How tidal erosion has shaped the relation between globular cluster specific frequency and galaxy luminosity

Abstract

Aims.We quantify to what extent tidal erosion of globular clusters (GCs) has contributed to the observed U-shaped relation between GC specific frequencies S N and host galaxy luminosity M V . Methods. We used our Muesli code to calculate GC survival rates for typical early-type galaxy potentials covering a wide range of observed galaxy properties. We do this for isotropic and radially anisotropic GC velocity distributions. Results. We find that the calculated GC survival fraction, f s , depends linearly on the logarithm of the 3D mass density, ρ 3D , within the galaxy's half-light radius, with f s ∝ ρ −0.17 3D . For a given galaxy, survival rates are lower for radially anisotropic configurations than for the isotropic GC cases. We apply these relations to a literature sample of 219 early-type galaxies from Harris et al. (2013, ApJ, 772, 82) in the range M V = [−24.5 : −15.5] mag. The expected GC survival fraction ranges from 50% for the most massive galaxies with the largest radii to 10% for the most compact galaxies. We find that intermediate luminosity galaxies M V = [−20.5 : −17.5] mag have the strongest expected GC erosion. Within the literature sample considered, the predicted GC survival fraction therefore defines a U-shaped relation with M V , similar to the relation between specific frequency S N and M V . As a consequence, the U-shape of S N vs. M V gets erased almost entirely when correcting the S N values for the effect of GC erosion. Conclusions. Tidal erosion is an important contributor to the U-shaped relation between GC specific frequency and host galaxy luminosity. It must be taken into account when inferring primordial star cluster formation efficiencies from observations of GC systems in the nearby universe.

The effect of primordial mass segregation on the size scale of globular clusters

“…Such a steepening of the relation with growing galactocentric radius can have significant implications for estimates of the initial number of GCs in galactic GC systems (e.g. Mieske, Küpper & Brockamp 2014).…”

Massive Star Clusters in Dwarf Galaxies

“…The overall variation of S N vs. host galaxy M V is U -shaped, with a broad minimum between M V ∼ −18 and M V ∼ −20 where S N is typically of order unity, but reaching S N > 20-30 for some cD galaxies and dwarf galaxies (e.g., Peng et al 2008;Harris et al 2013). This trend may be driven partly by dynamical effects that lead to more efficient cluster disruption at intermediate host galaxy masses (e.g., Mieske et al 2014) and partly by variations in the "efficiency" of GC formation, relative to field stars (Peng et al 2008;Georgiev et al 2010). Interestingly, the trend of S N vs. host galaxy mass resembles that of total (dark matter) halo mass vs. stellar mass inferred from abundance matching (e.g.…”

Globular clusters in M31, Local Group, and external galaxies

“…However, when normalising the numbers of GCs to the host galaxy luminosities, expressed by the GC specific frequency (S N ≡ N GC × 10 0.4(M V +15) ; Harris & van den Bergh 1981), the well-known trend for S N to increase for lower luminosity galaxies becomes apparent. Data for larger samples of galaxies show that the behaviour of S N versus host galaxy absolute magnitude is actually U -shaped with a minimum between M V ∼ −18 and M V ∼ −20 (Harris et al 1991;Miller & Lotz 2007;Peng et al 2008;Georgiev et al 2010;Harris et al 2013;Mieske et al 2014).…”