The ΛCDM theory of galaxy formation and evolution predicts that in dark matter-dominated galaxies the tracers of the potential should indicate a cuspy NFW profile (Navarro et al. 1996; 1997). However, this has not been observed, as already remarked by Moore (1994) and Flores and Primack (1994). Observations of late-type low surface brightness disk galaxies were done by a number of groups, first in Hi, and later augmented with long-slit Hα observations in the inner parts (e.g., de Blok et al. 2001; de Blok and Bosma 2002; de Blok et al. 2003). These confirmed the presence of cores in such galaxies, or, at the most, mildly cusp slopes with α = −0.2 ± 0.2, not compatible with the NFW profiles. These results were (e.g., Swaters et al. 2003) and still are the subject of intense debate. CO and three-dimensional Hα observations (Simon et al. 2003; 2005; Blais-Ouellette et al. 2004; Kuzio de Naray et al. 2006; 2008) were also brought to bear on this problem. A review has been given in de Blok (2010).
Projects such as THINGS, and LITTLE THINGS, using Hi observations at higher resolution and sensitivity, keep finding cores (Oh et al. 2008, 2011, 2015). These observations can now be compared with modified predictions of the ΛCDM theory of galaxy formation and evolution, where star formation and feedback have been added to the ingredients (“subgrid physics”) of the numerical simulations. The results are given in Fig. 12, together with the results from cosmological zoom simulations of the NIHAO project (Tollet et al. 2016). The addition of baryonic physics changes the prediction for the dark matter profile towards a slope shallower than the NFW profile. However, the current resolution achieved in the NIHAO project does not yet probe the full range in inner radii comparable to those of the observations. The debate is ongoing about whether the ΛCDM theory should be further revised to accommodate the new observational results. I select here a couple of issues which can be addressed with Hi data in the context of galaxy outskirts.
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Figure 12. Left: results from Oh et al. (2011, 2015) for the slope of the dark matter density profile as function of the radius of the innermost point on the rotation curve. The orange points are from hydrodynamical zoom simulations from the NIHAO project (Tollet et al. 2016, their Fig. 13). The inset shows the current data for IC 2574 and the APOSTLE simulation result for it (reproduced with permission from Oman et al. 2016). Right: a similar plot which collects older data (de Blok et al. 2001; de Blok and Bosma 2002; Swaters et al. 2003), the data from Oh et al. (2011), data based on stellar and gas velocity dispersions (Adams et al. 2014), and the selected data for 15 galaxies from Oh et al. (2015) as described in the text. The dotted lines converging on α = 0 represent the theoretical variations in slope for ISO haloes with RC = 0.5, 1 and 2 kpc. The line converging on α = −1 shows the variation in slope for c / V200 = 8.0/100. |
Oman et al. (2015; 2016) emphasize that there is a large variety in the data of late-type low surface brightness dwarfs, and find that the observations of the rotation properties of some dwarfs are closer to their models than others. They suggest that observers somehow do not have the systematics of galaxy inclinations under control. Read et al. (2016) claim good agreement with ΛCDM by discarding half their sample of four galaxies: IC 1613 is thought to be in disequilibrium due to starburst activity, and for DDO 101 the distance is too uncertain.
To examine the problem further, I looked at some of the underlying assumptions in the modelling of the observational data. One is that galaxy disks are thin, with a typical vertical axial ratio of 0.2. Such a value can be checked statistically, as has been done in the exemplary work of Sandage et al. (1970). For data in the Second Reference Catalog of Bright Galaxies (de Vaucouleurs et al. 1976), Binney and de Vaucouleurs (1981) point out that for Hubble types close to the end of the sequence (type 10), the distribution of apparent axial ratios does not indicate flattened disks. This was discussed further in Bosma (1994), and is illustrated here again in Fig. 13, now using data from the Local Volume Galaxy catalogue (Karachentsev et al. 2013), split by morphological type for the later types. While Scd, Sd and Sdm galaxies have histograms that seem compatible with those for flattened disks viewed from different orientation angles, the data for Sm and in particular Im galaxies show an apparent axial ratio distribution not compatible with this. It is thus likely that some of the dwarf galaxies used in the core-cusp debate are not modelled correctly when it is assumed that they are thin disks: instead, models with a considerable thickness should be explored. The results from the FIGGS sample (Begum et al. 2008; Roychowdhury et al. 2010) confirm this, and show that the thickness of the Hi maps peaks around 0.5. Roychowdhury et al. (2013) also analyze the Local Volume catalogue, and find a similar thickening of the galaxies of later type, but their analysis considers only a few bins. As discussed further in Sect. 9.2, thick Hi disks have been recognized as such by Puche et al. (1992), and even earlier by Bottema et al. (1986).
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Figure 13. Statistics of axial ratios for late-type galaxies (numerical Hubble type ≥ 6) in the Local Volume Galaxy catalogue (Karachentsev et al. 2013), split out by morphological type |
In Fig. 14 I use data from the recent collection of rotation curves studied by Lelli et al. (2016) concerning the mean velocity in the outer parts, Vflat, if defined. For the thin disk galaxies of type Sd and Sdm (numerical Hubble type 7 and 8) the range in Vflat overlaps the one of the thicker disk galaxies of type Sm, Im and BCD (types 9, 10 and 11, resp.). There is thus more to a galaxy than just its rotation curve, since the three-dimensional morphology of a galaxy does not follow automatically from the one-dimensional rotation curve. Therefore, for galaxies with Vflat between 70 and 110 km/s, corresponding to a stellar mass range of ∼ 5 × 108 − 4 × 109 M⊙, numerical simulations of galaxy formation and evolution ought to reproduce a variety of shapes in the stellar mass distribution, rather than a single one, and for smaller galaxies a thicker stellar disk should be produced.
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Figure 14. Statistics of the Vflat value from the SPARC sample (Lelli et al. 2016) split out by morphological type. The number of galaxies not reaching a Vflat value, and the total number per type bin, are indicated at the right. Note the overlap in Vflat for types 7 − 10 |
I further consider the data on the LITTLE THINGS project discussed by Oh et al. (2015). In that paper, the Hi layer is assumed to be infinitesimally thin, and the thickness of the stellar component is computed from the ratio of disk scale length to disk scale height (h/z0) of 5.0, which holds for large spiral galaxies seen edge-on, but not necessarily for dwarfs. To minimize problems, I selected only galaxies for which the difference in position angle and inclination derived from the Hi data and those from the axial ratio of the optical images, as given in Hunter et al. (2012), is less than 25 degrees (as √Δ(PA)2 + Δ(Inc)2 ). This leaves 15 galaxies, which are shown in Fig. 12 (right panel). Selecting “better behaving” dwarf galaxies, with little warping of the Hi disk, thus does not alleviate the core-cusp problem. A more elaborate analysis is beyond the scope of this review.