Imprint of the galactic acceleration scale on globular cluster systems

We report that the density profiles of globular cluster (GC) systems in a sample of 17 early-type galaxies (ETGs) show breaks at the radii where the gravitational acceleration exerted by the stars equals the galactic acceleration scale $a_0$ known from the radial acceleration relation or MOND. The match with the other characteristic radii in the galaxy is not that close. We propose possible explanations in the frameworks of the $\Lambda$CDM model and MOND. We find tentative evidence that in the $\Lambda$CDM context, GCs reveal not only the masses of the dark halos through the richness of the GC systems but also the concentrations through the break radii of the GC systems.

All galaxies, with the exception of the smallest dwarfs, are orbited by globular clusters (GCs, see, e.g., Brodie & Strader 2006 for a review). The GCs are compact (∼ 3 pc) massive (10 4 − 10 7 M ) spherically symmetric star clusters. Their ages typically exceed 10 Gyr, but GCs keep forming until today. The colors of old GCs follow a bimodal distribution. We thus divide GCs in the red (metal-rich) and blue (metal-poor) subpopulations, since they probably have different origins. The collection of all GCs that a galaxy has is called a GC system (GCS).
Gravitational fields of galaxies show an interesting regularity: assuming Newtonian gravity, we need dark matter only in the regions of galaxies where the strength of gravitational field generated by the observable matter a N  equals the constant a 0 = 1.2 × 10 −10 m s −2 and in these regions, the gravitational acceleration follows √ a N a 0 . This behavior has been confirmed for a wide variety of galaxies through different methods (e.g., Lelli et al. 2017), and was originally predicted theoretically by the MOND theory of modified gravity and/or inertia (Milgrom 1983). The constant a 0 is called the galactic acceleration scale. We call the radius at which the gravitational acceleration generated by baryons equals a 0 the a 0 radius.
As we detail below, we found in Bílek et al. (2019a) (BSR19 hereafter) that the density profiles of GCSs of massive early-type galaxies follow broken power laws, while the breaks occur at the a 0 radii. Later, we verified this for a larger variety of galaxies and blue and red GC subpopulations.
We came to our finding by fitting the radial profiles of the number-density of GCSs by a broken power law in the form: The reason why we chose this profile stems from Bílek et al. (2019b), where it was chosen because it allowed simple dynamical modeling of the GCSs and it described the data well. We call the parameter r br at which the profile changes the slope as the break radius. Its physical meaning is not clear yet.
So far, we have analyzed the profiles of about 40 GCS of elliptical and lenticular galaxies. The first sample of 17 massive early-type galaxies (ETGs) with spectroscopically confirmed GCs was presented in BSR19. The stellar galaxy masses ranged almost only between 10 10 − 10 11 M . The sample was a compilation of galaxies with a large number of spectroscopic GCs coming from different sources, often from the SLUGGS survey (Brodie et al. 2014). In a submitted work (Bílek et al.), we used photometric catalogs of GC candidates for galaxies in the Fornax cluster, coming from ground-based Fornax Deep Survey (FDS) (Cantiello et al. 2020) and HST observations (Jordán et al. 2007). We used all ETGs covered by the FDS whose stellar masses exceed 10 8 M (like the Magellanic clouds). The most massive galaxies had stellar masses of 10 11 M . The GCSs of dwarf galaxies of similar masses were stacked. We divided the GCs into blue and red according to their g − z color (Fahrion et al. 2020).
We derived a (complex) expression that gives the surface number-density profile associated to Eq. 1. We divided the area around each investigated galaxy in annuli containing a fixed number of GCs. The observed surface number-density of GCs was then fitted by the analytic expression for the surface numberdensity profile using the maximum likelihood method. The uncertainties of the fit parameters were derived using the method of support.
For each galaxy, we considered a 0 radii calculated in two different ways: first, by using the Newtonian prescription for the gravitational field and second, by using the MOND prescription for the gravitational field, even though the two types of a 0 radii come out rather similar. We found that the break radii occur near the a 0 radii (calculated in either way), see Fig. 1. The break and a 0 radii agree within the factor of two (the intrinsic scatter). This holds true for the total population of GCs and the red and blue GC subpopulations and this does not depend on whether we consider the a 0 radius calculated from the Newtonian or MOND gravity. The ratio of the break and a 0 radii is closer to unity for the MOND a 0 radii.
The difference between the break radii of the red and blue GCs is not statistically significant. We found this by fitting the distribution of this difference by a Gaussian distribution. The average is −0.3 +0.2 −0.2 kpc, meaning that the break radius is insignificantly higher for the blue subpopulation. The intrinsic scatter of the distribution came out 0.03 +0.3 −0.02 kpc. This result is based on a sample of 11 galaxies for which the break radii were available for both GC subpopulations.
We considered many possible interpretations of the match between the break and a 0 radii, such as the consequence of galaxy mergers, of the MOND external field effect (Bekenstein & Milgrom 1984), dynamical friction, and others. Some of them have been proposed already in BSR19. In the submitted work, these and additional interpretations were explored in more detail. It turned out that none of them is perfect. For example, they do not induce broken power-law number-density profiles or cannot account for the fact that even dwarf galaxies, that are not expected to have experienced many mergers, have GCS number density profiles that follow broken power laws.