In this chapter I have modelled the dark matter density profile of Tucana from its stellar kinematics, and shown that it has a high central density which may be consistent with the presence of a pristine cusp. If such a cusp is indeed present, it has been shown that dynamical friction would likely cause any globular clusters in the system to sink towards the centre of the galaxy, eventually becoming tidally destroyed (Goerdt et al., 2006; S´anchez-Salcedo et al., 2006). If the dark matter profile is cored, dynamical friction is suppressed (Petts et al., 2015, 2016) and the globular clusters survive to the present day. Contenta et al. (2018) developed an N–body model of the star cluster accounting for stellar evolution and two–body effects, from which the central density of the host dwarf galaxy can be constrained. Observations of the globular cluster distribution in a dwarf galaxy can therefore provide clues as to the nature of its dark matter density profile.
Tucana has no known globular clusters. This is consistent with the idea that they may have been dissolved by the presence of a dark matter cusp. However, to test this one would need to prove that globular clusters had once existed in Tucana, and have been destroyed by dynamical friction, as opposed to having never formed at all (which would not be symptomatic of a central cusp). To do so, a tracer must be found which unambiguously confirms the presence of a globular cluster, and which would be detectable in the field of a cusped galaxy such as Tucana following the destruction of its clusters. This could provide a new technique for determining the nature of the dark matter density profile, independent of the stellar kinematics.
It is possible that one such tracer may be found in the variable stars of the galaxy. Tucana has a significant population of type c RR Lyrae. RRc variables oscillate in the first overtone, with a shorter period than RRab stars. Bernard et al. (2009) found that out of 358 RR Lyrae stars in Tucana, 82 are RRc. A high density of RRc stars is also found in the Sculptor dwarf galaxy, where 197 out of 536 RR Lyrae are type c (Mart´ınez-V´azquez et al.,2016). Both of these galaxies are suspected to host a pristine cusp (Read et al., 2019). By contrast, Bernard et al.(2009) found only 8 RRc in a population of 172 RR Lyrae in the cored dwarf Cetus. This could indicate that RRc are more prevalent in cusped galaxies than cored galaxies. Furthermore,
Mackey and Gilmore (2003) found a large RRc fraction in the globular clusters of Fornax, which is known to be cored. Naively, it would appear from these studies that there may be an excess of type c RR Lyrae in the globular clusters of a cored galaxy, and the fields of cusped galaxies, relative to the field population of cored galaxies.
To investigate the possibility of using the RRc population to trace the destruction of globular clusters in a cusped galaxy, I consider the RR Lyrae population of a number of Local Group dwarf galaxies, and the Fornax globular clusters. I define η
10−7 10−6 10−5 10−4 η = NRRc M ∗ Tucana Draco Sculptor Fornax GC Fornax Field Cusped GC Cored 106 107 M∗ 0.1 0.2 0.3 0.4 0.5 NRRc NRR Tucana Draco Sculptor Fornax GC Fornax Field
Figure 2.12: Top: Number of RRc stars per unit stellar mass as a function of M∗ for a selection of Local Group stellar systems. Bottom: Fraction of RR Lyrae population which is RRc as a function of stellar mass. Red circles mark dwarf galaxies with a cusped halo; blue squares those with central cores. Green triangles indicate globular clusters. Stellar masses (and errors) assume a stellar mass–to–light ratio of 1, except Tucana, which is taken from Hidalgo et al. (2013). Only variable stars within the central 200 pc of a galaxy are considered.
as the number of RRc stars per unit stellar mass in a system, such that
η = NRRc
M∗ , (2.4.8)
where NRRc is the total number of known RRc in the system, and M∗ is the total stellar mass. I normalise by stellar mass to account for the size of the system. I consider only the RR Lyrae population within the central 200 pc of the galaxy, as the remnants of dissolved clusters would be concentrated in the central regions.
In the top panel of Fig. 2.12 I plot η as a function of stellar mass for a selection of stellar systems in the Local Group. Blue squares are used to mark galaxies with a central core; red circles for those suspected of hosting a central cusp. Globular clusters are plotted as green triangles. Cusped galaxies are chosen on the basis of a significant variable star study, and a robust measurement of their cusp/ core nature. In the case of Fornax, there has been a dedicated study of the stellar population of four of the five known globular clusters (Mackey and Gilmore, 2003). I therefore show the field RRc population and the globular cluster RRc population of Fornax as separate points.
If there is an excess of RRc in globular clusters relative to the field, one would expect globular clusters to have a high value of η, and cored galaxies to have a low η. In cusped galaxies such as Tucana, the disruption of the globular clusters should have redistributed their RRc population throughout the field, resulting in a higher value of η (intermediate between the value for clusters and the value for cored dwarfs). Within the chosen sample, there is an indication that the fractional RRc population may be higher in cusped galaxies than in the field of cored galaxies. However, the RRc population strongly correlates with stellar mass, with higher mass systems hosting fewer RRc per unit mass. There are two possible reasons for this. Firstly, if the RR Lyrae survey is incomplete, then the plot is essentially M∗ vs. 1
M∗,
and so a negative correlation would be anticipated. Secondly, RR Lyrae are known to represent an old stellar population. As low mass galaxies generally host older populations, one might expect a stronger RRc population at lower masses.
I also consider the proportion of RR Lyrae in the system which are type c. The bottom panel of Fig. 2.12shows the fraction of RRc stars out of the total RR Lyrae population (RRab + RRc + RRd) as a function of stellar mass. Once again, if the above hypothesis is true, one would expect a higher fraction of RRc in cusped dwarfs than in the field of cored dwarfs. Fig. 2.12 shows that this is not the case, with Draco hosting a smaller RRc population than the field of Fornax.
These results suggest that the RRc population is unlikely to be useful as a tracer of the disrupted globular cluster population. However, my investigation is limited by the small number of RR Lyrae surveys completed for galaxies with a robust cusp/ core measurement, and much more data is required to confirm the result. Future surveys such as LSST, combined with improved constraints on the density profiles of Local Group dwarfs, may be able to provide this analysis.