Evolution of galactic planes of satellites in the EAGLE simulation

TL;DR

This study uses the EAGLE simulation to analyze the formation and evolution of satellite galaxy planes around Milky Way-like haloes, revealing their transient nature and the influence of host halo shape on satellite orbits.

Contribution

It introduces a robust method to identify co-planar satellite orbits and demonstrates the transient and anisotropic nature of satellite planes in galaxy formation simulations.

Findings

Most MW satellites have highly clustered orbital planes.

Satellite planes are short-lived, lasting less than 1 Gyr.

Satellite systems were flatter in the past, around 9 Gyr ago.

Abstract

We study the formation of planes of dwarf galaxies around Milky Way (MW)-mass haloes in the EAGLE galaxy formation simulation. We focus on satellite systems similar to the one in the MW: spatially thin or with a large fraction of members orbiting in the same plane. To characterise the latter, we introduce a robust method to identify the subsets of satellites that have the most co-planar orbits. Out of the 11 MW classical dwarf satellites, 8 have highly clustered orbital planes whose poles are contained within a $22^\circ$ opening angle centred around $(l,b)=(182^\circ,-2^\circ)$. This configuration stands out when compared to both isotropic and typical $\Lambda$CDM satellite distributions. Purely flattened satellite systems are short-lived chance associations and persist for less than $1~\rm{Gyr}$. In contrast, satellite subsets that share roughly the same orbital plane are longer lived, with half of the MW-like systems being at least $4~\rm{Gyrs}$ old. On average, satellite systems were flatter in the past, with a minimum in their minor-to-major axes ratio about $9~\rm{Gyrs}$ ago, which is the typical infall time of the classical satellites. MW-like satellite distributions have on average always been flatter than the overall population of satellites in MW-mass haloes and, in particular, they correspond to systems with a high degree of anisotropic accretion of satellites. We also show that torques induced by the aspherical mass distribution of the host halo channel some satellite orbits into the host's equatorial plane, enhancing the fraction of satellites with co-planar orbits. In fact, the orbital poles of co-planar satellites are tightly aligned with the minor axis of the host halo.

Tables

Table 1. Table 1: The distribution of the orbital poles of the classical satellites, given in terms of Galactic longitude, l 𝑙 l , and latitude, b 𝑏 b . The first 8 satellites in this table orbit in approximately the same plane whose normal is given by ( l , b ) = ( 182.3 ∘ , − 1.8 ∘ ) 𝑙 𝑏 superscript 182.3 superscript 1.8 (l,b)=(182.3^{\circ},-1.8^{\circ}) (see Fig. 2 ). The last column gives the angle, Δ Δ \Delta , between each orbital pole and the normal to this plane (see Eq. 2 ). The satellites are ordered in ascending order of the Δ Δ \Delta values.

Name	$l{[}^{\circ }]$	$b{[}^{\circ }]$	$\Delta {[}^{\circ }]$
Satellites orbiting in nearly the same plane
LMC	175.3	-6.0	8.2
Sculptor†	353.0	-2.7	10.3
SMC	192.0	-10.3	12.9
Ursa Minor	198.3	-5.1	16.3
Draco	171.7	-17.1	18.5
Carina	161.9	-8.5	21.3
Fornax	186.8	19.3	21.6
Leo II	191.0	-22.0	21.9

Equations

$$I_{ij}\equiv \sum _{k=1}^N{x}_{k,i}{x}_{k,j},$$

$${\Delta }_{ij}=\arccos \left(|{\hat{n}}_i\cdot {\hat{L}}_j|\right),$$

Full text

††pubyear: 2019††pagerange: Evolution of galactic planes of satellites in the eagle simulation–3.2

1 Introduction

The Milky Way (MW) satellites have a highly inhomogeneous and anisotropic phase-space distribution whose origin remains one of the most baffling cosmological mysteries. All the classical dwarfs and many of the ultra-faint ones lie on a plane which shows an unexpectedly high degree of flattening (e.g. Kunkel & Demers, 1976; Lynden-Bell, 1976, 1982; Kroupa et al., 2005; Pawlowski, 2016). Many of the satellites have orbits within this plane (e.g. Metz et al., 2008; Pawlowski & Kroupa, 2013; Fritz et al., 2018) and the classical dwarfs have orbits that are more circularly biased than predicted by the current cosmological model (Cautun & Frenk, 2017). Furthermore, the plane in which most of the satellites reside is nearly perpendicular to the MW disc (e.g. Lynden-Bell, 1982; Libeskind et al., 2007; Deason et al., 2011; Shao et al., 2016), in contrast with observations of external galaxies where most satellites are found within the disc plane of the central galaxy (e.g Brainerd, 2005; Yang et al., 2006; Agustsson & Brainerd, 2010; Nierenberg et al., 2012).

Observational studies have reveal that flattened satellite distributions similar to the MW system are ubiquitous. Our two nearest giant neighbours, M31 and Centaurus A, both have one or more planes of satellite galaxies (e.g. Conn et al., 2013; Shaya & Tully, 2013; Tully et al., 2015), with many of their members showing correlated line-of-sight velocities that potentially a indicate co-rotating configuration (Ibata et al., 2013; Müller et al., 2018; Hodkinson & Scholtz, 2019). Farther afield, Cautun et al. (2015a) have shown that external galaxies also have anisotropic satellite distributions.

Within the standard cosmological model, the anisotropic distribution of satellites is a manifestation of the preferential direction of accretion into haloes (e.g. Aubert et al., 2004; Knebe et al., 2004; Zentner et al., 2005; Deason et al., 2011; Wang et al., 2014; Shi et al., 2015; Buck et al., 2015). The plane of satellites most likely reflects the connection between a galaxy and its cosmic web. Multiple satellites are accreted along the same filament (Libeskind et al., 2005; Buck et al., 2015) which leads to a significant population of co-rotating satellites (Libeskind et al., 2009; Lovell et al., 2011; Cautun et al., 2015a). Correlated satellite orbits can arise from the accretion of dwarf galaxy groups (e.g. Li & Helmi, 2008; Wang et al., 2013; Smith et al., 2016; Shao et al., 2018a). However, the MW plane of satellites is unlikely to have originated from the accretion of most of the satellites either in one group or along one filament (Shao et al., 2018a, see also Metz et al. 2009; Pawlowski et al. 2012).

Most studies of the MW plane of satellites have focused on the population of classical satellites because these objects are the ones with the most precise proper motion measurements (e.g. Gaia Collaboration et al., 2018) and because we have only a partial census of fainter satellites, with more than half of the predicted population of MW ultra-faint dwarfs awaiting discovery (Newton et al., 2018). While most $\Lambda$CDM haloes have planes of satellite galaxies, the properties of each plane vary from system to system (Cautun et al., 2015b) indicating that the planes encode information about the formation history of the host. For example, Shao et al. (2016) showed that while most dark matter haloes are aligned with their central galaxies, this might not be the case for the MW, and is a consequence of the Galactic plane of satellites being nearly perpendicular on the MW disc. A plane of satellites could also indicate a major merger during the evolution of the host (e.g. Hammer et al., 2013; Smith et al., 2016; Banik et al., 2018).

Most $\Lambda$CDM planes of satellite galaxies are transient features, with their thickness and orientation varying in time (Bahl & Baumgardt, 2014; Buck et al., 2016). This is a result of many of the members not moving within the plane and also due to gravitational interactions between satellites, which have the net effect of diminishing phase space correlations (e.g. Fernando et al., 2017, 2018). The same holds true for the Galactic plane of satellites, since several of the classical dwarfs orbit outside the plane (e.g. Gaia Collaboration et al., 2018). Moreover the MW has the Large Magellanic Cloud (LMC) which is thought to be massive (Peñarrubia et al., 2016; Shao et al., 2018b; Cautun et al., 2019) and thus might also perturb the obits of the other satellites (e.g. Gómez et al., 2015). Even in the ideal case, that is when assuming a spherical MW halo and when neglecting satellite interactions, the Galactic plane of satellites is short lived and loses its thinness in ${\sim}1~{}\rm Gyr$ (Lipnicky & Chakrabarti, 2017, the proper motion errors make the timescale somewhat uncertain – e.g. see Pawlowski et al. 2017).

In this paper we study the formation and evolution of planes of satellite galaxies similar to the one observed in our galaxy. For this, we use the eagle galaxy formation simulation (Schaye et al., 2015) which is ideal for this study since it contains a large sample of MW-mass haloes with satellite populations similar to the MW classical dwarfs. We start by identifying analogues of the MW system in terms of either the thinness or the degree of coherent rotation of the satellite distribution. We study the stability of the planes of satellites and how the phase-space distribution of satellites in these systems compares with that of the overall population of MW-mass haloes. In particular, we focus the analysis on systems where most satellites orbit roughly in the same plane, since these are both the most stable planes and also the ones that contain the largest amount of information about the accretion history of the MW satellites.

The paper is organised as follows. Section 2 reviews the eagle simulation and describes our sample selection; Section 3 introduces the two methods we use for identifying planes of satellite galaxies; Section 4 presents our results on the formation and evolution of planes of satellites; we conclude with a short summary in Section 5.

2 Observational and simulation data

Here we give an overview of the MW data and the galaxy formation simulation used in our study. We also describe the selection criteria of our sample of MW-like systems and how we follow the evolution of these systems across multiple simulation outputs.

2.1 Observational data

We study the spatial and orbital distribution of the 11 classical dwarfs of our galaxy. This choice is motivated by two considerations. Firstly, it is thought that the classical dwarfs are bright enough that we have a nearly complete census of them. Secondly, we need galaxy formation simulations that contain a large number of MW-mass haloes. Such simulations have limited resolution, and even state-of-the-art ones, such as eagle, resolve only the most massive substructures of MW-mass haloes.

We use the sky coordinates, distances and radial velocities of the classical dwarfs from the McConnachie (2012) compilation. The satellite proper motion are taken from the Gaia DR2 release (Gaia Collaboration et al., 2018), except for the Leo I and II satellites, for which we use the HST proper motions since they have lower uncertainties (Sohn et al., 2013; Piatek et al., 2016). We then transform the satellite coordinates and velocities to the Galactic Centre reference frame (for details see Cautun et al., 2015b). The thickness of the satellite plane (see Eq. 1) and the orbital pole directions are calculated in this Galactic Centre frame.

2.2 The EAGLE simulation

We make use of the main cosmological hydrodynamical simulation (labelled Ref-L0100N1504) performed as part of the eagle project (Schaye et al., 2015; Crain et al., 2015). The main eagle run is ideal for this work since: i) due to its large volume, it contains a large number of MW-mass haloes, ii) it has a high enough resolution to resolve satellites similar to the classical dwarfs and follow their orbits, and iii) resolves the baryonic processes that affect the orbits of satellites, such as torquing and tidal stripping due to the presence of a central galaxy disc (see e.g. Ahmed et al., 2017).

The main eagle run simulates a periodic cube of $100~{}\rm Mpc{}$ side length using $1504^{3}$ dark matter particles and an equal number of baryonic particles. The dark matter particles have a mass of $9.7\times 10^{6}{~{}\rm M_{\odot}}$, while the gas particles have an initial mass of $1.8\times 10^{6}{~{}\rm M_{\odot}}$. eagle assumes a Planck cosmology (Planck Collaboration XVI, 2014) and uses galaxy formation models calibrated to reproduce: the stellar mass function, the distribution of galaxy sizes, and the relation between supermassive black hole mass and host galaxy mass.

We make use of the eagle halo and galaxy merger trees described in McAlpine et al. (2016). Haloes and galaxies were identified using the subfind code (Springel et al., 2001; Dolag et al., 2009) applied to the full matter distribution (dark matter, gas and stars). It consist of first identifying friends-of-friends (FOF) haloes using a linking length of $0.2$ times the mean particle separation (Davis et al., 1985), after which each FOF halo is split into gravitationally bound substructures. The most massive subhalo is classified as the main halo and its stellar distribution as the central galaxy. The main haloes are characterized by the mass, $M_{200}$, and radius, $R_{200}$, that define an enclosed spherical overdensity of $200$ times the critical density. The position of each subhalo and galaxy is given by the particle that has the lowest gravitational potential energy. The merger tree was built on top of the subfind catalogues using the D-Trees algorithm (Jiang et al., 2014). The method works by tracing the most bound particles associated with each subhalo, and identifying in the subsequent simulation outputs the subhalo which contains the largest fraction of these particles.

2.3 Sample selection

To identify systems similar to the MW, we start by selecting the 3209 present day haloes with mass, $M_{200}\in[0.3,3]\times 10^{12}{~{}\rm M_{\odot}}$. The wide mass range is motivated by the large uncertainties in the mass of the MW (e.g. see Fig. 7 of Callingham et al., 2019) and the need to have a large sample of such systems. We require that any such halo be isolated and thus we remove any galaxy that has a neighbour within $600~{}\rm kpc$ that has a stellar mass larger than half their mass. We also restrict our selection to systems that, like the MW, have at least 11 luminous satellites within a distance of $300~{}\rm kpc$ from the central galaxy. We define luminous satellites as any subhaloes that has at least one stellar particle associated to them; this corresponds to objects with stellar mass higher than ${\sim}1\times 10^{6}{~{}\rm M_{\odot}}$. We find 1080 host haloes that satisfy all three selection criteria, with the resulting sample having a median halo mass, $M_{200}\sim 1.2\times 10^{12}{~{}\rm M_{\odot}}$ (the distribution of host halo masses is shown in Fig. A1 of Shao et al. 2016).

To study the evolution of satellite systems, we make use of the eagle snipshots, which are finely spaced (about every 70 Myrs) simulation outputs that allow us to trace the orbits of satellites with very good time resolution. For each satellite and its central galaxy, we trace their formation history using the most massive progenitor in the merger trees. Starting at high redshift, we follow forward the merger tree of each satellite in tandem with the merger tree of its present day central galaxy, until we find the first snapshot where the satellite and the central are part of the same FOF group; we then define the epoch of that snapshot as the infall time for the satellite. In a small number of cases satellite galaxies may drift in and out of the host FOF halo. Even in those cases, we define the accretion time as the first time the satellite enters the progenitor of the $z=0$ host halo.

3 Methods

Here we describe the two approaches we use to identify analogues of the MW planes of satellite galaxies: i) using the spatial distribution of satellites, which leads to determining MW-like-thin planes, and ii) using the orbital pole distribution, which leads to determining MW-like-orbit planes.

3.1 MW-like-thin planes of satellite galaxies

We wish to identify planes of satellite galaxies that have a similar spatial distribution to the Galactic classical dwarfs, which we refer to as MW-like-thin planes. To find Galactic analogues, we calculate the thickness of the satellite systems using the mass tensor,

[TABLE]

where the sum is over the $N=11$ most massive satellites by stellar mass (hereafter the “top 11”). The quantity $x_{k,i}$ denotes the $i$-th component ($i=1,2,3$) of the position vector of satellite $k$ with respect to the central galaxy. The shape and the orientation are determined by the eigenvalues, $\lambda_{i}$ ($\lambda_{1}\geqslant\lambda_{2}\geqslant\lambda_{3}$), and the eigenvectors, $\boldsymbol{\mathit{\hat{e}}}_{i}$, of the mass tensor. The major, intermediate and minor axes of the corresponding ellipsoid are given by $a=\sqrt{\lambda_{1}}$, $b=\sqrt{\lambda_{2}}$, and $c=\sqrt{\lambda_{3}}$, respectively. We refer to $c/a$ as the thickness of the satellite system and to $\boldsymbol{\mathit{\hat{e}}}_{3}$, which points along the minor axis, as the normal to the plane of satellites.

The distribution of plane thicknesses, $c/a$, for the top 11 satellites of MW-mass hosts is shown in Fig. 1. The satellite systems have a large spread in $c/a$ values ranging from ${\sim}0.15$ to ${\sim}0.9$ and a most likely value of $c/a\approx 0.45$. For comparison, we also show the shape, $c/a$, of their haloes, which is calculated by applying Eq. (1) to the distribution of dark matter particles within $R_{\rm 200}$ from the halo centre (see dotted line in Fig. 1). On average, the satellites are more flattened and have a wider distribution of $c/a$ values than their host haloes (e.g. see also Libeskind et al., 2005; Kang et al., 2005).

The 11 classical dwarfs of the MW have an axis ratio, $c/a=0.183$, which is shown by the vertical arrow in Fig. 1. This value is very low when compared with the typical expectation in eagle, with only ${\sim}1$ percent of eagle MW-mass haloes having thinner satellite distributions (see also Wang et al., 2013; Pawlowski et al., 2014). To obtain analogues to the MW planes of satellites, we select eagle systems with $c/a<0.3$, which represents our sample of MW-like-thin planes. There are 134 such systems and they represent $12$ percent of the total sample of eagle MW-mass haloes. Note that while most of the MW-like-thin planes are thicker than the MW one, the thickness of the MW plane of satellites is predicted to increase rapidly with time (e.g. see Lipnicky & Chakrabarti, 2017) and thus our selection procedure is reasonable.

3.2 MW-like-orbit planes of satellite galaxies