The missing massive satellites of the Milky Way

“The normalization of the power spectrum adopted in these simulations is slightly higher than that favoured by the latest WMAP data set (WMAP7; Komatsu et al. 2011), but this is expected to affect the abundance of haloes of given virial mass rather than the mass function of subhaloes, which is the…”

“We address these issues here by using large numbers of well-resolved halos identified in the Millennium Simulation series (Springel et al. 2005; Boylan-Kolchin et al. 2009).”

“This seems at odds with results from some semianalytic models of galaxy formation that attempt simultaneously to match the Tully-Fisher relation and the galaxy stellar mass function: agreement with observation seems to require Vrot ≈ V200 (see, e.g., Cole et al. 2000; Croton et al. 2006).”

“This is possible because, in agreement with earlier work, we find that the abundance of subhalos, when scaled appropriately, is independent of halo mass (see, e.g., Moore et al. 1999; Kravtsov et al. 2004; Springel et al. 2008).”

“…difference between the relatively flat faint-end slope of the galaxy stellar mass function and the much steeper cold dark matter halo mass function is usually reconciled by assuming that the efficiency of galaxy formation drops sharply with decreasing halo mass (see, e.g., White & Frenk 1991).”

“These results confirm earlier work (see, e.g., Moore et al. 1999; Kravtsov et al. 2004; Zheng et al. 2005; Weinberg et al. 2008; Springel et al. 2008), and imply that we can combine all well-resolved halos into one large sample to derive robust estimates of the statistical distribution of Nsub(> ν).”

“…models, the small number of MW satellites reflects the relatively small number of subhalos massive enough to host luminous galaxies (see, e.g., Kauffmann et al. 1993; Bullock et al. 2000; Benson et al. 2002; Somerville ⋆ Email: jie.wang@durham.ac.uk 2002; Cooper et al. 2010; Li et al. 2010;…”

“The particle mass in this run is 6.20×106 M⊙/h and gravitational interactions were softened with ǫP = 1 kpc/h. Halos and subhalos are identified in all simulations by subfind (Springel et al. 2001), a recursive algorithm that identifies self-bound structures and substructures in N-body simulations.”

“This, in turn, affects the expected dark-matter annihilation signal (Finkbeiner et al. 2009), increases the “missing satellite” problem (Wang et al. 2012), and increases the likelihood that the Magellanic Clouds are bound to the Milky Way (Shattow & Loeb 2009).”

“This discrepancy was called the ‘too big to fail problem’ by Boylan-Kolchin et al. Subsequently Wang et al. (2012) showed that the extent of the discrepancy depends strongly on the mass of the Galactic halo and all but disappears if the Milky Way’s halo has a mass of 1 × 1012M⊙,. Alternatively,…”

“…of the too big to fail problem in CDM depends on the mass of the MW halo, if it is in the low end of current estimates, .1012 M , the problem may be resolved (e.g. Wang et al. 2012), although a low halo mass may generate other difficulties such as explaining the presence of the Magellanic Clouds.”

“1× 1012 M ), or if the MW was a statistical outlier [802, 803, 1052].”

“In order to alleviate tensions due to the “missing massive satellites problem” pointed out by Boylan-Kolchin et al. (2011, 2012), a recent analysis by Wang et al. (2012) favours masses at the lower end of this interval, at around 1012 M , which is also the centre of the narrow mass interval that we…”

“E-mail: cautun@strw.leidenuniv.nl host halo mass (e.g. Purcell & Zentner 2012; Wang et al. 2012; Cautun et al. 2014a; Hellwing et al. 2016) while the radial mass profile plays a key role in determining the orbits of satellite galaxies and tidal streams (e.g. Barber et al. 2014; Monachesi et al.…”

“…excess of predicted massive subhalos around Milky Way-mass galaxies may disappear if satellites are modelled with Einasto (versus NFW) density profiles, or if the Milky Way’s true virial mass is ∼ 8 × 1011 M⊙, rather than ∼ 1012 M⊙ (Di Cintio et al. 2012; Vera-Ciro et al. 2012; Wang et al. 2012).”

“E-mail: cautun@strw.leidenuniv.nl host halo mass (e.g. Purcell & Zentner 2012; Wang et al. 2012; Cautun et al. 2014a; Hellwing et al. 2016) while the radial mass profile plays a key role in determining the orbits of satellite galaxies and tidal streams (e.g. Barber et al. 2014; Monachesi et al.…”

“Similarly, while large TBTF subhalos become increasingly infrequent as the mass of the MW and M31 host halos decrease (Purcell & Zentner, 2012; Wang et al., 2012; Rodrı́guez-Puebla et al., 2013; Cautun et al., 2014), solutions of this kind appear less likely in the face of evidence that the TBTF…”

“Specifically, if the Milky Way mass is approximately 1012 M , the number of subhalos with maximum circular velocity & 30 km/s can be made consistent with observations (Wang et al., 2012).”

“8 × 1011M , the problem disappears (e.g. Wang et al. 2012).”

“Others have argued that TBTF is a result of the mass of the targeted haloes, pointing to simulations that indicate that smaller hosts, Mv ∼ 8 × 1011 M , do not typically contain these large, dense subhaloes (Di Cintio et al. 2011; Wang et al. 2012; Vera-Ciro et al. 2013).”

“Using a larger statistical sample, both Wang et al. (2012) and Purcell & Zentner (2012) find a 10-20% probability of finding a subhalo population similar to the MW’s at a halo mass of 1012M⊙.”

“For example, Wang et al. (2012) & Vera-Ciro et al. (2013) have argued that if Article number, page 7 of 16 the mass of the MW halo isMvir < 1× 1012 M⊙ then the TBTF problem would likely not occur.”

“Figure 5 in Wang et al. (2012) allows us to directly compare the host halo mass against the probability of containing three or less than three subhalos withvmax > 30 kms−1 (maximum value of the circular velocity).”

“…would likely lead to variations of the same magnitude in the predicted number of satellites of such systems (Boylan-Kolchin, Besla & Hernquist 2011; Wang et al. 2012; Cautun et al. 2014), limiting the insight that may be gained from direct quantitative comparison between simulations and…”

“Based on our analysis of the eight highest resolution ΛCDM N-body simulations of MW-sized dark matter halos performed to date, it is very unlikely that Leo I is on an unbound orbit.”

“these simulations (but still within the range allowed from observational constraints), then the number of discrepant (too dense) halos may be small enough to not be a major worry [279, 280].”

“At slightly brighter magnitudes, it becomes harder to justify differences from theory (Boylan-Kolchin et al. 2012), although Wang et al. (2012) find some differences may be accounted for by assuming a slightly lower halo mass for the host galaxy.”

“Other authors have pointed out that a statistically rare or low-mass Milky Way (e.g. Purcell & Zentner 2012; Wang et al. 2012) can also explain the discrepancy; however, the former option is called into question by Strigari & Wechsler (2012) and the latter is in conflict with constraints derived by…”

“…Newman et al. 2009, 2011; de Blok 2010; Kuzio de Naray & Kaufmann 2011; Kuzio de Naray & Spekkens 2011; Salucci et al. 2012; Wolf & Bullock 2012) and the apparent paucity of bright satellites around the Milky Way (Boylan-Kolchin, Bullock & Kaplinghat 2011, 2012; although see Wang et al. 2012).”

“Indeed, Wang et al. (2012) showed that approximately 40% of haloes with mass Mhalo ∼ 1012 M in ΛCDM dark matter only simulations have three or fewer subhaloes with Vmax > 30 km/s (the threshold used by Boylan-Kolchin et al. 2011 to define massive failures).”

“…Milky Way is currently uncertain at a factor of two, and its more precise measurement using stellar streams may help resolve (or further aggravate) some apparent issues in the theory of galaxy formation, such as the so-called “Too-BigTo-Fail” problem (Boylan-Kolchin et al. 2011; Wang et al. 2012).”

“Several have suggested that a Milky Way halo mass of ∼ 8× 10(11)M has no TBTF problem if CDM-only simulations are to be believed [329, 330, 331, 332].”

“Even in the case of CDM, the ‘too big to fail’ problem disappears if the mass of the Milky Way halo is less than about 1.5 × 1012 M (Purcell & Zentner 2012; Wang et al. 2012).”

“The MW halo mass has been suggested to fall anywhere in the range of 5 × 1011 − 2 × 1012M , depending on the choice of method and the definition of the MW halo mass itself (Kahn & Woltjer 1959; Kahn & Woltjer 1959; Sales et al. 2007a,b; Li & White 2008; Busha et al. 2011; Deason et al. 2012; Wang et al. 2012;González…”

“The expected subhalo abundance increases roughly in proportion to the mass of the parent halo [327] so, in reality, the observed abundance of satellites constrains both the particle mass and the host halo mass simultaneously.”

“Alternatively, since the DM halo mass has a significant impact on the expected number of satellites, one may argue that the severity of the problem depends upon the choice of MW halo mass, which remains difficult to determine (Wang et al. 2012; Cautun et al. 2014).”

“We find that doubling the halo mass roughly doubles the number of subhaloes (Wang et al. 2012; Cautun et al. 2014a), so that there are more of them at fixed vpeak.”

“For example, di Cintio et al. (2011), Wang et al. (2012), Boylan-Kolchin et al. (2012), and Vera-Ciro et al. (2013) pointed out that reducing the assumed mass of the MW host halo to Mhalo ∼ 8 × 1011M will reduce the number of problematic subhalos.”

“On the other hand, if the host halo in our simulation is slightly less massive, similar to the halo masses used by other groups (e.g. Guedes et al. 2011; Sawala et al. 2014), one may not have a ‘too big to fail’ problem at all to begin with (Wang et al. 2012).”

“Since the subhalo abundance increases rapidly with increasing host halo mass (e.g. De Lucia et al. 2004; Gao et al. 2004; Zentner et al. 2005; Wang et al. 2012), the adoption of subhalo populations hosted by Milky Way-sized halos could underestimate the probability of flux-ratio anomalies.”

“In these simulations, the number of massive subhaloes depends strongly on the assumed MW halo mass and the problem disappears if the MW halo mass is sufficiently small ( 1 × 1012 M ; Wang et al. 2012; Cautun et al. 2014a).”

“That is, if the MW’s halo mass is low, the typical mass of a subhalo hosting a MW satellite is lower, and this can render the dynamics of MW satellites consistent with the subhaloes (Wang et al. 2012).”

“However, as argued by Wang et al. (2012) and Vera-Ciro et al. (2012), the number of massive satellites is a stochastic quantity that also depends on the mass of the host.”

“To resolve this so-called missing satellite problem various studies have shown that the tension is eased for lower halo masses of the Milky Way (e.g. Wang et al. 2012; Vera-Ciro et al. 2013).”

“…works (Salvadori & Ferrara 2009, 2012; Salvadori et al. 2014), along with Via Lactea II, Aquarius, and CLUES simulations (e.g. Madau et al. 2008; Wang et al. 2012; Beńıtez-Llambay et al. 2015), we adopt a Lambda Cold Dark Matter (ΛCDM) cosmology with Ωm = 0.24, ΩΛ = 1 − Ωm = 0.76, Ωb = 0.04,…”

“…of numerous cosmological studies based on the stellar kinematics of Local Group dwarf galaxies (see e.g. Boylan-Kolchin, Bullock & Kaplinghat 2011, 2012; Sawala et al. 2013, 2016, 2015, 2014; Wang et al. 2012; Cautun et al. 2014a; Di Cintio et al. 2013; Zolotov et al. 2012; Arraki et al. 2014).”

“…11 classical MW satellites (rper = 19.6 kpc, e.g. Kroupa et al. 2005; Zentner et al. 2005; Metz et al. 2007; Metz et al. 2009; Kroupa et al. 2010; Wang et al. 2012; Pawlowski et al. 2013; Pawlowski et al. 2014), or as a relative flattening of the distribution’s minor-tomajor axis ratio…”

“On the other hand, if the mass of the Milky Way halo has been overestimated, this apparent lack of high mass sub-halos may be due to a statistical anomaly (Wang et al. 2012).”

“Also, the problem would disappear if the total Milky Way halo mass were considerably smaller than currently expected (Rashkov et al. 2012; Wang et al. 2012; Purcell & Zentner 2012), but this seems rather unlikely (Boylan-Kolchin et al. 2013).”

“…scales linearly with the host halo mass. Lowering the mass of the MW by∼ 20 per cent, fromMvir ∼ 1012 to Mvir 6 8 × 1011 M⊙, reduces the abundance of massive, dense subhaloes such that their absence around the MW can be attributed to a statistical fluke (Wang et al. 2012; Vera-Ciro et al. 2013).”

“An excess of satellites around red primaries at fixed luminosity had previously been reported in a number of other studies (Sales et al. 2007; Guo et al. 2012; Wang et al. 2012).”

“4 and 5, confirming the earlier results of Moore et al. (1999); Kravtsov et al. (2004); Zheng et al. (2005); Springel et al. (2008); Weinberg et al. (2008); Klypin et al. (2011); Wang et al. (2012); Cautun et al. (2014) It is clear from Figs.”

“Wang et al. (2012) find that a smaller halo mass∼ (0.8 − 1) × 1012M⊙ will reduce the probability of massive subhalo withVmax > 30 km/s significantly, but the probability of having Magellanic-cloud-like systems is also reduced.”

“…(Deason et al. 2012; Piffl et al. 2014; Wang et al. 2015), the kinematics of bright Milky Way satellites, (Sales et al. 2007a,b; Busha et al. 2011; Wang et al. 2012; Boylan-Kolchin et al. 2013; González et al. 2013; Cautun et al. 2014) and the timing argument (Kahn & Woltjer 1959; Li & White…”

“…halos by tidal forces and ram-pressure stripping upon their entry in the MW virial region (e.g., Mayer et al. 2007), modifications of the cold dark matter structure formation paradigm (e.g., Lovell et al. 2012), and others (e.g., Bovy & Dvorkin 2012; Vera-Ciro et al. 2012; Wang et al. 2012).”

“These values are inconsistent with the WMAP 7 data at about the 2σ level, but this discrepancy is of no consequence for the analysis of this paper (see Wang et al. 2012).”

“Within the collisionless CDM model, these explanations fall into two camps: (i) invoking baryonic physics to reduce the efficiency of galaxy formation in low-mass DM haloes (Sawala et al. 2016a,b), and (ii) exploiting the uncertainty in the mass of the MW DM halo (Wang et al. 2012).”

“…to the TBTF problem in the MW context have been put forward, related for example to the uncertainty in the mass of the halo hosting our Galaxy or pointing out the statistical weakness of this “sample of one” challenge (e.g., Wang et al. 2012; Vera-Ciro et al. 2013; Purcell & Zentner 2012).”

“To combine the satellite luminosity functions of the Milky Way and M31 we assume that the abundance of satellites scales with the mass of the central galaxy’s halo (Wang et al. 2012).”

“…are essential for studies of the Galaxy in the contexts of galaxy evolution and cosmology (Abadi et al. 2010; Boylan-Kolchin et al. 2010; Wang et al. 2012) and to the analysis of the 6D motions of high-velocity stars in the tails of the velocity distribution and the local escape speed…”

“This has been achieved for satellites with Vmax > 30 kms −1by invoking a relatively low mass for the Milky Way halo (Wang et al. 2012; Cautun et al. 2014); less massive (Vmax < 20 kms −1) subhaloes are prevented from forming galaxies by reionisation and supernova feedback (e.g. Bullock et al. 2000;…”

“…2011; Kuzio de Naray & Kaufmann 2011; Salucci et al. 2012; Wolf & Bullock 2012) and the missing satellite problem (Boylan-Kolchin et al. 2011, 2012; Wang et al. 2012), but these observations may be the result of galaxy formation physics that is not yet well understood (Benson et al. 2002a;…”

“…et al. 2019), disfavouring a low mass Milky Way solution to the ‘too big to fail’ (TBTF) problem (Boylan-Kolchin et al. 2011; di Cintio et al. 2011; Wang et al. 2012; Vera-Ciro et al. 2013), indicating the need for other solutions such as feedback (e.g. Brook & Di Cintio 2015; Wetzel et al.…”

“This could suggest that these dark haloes are too massive to host the Milky Way (in agreement with Battaglia et al. 2005; Sales et al. 2007; Smith et al. 2007; Wang et al. 2012; Vera-Ciro et al. 2013).”

“…by a variety of baryonic mechanisms, including tidal stripping by the central galactic disk and internal feedback (e.g., Brook & Di Cintio 2015; GarrisonKimmel et al. 2019), or simply if the mass of the MW halo is lighter than commonly assumed (e.g., Wang et al. 2012; Jiang & van den Bosch 2015).”

“…Koposov et al. 2009; Muñoz et al. 2009; Busha et al. 2010; Cooper et al. 2010; Macciò et al. 2010; Li, De Lucia, & Helmi 2010; Font et al. 2011; Wang et al. 2012) and full N-body/gasdynamic simulations to investigate the physics of satellite galaxies (e.g. Libeskind et al. 2007; Okamoto &…”

“Moreover, the discrepancy between observed and simulated sllite galaxies may reflect the fact that the MW is less massive than is commonly thought: a total mass between8 · 1011 ∼ < M/M⊙ ∼ < 1012 has been argued in Vera-Ciro et al. (2013) and Wang et al. (2012).”

“Wang et al. (2012) argue the low velocities of the MW satellites may be an indication the MW is less massive than typically thought.”

“Even at fixed mass, observations find a large degree of scatter in the abundance of satellites surrounding galaxies similar to our own (e.g. Zaritsky et al. 1993; Guo et al. 2011; Wang et al. 2012; Geha et al. 2017; Kondapally et al. 2018; Bennet et al. 2019).”

“Wang et al. (2012) argue that the missing satellite problem is not serious enough to motivate a revision to the CDM paradigm, but what we saw above in Fig.”

“One caveat in this debate is that some satellite properties depend sensitively on the MW halo mass (e.g., Wang et al. 2012).”

“Wang et al. (2012) showed that taking into account the uncertainty on the measured Milky Way virial mass, the observed subhalo circular velocity function was consistent with that observed in ensemble simulations of dark matter halos.”

“…(2014) D ow nloaded from https://academ ic.oup.com /m nras/article-abstract/445/2/1820/1404326 by U niversity of G roningen user on 15 N ovem ber 2018 assumption that the mean subhalo count is self-similar amongst host haloes of different masses (see Wang et al. 2012, and references therein).”

“For example, Wang et al. (2012) express it as a problem of missing massive satellites; high-resolution N-body simulations of Milky-Way (MW) size host haloes reveal of the order of 10 subhaloes per host with a maximum circular velocity Vmax >∼ 25km s −1 (e.g., Strigari et al. 2007; Madau, Diemand &…”

“Another would be to explore whether satellite alignments may be used to improve the reliability of algorithms that search for primary-satellite associations, especially when applied to large datasets like the c© 2014 RAS, MNRAS 000, 1–16 SDSS (see, e.g., Wang et al. 2012; Sales et al. 2013).”

“…M = 5 × 1011 M ) and 16% (at 2×1012 M ); (2) eliminating the too-big-to-fail problem (Boylan-Kolchin et al. 2011b, 2012) and severely exacerbating it (Wang et al. 2012; Vera-Ciro & Helmi 2013; Jiang & van den Bosch 2015); and (3) placing the Large Magellanic Cloud and the Leo I dwarf spheroidal…”

“Several solutions have been proposed to both problems (Strigari et al. 2007; Simon & Geha 2007; Madau et al. 2008; Zolotov et al. 2012; Brooks & Zolotov 2012; Purcell & Zentner 2012; Vera-Ciro et al. 2012; Di Cintio et al. (2012); Wang et al. 2012).”

“…al. 1999; Swaters et al. 2003; Simon et al. 2005), the number of observed satellite galaxies in our Galaxy is too small (Klypin et al. 1999; Moore et al. 1999), and the observed circular velocities of most massive subhaloes in our Galaxy are too small (Boylan-Kolchin et al. 2011; Wang et al. 2012).”

“For example, if the Milky Way were to have a smaller virial mass, then it would also host a smaller number of massive subhalos (Wang et al. 2012).”

“8 shows the well-known correlation between the number of satellites and the halo mass (Wang et al. 2012).”