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.”

“For example, Wang et al. (2012) and Cautun et al. (2014b) reported that the MW satellites are consistent with ΛCDM predictions at the 10% confidence level if the MW halo has a virial mass smaller than 1.3× 1012M .”

“This may seem somewhat at odds with the conclusions of Wang et al. (2012) and Cautun et al. (2014a), who found that the abundance of subhaloes at high Vmax is proportional to the host halo mass.”

“This argumentation c© 2015 The Authors has since been both challenged (e.g. Zentner et al. 2005; Libeskind et al. 2009; Wang et al. 2012) and supported (Metz et al. 2008; Ibata et al. 2014b; Pawlowski et al. 2014; Pawlowski & McGaugh 2014).”

“However, since the number of satellites scales with the host halo mass (Wang et al. 2012; Cautun et al. 2014), our sterile neutrino models would be increasingly in conflict with the observed luminosity functions for Mhosthalo 6 10 12 M .”

“While this system has been used in attempts to constrain the cosmological model (e.g. Bullock, Kravtsov & Weinberg 2000; Benson et al. 2002; Klypin, Zhao & Somerville 2002; Lovell et al. 2012; Wang et al. 2012), it is not clear that it is typical of the population as a whole.”

“Cold dark matter models predict the structure of halos to be self-similar; in such a way that, when properly scaled, a Milky Way-sized halo looks comparable to one hosting a faint dwarf galaxy (Moore et al. 1999; Springel et al. 2008; Klimentowski et al. 2010; Wang et al. 2012).”

“This provides evidence that dwarf galaxy halos also harbor satellite galaxies of their own, supporting predictions from Λ Cold Dark Matter (ΛCDM) numerical simulations (e.g., Moore et al. 1999; Gao et al. 2004; Kravtsov et al. 2004; Guo et al. 2011; Wang et al. 2012; Sales et al. 2011, 2013).”

“As discussed by Wang et al. (2012), a few of the bright satellites in Aquarius were accreted in groups, but the accretion happened early and the groups have long been disrupted by the tidal field of the main halo.”

“Using the results of cosmological N-body simulations, Wang et al. (2012) demonstrate that the number of subhaloes which can be regarded as massive failures increases roughly linearly with the mass of the host haloes.”

“The number of massive subhaloes in these simulations, which are inconsistent with the observed structure, is sensitive to the assumed MW halo mass, and the problem would disappear if the MW halo mass is sufficiently small (<1 × 1012M ; Wang et al. 2012; Cautun et al. 2014).”

“However, such a comparison relies (i) on the hope that the MW satellite CSMF is not atypical and (ii) on the assumed halo mass for the MW (the subhalo abundance strongly depends on Mh, e.g., Gao et al. 2011; Wang et al. 2012).”

“We find that this Vmax function is consistent with being independent of the variation in cosmological parameters considered, confirming the result of Wang et al. (2012).”

“…Milky Way (MW), a number of theoretical predictions or interpretations of observations, for example, the baryon fraction (e.g. Zaritsky & Courtois 2017) and the problem of missing massive satellites (e.g. Boylan-Kolchin et al. 2011; Wang et al. 2012; Cautun et al. 2014), depend on the MW halo mass.”

“The mass of the MW plays a crucial role in interpreting many of the Local Group observations (Wang et al. 2012; Kennedy et al. 2014; Cautun et al. 2014).”

“Moreover, if the mass of the Milky Way host halo is higher than that assumed in our simulations, the low-concentration rapid-accretion hosts could achieve better fits to the Milky Way kinematic constraints (e.g. Wang et al. 2012; Cautun et al. 2014a).”

“E-mail:sy1823@nyu.edu † E-mail:xdu@carnegiescience.edu lem (Kauffmann et al. 1993; Klypin et al. 1999b; Bullock 2010; Boylan-Kolchin et al. 2011, 2012; Wang et al. 2012) still remain to be fully explained.”

“In Wang et al. (2012), too–big–to–fail is restated in terms of the galaxies’ maximum circular velocities; all known satellites are observed MNRAS 000, 1–16 (2019) with vmax < 30 kms−1 (with the exception of the Magellanic Clouds— Jiang & van den Bosch 2015), yet the simulated halos should host…”

“However, whether these inconsistencies exist (when observational uncertainties and baryonic physics are taken into account) [8–12] and whether they can be solved with SIDM remain disputable [13, 14].”

“Others (e.g., Wang et al. 2012; Vera-Ciro et al. 2013) attempt to address the problem by invoking the possibility that the mass of the Milky Way halo is lower than normally assumed, which reduces the expected number of satellites with high maximum circular velocities.”

“…an active debate in the literature, with some authors pointing out that a reduced MW mass would effectively eliminate the problematic halos (e.g. Wang et al., 2012; Cautun et al., 2014) and others arguing that baryonic processes, such as reionization, supernovae feedback, tidal interactions,…”

“The absence of massive subhaloes in the Milky Way could be also interpreted as an indication that the MW halo is less massive than is commonly assumed [13].”

“The fact that the number of particles within the virial radius in Busha et al. (2011) is smaller than the minimum number needed to achieve convergence as listed in Wang et al. (2012) may account for part of the difference in the probability of finding two subhalos like Magellanic Clouds.”

“The MW halo mass and the inferred satellite galaxy properties, however, play a crucial role in many inferences derived from the properties of the MW or Local Group system (e.g.Boylan-Kolchin et al. 2011; Wang et al. 2012; Pawlowski et al. 2012; Cautun et al. 2014, 2015a,b).”

“…2015; Jiang & van den Bosch 2015), or to attempt solving it (Del Popolo & Le Delliou 2014; Ogiya & Burkert 2015; Elbert et al. 2015; Dutton et al. 2016; Oñorbe et al. 2015; Chan et al. 2015; Read et al. 2015; Sawala et al. 2014; Brook & Di Cintio 2015; Wang et al. 2012; Zolotov et al. 2012).”

“However, recent analyses of Gao et al. (2012) and Wang et al. (2012) show that substructure abundances are not very sensitive to cosmological models.”

“constant. There are several factors that can yet affect the particle energy distribution of the formed halo. I. An already formed halo may gravitationally capture more substance from the surroundings(Wang et al. 2012; Baushev 2013b). The accretion of the additional mass can lead to the ’secondary violent relaxation’ II…”

“Recent studies claim that the missing massive satellites problem would disappear if the assumed mass of the MW halo is less than 1 × 1012 M⊙ through analysis of MW-like simulations (Wang et al. 2012; Cautun et al. 2014).”

“…so, this dramatically lessens tensions between predictions of large numbers of massive dwarfs and the modest number of observed dwarf galaxies at such velocity scales (the evidence for an uncertain Milky Way mass and its consequences are discussed by e.g., Wang et al. 2012; Vera-Ciro et al. 2013).”

“On the observational side, this problem could be due to the inability of modern telescopes to detect the faintest galaxies (Bullock et al. 2010), or to an overestimate of the virial mass of the Milky-Way dark matter halo (Wang et al. 2012).”

“For the case of the TBTF problem, CDM models can resolve the issue if the mass of the MW halo is less than ∼ 1.5× 1012M⊙ (Wang et al. 2012).”

“However the jury on this is still out: the Milky Way’s halo may simply be of lower mass than those of the Aquarius haloes and hence have fewer massive satellites (Wang et al. 2012).”

“Some of these discrepancies can be alleviated by reducing the expected host halo mass, for example, having fewer (massive) substructures in less-massive halos so that both the ‘missing-satellite’ problem and the ‘too-big-tofail’ problem could be less severe (Wang et al. 2012; Cautun et al. 2014a).”

“However, since the amplitude of the subhalo mass function scales approximately linearly with halo mass (Wang et al. 2012), our conclusions from comparing this simulated cluster (the only one available with the required resolution) with Abelll 2744 are conservative.”

“…has been reduced over the past decade with the discovery of many more faint Milky Way satellites (Belokurov et al. 2006; Zucker et al. 2006; Koposov et al. 2015), and new estimates of our halo mass predict fewer high-mass satellites (Wang et al. 2012; Kafle et al. 2014), it still exists.”

“The host halo has a mass of M = 1.1×1012M⊙ (Watkins et al. 2010; Deason et al. 2012; Wang et al. 2012) and a concentration parameter of c = 9.39.”

“Moreover, a significant part of the dark matter gradually accretes onto the already formed halo, when the strong gravitational field inhomogeneities have already disappeared (Wang et al. 2012).”

“The absence of massive subhaloes in the Milky Way could be also interpreted as an indication that the MW halo is less massive than is commonly assumed [14].”

“…of the more massive subhaloes remain dark (e.g. Purcell & Zentner 2012; Rodŕıguez-Puebla et al. 2013a,b), lowering the mass of the MW host halo (e.g. Wang et al. 2012; Vera-Ciro et al. 2013) to better fit the observed MW’s velocity function or tidal interactions (Wang et al. 2017; Sawala et…”

“In terms of substructure, the similarity implies that the mass function of subhalos (“satellites”) is independent of halo mass when scaled to the mass of the host (see; e.g., Moore et al 1999, Wang et al 2012).”

“This agreement supports the expectation that the number of subhaloes, and thus satellites, scales approximately linearly with host halo mass (Wang et al. 2012).”

“Third, the observed circular velocities of most massive subhalos in our Galaxy are also significantly smaller than the predicted values, which is called the ’too big to fail problem’ (Boylan-Kolchin et al. 2011; Wang et al. 2012).”

“Moreover, simulations show that a significant part of the total mass of the halo accretes to the already collapsed halo (Wang et al. 2012).”

“The host halo has a mass of M = 1.1× 1012 M (Watkins et al. 2010; Deason et al. 2012; Wang et al. 2012) and a concentration parameter of c = 9.39.”

“Subhalo abundance is known to scale linearly with host halo mass (J. Wang et al. 2012 We assign a log-normal prior within a 2 σ range to the M host parameter, so its role is to linearly scale M 50 and M hm using the mass prior information, effectively accounting for the uncertainties in the MW and…”

“4This observation was already pointed out in [81] as a possible explanation for the former missing satellites problem.”

“By the mere assumption that Leo I is bound, one would have to accept a lower limit for the MW mass of at least 1.16 × 1012, even though motions of a vast majority of remaining tracers or other arguments as in Wang et al. (2012) might point to a lower mass, insufficient to bind Leo I.”

“It was also shown that there might not be a TBTF problem if the CDM halo of the MW has a relatively low mass of ≈ 1012 M (e.g., Wang et al. 2012).”

“In the Λ CDM framework, the subhalo mass function is approximately scale-free, following a power law in the mass ratio between subhalos and their host halos ( J. Wang et al. 2012 ) .”

“…could be another manifestation of the “Too Big to Fail” problem (however see Papastergis et al. 2015), although the two issues are not necessarily strictly related, since other solutions to this problem exist (Wang et al. 2012; Vera-Ciro et al. 2013; Brooks & Zolotov 2014; Arraki et al. 2014).”

“The statistics of satellite galaxies around Milky-Way like hosts have been studied in the Millennium simulation (Springel et al., 2005b; Wang et al., 2012) where the brightest satellites were determined to be more massive than those found in observations.”

“Since Pal 5 is at most 20 kpc from the Galactic Center, it is not useful to obtain the full mass of the Milky Way.”