In this paper, globular star clusters which contain a sub-system of stellar-mass black holes (BH) are investigated. This is done by considering two-component models, as these are the simplest approximation of more realistic multi-mass systems, where one component represents the BH population and the other represents all the other stars. These systems are found to undergo a long phase of evolution where the centre of the system is dominated by a dense BH sub-system. After mass segregation has driven most of the BH into a compact sub-system, the evolution of the BH sub-system is found to be influenced by the cluster in which it is contained. The BH sub-system evolves in such a way as to satisfy the energy demands of the whole cluster, just as the core of a one component system must satisfy the energy demands of the whole cluster. The BH sub-system is found to exist for a significant amount of time. It takes approximately 10t rh,i , where t rh,i is the initial half-mass relaxation time, from the formation of the compact BH sub-system up until the time when 90% of the sub-system total mass is lost (which is of order 10 3 times the half-mass relaxation time of the BH subsystem at its time of formation). Based on theoretical arguments the rate of mass loss from the BH sub-system (Ṁ 2 ) is predicted to be −βζM/(αt rh ), where M is the total mass, t rh is the half-mass relaxation time, and α, β, ζ are three dimensionless parameters (see Section 2 for details). An interesting consequence of this is that the rate of mass loss from the BH sub-system is approximately independent of the stellar mass ratio (m 2 /m 1 ) and the total mass ratio (M 2 /M 1 ) (in the range m 2 /m 1 10 and M 2 /M 1 ∼ 10 −2 , where m 1 , m 2 are the masses of individual low-mass and high-mass particles respectively, and M 1 , M 2 are the corresponding total masses). The theory is found to be in reasonable agreement with most of the results of a series of N-body simulations, and with all of the models if the value of ζ is suitable adjusted. Predictions based on theoretical arguments are also made about the structure of BH sub-systems. Other aspects of the evolution are also considered such as the conditions for the onset of gravothermal oscillation. out any supernova explosion (Fryer 1999). Uncertainty in the natal kicks leads to uncertainty in the initial size of the BH population. As the BH are more massive than the other stars in the system, any retained BH will undergo mass segregation and almost all are likely to become concentrated in the centre of the system, eventually forming a compact sub-system.The mass of the BH sub-system decreases over time because BH binaries form in the dense core of the BH subsystem, causing the ejection of single BH and ultimately the binaries themselves through super-elastic encounters (see

Genome-wide association studies (GWAS) have identified thousands of genomic regions affecting complex diseases. The next challenge is to elucidate the causal genes and mechanisms involved. One approach is to use statistical colocalization to assess shared genetic aetiology across multiple related traits (e.g. molecular traits, metabolic pathways and complex diseases) to identify causal pathways, prioritize causal variants and evaluate pleiotropy. We propose HyPrColoc (Hypothesis Prioritisation for multi-trait Colocalization), an efficient deterministic Bayesian algorithm using GWAS summary statistics that can detect colocalization across vast numbers of traits simultaneously (e.g. 100 traits can be jointly analysed in around 1 s). We perform a genome-wide multi-trait colocalization analysis of coronary heart disease (CHD) and fourteen related traits, identifying 43 regions in which CHD colocalized with ≥1 trait, including 5 previously unknown CHD loci. Across the 43 loci, we further integrate gene and protein expression quantitative trait loci to identify candidate causal genes.

1Genome-wide association studies (GWAS) have identified thousands of genomic regions 2 affecting complex diseases. The next challenge is to elucidate the causal genes and mechanisms 3 involved. One approach is to use statistical colocalization to assess shared genetic aetiology 4 across multiple related traits (e.g. molecular traits, metabolic pathways and complex diseases) 5 to identify causal pathways, prioritize causal variants and evaluate pleiotropy. We propose 6HyPrColoc (Hypothesis Prioritisation in multi-trait Colocalization), an efficient deterministic 7Bayesian algorithm using GWAS summary statistics that can detect colocalization across vast 8 numbers of traits simultaneously (e.g. 100 traits can be jointly analysed in around 1 second). 9We performed a genome-wide multi-trait colocalization analysis of coronary heart disease 10 (CHD) and fourteen related traits. HyPrColoc identified 43 regions in which CHD colocalized 11 with ≥1 trait, including 5 potentially new CHD loci. Across the 43 loci, we further integrated 12 gene and protein expression quantitative trait loci to identify candidate causal genes. 13

We show that hard encounters in the central regions of globular clusters embedded in dark matter (DM) haloes necessarily lead to the formation of gravitationally-bound stellar envelopes that extend far beyond the nominal tidal radius of the system. Using statistical arguments and numerical techniques we derive the equilibrium distribution function of stars ejected from the centre of a non-divergent spherical potential. Independently of the velocity distribution with which stars are ejected, GC envelopes have density profiles that approach asymptotically ρ ∼ r −4 at large distances and become isothermal towards the centre. Adding a DM halo component leaves two clear-cut observational signatures: (i) a flattening, or slightly increase of the projected velocity dispersion profile at large distances, and (ii) an outer surface density profile that is systematically shallower than in models with no dark matter.