A family of lowered isothermal models

We present a family of self-consistent, spherical, lowered isothermal models, consisting of one or more mass components, with parameterised prescriptions for the energy truncation and for the amount of radially biased pressure anisotropy. The models are particularly suited to describe the phase-space density of stars in tidally limited, mass-segregated star clusters in all stages of their life-cycle. The models extend a family of isotropic, single-mass models by Gomez-Leyton and Velazquez, of which the well-known Woolley, King and Wilson (in the non-rotating and isotropic limit) models are members. We derive analytic expressions for the density and velocity dispersion components in terms of potential and radius, and introduce a fast model solver in PYTHON (LIMEPY), that can be used for data fitting or for generating discrete samples.Comment: 17 pages, 10 figures, 4 appendices, MNRAS, updated to match final journal styl

On the uniqueness of kinematical signatures of intermediate-mass black holes in globular clusters

Finding an intermediate-mass black hole (IMBH) in a globular cluster (GC), or proving its absence, is a crucial ingredient in our understanding of galaxy formation and evolution. The challenge is to identify a unique signature of an IMBH that cannot be accounted for by other processes. Observational claims of IMBH detection are often based on analyses of the kinematics of stars, such as a rise in the velocity dispersion profile towards the centre. In this contribution we discuss the degeneracy between this IMBH signal and pressure anisotropy in the GC. We show that that by considering anisotropic models it is possible to partially explain the innermost shape of the projected velocity dispersion profile, even though models that do not account for an IMBH do not exhibit a cusp in the centre.Comment: 4 pages, 2 figures. To be published in the Proceedings IAU Symposium No. 312, Star Clusters and Black Holes in Galaxies Across Cosmic Tim

The effect of stellar-mass black holes on the central kinematics of omega Cen: a cautionary tale for IMBH interpretations

The search for intermediate-mass black holes (IMBHs) in the centre of globular clusters is often based on the observation of a central cusp in the surface brightness profile and a rise towards the centre in the velocity dispersion profiles. Similar signatures, however, could result from other effects, that need to be taken into account in order to determine the presence (or the absence) of an IMBH in these stellar systems. Following our previous exploration of the role of radial anisotropy in shaping these observational signatures, we analyse here the effects produced by the presence of a population of centrally concentrated stellar-mass black holes. We fit dynamical models to omega Cen data, and we show that models with ~5% of their mass in black holes (consistent with ~100% retention fraction after natal kicks) can reproduce the data. When simultaneously considering both radial anisotropy and mass segregation, the best-fit model includes a smaller population of remnants, and a less extreme degree of anisotropy with respect to the models that include only one of these features. These results underline that before conclusions about putative IMBHs can be made, the effects of stellar-mass black holes and radial anisotropy need to be properly accounted for.Comment: 13 pages, 5 figures. Accepted for publication in MNRA

Testing lowered isothermal models with direct N-body simulations of globular clusters - II: Multimass models

Lowered isothermal models, such as the multimass Michie-King models, have been successful in describing observational data of globular clusters. In this study we assess whether such models are able to describe the phase space properties of evolutionary $N$-body models. We compare the multimass models as implemented in (Gieles \& Zocchi) to $N$-body models of star clusters with different retention fractions for the black holes and neutron stars evolving in a tidal field. We find that multimass models successfully reproduce the density and velocity dispersion profiles of the different mass components in all evolutionary phases and for different remnants retention. We further use these results to study the evolution of global model parameters. We find that over the lifetime of clusters, radial anisotropy gradually evolves from the low-mass to the high-mass components and we identify features in the properties of observable stars that are indicative of the presence of stellar-mass black holes. We find that the model velocity scale depends on mass as $m^{-\delta}$, with $\delta\simeq0.5$ for almost all models, but the dependence of central velocity dispersion on $m$ can be shallower, depending on the dark remnant content, and agrees well with that of the $N$-body models. The reported model parameters, and correlations amongst them, can be used as theoretical priors when fitting these types of mass models to observational data.Comment: 28 pages, 22 figures, published in MNRA

A stellar-mass black hole population in the globular cluster NGC 6101?

Dalessandro et al. observed a similar distribution for blue straggler stars and main-sequence turn-off stars in the Galactic globular cluster NGC 6101, and interpreted this feature as an indication that this cluster is not mass-segregated. Using direct N-body simulations, we find that a significant amount of mass segregation is expected for a cluster with the mass, radius and age of NGC 6101. Therefore, the absence of mass segregation cannot be explained by the argument that the cluster is not yet dynamically evolved. By varying the retention fraction of stellar-mass black holes, we show that segregation is not observable in clusters with a high black hole retention fraction (>50% after supernova kicks and >50% after dynamical evolution). Yet all model clusters have the same amount of mass segregation in terms of the decline of the mean mass of stars and remnants with distance to the centre. We also discuss how kinematics can be used to further constrain the presence of a stellar-mass black hole population and distinguish it from the effect of an intermediate-mass black hole. Our results imply that the kick velocities of black holes are lower than those of neutron stars. The large retention fraction during its dynamical evolution can be explained if NGC 6101 formed with a large initial radius in a Milky Way satellite.Comment: 10 pages, 7 figure

Mass models of NGC 6624 without an intermediate-mass black hole

An intermediate-mass black hole (IMBH) was recently reported to reside in the centre of the Galactic globular cluster (GC) NGC 6624, based on timing observations of a millisecond pulsar (MSP) located near the cluster centre in projection. We present dynamical models with multiple mass components of NGC 6624 - without an IMBH - which successfully describe the surface brightness profile and proper motion kinematics from the Hubble Space Telescope (HST) and the stellar mass function at different distances from the cluster centre. The maximum line-of-sight acceleration at the position of the MSP accommodates the inferred acceleration of the MSP, as derived from its first period derivative. With discrete realizations of the models we show that the higher-order period derivatives - which were previously used to derive the IMBH mass - are due to passing stars and stellar remnants, as previously shown analytically in literature. We conclude that there is no need for an IMBH to explain the timing observations of this MSP.Comment: 8 pages, 7 figures, MNRAS. Updated to match final journal styl

Investigating black hole accretion disks as potential polluter sources for the formation of enriched stars in globular clusters

Accretion disks surrounding stellar mass black holes (BHs) have been suggested as potential locations for the nucleosynthesis of light elements, which are our primary observational discriminant of multiple stellar populations within globular clusters. The population of enriched stars in globular clusters are enhanced in N14, Na23, and sometimes in Al27 and/or in K39. In this study, our aim is to investigate the feasibility of initiating nucleosynthesis for these four elements in BH accretion disks, considering various internal parameters such as the temperature of the gas and timescale of the accretion. To achieve this, we employed a 132-species reaction network. We used the slim disk model, suitable for the Super-Eddington mass accretion rate and for geometrically and optically thick disks. We explored the conditions related to the mass, mass accretion rate, viscosity, and radius of the BH-accretion disk system that would allow for the creation of N14, Na23, Al27, and K39 before the gas is accreted onto the central object. Our findings reveal that there is no region in the parameter space where the formation of Na23 can occur and only a very limited region where the formation of N14, Al27, and K39 is plausible. Specifically, this occurs for BHs with masses lower than 10 solar masses, with a preference toward even lower mass values and extremely low viscosity parameters ($\alpha <10^{-3}$). Such values are highly unlikely based on current observations of stellar mass BHs. However, such low mass BHs could actually exist in the early universe, as so-called primordial BHs. In conclusion, our study suggests that the nucleosynthesis within BH accretion disks of four elements of interest for the multiple stellar populations is improbable, but not impossible, using the slim disk model.Comment: 11 pages, 7 figures, 2 tables, Accepted by A&

Spherical models of star clusters with potential escapers

An increasing number of observations of the outer regions of globular clusters (GCs) have shown a flattening of the velocity dispersion profile and an extended surface density profile. Formation scenarios of GCs can lead to different explanations of these peculiarities, therefore the dynamics of stars in the outskirts of GCs are an important tool in tracing back the evolutionary history and formation of star clusters. One possible explanation for these features is that GCs are embedded in dark matter haloes. Alternatively, these features are the result of a population of energetically unbound stars that can be spatially trapped within the cluster, known as potential escapers (PEs). We present a prescription for the contribution of these energetically unbound members to a family of self-consistent, distribution function-based models, which, for brevity, we call the Spherical Potential Escapers Stitched (SPES) models. We show that, when fitting to mock data of bound and unbound stars from an N-body model of a tidally limited star cluster, the SPES models correctly reproduce the density and velocity dispersion profiles up to the Jacobi radius, and they are able to recover the value of the Jacobi radius itself to within 20 per cent. We also provide a comparison to the number density and velocity dispersion profiles of the Galactic cluster 47 Tucanae. Such a case offers a proof of concept that an appropriate modelling of PEs is essential to accurately interpret current and forthcoming Gaia data in the outskirts of GCs, and, in turn, to formulate meaningful present-day constraints for GC formation scenarios in the early Universe

Concurrent formation of supermassive stars and globular clusters : implications for early self-enrichment

19 pages, 5 figures, accepted to MNRAS (shortened abstract and included feedback from the community)We present a model for the concurrent formation of globular clusters (GCs) and supermassive stars (SMSs, ≳10 3M ⊙) to address the origin of the HeCNONaMgAl abundance anomalies in GCs. GCs form in converging gas flows and accumulate low-angular momentum gas, which accretes on to protostars. This leads to an adiabatic contraction of the cluster and an increase of the stellar collision rate. A SMS can form via runaway collisions if the cluster reaches sufficiently high density before two-body relaxation halts the contraction. This condition is met if the number of stars ≳10 6 and the gas accretion rate ≳10 5M ⊙ Myr -1, reminiscent of GC formation in high gas-density environments, such as - but not restricted to - the early Universe. The strong SMS wind mixes with the inflowing pristine gas, such that the protostars accrete diluted hot-hydrogen burning yields of the SMS. Because of continuous rejuvenation, the amount of processed material liberated by the SMS can be an order of magnitude higher than its maximum mass. This 'conveyor-belt' production of hot-hydrogen burning products provides a solution to the mass budget problem that plagues other scenarios. Additionally, the liberated material is mildly enriched in helium and relatively rich in other hot-hydrogen burning products, in agreement with abundances of GCs today. Finally, we find a super-linear scaling between the amount of processed material and cluster mass, providing an explanation for the observed increase of the fraction of processed material with GC mass. We discuss open questions of this new GC enrichment scenario and propose observational tests.Peer reviewe

Asking gender questions

We report on a survey of astronomers asking questions at the most recent National Astronomy Meeting (NAM2014). The gender balance of both speakers and session chairs at NAM (31% and 29% women respectively) closely matched that of attendees (28% female). However, we find that women were under-represented among question askers (just 18% female). Women were especially under-represented in asking the first question (only 14% of first questions asked by women), but when the Q&A session reached four or more questions, women and men were observed to ask roughly equal numbers of questions. We found a small, but statistically insignificant, increase in the fraction of questions from women in sessions where the chair was also female. On average $2.2\pm0.1$ questions were asked per talk, with no detectable difference in the number of questions asked of female and male speakers, but on average female chairs solicited slightly fewer questions than male chairs. We compare these results to a similar study by Davenport et al. (2014) for the AAS, who also found under-representation of women amongst question askers, but saw more pronounced gender effects when a session chair or speaker were female. We conclude with suggestions for improving the balance of questions at future astronomy meetings.Comment: 15 pages, 7 figures, comments welcom