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.”

“…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; Macciò et al. 2010; Guo et al. 2011; Font et al. 2011).”

“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).”

“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).”

“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).”

“…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; Macciò et al. 2010; Guo…”

“One is that a 1012 M⊙ halo has a virial velocity of only ∼ 150 km/s, well below the rotation speed of the Milky Way disk, usually assumed to be Vrot = 220 km/s, or even higher (Reid et al. 2009).”

“…reported by estimates based on (i) the radial velocity dispersion of Milky Way satellites and halo stars (Battaglia et al. 2005; Sales et al. 2007); (ii) the escape speed in the solar neighbourhood (Smith et al. 2007); or (iii) the kinematics of halo blue horizontal branch stars (Xue et al. 2008).”

“…reported by estimates based on (i) the radial velocity dispersion of Milky Way satellites and halo stars (Battaglia et al. 2005; Sales et al. 2007); (ii) the escape speed in the solar neighbourhood (Smith et al. 2007); or (iii) the kinematics of halo blue horizontal branch stars (Xue et al. 2008).”

“…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; Macciò et al. 2010; Guo et al. 2011; Font et al. 2011).”

“…the best-studied nine brightest dwarf spheroidal MW companions: Draco, Ursa Minor, Fornax, Sculptor, Ca- c© 2012 RAS rina, Leo I, Leo II, Canis Venatici I, and Sextans (see, e.g., Peñarrubia et al. 2008; Strigari et al. 2008; Lokas 2009; Walker et al. 2009; Wolf et al. 2010; Strigari et al. 2010).”

“…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; Macciò et al. 2010; Guo et al. 2011; Font et…”

“Assuming that Vmax for the LMC and SMC can be identified with the rotation speed of their HI disks, or 60 and 50 km/s, respectively (Kim et al. 1998; Stanimirović et al. 2004), we find, using the data in Table 1, that only ∼ 62% of V200 = 150 km/s halos would be expected not to host an LMC-like…”

“…the baryon adiabatic contraction and feedback (di Cintio et al. 2011), reducing the central density of subhalos through tidal stripping (Di Cintio et al. 2012; Vera-Ciro et al. 2012), or positing radical revisions to the nature of dark matter (Lovell et al. 2012; Vogelsberger et al. 2012).”

“…agreement with the lower virial masses reported by estimates based on (i) the radial velocity dispersion of Milky Way satellites and halo stars (Battaglia et al. 2005; Sales et al. 2007); (ii) the escape speed in the solar neighbourhood (Smith et al. 2007); or (iii) the kinematics of halo blue…”

“Assuming that Vmax for the LMC and SMC can be identified with the rotation speed of their HI disks, or 60 and 50 km/s, respectively (Kim et al. 1998; Stanimirović et al. 2004), we find, using the data in Table 1, that only ∼ 62% of V200 = 150 km/s halos would be expected not to host an LMC-like…”

“This is well within the range of halo masses allowed by the latest estimates based on either the timing argument (Li & White 2008) or on abundancematching methods (Guo et al. 2010).”

“…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; Macciò et al. 2010; Guo et al. 2011; Font et al. 2011).”

“The latter correlates strongly with the total dark mass of the dwarf, which is usually expressed in terms of its maximum circular velocity, Vmax, a quantity less affected than mass by tidal stripping (Peñarrubia et al. 2008).”

“…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; Macciò et al. 2010; Guo et al. 2011; Font et al. 2011).”

“…the best-studied nine brightest dwarf spheroidal MW companions: Draco, Ursa Minor, Fornax, Sculptor, Ca- c© 2012 RAS rina, Leo I, Leo II, Canis Venatici I, and Sextans (see, e.g., Peñarrubia et al. 2008; Strigari et al. 2008; Lokas 2009; Walker et al. 2009; Wolf et al. 2010; Strigari et al. 2010).”

“…lower virial masses reported by estimates based on (i) the radial velocity dispersion of Milky Way satellites and halo stars (Battaglia et al. 2005; Sales et al. 2007); (ii) the escape speed in the solar neighbourhood (Smith et al. 2007); or (iii) the kinematics of halo blue horizontal branch…”

“…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; Macciò et al. 2010; Guo et al. 2011; Font et al. 2011).”

“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).”

“As discussed by Parry et al. (2012) and Boylan-Kolchin et al. (2012), the discrepancy can be traced to the fact that the largest Aquarius subhalos are significantly more massive or, equivalently, have too large a value of Vmax to be compatible with the measured kinematics of the brightest dwarf…”

“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.”