in baryonic versus dark matter-only (DMO) simulations. We compare the 14 most massive baryonic satellites and subhalos to DMOsubhalos within 𝑑 host ≤
300 kpc. We rank order subhalos by M peak and satellites by M ∗ . We generate KDEs using 114 snapshots per host over 𝑧 = − . planes in our baryonic simulations to planes in their DMO coun-terparts by selecting luminous satellites and dark matter subhaloswithin 𝑑 host ≤
300 kpc. We choose the 14 most massive object fromeach sample by rank ordering satellite galaxies by M ∗ and subhalosusing M peak .Figure 8 shows the distributions of planarity for satellite galax-ies and subhalos, both selecting the top 14 subhalos by M peak andthe top satellite galaxies by M ∗ , which are not identical samplesbecause of scatter in the M ∗ − M peak relation. The satellite galaxydistributions (red) are identical to those in Figure 6. While the threedistributions have slightly different shapes, they have almost thesame ranges and medians. Using a rank ordering selection, the pla-narity of DMO subhalos is essentially identical to that of baryonicsatellites. We find that this general result is robust with respect torank ordering subhalos by different properties such as M halo , V peak ,and V circ . The one exception is a small population of baryonic satel-lites that extend to lower orbital dispersion values due to the passageof an LMC-like satellite (see Section 5.4.1).These results are surprising in light of the differences in theradial distributions of satellites and subhalos in our simulations,wherein DMO subhalos are more radially concentrated around theirhost than luminous satellites (Samuel et al. 2020). One might expectto find thinner planes in DMO simulations because subhalos residespatially closer to the host halo. Alternatively, one might expectbaryonic simulations to show greater planarity, given that the sur-viving population is biased to more tangential orbits (e.g. Garrison-Kimmel et al. 2017). Ahmed et al. 2017 observed both a differencein the significance and satellite membership of their planes in bary-onic versus DMO simulations of the same four systems. Satellitemembership here refers to whether the satellites contributing toplanes belong to the same subhalos in baryonic and DMO runsof the same systems. While we do not explicitly consider differ-ences in satellite membership, we do find that our DMO spatialplanes are also typically more significant relative to a statisticallyisotropic distribution of satellites than their baryonic counterparts,with most having 𝑃 < . 𝑧 = − .
2. However, the sig-nificance of DMO kinematic planes is on par with the baryonicsimulations. So while we find that the significance of spatial planesmay be slightly overestimated in DMO simulations relative to bary-onic simulations, the absolute planarity is not much different fromthat in baryonic simulations. If, instead, we select subhalos at a
Table 2.
Correlations between planarity in simulations and properties ofthe host and radial distribution of satellites. We select satellite galaxies byrank ordering them by stellar mass at each snapshot and choosing the 14most massive. We measure host halo properties using only dark matter. Wequote the correlation coefficients ( 𝑟 ) and 𝑝 -values given by the Spearmancorrelation test. For brevity, we only show correlations with 𝑝 < .
1, thoughwe note that only 𝑝 (cid:46) .
01 indicates a significant correlation in our sample.Planarity metric Host/system property 𝑟 𝑝 -valueRMS height Host halo concentration 0.49 0.07Host M ∗ ∗ / M halo 𝑅 𝑅 / 𝑅 𝑅 / 𝑅 fixed value of 𝑀 peak ≥ × M (cid:12) , DMO simulations typicallyhave many more subhalos meeting this criteria. This difference innumber of subhalos in the plane sample reduces planarity in DMOsimulations, because planes with more members are general lessplanar (Pawlowski et al. 2019). Finally, we explore relationships between satellite planarity and hostand satellite system properties, but we find few correlations. Wequantify correlation using the Spearman correlation coefficient ( 𝑟 )and 𝑝 -value, applied to the median value of each plane metric andhost property over 𝑧 = − . 𝑟 < .
7. Wesummarize correlations in Table 2, where we only show correlationswith 𝑝 < . 𝑝 (cid:46) .
01 indicatea statistically significant correlation in our sample, and there is onlyone correlation meeting this criteria.We considered four host properties: stellar mass, dark matterhalo mass (M ), stellar-to-total mass ratio, and halo concentra-
MNRAS000
MNRAS000 , 1–16 (2020) J. Samuel et al. tion. Both of the spatial metrics correlate with the host halo axisratio, such that more triaxial host halos are more likely to havethinner satellite planes. RMS height is also correlated with hoststellar mass, whereby more massive host disks may act to disruptrather than promote thin planes. Orbital dispersion does not cor-relate significantly with any of the host properties. While there issome evidence for spatial planarity correlating with host halo axisratio, the correlations are not strong (0 . < 𝑟 < . 𝑟 = .
68 and 𝑝 = .
01) exists between RMS height and 𝑅 , the radiusenclosing 50 per cent of the satellites. This correlation may arisefrom more satellites being near pericenter, rather than actually beingflattened into a thin plane, because RMS height is a dimensionalquantity (unlike dimensionless axis ratio), so we would expect it tocorrelate with satellite distances. We also examine planarity as afunction of 𝑅 / 𝑅 and 𝑅 / 𝑅 , where 𝑅 / 𝑅 is the ratio ofthe distance from the host that encloses 90 per cent of the satellitepopulation to the distance from the host that encloses 50 per centof the satellite population, and 𝑅 / 𝑅 is similarly defined. Theseratios describe the radial concentration of the satellites around theirhost, and they are the only metrics that significantly correlate withorbital dispersion. In both cases, more concentrated satellite systemsare correlated with less kinematically coherent planes. We explored the incidence and origin of planes of satellite galaxiesin the FIRE-2 simulations, using satellites around 14 MW/M31-mass galaxies over 𝑧 = − .
2. We compared to and provided contextfor satellite planes in the Local Group, including all satellites with 𝑀 ∗ ≥ M (cid:12) around the MW and within the PAndAS survey ofM31. We summarize our main results as follows. • MW-like planes exist in our simulations, but they are relativelyrare among our randomly selected ∼ 𝑀 (cid:12) halos at 𝑧 = − . ∼ − spatial and kinematic metrics simultaneously occur in ∼ . • However , if we select halos that feature a LMC-mass satelliteanalogue near its first pericentric passage, then the frequency ofMW-like or thinner planes dramatically increases to 7 −
16 per cent,with ∼
5% at least as thin as the MW plane by spatial and kinematicmetrics simultaneously. • If we consider M31’s satellite population as a whole, the pla-narity of satellites around M31 is common in our simulations. Byevery spatial or kinematic (or simultaneous) measure we consider, M31’s satellites lie within ∼ 𝜎 of the median of randomly selectedhalos of similar mass that we simulated. • Most of our simulations are not significantly planar relative toa statistically isotropic distribution of satellites. • Most MW-like thin satellite planes are transient and last < ∼ . − ∼ − • We do not find significant differences in planarity of satellitesaround hosts in Local Group-like pairs versus isolated hosts. • Dark matter-only (DMO) simulations show no significant dif-ferences in planarity compared to their baryonic-simulation coun-terparts, when selecting a fixed number of satellites in each sample. • Correlations between plane thickness and other satellite pop-ulation properties (radial concentration) or host properties (mass,concentration, size, axis ratio) are generally modest or weak. Planethickness is generally larger for more radially extended satellitedistributions, as expected. The one property that strongly correlateswith the presence of spatially thin and kinematically coherent planesis the presence of an LMC analogue near first pericentric passage. • Plane metrics can be sensitive to the satellite selection methodin simulations and observations. Selecting just the 14 satellite galax-ies with the highest stellar mass in the simulation produces thinnerplanes compared to selecting all satellites with 𝑀 ∗ > 𝑀 (cid:12) ,because the latter tends to select more satellites, which producesthicker planes. • Incompleteness from the inability to see through the hostgalaxy disk (as in the MW) can increase the probability of mea-suring MW-like spatial planes by as much as a factor ∼
10. Thisbias is opposite in sign but much smaller for kinematic planes. • We have not corrected in any of our analysis for any ‘look-elsewhere’ effects, including the choice to look for ‘planes’, thechoice of definition of ‘plane’, sample selection, number of satel-lites, etc. These corrections only would decrease the statistical sig-nificance of the observed planes, as outliers from simulations.
While only 1-2 percent of snapshots for all 14 hosts during z=0-0.2contain planes at least as thin as the MW’s, we do not interpretthis as a tension with Λ CDM cosmology. Instead, we identify themere presence of MW-like planes in the simulations as evidence thatcosmological simulation indeed can form thin planes of satellites, aslong as they have adequate mass and spatial resolution. We find thatplanes are much more common in the presence of LMC analogues,as suggested by Li & Helmi 2008; D’Onghia & Lake 2008, whichprovides evidence that future work should prioritize comparingthe MW against simulations with an LMC analog. Consideringthe entire M31 satellite population, M31-like satellite planes arecommon in our simulations, and combined with the fact that oursimulations are only marginally more planar than a statisticallyisotropic distribution of satellites, this may indicate that M31’ssatellites as a whole are not significantly planar. The lack of strong
MNRAS , 1–16 (2020) atellite planes in FIRE correlations between planarity and other properties of the host-satellite systems leaves us with few physical explanations for theMW’s highly coherent satellite plane. Our most promising resultpoints to the presence of the LMC near first pericenter as a likelyprimary driver of planarity. If our simulations are representative ofthe MW, then the observed MW plane is likely to be a temporaryeffect that will wash out in subsequent orbits of the LMC (Deasonet al. 2015).We have deliberately approached our analysis of satellite planesas agnostically as we can. In choosing a fixed number of satellitesfor our nominal selection method, we have tried to both show theclearest comparisons between our simulations and LG observations,as well as mitigate the confounding effects of correlations betweenN sat and planarity. Further studies of the most-planar subsamplesof simulated satellites, as examined in Pawlowski et al. 2013 andextended in Santos-Santos et al. 2020, may yield more insight intothe nature of satellite planes. We defer an analysis of satellite sub-samples to future work.We also have not yet considered a comparison to satellite sys-tems outside of the LG. There is evidence for satellite planes out-side of the LG around Centaurus A (Müller et al. 2018), and recentstudies have examined planarity around hosts in SDSS (Ibata et al.2014a; Brainerd & Samuels 2020) and the SAGA survey (Mao et al.2020). Connecting LG hosts to a statistical sample of similar hostswill be crucial in evaluating the significance of planar alignmentsand the validity of proposed formation mechanisms, demonstratingthe need for large surveys with e.g., the Nancy Grace Roman SpaceTelescope, which promises to significantly augment the observa-tional sample of MW analogues. LG galaxies are also aligned withlarge scale structure, along a local sheet, which is not captured inour simulations and may play a part in the formation of satelliteplanes (Neuzil et al. 2020). Simulations that can accurately repro-duce this large scale structure may offer new insight into satelliteplanes (Libeskind et al. 2020). ACKNOWLEDGEMENTS
We thank Marcel Pawlowski for insightful comments and discussionthat improved this manuscript.This research made use of Astropy, a community-developedcore Python package for Astronomy (Astropy Collaboration et al.2013, 2018), the IPython package (Pérez & Granger 2007), NumPy(Harris et al. 2020), SciPy (Jones et al. 2001), Numba (Lam et al.2015), and matplotlib, a Python library for publication qualitygraphics (Hunter 2007).JS, AW, and SC received support from NASA through ATPgrants 80NSSC18K1097 and 80NSSC20K0513; HST grants GO-14734, AR-15057, AR-15809, and GO-15902 from the Space Tele-scope Science Institute (STScI), which is operated by the Associ-ation of Universities for Research in Astronomy, Inc., for NASA,under contract NAS5-26555; the Heising-Simons Foundation; anda Hellman Fellowship. We performed this work in part at the AspenCenter for Physics, supported by NSF grant PHY-1607611, and atthe KITP, supported NSF grant PHY-1748958. PFH was providedby an Alfred P. Sloan Research Fellowship, NSF grant from NASA grants NNX17AG29G and HST-AR-13888, HST-AR-13896, HST-AR-14282, HST-AR-14554, HST-AR-15006, HST-GO-12914, and HST-GO-14191 from STScI. CAFG was supportedby NSF through grants AST-1517491, AST-1715216, and CAREERaward AST-1652522, by NASA through grant 17-ATP17-0067, andby a Cottrell Scholar Award from the Research Corporation forScience Advancement. We ran simulations using the Extreme Sci-ence and Engineering Discovery Environment (XSEDE) supportedby NSF grant ACI-1548562, Blue Waters via allocation PRACNSF.1713353 supported by the NSF, and NASA’s HEC Programthrough the NAS Division at Ames Research Center. DATA AVAILABILITY
Full simulation snapshots at 𝑧 = ananke.hub.yt . The publicly availablesoftware packages used to analyze these data are availble at: https://bitbucket.org/awetzel/gizmo_analysis , https://bitbucket.org/awetzel/halo_analysis , and https://bitbucket.org/awetzel/utilities . REFERENCES
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APPENDIX A: COMPARISON TO STATISTICALLYISOTROPIC REALIZATIONS
We provide a visual representation of how planar each host’s satellitesystem is relative to 10 statistically isotropic random realizationsof satellite positions and velocities. We describe this calculation indetail in Sections 4.3 and 5.2.1. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS , 1–16 (2020) atellite planes in FIRE Figure A1.
The significance of simulated and observed plane metrics from Figure 2 relative to 10 statistically isotropic realizations of satellite positions(keeping radial distance fixed) and velocities (considering only their directions). For each simulated host we plot the median and 95 per cent scatter during 𝑧 = − . 𝑓 iso ) of isotropic realizations that are more planar than the true plane. We consider hosts with median 𝑓 iso ≤ .
25 and lower 95per cent limit 𝑓 iso ≤ .
05 to have significant planes (blue). The MW’s plane is highly significant relative to its statistically isotropic distribution, both spatially( 𝑓 iso = . 𝑓 iso = . 𝑧 = − .
2. None of the simulated hosts are significant in botha spatial and kinematic sense, and most hosts are consistent with a statistically isotropic distribution. While MW-like planes do occur in the simulations, theyare not as significant as the MW’s plane.MNRAS000