4U 1820-30 is a low-mass X-ray binary near the center of the globular cluster NGC 6624 consisting of, at least, one neutron star and one helium white dwarf. Analyzing 16 years of data from the Rossi X-ray Timing Explorer (RXTE) allows us to measure i
ts orbital period and its time derivative with unprecedented accuracy to be P = 685.01197 +- 0.00003 s and dP/dt /P = -5.3 +- 0.3x10^-8 yr^-1. Hence, we confirm that the period derivative is significantly negative at the >17 sigma level, contrary to theoretical expectations for an isolated X-ray binary. We discuss possible scenarios that could explain this discrepancy, and conclude that the center of NGC 6624 most likely contains large amounts of non-luminous matter such as dark remnants. We also discuss the possibility of an IMBH inside NGC 6624, or that a dark remnant close to 4U 1820-30 causes the observed shift.
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. We used our MUESLI code to calculate GC survival rates for typic
al early-type galaxy potentials covering a wide range of observed galaxy properties. We do this for isotropic and radially anisotropic GC velocity distributions. We find that the calculated GC survival fraction, f_s, depends linearly on the logarithm of the 3D mass density, rho_3D, within the galaxys half light radius, with f_s proportional to (rho_3D)^(-0.17). 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) 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 considered literature sample, 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. We conclude that 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.
