Massive dark subhaloes in the Milky Way

Too big to fail? The puzzling darkness of massive Milky Way subhaloes

Abstract

We show that dissipationless CDM simulations predict that the majority of the most massive subhaloes of the Milky Way are too dense to host any of its bright satellites (). These dark subhaloes have peak circular velocities at infall of and infall masses of . Unless the Milky Way is a statistical anomaly, this implies that galaxy formation becomes effectively stochastic at these masses. This is in marked contrast to the well-established monotonic relation between galaxy luminosity and halo circular velocity (or halo mass) for more massive haloes. We show that at least two (and typically four) of these massive dark subhaloes are expected to produce a larger dark matter annihilation flux than Draco. It may be possible to circumvent these conclusions if baryonic feedback in dwarf satellites or different dark matter physics can reduce the central densities of massive subhaloes by order unity on a scale of 0.3 – 1 kpc.

keywords:
Galaxy: halo – galaxies: abundances – dark matter – cosmology: theory
12

1 Introduction

The cold dark matter (CDM) paradigm has been demonstrably successful at explaining a variety of observations on cosmological scales. Tests on smaller scales are often complicated by the physics of galaxy formation, but are crucial for verifying the CDM model. Perhaps the most prominent issue facing CDM on galactic scales is the large discrepancy between the number of observed and expected satellite galaxies of the Milky Way (Kauffmann et al. 1993; Klypin et al. 1999; Moore et al. 1999; see Bullock 2010 for a recent review). Accordingly, much theoretical work has been devoted to understanding how to reproduce the satellite population of the Milky Way (MW).

While some CDM models of the MW’s satellite population place the most luminous dwarf galaxies in the most massive subhaloes at redshift zero (Stoehr et al., 2002; Hayashi et al., 2003; Peñarrubia et al., 2008), recent kinematic studies of the satellites have shown that this is unlikely to be the case (Walker et al., 2009; Strigari et al., 2010). Other models postulate that MW satellite galaxies correspond to subhaloes that were the most massive at some earlier time (Bullock et al., 2000; Kravtsov et al., 2004b; Ricotti & Gnedin, 2005; Koposov et al., 2009; Okamoto & Frenk, 2009; Busha et al., 2010), often the epoch of reionization, with galaxy formation strongly suppressed in lower mass subhaloes (see Kravtsov 2010 for a recent review). In addition, many faint MW satellites have been discovered in the SDSS (e.g., Willman et al. 2005; Belokurov et al. 2007), and it has become clear that up to a factor of times as many faint galaxies could remain undetected at present owing to incomplete sky coverage, luminosity bias, and surface brightness limits (Tollerud et al., 2008; Walsh et al., 2009; Bullock et al., 2010).

While this theoretical and observational progress has alleviated – though not eliminated – concerns about the mismatch between the number of low-mass subhaloes and faint MW satellites, a pressing question remains: what is the stellar content of massive Milky Way subhaloes at redshift zero? In this Letter, we focus on properties of massive subhaloes in CDM galaxy-mass haloes, and examine which Milky Way satellites – if any – can be hosted by such subhaloes.

2 Simulations and Data

Our CDM predictions are based on dark matter subhaloes from the Aquarius project (Springel et al., 2008) and the Via Lactea II simulation (Diemand et al., 2008, 2007). The Aquarius project consists of six galaxy-mass haloes – denoted A through F – simulated at a series of increasingly high mass and force resolution. Although only halo A was simulated at the highest resolution level, all six haloes were simulated with particle mass and Plummer-equivalent gravitational softening pc; it is this set of “level 2” simulations that we use in this paper. The Via Lactea II simulation (VL-II) of one galaxy-mass halo used and pc. A notable difference between the simulations is the background cosmological model: the Aquarius simulations used a value of 0.9 for the power spectrum normalization and 1.0 for the spectral index of the primordial power spectrum , while VL-II used and . The best current estimates of these parameters, and (Komatsu et al., 2011), fall in between those used for the simulations.

In each simulation, we select every subhalo that lies within 300 kpc of the host’s center and has a maximum circular velocity exceeding . We characterize a subhalo prior to infall onto its host via , which we define to be the value of when the subhalo’s mass was at a maximum (over its entire evolution) in Aquarius and the maximum value of over the subhalo’s entire history for VL-II. The measured values of and (the radius at which is attained) at redshift zero are used to determine each subhalo’s inner mass distribution by assuming that the subhalo’s density structure can be modeled by a Navarro, Frenk, & White (1997, hereafter NFW) profile with the same and . Using subhaloes extracted from the Millennium-II Simulation (Boylan-Kolchin et al., 2009), we have verified that this approach gives the correct mass to better than 10% at radii that are well resolved3 (as expected from earlier work by Kazantzidis et al. 2004).

To connect the -body subhaloes to the bright () dwarf spheroidal galaxies of the Milky Way, we turn to kinematic measurements of the dwarfs’ masses. Walker et al. (2009) and Wolf et al. (2010) have recently shown that dispersion-supported galaxies such as the MW dwarf spheroidals have dynamical masses within their deprojected half-light radii that are well-constrained by line-of-sight velocity measurements. Since these galaxies are all strongly dark matter-dominated even within (e.g., Mateo 1998), observed values of are effectively measurements of the dark matter mass within . A necessary, but not sufficient, condition for a subhalo to possibly host a given dwarf is that agree with . Conversely, a dwarf cannot live in a subhalo if and differ substantially.

Figure 1: Constraints on the values (assuming NFW profiles) of the hosts of the nine bright () MW dwarf spheroidal galaxies. The colored bands show confidence intervals based on measured values of and from Wolf et al. (2010).

Given the values of calculated by Wolf et al. (2010), we can therefore investigate what values of NFW subhaloes are consistent with the observed dynamics of the bright MW dwarf spheroidals. We exclude Sagittarius, which is far from dynamical equilibrium, for the present. Figure 1 shows the resulting confidence regions in - space for these nine dwarfs. The behavior of the contours for each of the dwarfs is qualitatively similar: there is a global minimum in , corresponding to and (Wolf et al., 2010), with allowed values of increasing for both smaller and larger values of (corresponding to and , respectively). The lower portions of the curves, where , are unlikely to be physically plausible models for the hosts of dwarfs, as they require that the dark matter subhalo has been strongly affected by tides on the scale of the luminous matter in the dwarf.

3 Results

Figure 2: Subhaloes from all six Aquarius simulations (circles) and Via Lactea II (triangles), color-coded according to . The shaded gray region shows the confidence interval for possible hosts of the bright MW dwarf spheroidals (see Fig. 1).

In Figure 2, we plot data for all subhaloes from the six Aquarius simulations (circles) and from the VL-II simulation (triangles), color-coded by . The gray shaded band corresponds to constraints from the MW dwarf spheroidal galaxies in Fig. 1. In terms of the total mass within 300 parsecs (; Strigari et al. 2008), this gray shaded region is almost exactly the same as . Many of the subhaloes lie in the range that is consistent at the level with the dwarfs, but there is a large population of subhaloes that does not. These subhaloes all have central densities that are too high to host any of the bright MW dwarf spheroidals; they also have higher values of both and , on average.

The Milky Way contains three additional satellites that are brighter than the nine dwarf spheroidals included in Figs. 1-2: the Large Magellanic Cloud (LMC), the Small Magellanic Cloud (SMC), and the Sagittarius dwarf spheroidal. In the context of CDM models of galaxy formation, the Magellanic Clouds are expected to reside in subhaloes with large values of : using abundance matching (e.g., Kravtsov et al. 2004a; Conroy et al. 2006; Guo et al. 2010) to assign stellar mass to subhaloes4, we find that the SMC should have and the LMC should have . Conservatively, we estimate that the Magellanic Clouds have and (Stanimirović et al., 2004; Olsen & Massey, 2007) and remove all subhaloes with these properties from our sample of subhaloes that are inconsistent with the dynamics of the bright MW dwarfs. Sagittarius is in the process of being completely disrupted by the disk, but estimates of its pre-interaction properties give it a total stellar mass similar to the SMC (Niederste-Ostholt et al., 2010). In the absence of the MW disk – e.g., in dissipationless simulations such as those used here – it is very likely that Sagittarius would be much more massive at , and our Magellanic Cloud exclusion criteria might also be appropriate for Sagittarius. Regardless, the inclusion or exclusion of one object does not alter the conclusions reached below. The remaining subhaloes are not compatible with hosting any of the bright () satellites of the Milky Way; we refer to these as massive dark subhaloes and focus the remainder of our analysis on them.

Figure 3: Cumulative function of massive subhaloes at that cannot host any MW satellite brighter than , including the Magellanic Clouds. Each of the seven high resolution simulations studied here has at least six such subhaloes with , and at least four with .

Figure 3 shows the cumulative velocity function of massive dark subhaloes as a function of for each of the seven simulations considered here. All of the dark subhaloes plotted in Fig. 3 have current values larger than 23 , and none meet our criteria for hosting galaxies similar to the Magellanic Clouds. In all cases, there are at least 6 – and up to 12 – subhaloes with that are not consistent with any of the bright MW satellites (i.e, any satellite with ). These subhaloes tend to be more massive than the possible hosts of the dwarf spheroidals, both today and at infall (see Fig. 4 below). Moreover, the three haloes with the fewest massive dark subhaloes (Aq-B, Aq-C, and VL-II) do not contain any potential Magellanic Cloud hosts. If we restrict ourselves to the simulations that do contain reasonable Magellanic Cloud analogs, then the predicted number of massive dark subhaloes is closer to 10, including several with .

The luminosity - relation for a representative halo is shown in Figure 4. The MW dwarfs (red symbols) were assigned their values by placing the most luminous dwarf spheroidal (Fornax) in the subhalo with the largest value of that has within of the measured of Fornax, then repeating the process for each of the other dwarfs in order of decreasing luminosity. For each dwarf, the assigned value of can therefore be considered an upper limit at confidence within this realization. The massive dark subhaloes (black symbols) are placed on the same plot according to their . These subhaloes must all have luminosities less than in order to have escaped detection in all-sky optical surveys (Whiting et al., 2007). The dotted blue line shows an extrapolation of abundance matching, assuming . It is clear that neither the bright dwarf spheroidals nor the dark subhaloes described in this paper can be easily accommodated by galaxy formation models in which luminosity is a monotonic function of halo mass or .

Figure 4: Relation between and for Milky Way dwarf spheroidals (red points) and massive dark subhaloes (black points) for one representative halo realization (Aq-A).

If massive, dark subhaloes do exist in the Milky Way halo, their presence has important implications for indirect dark matter searches. Denser subhaloes produce a larger luminosity from dark matter annihilation; from Fig. 2, the dark subhaloes expected in the Milky Way are denser than their potentially luminous counterparts and therefore may be bright in -rays due to annihilations. In Fig. 5, we plot the annihilation flux, , within steradians (a circular region with radius 0.5 degrees) of the center of each massive dark subhalo relative to the predicted flux within the same angular radius originating from Draco, one of the most promising targets among the MW dwarfs for Fermi (Abdo et al., 2010). The horizontal error bars on the data points show 68% confidence intervals based on 1000 random realizations for the observer’s location (constrained to have a galactocentric distance of 8 kpc). Dark subhaloes are promising indirect detection candidates: each halo has at least two dark subhaloes with annihilation fluxes larger than that of Draco, and four of the seven haloes have at least one dark subhalo with .

Figure 5: Distribution of annihilation fluxes from dark subhaloes, normalized to a typical scenario for the annihilation flux from Draco. Error bars reflect 68% confidence levels for varying the specific angular location of the observer on the solar circle. The typical halo has approximately four dark subhaloes with annihilation fluxes exceeding that of Draco.

Our division between dark and bright subhaloes is very conservative: rather than requiring at most one subhalo that is consistent with each of the bright MW dwarf spheroidals, we require that all of the dark subhaloes are inconsistent with all of the bright dwarfs at the level. While the quantitative results may, in principle, change slightly if systematic errors in the determination for the densest MW dwarfs (Draco and Ursa Minor) have resulted in an underestimate of , our general result – that many of the most massive simulated subhaloes are too dense to host any bright MW satellite – will be unaffected unless all of the measured values change substantially.

4 Discussion

The results of Section 3 show that high resolution CDM simulations of individual galactic haloes generically predict that the Milky Way should host at least six subhaloes that, at one point, had maximum circular velocities in excess of 30 and yet are incompatible with any known MW satellite (including the Magellanic Clouds) having . Either these subhaloes actually exist as predicted in the Milky Way, requiring us to understand their properties and stellar content, or they do not exist, in which case we must understand the mechanism(s) that suppress their formation or survival.

If massive dark subhaloes exist as predicted:
Detecting massive dark subhaloes would be a strong confirmation of the standard CDM paradigm. These dark subhaloes might host at least some of the recently discovered ultra-faint galaxies, all of which have luminosities lower than . Kinematic constraints favor masses and densities for the ultra-faints that are indicative of fairly massive subhaloes (Strigari et al., 2008; Walker et al., 2009; Simon et al., 2010), albeit with large uncertainties at present (e.g., Wolf et al. 2010; Martinez et al. 2010). If some of the ultra-faints are hosted by the massive subhaloes described here, they would have total mass-to-light ratios of . The ultra-faints would be excellent candidates for indirect dark matter detection in this scenario (Fig. 5). An alternate detection method could be through the subhaloes’ tidal influence on the MW’s HI disk (Chakrabarti et al., 2011). While the existence of effectively dark subhaloes with low masses is perhaps not surprising given the standard CDM power spectrum and the variety of effects that can impede cooling and star formation in shallow gravitational potential wells, the prospect of subhaloes more massive than the hosts of bright dwarf spheroidals but with is intriguing.

The existence of massive dark subhaloes requires that the fundamental assumption of abundance matching models – that galaxy stellar mass or luminosity is a monotonic function of – does not hold for ; Fig. 4 illustrates this point. Galaxy formation on scales below should therefore be effectively stochastic, with stellar mass depending sensitively on specific details of a subhalo’s environment, formation history, etc. rather than primarily determined by host halo mass or .

If massive dark subhaloes do not exist as predicted:
The most prosaic explanation is that the haloes studied here are not representative of the MW-mass halo population at large in CDM. This is unlikely to be the case for the Aquarius haloes, however, since they have substructure abundances typical of the full sample of over 2000 MW-mass haloes from the Millennium-II Simulation’s volume (Boylan-Kolchin et al., 2010). The subhalo mass function of the Milky Way could also be a statistical anomaly with respect to CDM expectations, in the sense that massive MW subhaloes are all less concentrated than expected, or that there are zero massive dark subhaloes in the MW when we expect at least six (Fig. 3). Perhaps the best way to investigate this possibility is to obtain detailed kinematic measurements of M31’s satellites: if the M31 satellite system does not require massive dark subhaloes in CDM simulations, then the statistical anomaly explanation would gain more traction.

If the MW’s subhalo mass function is not aberrant, then understanding why there are no massive dark subhaloes would likely result in important insight into the physics governing structure formation. One possible CDM-based explanation is that the dark matter distribution in satellites of the MW is substantially less concentrated than current dissipationless simulations predict.5 Baryonic processes may affect the dark matter distribution on small scales by heating it to larger radii, which would have the desired effect of lowering the dark matter density. For such a solution to work, it would have to substantially lower the dark matter density on scales of 0.3 – 1 kpc (corresponding to the deprojected half-light radii of the bright dwarf spheroidals) while not strongly impacting the dark matter on smaller scales (, corresponding to the half-light radii of the ultra-faint dwarfs), as ultra-faints seem to have high central dark matter densities (Simon et al., 2010). It is not clear that this could produce nearly identical average dark matter densities on scales of 300 pc in galaxies spanning a factor of in luminosity (Strigari et al., 2008).

Gravitational shocks from encounters with the MW disk may also destroy some fraction of satellites (D’Onghia et al., 2010). This mechanism works most efficiently at destroying low-mass subhaloes, however. Furthermore, it would not affect subhaloes that have larger pericenters or were accreted recently; many massive dark subhaloes in the simulations studied here fall into these two categories.

If the Milky Way’s dark matter subhalo population is typical of CDM predictions, and baryonic physics has not strongly modified the internal structure or abundance of massive subhaloes, then the more drastic solution of modifying the underlying cosmology may be required in order to circumvent our primary conclusions that massive dark subhaloes should exist and that galaxy formation on small scales is stochastic. Merely tweaking the cosmological parameters within the CDM model is unlikely to have an influence, as VL-II and Aquarius bracket current estimates of and . Modifying the dark matter power spectrum on sub-galactic scales – for example, through Warm Dark Matter (WDM) with a characteristic scale of 40 to 50 – would result in both fewer massive subhaloes (e.g., Zavala et al. 2009) and lower central densities in such subhaloes. Recent analyses of the Ly- forest put fairly stringent constraints on the mass of WDM particles, however (Boyarsky et al., 2009). Dark matter self-interactions would also reduce the central densities of subhaloes, and would additionally make them more vulnerable to tidal disruption. It is far from obvious that the abundance and dynamics of observed MW satellites would be correctly reproduced in the viable parameter space of these non-CDM models.

In summary, we find that the majority of the most massive subhaloes in dissipationless CDM simulations are too dense to host any of the bright Milky Way satellites. It follows that galaxy formation must be effectively stochastic in haloes with maximum circular velocities of . This conclusion may be circumvented if the Milky Way’s subhalo population differs substantially from the average CDM expectation, or if the abundance or structure of massive subhaloes in the Milky Way is strongly affected by baryonic processes or different dark matter physics.

Acknowledgments

We thank Louis Strigari for interesting discussions and the Aquarius and Via Lactea collaborations for providing access to their simulation data. The Aquarius Project is part of the program of the Virgo Consortium for cosmological simulations. The Millennium and Millennium-II simulation databases used in this paper were constructed as part of the activities of the German Astrophysical Virtual Observatory. JSB was supported by NSF AST-1009973; MK was supported by NASA grant NNX09AD09G.

Footnotes

  1. pagerange: Too big to fail? The puzzling darkness of massive Milky Way subhaloesReferences
  2. pubyear: 2011
  3. While both the host haloes and subhaloes from Aquarius are fit somewhat better by Einasto (1965) profiles than by NFW profiles (Navarro et al., 2010; Springel et al., 2008), we use NFW profiles here because they provide more conservative constraints: at fixed and , an Einasto profile contains more mass than an NFW profile within a given radius for reasonable values of the Einasto shape parameter when .
  4. We match from Li & White (2009) to that we have calculated from the Millennium and Millennium-II simulations (Springel et al., 2005; Boylan-Kolchin et al., 2009).
  5. Lower concentrations of dark matter are also favored by many observations of low-mass field galaxies (e.g., Kuzio de Naray et al. 2008), although these tend to be gas-rich, disk-dominated systems with higher luminosities than the bright MW dwarf spheroidals.

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