Imprint of the galactic acceleration scale on globular cluster systems

TL;DR

This study finds that the density profiles of globular cluster systems in early-type galaxies exhibit breaks at radii where the gravitational acceleration matches the galactic acceleration scale a_0, suggesting a link to fundamental galactic dynamics.

Contribution

It demonstrates a correlation between GC system profile breaks and the galactic acceleration scale, providing insights into galaxy structure within ΛCDM and MOND frameworks.

Findings

GC density profile breaks align with the acceleration scale a_0

GC systems may reveal dark halo masses and concentrations

Tentative evidence supports the role of GC profiles in understanding galaxy dynamics

Abstract

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.

Tables

Table 1. Table 1: Properties of the investigated galaxies and their GC systems.

Name	$d$	$\log L$	$\log M$	$R_e$	$n$	$r_{\mathrm{br}}$	$r_{\mathrm{acc},N}$	$r_{\mathrm{acc},M}$	$R_e$	$r_{s,s}$	$r_{s,f}$	$r_{\mathrm{sh},s}$	$r_{\mathrm{sh},f}$	$R_{\mathrm{RB}}$
	[Mpc]	[$L_{☉}$]	[$M_{☉}$]	[kpc]		[kpc]	[$r_{\mathrm{br}}$]	[$r_{\mathrm{br}}$]	[$r_{\mathrm{br}}$]	[$r_{\mathrm{br}}$]	[$r_{\mathrm{br}}$]	[$r_{\mathrm{br}}$]	[$r_{\mathrm{br}}$]	[$r_{\mathrm{br}}$]
N 821	24	10.5	11.2	4.7	4.7	16	0.73	1.1	0.30	13	4.0	0.61	0.85	6.2
N 1023	11.4	10.5	11.3	2.7	4.2	8.3	1.7	2.5	0.33	37	3.8	1.3	3.2	–
N 1399	20	10.7	11.5	3.5	5.6	43	0.43	0.63	0.082	18	19	0.15	0.28	–
N 1400	26	10.4	11.2	3.4	4.0	23	0.49	0.73	0.15	6.8	2.7	0.46	0.60	0.46
N 1407	29	11	11.9	9.4	8.3	46	0.52	0.77	0.21	3.6	8.7	–	0.34	0.58
N 2768	22	10.7	11.5	8.9	3.3	21	0.70	1.1	0.42	34	3.8	0.22	0.72	7.6
N 3115	9.7	10.2	11.0	4.8	4.4	9.5	0.85	1.3	0.50	8.0	8.3	0.97	0.95	–
N 3377	11.2	9.9	10.5	2.9	5.0	5.6	0.85	1.3	0.52	5.1	5.6	1.4	1.2	1.9
N 4278	16	10.2	11.0	2.5	4.8	15	0.61	0.90	0.16	5.0	6.6	0.70	0.56	0.48
N 4365	20	10.7	11.5	8.5	5.2	29	0.54	0.82	0.29	27	17	0.15	0.42	1.1
N 4472	16.3	10.9	11.7	3.9	3.0	24	1.0	1.5	0.16	21	33	–	0.44	–
N 4486	16	10.8	11.6	5.8	2.9	15	1.4	2.0	0.40	54	4.3	0.16	0.42	–
N 4494	17.1	10.4	11.1	3.7	3.4	10	1.0	1.5	0.36	11	3.9	1.0	1.5	–
N 4526	17	10.4	11.2	2.7	3.6	12	1.0	1.5	0.22	13	6.5	0.92	0.99	–
N 4649	17	10.8	11.6	5.1	3.6	30	0.69	1.0	0.17	25	11	0.074	0.53	–
N 5128	4.2	10.5	11.2	6.2	4.0	12	0.93	1.4	0.54	18	22	0.77	0.65	–
N 5846	25	10.7	11.6	8.1	3.9	37	0.44	0.68	0.22	21	8.5	0.099	0.30	0.77
R17x	19	10.2	11.0	1.5	2.6	2.0	5.2	7.4	0.75	38	16	6.0	10	–
R17y	19	10.2	11.0	1.7	2.0	3.0	3.6	5.1	0.57	26	13	4.1	5.7	–
R17z	19	10.2	11.0	2.0	2.0	3.4	3.1	4.4	0.58	22	9.2	3.5	4.3	–

Equations

$$\rho (r)$$

$$\int \frac{r^{\alpha }}{\sqrt{r^2-R^2}}\mathrm{d}r=R^{\alpha }u{}_2{F}_1\left(\frac{1}{2},-\frac{\alpha -1}{2};\frac{3}{2};-u^2\right)+const.,$$

$$\ln \mathcal{L}(p)=\sum _i-0.5\ln \left(2\pi \right)-\ln \left(\Delta {\Sigma }_i\right)-\frac{{\left[{\Sigma }_{\mathrm{m}}(r_i,p)-{\Sigma }_i\right]}^2}{2\Delta {\Sigma }_i^2},$$

Full text

1 Introduction

Radial surface density profiles of GC systems have traditionally been described either by a power law or by a Sérsic profile (see, e.g., the review Brodie & Strader, 2006). The papers investigating the kinematics of GC systems to perform Jeans analysis prefer instead a broken power law over the Sérsic profile for its easier computational implementation (e.g., Samurović, 2014). In our previous work, Bílek et al. (2019), dealing with kinematics of GC systems of 17 early-type galaxies (ETGs) we fitted the volume density profile $\rho(r)$ by a broken power law:

[TABLE]

Here we report that the break radii $r_{\mathrm{br}}$ are very close to the radii where the gravitational accelerations generated by the stars of the galaxies equal the much discussed galactic acceleration scale $a_{0}$ and suggest possible explanations in the frameworks of the Lambda cold dark matter ($\Lambda$CDM) model and modified Newtonian dynamics (MOND).

This scale, $a_{0}=1.2\times 10^{-10}$ m s*-1*, is revealed most clearly by rotation curves of spiral galaxies: Newtonian dynamics requires dark matter for the explanation of the rotation curves only beyond the galactocentric radii where the gravitational acceleration predicted by Newtonian dynamics, $a_{\mathrm{N}}$, is lower than $a_{0}$. In this weak field region, the measured accelerations of stars or gas turns out to be $\sqrt{a_{\mathrm{N}}a_{0}}$ (see, e.g., a recent study by McGaugh et al., 2016). This behavior was predicted by the MOND hypothesis before detailed rotation curves were available (Milgrom, 1983). According to MOND, the laws of physics need to be updated such that dynamics becomes nonlinear in the regions of space where all accelerations are below $a_{0}$. Assuming the standard $\Lambda$CDM framework, Navarro et al. (2017) proposed that the MOND-like behavior in spiral galaxies stems from the following factors: 1) the galaxies are embedded in dark halos with Navarro-Frenk-White (NFW) profiles (Navarro et al., 1996), 2) the mass of the halo correlates with the baryonic mass of the galaxy, 3) the baryonic mass of a disk galaxy correlates with the scale length of its exponential profile, and 4) the rotation curves can only be observed to about five scale lengths. How these suggestions compare to observational data has not yet been assessed quantitatively, and it has not been proven, for example, that the necessary stellar-to-halo mass relation is indeed a consequence of the $\Lambda$CDM theory (see Bílek et al., 2019 for details). The acceleration scale is present in the dynamics of some, if not all, ETGs as well (e.g., Durazo et al., 2017, 2018), although verifying this is observationally difficult (see, e.g., the reviews in Milgrom, 2012 and Bílek et al., 2019). Even the profiles of the stellar velocity dispersion of individual globular clusters usually become flat at the radii where $a_{\mathrm{N}}\approx a_{0}$ (Scarpa et al., 2003, 2007; Scarpa & Falomo, 2010; Hernandez & Jiménez, 2012; Hernandez et al., 2013a, 2017). The acceleration scale $a_{0}$ is reflected in several other laws, such as the Faber-Jackson relation, the baryonic Tully-Fisher relation, the Fish law, and the Freeman limit, and it even coincides with the natural acceleration scales in cosmology (see the review in Famaey & McGaugh 2012 for details).

In the present work we report that the galactic acceleration scale is imprinted even in the number density profiles of GC systems of ETGs since they show abrupt breaks near the radii where the gravitational accelerations caused by stars equal $a_{0}$. Other characteristic radii in the galaxies do not match the break radii that well. We discuss the possible reasons for this observation in $\Lambda$CDM and in MOND contexts. If larger galaxy samples confirm our observation, then the breaks in the density profiles of GC systems can be used to estimate the dark halo concentration when working in the $\Lambda$CDM framework.