In this section, we use the diagnostics in Section 3 to consider the classification of four populations of astrophysical objects: extreme ultra-faint dwarf galaxies, UCDs, GCs, and tidal dwarfs.
4.1. Ultra-faint dwarfs with rhalf < 50 pc
We begin our discussion with extreme ultra-faint dwarfs, because their classification is starting to converge in the literature. The term "ultra-faint dwarfs" refers to the dwarf galaxies with absolute magnitudes fainter than MV ~ -8. Currently, such objects are only known around the Milky Way and M31 because they are difficult to detect, although the Next Generation Virgo Cluster Survey should soon reveal them in Virgo. The most extreme of these objects (Segue 1, Segue 2, Boötes II, Willman 1) are observed to have MV ~ -2.5 and rhalf ~ 30 pc.
These extreme objects have total luminosities less than individual bright red giant branch stars. Their sizes are intermediate between typical GCs and low luminosity dwarf spheroidal galaxies. Despite their extreme and unusual properties, direct and/or indirect diagnostics support a galaxy definition for all four of these objects. With an (M / L)half ~ 3400 and [Fe / H] = 0.75-0.23+0.42 dex (Table 1), Segue 1 is a galaxy as diagnosed by both its kinematic and its [Fe / H]. Taken at face value, the dynamics of Willman 1's stars require a high dynamical mass relative to its stellar mass. However, its irregular kinematic distribution hinders drawing a robust classification from kinematics alone (Willman et al. 2011). Regardless, the substantial spread in [Fe/H] among three member stars in Willman 1 (0.56-0.23+0.58 dex, Table 1) demonstrates its galaxy classification. A dynamical study based on small numbers of stars in Segue 2 (Belokurov et al. 2009) is consistent with a galaxy classification, although the uncertainties are still large. Finally, tidal arguments for Boötes II have suggested that it may need a substantial dark matter component for it to be self-bound (Walsh et al. 2008).
It is essential that all (candidate) extreme ultra-faint dwarfs close enough to study with 10m-class telescopes are spectroscopically investigated. Surveys like DES and LSST have the potential to uncover large numbers of objects like Segue 1 to distances beyond the reach of today's spectroscopic resources. If a sufficient number of nearby Segue 1-like objects are demonstrated to be galaxies, then systems discovered to share that region of size-luminosity space in the future might be classified as galaxies without extensive follow-up. Even now, it is not yet certain whether Segue 2 and Boötes II should be counted as galaxies or remnants thereof. Their classifications will greatly impact the predicted number of luminous dwarfs orbiting the Milky Way and our (currently minimal) knowledge of the bottom of the galaxy luminosity function.
As a population, the MW's ultra-faint dwarfs follow luminosity-metallicity and luminosity-(M / L) relations (e.g., Geha et al. 2009). These scaling relations rule out pathological explanations for the ultra-faints as a population, such as clumps in tidal streams or stellar streams at orbital apocenter. When in doubt for any particular object, hypothesis testing against the spatial-kinematic predictions of a specific model can be used to effectively vet a galaxy classification. For example, Zolotov et al. 2011 showed that the highly elliptical Hercules dwarf spheroidal is inconsistent with a cusp catastrophe hypothesis.
Like "ultra-faint dwarf", the term UCD has no formal definition. It is generally used to refer to systems with -13 MV -9 and 10 pc < rhalf < 100 pc. This population of objects has proved particularly challenging to classify. With up to 100 UCDs possibly orbiting M87 alone (Brodie et al. 2011), whether or not these should be counted as galaxies bears great importance for understanding the dwarf galaxy population of the Virgo Cluster in a cosmological context. Thus far, studies seem to be converging on the conclusion that multiple formation channels may be required to explain the UCDs as a population, such as very massive star clusters or as the stripped nuclei of dwarf galaxies (Brodie et al. 2011, Chiboucas et al. 2011, Chilingarian et al. 2011, Da Rocha et al. 2011). In this section, we do not review the work relying on population arguments or detailed studies of individual UCDs (e.g., Maraston et al. 2004, Fellhauer & Kroupa 2005, Norris & Kannappan 2011) to reach this conclusion. We instead discuss the efficacy of UCD kinematic studies in a cosmological context and consider possible future kinematic and [Fe/H] UCD classification diagnostics.
4.2.1. UCD Kinematics
Dynamical studies of UCDs do not provide a clear diagnosis of a galaxy classification. UCD3, the most luminous UCD in the Fornax cluster (MV = -13.55, rhalf = 87 pc), is the only UCD with spatially resolved kinematics (Frank et al. 2011). UCD3 has less than a 33% mass contribution from dark matter within 200 pc, and M / L = 3.6 ± 0.3, if it is assumed that mass follows light. This M / L may be consistent with the M / L of its stellar population (Chilingarian et al. 2011, however see Mieske et al. 2006 and Firth et al. 2009 who estimate a lower stellar M / L). The spatially unresolved dynamical studies of other UCDs yield dynamical M / L = 2-5, plausibly (but not certainly) consistent with their stellar M / L (e.g., Hilker et al. 1999, Drinkwater et al. 2003, Hasegan et al. 2005, Evstigneeva et al. 2007, Mieske et al. 2008, Chilingarian et al. 2011). The dynamical M / L of Virgo cluster UCDs seem to be systematically higher than Fornax cluster UCDs (Mieske et al. 2008). The inflated Virgo UCD M / Ls may be explained by unusual IMFs; a top-heavy IMF can yield a large fraction of dark stellar remnants (Dabringhausen et al. 2009, Dabringhausen et al. 2012), while a bottom-heavy IMF is rich in low-mass M dwarfs with high individual M / L.
It is not surprising that dynamical studies of UCDs do not easily yield a galaxy classification, even if (for example) they do presently reside in dark matter halos. To quantify this, we must begin with a reasonable hypothesis for the amount of dark matter expected within the half-light radii of UCDs if they reside in dark matter halos. There are no simulations of sufficient spatial resolution to predict the expected amount of dark matter in the innermost ~30 pc of a dark matter halo, and the highest resolution simulations do not include the effect of baryons, star formation, or feedback. Moreover, there are known differences between the central mass densities observed for dwarf galaxies and the central dark matter densities predicted for dwarf galaxies using dark matter only simulations (Boylan-Kolchin et al. 2011, Boylan-Kolchin et al. 2012) that have, in some cases, been resolved with baryonic physics (e.g., Governato et al. 2010, Pontzen & Governato 2012). Similarly, Tollerud et al. (2011) find that the observed central mass densities of UCDs are not consistent with residing in the Navarro-Frenk-White profile dark matter halos predicted by dark matter simulations.
We therefore rely on an empirical hypothesis for the possible dark matter content of UCDs: they contain the same amount of dark matter within their half-light radii as known dwarf galaxies with the same half-light radii. We consider two MW dwarfs: Segue 1 (Martin et al. 2008, Simon et al. 2011, los = 3.7-1.1+1.4 km s-1, MV = -1.5-0.8+0.6, rhalf= 29 ± 6 pc) and Coma Berenices (Simon & Geha 2007, Muñoz et al. 2010, MV = -3.6 ± 0.6, rhalf = 74 ± 4 pc). Using the Wolf et al. (2010) formula, we calculate MSegue 1,half = 3.7-2.3+2.9 × 105 M and MComBer,half = 1.5 ± 0.5 × 106 M. To obtain the half-light dark matter masses of these objects, we simply subtract out their approximate stellar masses assuming a stellar M / L of 2. Because Segue 1 and Coma Berenices are highly dark matter dominated, the derived dark matter masses depend little on our assumed value of (M / L)star.
We use the half-light dark matter masses of Segue 1 and Coma Berenices to predict the possible dynamical (M / L)half of UCD-luminosity systems with half-light radii of 30 pc and 75 pc. Figure 2 shows the resulting predictions, as a function of absolute magnitude and assuming a stellar M / L = 2 for the UCDs. UCDs are typically observed to have -13 < MV < -9 and 10 pc < rhalf < 100 pc (see e.g. Madrid et al. 2010, Brodie et al. 2011, Misgeld et al. 2011). We predict that UCDs in dark halos would have dynamical M / L within their half-light radii of 2-3, consistent with observations. Given the large uncertainties in deriving stellar M / L, this prediction confirms that dynamics will not be able to unambiguously reveal the presence of dark matter in most individual UCDs. Less luminous UCDs have less baryonic mass, and so will be more dynamically affected by the presence of dark matter if they reside in halos similar to those of more luminous UCDs. We also predict that among UCDs of similar luminosity, those with larger scale-sizes should have systematically higher dark matter fractions. This prediction makes sense, because larger half-light radii enclose a larger fraction of an object's dark matter halo, if UCDs of similar luminosity reside in similar dark matter halos. Current observations do not bear a clear signature of this predicted relationship (Mieske et al. 2008). However, because of possible system-to-system variations and uncertainties in stellar M / L, it is impossible (to date) to draw robust conclusions about the dynamical evidence for dark matter or lack thereof.
In making the quantitative predictions in Figure 2, we have assumed that UCDs contain the same amount of dark matter within their half-light radii as known dwarf galaxies with the same half-light radii. The dark matter halos inhabited by UCDs may instead have higher mass density than those inhabited by MW ultra-faint dwarfs, owing to gravitational contraction. Alternatively they may have lower mass density, owing to the far greater amount of feedback from star formation and death experienced by UCDs with orders of magnitude more stars than ultra-faint dwarfs. Nevertheless, Figure 2 demonstrates a reasonable model in which dark matter is not dynamically detectable in most UCDs, but may be detectable in the least luminous UCDs. The relationship we predict between half-light radius and dynamical mass is dependent only on the assumption that similar luminosity UCDs inhabit similar dark matter halos.
Figure 2. The predicted (M / L)half of UCDs with rhalf = 30 or 75 pc, assuming they reside in dark matter halos like those inferred for Segue 1 and ComBer, respectively. Typical UCDs should not display dynamical evidence for dark matter, even if they do reside in the centers of dark matter halos.
4.2.2. UCD [Fe/H]
Even if it is possible to assess [Fe / H] in UCDs with MV < -10, it would not easily aid in their classification (see Section 3.2). Brodie et al. (2011) have recently argued that objects with lower stellar masses are also part of the UCD population around M87 in Virgo. NGC 2419, a MW GC, has a size (21 pc, Harris 1996) and absolute magnitude (MV = -9.42, Harris 1996) consistent with the lower luminosity UCDs around M87. At face value, NGC 2419's lack of an [Fe/H] spread (Table 1) suggests that star clusters may form with the sizes and luminosities of at least some UCDs. However, NGC 2419's spread in Ca (~0.2 dex) may be difficult to reconcile with the inferred depth of its potential well. Unlike spreads in lighter elements, a Ca spread might require enrichment by supernovae (Cohen et al. 2010).
It would be extremely interesting if future studies could measure (or set limits on) the [Fe/H] spread of a set of lower luminosity UCDs to see whether they all lack a spread in [Fe/H], as observed for typical star clusters. Another hint to a possible UCD-dwarf galaxy connection - or lack thereof - may be their average [Fe/H]. UCDs fall above the metallicity-luminosity relationship followed by dwarf galaxies (e.g., Chilingarian et al. 2011, see also discussion in Section 3.3). If the UCDs are stripped remnants of nucleated dwarfs then they once would have been more luminous and may have fallen on observed metallicity-luminosity relationships.
4.3. Globular Clusters
A combination of dynamics, [Fe / H], and several indirect diagnostics show that GCs, as a population, do not satisfy our definition of galaxy and do not presently inhabit dark matter halos. We briefly discuss this evidence here, because we should neither take for granted that canonical GCs do not satisfy our proposed definition of galaxy, nor take for granted that they should be ignored in efforts to map dark matter substructure around the MW and other galaxies. For example, the spatial distribution of MW halo GCs is consistent with the predicted present-day distribution of early forming dark matter peaks (Brodie & Strader 2006, Moore et al. 2006). This similarity could be interpreted as evidence that GCs themselves reside in the center of present day dark matter halos and, if so, should be included in studies that rely on dwarf galaxies as luminous tracers of the spatial and mass distribution of dark matter.
No dynamical study of GCs has yielded a dynamical mass in excess of stellar mass, even for lower surface density (Palomar 13, Bradford et al. 2011) and tidally disrupting clusters (Palomar 5, Odenkirchen et al. 2002). In light of the dynamical arguments presented for UCDs, GCs would be unlikely to exhibit straightforward dynamical evidence for dark matter even if they did reside in dark matter halos. The [Fe/H] analysis in Section 3.2 and shown in Figure 1 instead provides direct evidence that GCs do not satisfy the definition of a galaxy - the iron abundances of their stars is explicable with only stellar mass and Newtonian gravity.
Additional indirect diagnostics also demonstrate that GCs would be classified as star clusters with our proposed definition. The presence of tidal streams around numerous MW GCs (e.g. Leon et al. 2000) provides upper limits to their present-day masses; this is additional evidence that their present-day dynamics are consistent with their observed stellar masses and Newtonian gravity. Another diagnostic is the existence of GCs in low-mass dwarf galaxies, such as the Fornax dwarf spheroidal. If its GCs were embedded in dark matter halos, then their dynamical friction timescale for destruction would be <1 Gyr, far shorter than their observed ages (Conroy & Spergel 2011). One final diagnostic may be the outer density profiles of GCs, as demonstrated by Conroy et al. (2011) for the case of NGC 2419 and MGC1.
Light element abundance spreads are common in GCs, and usually attributed to enrichment by asymptotic giant branch stars or the winds of rotating massive stars (e.g., Renzini 2008, Ventura & D'Antona 2009). These ejecta are less energetic than those of supernovae and can be retained by the gravity of stars alone. The ubiquity of these abundance variations, often identified through the anti-correlation of Na and O, has led to the suggestion that such variations should define the class of GCs (Carretta et al. 2010b). We do not advocate for this suggestion, since little is known about the abundance patterns of low-mass GCs, which may differ from those of more massive clusters, and star clusters with masses 104 M in the Large Magellanic Cloud do not appear to self-enrich (Milone et al. 2009). Furthermore, more massive objects that might be confused with GCs, such as UCDs or dwarf nuclei, lack detailed abundance observations.
Existing diagnostics do not preclude the hypothesis that some massive (MV < -10) GCs may reside in dark matter halos. This possibility must be considered when comparing observations against cosmological models. Extended star clusters (MV ~ -7 to -8, rhalf ~ 20 - 30 pc, Tanvir et al. 2012), such as those observed around M31 (Huxor et al. 2005), also present a challenge to classification. The M31 extended GCs would make particularly interesting targets for spectroscopic [Fe/H] studies, because their current stellar masses and escape velocities are too low to expect self-enrichment in iron.
4.4. Tidal Dwarfs
The term "tidal dwarf" (TD) refers to a gravitationally bound, galaxy-sized object (few kpc scale) formed as a result of the tidal interaction of two galaxies (Bournaud 2010). These objects form from a combination of star formation in gaseous tidal tails and of the agglomeration of existing stars from the interacting parent galaxies (Kaviraj et al. 2012). Candidates for such objects were originally observed in the Antennae and in compact galaxy groups (Mirabel et al. 1992, Hunsberger et al. 1996). Although many candidate TDs have been discovered since then, it remains difficult to determine whether TD candidates are truly self-bound (Duc et al. 2000).
Dynamical studies of TDs do not provide a definitive classification of these objects. Their kinematic properties are difficult to study, in part because TDs are typically observed while still embedded in ambient tidal material from which they formed/are forming. Some studies find their dynamical masses to be consistent with their stellar and gas (both neutral and molecular) contents (Duc et al. 2000, Braine et al. 2001, Bournaud et al. 2004, Duc et al. 2007), while others find dynamical masses 2-3 times higher than expected from observed stars and gas (Bournaud et al. 2007). In all cases, the uncertainties are substantial. Even in a cold dark matter interpretation of galaxies, TDs are not expected contain (much) dark matter (e.g., Barnes & Hernquist 1992). Unlike gas, the dark matter in TD progenitor material cannot dissipate energy and has a velocity dispersion exceeding the escape velocity of the forming TD (Bournaud 2010), unless some dark matter is present in a cold, rotating, galaxy disk (Purcell et al. 2009, Read et al. 2009). Identifying a sample of relatively older (> 1 Gyr) TDs and conducting uniform dynamical studies will help reveal whether: (i) TDs are simply composed of gas and stars orbiting in a Newtownian potential, (ii) galaxy disks do contain a dark matter component which can be accreted by forming TDs, or (iii) TDs demonstrate a dynamical regime governed by non-Newtonian gravity. If (ii) or (iii) is verified, then TDs would be classified by galaxies by our definition.
The possible contribution of ancient TDs formed at high redshift to today's dwarf galaxy population, in particular around the Milky Way, is controversial. Observations of the universe at low or intermediate redshift imply that that TDs could not contribute more than ~ 10% of the dwarf galaxies in the local universe (e.g., Wen et al. 2012, Kaviraj et al. 2012). TDs forming in the local universe also do not exhibit the relationship between stellar mass and metallicity (Weilbacher et al. 2003) that is observed in the MW dwarfs (Kirby et al. 2011). Moreover, kinematic studies of nearby TDs do not imply the high dynamical M / L observed for MW dwarf satellites. Others propose that the MW's dwarf galaxies may be dominated by tidal dwarfs formed at very high redshift when merger rates were far higher, and that the high M / L inferred for MW dwarfs are actually a misinterpretation of the observed kinematics (e.g. Kuhn & Miller 1989, Metz & Kroupa 2007, Kroupa et al. 2010). It remains to be seen whether models of ancient TDs evolving into z = 0 dwarfs could fall on the same metallicity-luminosity relation followed by both MW dwarfs and spheroidal galaxies over a wide range of masses.