No Globular Cluster Progenitors in Milky Way Satellite Galaxies

MNRAS 000,1–7 (2021) Preprint 18 June 2021 Compiled using MNRAS LATEX style ﬁle v3.0

No globular cluster progenitors in Milky Way satellite galaxies

Pierre Boldrini1★ and Jo Bovy2 1Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France 2Department of Astronomy and Astrophysics, University of Toronto, 50 St George Street, Toronto, ON M5S 3H4, Canada

18 June 2021

ABSTRACT In order to ﬁnd the possible progenitors of Milky Way globular clusters, we perform orbit integrations to track the orbits of 151 Galactic globular clusters and the eleven classical Milky Way satellite galaxies backward in time for 11 Gyr in a Milky- Way-plus-satellites potential including the eﬀect of dynamical friction on the satellites. To evaluate possible past associations, we devise a globular-cluster–satellite binding criterion based on the satellite’s tidal radius and escape velocity and we test it on globular clusters and satellites associated with the Sagittarius dwarf and with the Large Magellanic Cloud. For these, we successfully recover the dynamical associations highlighted by previous studies and we derive their time of accretion by the Galaxy. Assuming that Milky Way globular clusters are and have been free of dark matter and thus consist of stars alone, we demonstrate that none of the globular clusters show any clear association with the eleven classical Milky Way satellites even though a large fraction of them are believed to be accreted. This means that accreted globular clusters either came in as part of now-disrupted satellite galaxies or that globular clusters may have had dark matter halos in the past – as suggested by the similar metallicity between globular clusters and dwarf galaxies. Key words: galaxy dynamics - methods: orbital integrations - globular clusters - Milky Way - dwarf galaxies

1 INTRODUCTION possible to assess whether GCs formed in the MW or in a satellite galaxy that was later accreted. The origin of compact stellar clusters, also known as globular clusters (GCs), is one of the open questions in modern astrophysics. Many It was found that 62 of the present-day MW GCs likely formed years now since their first discovery, it is still unclear whether they in the MW, ∼55–65 have an extragalactic origin and the rest likely formed within dark matter minihalos or as gravitationally bound has a more heterogeneous origin (Kruĳssen, et al. 2019; Massari et clouds in the early universe (Peebles & Dicke 1968; Kravtsov & al. 2019). It was established that the main contribution to the MW Gnedin 2005; Kruĳssen 2015; Peebles 1984; Peñarrubia et al. 2017). came from three major accretion events: Sagittarius (Ibata, Gilmore Despite ongoing debates about their origin (Kruĳssen 2015; Forbes & Irwin 1994; Law & Majewski 2010), Gaia-Enceladus (Belokurov, et al. 2018), these gravitationally-bound groupings of mainly old et al. 2018; Helmi, et al. 2018), and Sequoia (Myeong, et al. 2019). stars also have a similarly long history of being used as probes of In fact, numerous pieces of evidence indicate that 35% of the clusters the galaxy formation and assembly process, particularly in the Milky are possibly associated with these merger events and then are formed Way (MW) (Searle & Zinn 1978; Dinescu, Girard & van Altena in accreted dwarf galaxies (Leaman, VandenBerg & Mendel 2013; 1999; Brodie et al. 2006). Massari et al. 2019). It has long been recognized that the accretion of satellite galaxies A particularly intriguing set of GCs is the population of eleven has contributed to the growth of the MW (Searle & Zinn 1978)and the loosely bound GCs or at high energies in the MW as defined by Galaxy has accreted around one hundred satellite galaxies (Bland- arXiv:2106.09419v1 [astro-ph.GA] 17 Jun 2021 Massari et al.(2019). These GCs (AM1, Eridanus, Pyxis, Palomar Hawthorn et al. 2016). As a natural result of such events, GCs may 3, Palomar 4, Crater, NGC 6426, NGC 5694, NGC 6584, NGC 6934 have been accreted by the MW (Peñarrubia, Walker & Gilmore 2009). and Palomar 14) do not seem to have formed in situ in the Galaxy Indeed, several authors have used metallicities and horizontal-branch (Massari et al. 2019). In the E-MOSAICS simulations, high-energy morphologies to distinguish GC origin; those formed in satellite GCs are generally old and metal-poor and then it may not be pos- galaxies and those formed in situ within the Galaxy (Zinn 1999; van sible to unambiguously determine their origin (Pfeffer, et al. 2020). den Bergh 1993; Mackey & Gilmore 2004). Some of the 11 GCs have previously been tentatively associated with Recently, full six-dimensional phase-space information for almost MW satellite galaxies such as Fornax, Sculptor, or the Large Magel- all of the Galactic GCs from the second data release of the Gaia lanic Cloud (Irwin, Demers & Kunkel 1995; Koposov, et al. 2014). mission has offered unique insights into their dynamics (Gaia Col- Intriguingly, Fornax is the only one of the classical dwarfs to have laboration, et al. 2018; Vasiliev 2019). Thanks to these data, it is now six GCs in orbit (Wang, et al. 2019), thus demonstrating that most classical dwarfs can have hosted GCs in the past that now have been stripped. Indeed, as the 11 loosely-bound GCs reach far distances from the MW centre over their history, they could have interacted ★ Contact e-mail: [email protected] with or belonged to MW satellites.

In this paper, we examine if the eleven satellite galaxies of the dSph Mmin Mmax tinfall 9 9 MW could be progenitors of some of the 151 GCs. We follow the dy- [10 M ][10 M ] [Gyr] 푎 namical history backward in time of these GCs in the MW+satellite LMC 100 198.8 4.0 푎 environment by using orbital integration methods. The paper is or- SMC 26 73.9 4.0 Sgr 14 62 7.48푏 ganized as follows. Section 2 provides a description of our orbital- UMi 0.79 2.8 10.7푐 integration method. In Section 3, we discuss how we decide whether Draco 3.16 3.5 10.4푐 or not a GC was associated with a satellite galaxy in the past and Sculptor 1.99 5.7 9.9푐 present our results on associations between GCs and the Sagittarius Sextans 0.316 2.0 8.4푐 dwarf, satellites of the Large Magellanic Cloud and the Cloud itself, Leo I 1.99 5.6 2.3푐 and ﬁnally all Milky-Way GCs and the classical satellites. Section 4 Leo II 0.316 1.6 7.8푐 presents our conclusions. Carina 0.398 0.8 9.9푐 Fornax 0.79 21.9 10.7푐

Table 1. MW satellite properties: From left to right, the columns give for 2 METHOD each classical satellites: the current mass 푀200 (Errani, Peñarrubia & Walker 2018) and the pre-infall mass 푀pi (Read & Erkal 2019); the infall time from: In order to find the possible progenitors of the 151 Galactic GCs, (a) Rocha, Peter, & Bullock(2012), (b) Dierickx & Loeb(2017) and (c) we take their present-day phase-space position derived from Gaia (Fillingham, et al. 2019). DR2 data (Vasiliev 2019) and integrate them backward in time for 11 Gyr in a model for the Milky Way’s gravitational potential. It was recently demonstrated that interactions with MW satellites can orbits backwards in time for 11 Gyr in MWPotential2014 by ap- cause the orbital properties of Galactic GCs to evolve significantly plying dynamical friction to them with a constant mass of Mmin or over time (Garrow, Webb, & Bovy 2020). Therefore, we include the Mmax, given their current positions and proper motions from Fritz, gravitational potential of the eleven classical satellites in the potential et al.(2018). Dynamical friction is implemented by following the model (see Table1). semi-analytic model of Petts, Gualandris, & Read(2015). The GCs We assume that the main component of the Galactic potential is are then integrated in the combined MWPotential2014 plus the well represented by the MWPotential2014 mass model from Bovy time-dependent potential of each of the 11 classical satellites. (2015). Much of the stellar halo was likely accreted between 9 and 11 A mass of 6 × 106 M corresponds to the upper limit of the Gyr ago (Di Matteo, et al. 2019; Mackereth & Bovy 2020). Moreover, stellar mass of Galactic GCs 12 Gyr ago (Baumgardt, et al. 2019). cosmological simulations of the formation of Milky-Way-like galax- The time to change the GC apocentre substantially due to dynamical ies show that the main halo mass, which grows with time, reaches its friction is ≈ 푀enclosed/푀GC ×푡dyn where 푀enclosed is the host galaxy asymptotic value 9-10 Gyr ago (Diemand, Kuhlen & Madau 2007; mass enclosed within the orbit and 푡dyn is the orbital time (Binney Lux, Read & Lake 2010). As a consequence, we establish that our & Tremaine 2008). As the mass ratio between MW enclosed mass model describes the Galaxy well until 9-10 Gyr ago. and GC masses is large, dynamical friction is inefficient over our For the satellites, we assume a Hernquist(1990) density profile timescale (11 Gyr). We thus neglect the mass loss to the clusters for the DM component. Given the halo mass and redshift, both halo assuming that the GC mass remains constant during integrations. concentrations 푐200 can be estimated from cosmological 푁-body Orbit integrations are performed with a time step of 10 Myr us- simulations (Dutton & Macciò 2014). We neglect the stellar contri- ing the publicly available code galpy1 (Bovy 2015) by applying bution of satellites as their dynamics is largely governed by the dark dynamical friction to the clusters and dwarfs. As proper motion un- component. The mass loss histories of satellite galaxies are poorly certainties and measurement errors could affect the results and thus constrained, but we can write down a simple mass-loss model by also the possible close encounters between GCs and satellite galaxies, connecting the pre-infall mass 푀pi and the satellite mass 푚(푡) as: our analysis takes account of uncertainties and measurement errors as follows. In order to establish associations between MW satellites 푡 푚(푡) = 푀 1 − (1) and GCs, we Monte Carlo sample their 6D phase-space position by 200 푇 d sampling the distance, the radial velocity and proper motions includ- where 푇d is the characteristic time defined as 푚(−푡infall) = 푀pi. We ing the covariance using Gaussian error distributions with means and assume that the satellite mass remains constant before the infall time standard deviations given by Vasiliev(2019) for the GCs and by Fritz, constrained by Fillingham, et al.(2019) (see Table1). However, in- et al.(2018) for the satellite galaxies. We neglect the uncertainty in corporating this mass-loss model during all orbital integrations is the position on the sky. We then evaluate the association criterion computationally costly. As an alternative, we choose to assess the described below for all Monte Carlo samples. impact of mass loss by keeping the satellite masses constant during integrations and considering minimum and maximum values for the mass. They correspond to the current mass 푀200 (as the minimum 3 RESULT mass Mmin) and the pre-infall mass 푀pi (as the maximum mass Mmax) determined by Read & Erkal(2019) and Errani, Peñarrubia 3.1 Globular-cluster–satellite association criterion & Walker(2018), respectively (see Table1). Once they are falling In order to identify which GCs were associated with the eleven into the MW, the satellites loose mass due to tidal effects and dy- satellite galaxies as likely progenitors, we define two simple criteria namical friction. Taking into account the mass loss is crucial as it based on the tidal radius and the escape velocity of satellites. affects directly the orbital radius and hence the tidal radius. Below, The tidal radius is the distance to the last closed zero-velocity we therefore check that satellite orbits for these mass limits cover the surface surrounding a galaxy. Since the final closed surface passes same region as if we have considered a mass loss for all satellites. Table1 summarizes all the satellite properties adopted in the paper. We create the potential of the moving satellites by integrating their 1 Available at https://github.com/jobovy/galpy

MNRAS 000,1–7 (2021) No globular cluster progenitors in Milky Way satellite galaxies 3

Globular cluster 푝Sgr(Mmin) tacc(Mmin) 푝Sgr(Mmax) tacc(Mmax) Previously associated [Gyr] [Gyr] likely associated with Sgr Whiting 1 0.68 -0.26 0.83 -0.2 Yes Terzan 7 0.93 0.0 0.99 0.0 Yes Arp 2 0.96 0.0 0.98 0.0 Yes Pal 12 0.64 -0.19 0.93 -0.16 Yes Terzan 8 0.99 0.0 0.99 0.0 Yes NGC 6715 0.99 0.0 0.99 0.0 Yes not associated with Sgr NGC 5694 0.004 - 0.0 - No NGC 7006 0.02 - 0.0 - No Pal 4 0.009 - 0.0 - No Crater 0.004 - 0.0 - No Pal 15 0.005 - 0.006 - No NGC 5904 0.014 - 0.037 - No NGC 288 0.0 - 0.087 - No NGC 2298 0.0 - 0.21 - No

Table 2. Summary of results for the Sagittarius dwarf: From left to right, the columns give for each GCs: the probability of having been bound to the Sgr assuming Mmin and Mmax for the 11 satellite galaxies, with their respective times of the accretion by the MW if GCs were previously associated sith Sgr dwarf according to Law & Majewski(2010); Massari, et al.(2017); Sohn, et al.(2018); Bellazzini, et al.(2020). Only GCs with a non-zero probability for one of the dwarf masses are listed. We found that 6 GCs were eﬀectively associated with the Sgr dwarf galaxy. NGC6715, Arp 2, Terzan 7 and Terzan 8 still belong to Sgr, whereas Whiting 1 and Palomar 12 were accreted less than 0.3 Gyr ago by the MW galaxy. According to our results, the other 145 GCs have never been associated with the Sgr dwarf.

through a minimum of the combined effective potential of the satellite the GC relative velocity to its putative parent galaxy 푣GC: and the Galaxy Φ , the distance to this surface can be determined eff 푣GC (푡 ) < 푣SG (푡 ). (8) with the condition: i esc i This criterion and the escape velocity in it is evaluated at the mini- 푑Φeff (푟t, 0, 0) = 0, (2) mum separation between the GC and the satellite galaxy. The above 푑푥 criteria give the information needed to decide whether GCs were where the x-axis is taken to point away from the center of the Galaxy. bound or unbound to a satellite in the past. In order to determine Using the orbital radius 푅0 and the mass 푀SG, we calculate the the- the probability of a GC being bound to MW satellites, we count the oretical tidal radius of each satellite galaxies over 11 Gyr as derived fraction of the Monte Carlo samples that satisfy our criteria based by Bertin & Varri(2008) as on Equations (7) and (8) at each time. We assume that the most recent time 푡 , which satisfies the previous conditions, corresponds 퐺푀 1/3 i 푟DG = DG , (3) to the time of the GC accretion by the MW, t . Before this time, the t 2 acc Ω 휐 GC dynamics is no longer governed by the MW, but by the satellite where the orbital frequency Ω at 푅0, the epicyclic frequency 휅 at 푅0, galaxy. and a positive dimensionless coefficient 휐 are defined as: Ω2 = ( Φ ( )/ ) / 3.2 Sagittarius dwarf and its globular clusters 푑 MW 푅 푑푅 푅0 푅0 , (4) 2 2 2 2 First, we apply our method to the Sagittarius (Sgr) dwarf galaxy and 휅 = 3Ω + 푑 ΦMW (푅)/푑푅 , (5) 푅0 the full set of 151 GCs. The ongoing disruption of the Sgr dwarf 휐 = 4 − 휅2/Ω2 . (6) provides a formidable case study of GC accretions (Ibata, Gilmore & Irwin 1994). Six GCs such as NGC 6715, Ter 8, Ter 7, Arp 2, Pal Dynamical friction and mass-loss at pericentric passages act by re- 12 and Whiting 1 have been associated with this dwarf beyond any ducing the satellite tidal radius forward in time, thereby increasing reasonable doubt (Law & Majewski 2010; Massari, et al. 2017; Sohn, the probability of GC accretions by the MW. We, therefore, use the et al. 2018; Bellazzini, et al. 2020). However, there are still interesting orbital radii of GCs and the satellite tidal radii to define a simple candidates possibly associated with the Sgr stream such as NGC criterion to identify satellite galaxies as likely progenitors: 2419, NGC 5634 and NGC 4147 (Bellazzini, et al. 2020). Recently, GC SG it was confirmed that NGC 2419 was well associated with Sgr dwarf 푟 (푡i) < 푟 (푡i), (7) c t (Antoja, et al. 2020). Furthermore, NGC 5824 was also proposed as GC where 푟c and 푡i is the GC orbital radius centered on a galaxy and a a potential member of this system (Massari et al. 2019). We take the specific time, respectively. present-day phase-space position of these ten GCs derived from Gaia As the tidal radius criterion only considers an association in the DR2 data (Vasiliev 2019) and integrate them backward in time for 11 position space of both galactic objects, it is insufficient to identify Gyr in our MWPotential2014+satellites potential. Table2 shows the past bound associations. To do this, we need to establish an additional probability of having been bound to the Sgr dwarf, assuming Mmin criterion based on the escape velocity of likely progenitors. The and Mmax for the 11 satellite galaxies used in the time-dependent escape velocity is the maximum velocity that GCs could have if they MWPotential2014+satellites potential, with the respective times of had been bound to a MW satellite. As the next step, therefore, we the accretion by the MW for the full set of 151 GCs. Only GCs calculate the escape velocity of the satellite 푣esc and compare it with with a non-zero probability for one of the satellite masses are listed.

MNRAS 000,1–7 (2021) 4 P. Boldrini and J. Bovy

Sgr LMC 100 600 Mass loss Mass loss Max Max ] ] 500 c 80 Min c Min p p k k [ [ 400 s 60 s u u i i

d d 300 a a r 40 r l l

a a 200 t t i i b b

r 20 r 100 O O

0 0 0.5 0.4 0.3 0.2 0.1 0.0 5 4 3 2 1 0 t [Gyr] t [Gyr]

Figure 1. Mass loss impact: Orbital radius centered on the MW of the Sgr Figure 2. Mass loss impact: Orbital radius centered on the MW of the LMC dwarf backwards in time over 0.5 Gyr in our galactic potential assuming Mmin, backwards in time over 5 Gyr in our Galactic potential assuming Mmin,Mmax, Mmax and the mass loss model described by Equation. The bands correspond and the mass loss model described by Equation. The bands correspond to the to the bound region around Sgr delimited by its tidal radius, which depends bound region around the LMC delimited by its tidal radius, which depends on on its mass. Considering Mmin and Mmax masses for the orbital integrations is its mass. Beyond 0.5 Gyr backwards in time, it is necessary to take correctly suﬃcient to approximate the mass loss of Sgr dwarf over 0.5 Gyr backwards in account the mass loss for the LMC in order to ﬁnd associations with DES in time. dwarfs.

We found that 6 GCs were effectively associated with the Sgr dwarf galaxy. NGC6715, Arp 2, Terzan 7 and Terzan 8 still belong to Sgr, Kim & Jerjen 2015; Koposov et al. 2018; Laevens et al. 2015; Tor- whereas Whiting 1 and Palomar 12 were accreted less than 0.3 Gyr realba et al. 2016, 2018). Given the proximity of the DES survey ago by the MW galaxy, respectively (see Table2). According to our area to the clouds, these new dwarfs appear good candidates to have results, the other 145 GCs have never been associated with the Sgr been members of the LMC. One can easily imagine that some DES dwarf. dwarfs have been stripped during the last passage of LMC, i.e., 0.14 Gyr ago. According to previous studies, only about half of the DES Figure1 confirms that considering the M min and Mmax masses for the orbital integrations is sufficient to approximate the mass loss of dwarfs are very likely to have been associated with the LMC in the Sgr over 0.5 Gyr backwards in time. Our method remains valid as past (Jethwa, et al. 2016; Santos-Santos et al. 2021; Sales et al. 2017; long as the bound regions delimited by the satellite tidal radius for Kallivayalil et al. 2018; Jahn et al. 2019; Erkal & Belokurov 2020; Patel et al. 2020). Mmin and Mmax cover the same region as if we have considered our mass loss model for Sgr over a period which includes the times of To investigate possible associations of the DES dwarfs with the accretion that we found. LMC, we apply our method to the 26 DES dwarfs considered by Erkal In light of previous studies, our results state that our method based & Belokurov(2020). We similarly Monte Carlo the 6d position and on our criteria to associate GCs with Sgr as their progenitor works rewind these dwarfs and the LMC for 5 Gyr. As in Erkal & Belokurov well and provides also an estimate of the time of accretion for GCs. (2020), we consider a grid of LMC masses (see Table3). Our results suggest that the SMC, Tuc 3, and Car 2 were effectively associated with the LMC. As in Patel et al.(2020), we find that the 3 DES dwarfs were bound to the LMC in the last 0.5 Gyr. For a high LMC mass, 3.3 LMC and Dark Energy Survey dwarf galaxies we find that Car 2 still belongs to the LMC. In view of these recent The Large Magellanic Cloud (LMC) is the most massive satellite accretions by the MW, it is reasonable to assume that dynamical of the MW and it is currently at a particular stage of its orbit. The friction is negligible on this timescale (see Table3). Besides, we LMC and the Small Magellanic Cloud (SMC) have been identified stress that beyond 0.5 Gyr backwards in time, it is necessary to as a galaxy pair orbiting together in the MW (e.g. Westerlund 1990; correctly take the mass loss for the LMC in account in order to D’Onghia & Fox 2016; Kallivayalil, van der Marel, & Alcock 2006; find associations with DES dwarfs (see Figure2). Concerning the Kallivayalil et al. 2013). It has been suggested that the Clouds are dynamical associations, Table3 emphasises the impact of the LMC just past their first closest approach to the Galaxy (Besla et al. 2007; mass, which is still not sufficiently constrained, on the dynamical Boylan-Kolchin, Besla, & Hernquist 2011; Patel, Besla, & Sohn history of DES dwarfs. 2017). The orbital behaviour depending on the LMC mass can be In contrast to our results, previous studies based on orbital integra- seen in Figure2. We see that the LMC is close to the pericentre of a tions found five other DES dwarfs that were likely associated with highly eccentric orbit with long orbital times. Previous studies have the LMC in a combined MW+LMC potential (Erkal & Belokurov attempted to find tentative evidence of associated satellites with the 2020; Patel et al. 2020). One of the reasons that could explain this LMC (e.g. D’Onghia & Lake 2008; Sales et al. 2011). discrepancy is that, contrary to Erkal & Belokurov(2020) and Patel Recently, the Dark Energy Survey (DES) mapped out a large frac- et al.(2020), our MW satellites are modelled by a Herquist profile tion of the Southern Galactic hemisphere which uncovered 32 low- with a tidal-radius criterion for boundedness. Indeed, our criterion mass dwarf galaxies close to the LMC (e.g. Koposov et al. 2015; based on the tidal radius is more restrictive when we have determined Bechtol et al. 2015; Drlica-Wagner et al. 2015; Drlica-Wagner 2015; which galaxies are dynamically associated with the LMC. Erkal &

MNRAS 000,1–7 (2021) No globular cluster progenitors in Milky Way satellite galaxies 5

DES dwarf SMC Tuc 3 Car 2 Phe2 Car 3 Ret 2 Aqu 2 Hor 1 10 푝LMC (2 × 10 M ) 0.0 0.0 0.0 0.007 0.0 0.0 0.0 0.0 10 tacc(2 × 10 M )------10 푝LMC (5 × 10 M ) 0.0 0.007 0.0 0.04 0.003 0.003 0.0 0.0 10 tacc(5 × 10 M ) -0.22 ------10 푝LMC (10 × 10 M ) 0.08 0.12 0.0 0.18 0.021 0.26 0.006 0.0 10 tacc(10 × 10 M ) -0.1 ------10 푝LMC (15 × 10 M ) 0.32 0.38 0.0 0.24 0.023 0.38 0.011 0.006 10 tacc(15 × 10 M ) -0.08 ------10 푝LMC (20 × 10 M ) 0.65 0.76 0.0 0.29 0.017 0.3 0.016 0.01 10 tacc(20 × 10 M ) -0.06 -0.06 ------10 푝LMC (25 × 10 M ) 0.77 0.88 0.3 0.33 0.018 0.33 0.021 0.03 10 tacc(25 × 10 M ) -0.05 -0.054 ------10 푝LMC (30 × 10 M ) 0.79 0.97 0.99 0.38 0.015 0.38 0.025 0.06 10 tacc(30 × 10 M ) -0.012 -0.046 0.0 - - - - - Erkal & Belokurov(2020) Yes No Yes Yes Yes Yes No Yes Patel et al.(2020) Yes Yes Yes Yes Yes Yes No Yes This work Yes Yes Yes No No No No No

Table 3. Summary of results for the LMC: From top to bottow, the lines give for each DES dwarf: the probability of having been bound to the LMC 푝LMC depending on its mass with their respective times of the accretion by the MW tacc; if these dwarfs were previously associated with LMC according to the litterature. Only DES dwarfs with a non-zero probability are listed. We found that 3 DES dwarfs were effectively associated with the LMC. For a specific mass, we find that Car 2 still belongs to the LMC.

Belokurov(2020) have only verified whether the energy relative to Progenitor Globular cluster 푝DG(Mmin) 푝DG(Mmax) the LMC is less than the binding energy, while we take into account the influence of the MW on the LMC tidal radius. Even subject to Fornax E1 0.005 0.05 this condition, a satellite could be unbound if it is orbiting outside of Eridanus 0.0 0.003 the tidal radius. Patel et al.(2020) have considered an outer radius Pal 3 0.0 0.02 for the LMC, which is assumed to be constant over time. In addition, Crater 0.0 0.001 Pal 4 0.001 0.006 this specific radius is significantly greater than our LMC tidal radii Pal 14 0.0 0.001 in the first Gyr. That is the reason why we expect that their criterion gives a higher number of MW satellites that have interacted with the Carina E1 0.0 0.006 LMC. As depicted by Figure2, current orbital methods need to take Eridanus 0.001 0.0 into the mass loss for the LMC in order to investigate old accretions Pal 3 0.0 0.004 by the MW, i.e., 1-9 Gyr ago. Pal 4 0.0 0.006 Pal 14 0.0 0.007

3.4 Progenitors of 151 GCs Sculptor E1 0.0 0.003 Pal 3 0.0 0.004 By integrating orbits of the 151 GCs in our MW+satellites potential, we find that none of these GCs show any clear association with the Umi NGC 2419 0.002 0.004 eleven MW satellites. As for our previous tests applied on globular Pal 4 0.001 0.0 clusters and satellites associated with the Sagittarius dwarf and with Pal 14 0.002 0.0 the Large Magellanic Cloud, we stress that our two criteria do not lead to wrong associations. Table4 summarizes all the non-zero Sextans Pal 3 0.0 0.07 binding probabilities for possible satellite progenitors as a result of Draco Pal 14 0.0 0.003 the investigation of associations between satellite galaxies and GCs over 10 Gyr backwards in time. For instance, we find that none of 62 LMC NGC 7006 0.011 0.076 GCs likely formed in the MW was associated with MW satellites. According to our results, none of the MW satellites investigated Table 4. Absence of GC progenitors in MW satellites: From left to right, here appears to be progenitors of MW GCs even if some dynamical the columns give for each progenitor candidate: likely associated GCs; the properties of GCs, especially the population of eleven loosely bound probability of having been bound to the progenitor candidate assuming Mmin and M for the MW satellite galaxies. None of these GCs show any clear GCs defined by Massari et al.(2019), could support an accretion max association with the eleven MW satellites. origin. Even though there is no observation of stellar debris from dwarf progenitors, there are several indications that Eridanus might be accreted such as that the probably orbit of Eridanus passes close to Fornax and Sculptor (Myeong, et al. 2017). It was proposed that dwarf galaxy could explain the highly eccentric orbit of Palomar Pyxis probably originated in an unknown galaxy, which today is fully 4 (Zonoozi, et al. 2017). It was also suggest that Palomar 14 and disrupted by the MW (Fritz, et al. 2017). Moreover, this cluster is NGC 5694 have dynamical properties in favor of an accretion origin likely to be associated with a narrow stellar stream crossing the con- (Sollima, et al. 2011; Çalıs, kanet al. 2012; Frank, Grebel & Küpper stellations of Sculptor and Fornax (Irwin, Demers & Kunkel 1995; 2014; Lee, López-Morales & Carney 2006). We underline that the Koposov, et al. 2014). Being born in a now detached or disrupted hypothesis that these eleven GCs were stripped from dwarf galaxies

MNRAS 000,1–7 (2021) 6 P. Boldrini and J. Bovy is further supported by their metallicity indicating that these clus- Baumgardt H., Hilker M., Sollima A., Bellini A., 2019, MNRAS, 482, 5138 ters are metal-poor as MW dwarfs (Koch, Côté & McWilliam 2009; Bellazzini M., Ibata R., Malhan K., Martin N., Famaey B., Thomas G., 2020, Koch & Côté 2010; Da Costa, et al. 2009; Dotter, Sarajedini & An- A&A, 636, A107 derson 2011; Harris 2010; Sarajedini & Forrester 1995; Harris 1996; Belokurov V., Erkal D., Evans N. W., Koposov S. E., Deason A. J., 2018, Armandroff, Da Costa & Zinn 1992; Stetson, et al. 1999; Dotter, MNRAS, 478, 611 Bertin G., Varri A. L., 2008, ApJ, 689, 1005 Sarajedini & Yang 2008; Palma, Kunkel & Majewski 2000). Besla G., Kallivayalil N., Hernquist L., Robertson B., Cox T. J., van der Marel In this work, GCs were considered as purely stellar systems. Hov- R. P., Alcock C., 2007, ApJ, 668, 949. doi:10.1086/521385 ewer, it has also been proposed that GCs may have a galactic origin, Bechtol K., Drlica-Wagner A., Balbinot E., Pieres A., Simon J. D., Yanny B., where GCs are formed within small dark matter halos in the early Santiago B., et al., 2015, ApJ, 807, 50. doi:10.1088/0004-637X/807/1/50 Universe (e.g. Bromm & Clarke 2002; Mashchenko & Sills 2005a,b; Binney J., Tremaine S., 2008, gady.book Ricotti, Parry, & Gnedin 2016; Peebles 1984). By adding this dark Bland-Hawthorn J., Gerhard O., 2016, 54, 529 component, the dynamical friction acting on GCs with DM would Bovy J., 2015, ApJS, 216, 29 no longer be negligible and GCs could then have been orbiting in Boylan-Kolchin M., Besla G., Hernquist L., 2011, MNRAS, 414, 1560. the outer regions of the MW for a significant period in the past. This doi:10.1111/j.1365-2966.2011.18495.x would allow the GCs to have interacted even more with the satel- Brodie J. P., Strader J., 2006, 44, 193 lite galaxies, which populate the MW periphery. We leave a detailed Bromm V., Clarke C. J., 2002, ApJL, 566, L1. doi:10.1086/339440 Çalıskan Ş., Christlieb N., Grebel E. K., 2012, 537, A83 investigation of this possibility to future work. , Da Costa G. S., Grebel E. K., Jerjen H., Rejkuba M., Sharina M. E., 2009, AJ, 137, 4361 Diemand J., Kuhlen M., Madau P., 2007, ApJ, 657, 262 4 CONCLUSION Dierickx M. I. P., Loeb A., 2017, ApJ, 847, 42 Di Matteo P., et al., 2019, 632, A4 Using orbital integrations, we have tracked the orbits of the 151 Dinescu D. I., Girard T. M., van Altena W. F., 1999, AJ, 117, 1792 Galactic GCs and the eleven satellite galaxies backward in time D’Onghia E., Lake G., 2008, ApJL, 686, L61. doi:10.1086/592995 over 11 Gyr in a MW + satellites potential, including the effect D’Onghia E., Fox A. J., 2016, ARA&A, 54, 363. doi:10.1146/annurev-astro- of dynamical friction on the satellites. In order to associate Galactic 081915-023251 GCs and MW satellites, we apply a criterion based on the comparison Dotter A., Sarajedini A., Yang S.-C., 2008, AJ, 136, 1407 between the GC orbits and the satellite tidal radius, which evolves Dotter A., Sarajedini A., Anderson J., 2011, ApJ, 738, 74 with time. In addition, we establish a second criterion based on the Drlica-Wagner A., Bechtol K., Rykoff E. S., Luque E., Queiroz A., Mao Y.-Y., Wechsler R. H., et al., 2015, ApJ, 813, 109. doi:10.1088/0004- escape velocity of likely progenitors to test for boundedness. 637X/813/2/109 First of all, we have tested our method on the Sgr dwarf and its Drlica-Wagner A., 2015, APS..APR GCs. We successfully recovered the 6 GCs, which were previously Dutton A. A., Macciò A. V., 2014, MNRAS, 441, 3359. associated with the Sgr dwarf beyond any reasonable doubt, without doi:10.1093/mnras/stu742 finding any spurious associations. For the 6 associated GCs, we also Erkal D., Belokurov V. A., 2020, MNRAS, 495, 2554. derived their corresponding time of accretion by the MW. Further- doi:10.1093/mnras/staa1238 more, we have also re-investigated the possible associations between Errani R., Peñarrubia J., Walker M. G., 2018, MNRAS, 481, 5073 DES dwarfs and the LMC. Orbital integrations allow us to success- Fillingham S. P., et al., 2019, arXiv, arXiv:1906.04180 fully recover the recent dynamical associations, i.e in the last 0.5 Gyr, Forbes D. A., et al., 2018, Proceedings of the Royal Society of London Series where the mass loss of the LMC is negligible. A, 474, 20170616 A challenging problem is to fully and consistently model the MW’s Frank M. J., Grebel E. K., Küpper A. H. W., 2014, MNRAS, 443, 815 Fritz T. K., et al., 2017, ApJ, 840, 30 mass, which has drastically grown before 푧 = 1.3−1.7 due to mergers Fritz T. K., et al., 2018, A&A, 619, A103 (Renaud, Agertz & Gieles 2017). This will be crucial for investigating Gaia Collaboration, et al., 2018, 616, A12 GC accretions at this earlier epoch than we have considered in this Garrow T., Webb J. J., Bovy J., 2020, MNRAS, 499, 804. paper. doi:10.1093/mnras/staa2773 Harris W. E., 1996, AJ, 112, 1487 Harris W. E., 2010, arXiv, arXiv:1012.3224 5 ACKNOWLEDGMENTS Helmi A., Babusiaux C., Koppelman H. H., Massari D., Veljanoski J., Brown A. G. A., 2018, Natur, 563, 85 We thank David Valls-Gabaud and Joe Silk for illuminating discus- Hernquist L., 1990, ApJ, 356, 359 sions about globular clusters. Ibata R. A., Gilmore G., Irwin M. J., 1994, Natur, 370, 194 Irwin M. J., Demers S., Kunkel W. E., 1995, ApJL, 453, L21 Jahn E. D., Sales L. V., Wetzel A., Boylan-Kolchin M., Chan T. K., El-Badry K., Lazar A., et al., 2019, MNRAS, 489, 5348. 6 DATA AVAILABILITY doi:10.1093/mnras/stz2457 Jethwa P., Erkal D., Belokurov V., 2016, MNRAS, 461, 2212. This work has made use of data from the Milky-Way globular clusters doi:10.1093/mnras/stw1343 (Vasiliev 2019) and satellite galaxies (Fritz, et al. 2018) catalogs with Kallivayalil N., van der Marel R. P., Alcock C., 2006, ApJ, 652, 1213. data from Gaia DR2 (Gaia Collaboration, et al. 2018). doi:10.1086/508014 Kallivayalil N., van der Marel R. P., Besla G., Anderson J., Alcock C., 2013, ApJ, 764, 161. doi:10.1088/0004-637X/764/2/161 REFERENCES Kallivayalil N., Sales L. V., Zivick P., Fritz T. K., Del Pino A., Sohn S. T., Besla G., et al., 2018, ApJ, 867, 19. doi:10.3847/1538-4357/aadfee Antoja T., Ramos P., Mateu C., Helmi A., Anders F., Jordi C., Carballo-Bello Kim D., Jerjen H., 2015, ApJL, 808, L39. doi:10.1088/2041-8205/808/2/L39 J. A., 2020, A&A, 635, L3 Koch A., Côté P., McWilliam A., 2009, 506, 729 Armandroff T. E., Da Costa G. S., Zinn R., 1992, AJ, 104, 164 Koch A., Côté P., 2010, 517, A59

MNRAS 000,1–7 (2021) No globular cluster progenitors in Milky Way satellite galaxies 7

Koposov S. E., et al., 2014, MNRAS, 442, L85 Zinn R. J., 1999, AAS, 194, 40.02 Koposov S., Belokurov V., Torrealba G., Evans W., 2015, IAUGA Zonoozi A. H., Haghi H., Kroupa P., Küpper A. H. W., Baumgardt H., 2017, Koposov S. E., Walker M. G., Belokurov V., Casey A. R., Geringer- MNRAS, 467, 758 Sameth A., Mackey D., Da Costa G., et al., 2018, MNRAS, 479, 5343. doi:10.1093/mnras/sty1772 This paper has been typeset from a TEX/LATEX file prepared by the author. Kravtsov A. V., Gnedin O. Y., 2005, ApJ, 623, 650 Kruĳssen J. M. D., 2015, MNRAS, 454, 1658 Kruĳssen J. M. D., Pfeffer J. L., Reina-Campos M., Crain R. A., Bastian N., 2019, MNRAS, 486, 3180 Laevens B. P. M., Martin N. F., Ibata R. A., Rix H.-W., Bernard E. J., Bell E. F., Sesar B., et al., 2015, ApJL, 802, L18. doi:10.1088/2041-8205/802/2/L18 Law D. R., Majewski S. R., 2010, ApJ, 718, 1128 Lee J.-W., López-Morales M., Carney B. W., 2006, ApJL, 646, L119 Leaman R., VandenBerg D. A., Mendel J. T., 2013, MNRAS, 436, 122 Lux H., Read J. I., Lake G., 2010, MNRAS, 406, 2312 Mackereth, J. T. & Bovy, J. 2020, MNRAS, 492, 3631. doi:10.1093/mnras/staa047 Mackey A. D., Gilmore G. F., 2004, MNRAS, 355, 504 Mashchenko S., Sills A., 2005, ApJ, 619, 243. doi:10.1086/426132 Mashchenko S., Sills A., 2005, ApJ, 619, 258. doi:10.1086/426133 Massari D., Posti L., Helmi A., Fiorentino G., Tolstoy E., 2017, 598, L9 Massari D., Koppelman H. H., Helmi A., 2019, 630, L4 Myeong G. C., Jerjen H., Mackey D., Da Costa G. S., 2017, ApJL, 840, L25 Myeong G. C., Vasiliev E., Iorio G., Evans N. W., Belokurov V., 2019, MNRAS, 488, 1235 Palma C., Kunkel W. E., Majewski S. R., 2000, PASP, 112, 1305 Patel E., Besla G., Sohn S. T., 2017, MNRAS, 464, 3825. doi:10.1093/mnras/stw2616 Patel E., Kallivayalil N., Garavito-Camargo N., Besla G., Weisz D. R., van der Marel R. P., Boylan-Kolchin M., et al., 2020, ApJ, 893, 121. doi:10.3847/1538-4357/ab7b75 Peebles P. J. E., Dicke R. H., 1968, ApJ, 154, 891 Peebles P. J. E., 1984, ApJ, 277, 470 Peñarrubia J., Walker M. G., Gilmore G., 2009, MNRAS, 399, 1275 Peñarrubia J., Varri A. L., Breen P. G., Ferguson A. M. N., Sánchez-Janssen R., 2017, MNRAS, 471, L31 Petts J. A., Gualandris A., Read J. I., 2015, MNRAS, 454, 3778. doi:10.1093/mnras/stv2235 Pfeffer J. L., Trujillo-Gomez S., Kruĳssen J. M. D., Crain R. A., Hughes M. E., Reina-Campos M., Bastian N., 2020, arXiv, arXiv:2003.00076 Read J. I., Erkal D., 2019, MNRAS, 487, 5799 Renaud F., Agertz O., Gieles M., 2017, MNRAS, 465, 3622 Ricotti M., Parry O. H., Gnedin N. Y.,2016, ApJ, 831, 204. doi:10.3847/0004- 637X/831/2/204 Rocha M., Peter A. H. G., Bullock J., 2012, MNRAS, 425, 231. doi:10.1111/j.1365-2966.2012.21432.x Sales L. V., Navarro J. F., Cooper A. P., White S. D. M., Frenk C. S., Helmi A., 2011, MNRAS, 418, 648. doi:10.1111/j.1365-2966.2011.19514.x Sales L. V., Navarro J. F., Kallivayalil N., Frenk C. S., 2017, MNRAS, 465, 1879. doi:10.1093/mnras/stw2816 Santos-Santos I. M. E., Fattahi A., Sales L. V., Navarro J. F., 2021, MN- RAS.tmp. doi:10.1093/mnras/stab1020 Sarajedini A., Forrester W. L., 1995, AJ, 109, 1112 Searle L., Zinn R., 1978, ApJ, 225, 357 Sohn S. T., Watkins L. L., Fardal M. A., van der Marel R. P., Deason A. J., Besla G., Bellini A., 2018, ApJ, 862, 52 Sollima A., Martínez-Delgado D., Valls-Gabaud D., Peñarrubia J., 2011, ApJ, 726, 47 Stetson P. B., et al., 1999, AJ, 117, 247 Torrealba G., Koposov S. E., Belokurov V., Irwin M., Collins M., Spencer M., Ibata R., et al., 2016, MNRAS, 463, 712. doi:10.1093/mnras/stw2051 Torrealba G., Belokurov V., Koposov S. E., Bechtol K., Drlica-Wagner A., Olsen K. A. G., Vivas A. K., et al., 2018, MNRAS, 475, 5085. doi:10.1093/mnras/sty170 van den Bergh S., 1993, AJ, 105, 971 Vasiliev E., 2019, MNRAS, 484, 2832 Wang M. Y., et al., 2019, ApJ, 875, L13 Westerlund B. E., 1990, A&ARv, 2, 29. doi:10.1007/BF00873541

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