Binary-corrected velocity dispersions from single- and multi-epoch radial velocities: massive stars in R136 as a test case

Orbital motions from binary stars can broaden the observed line-of-sight velocity distribution of a stellar system, artificially inflating the measured line-of-sight velocity dispersion, which can in turn lead to erroneous conclusions about the dynamical state of the system. Cottaar et al. (2012b) proposed a maximum likelihood procedure to recover the intrinsic velocity dispersion of a resolved star cluster from a single epoch of radial velocity data of individual stars, which they achieved by simultaneously fitting the intrinsic velocity distribution of the single stars and the centres of mass of the binaries along with the velocity shifts caused by binary orbital motions. Assuming well-characterized binary properties, they showed that this procedure can accurately reproduce intrinsic velocity dispersions below 1 km s$^{-1}$ for solar-type stars. Here we investigate the systematic offsets induced in cases where the binary properties are uncertain, and we show how two epochs of radial velocity data with an appropriate baseline can help to mitigate these systematic effects. We first test the method above using Monte Carlo simulations, taking into account the large uncertainties in the binary properties of OB stars. We then apply it to radial velocity data in the young massive cluster R136, an example for which the intrinsic velocity dispersion of O-type stars is known from an intensive multi-epoch approach. For typical velocity dispersions of young massive clusters ($\gtrsim 4$ km s$^{-1}$) and with a single epoch of data, we demonstrate that the method can just about distinguish between a cluster in virial equilibrium and an unbound cluster. This is due to the higher spectroscopic binary fraction and more loosely constrained distributions of orbital parameters of OB stars compared to solar-type stars. By extending the maximum likelihood method to multi-epoch data, Comment: Accepted by A&A; minor corrections made on November 2

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

Synthesis studies to single stereoisomers of the vicinal trifluoroalkane motif

This thesis focuses on the construction of individual isomers of the R-CHF-CHF-CHF-R’ motif. The multi-vicinal fluorine motif is new in organic chemistry and therefore stereoselective methods giving rapid access to these motifs and with flexibility need to be explored. The research in the thesis succeeded in the preparation of (2S,3R,4S)-314 and (2S,3S,4R)-328. In Chapter 1, an overview of the impact of fluorine in organic molecules is given. Recent developments in asymmetric electrophilic and nucleophilic fluorination are described, as well as the preparation of multivicinal fluoroalkane motifs. Aldol reactions of either (R)- or (S)-N-(α-fluoropropyl)-2-oxazolidinones, mediated by TiCl 4 are reported in Chapter 2. Such aldol reactions gave rise to identical α-fluoro-β-hydroxy- aldol products with high diastereoselectivities (95% dr). After removal from the auxiliary α- fluoro-β-hydroxy- products were converted to the corresponding α,β-difluoro products. The synthesis of non symmetric vicinal trifluoro motifs (2S,3R,4S)-314 and (2S,3S,4R)-328 is described in Chapter 3. They were prepared by direct fluorination in three steps of the corresponding (2R,3R,4R)-erythro and (2R,3S,4S)-threo enantio-enriched epoxy-alcohols. The two erythro and threo epoxy-alcohol isomers behave very differently during the first fluorination step and then an attempt to study and rationalise this difference in behaviour is made

Multiple populations in globular clusters: the distinct kinematic imprints of different formation scenarios

Several scenarios have been proposed to explain the presence of multiple stellar populations in globular clusters. Many of them invoke multiple generations of stars to explain the observed chemical abundance anomalies, but it has also been suggested that self-enrichment could occur via accretion of ejecta from massive stars onto the circumstellar disc of low-mass pre-main sequence stars. These scenarios imply different initial conditions for the kinematics of the various stellar populations. Given some net angular momentum initially, models for which a second generation forms from gas that collects in a cooling flow into the core of the cluster predict an initially larger rotational amplitude for the polluted stars compared to the pristine stars. This is opposite to what is expected from the accretion model, where the polluted stars are the ones crossing the core and are on preferentially radial (low-angular momentum) orbits, such that their rotational amplitude is lower. Here we present the results of a suite of $N$-body simulations with initial conditions chosen to capture the distinct kinematic properties of these pollution scenarios. We show that initial differences in the kinematics of polluted and pristine stars can survive to the present epoch in the outer parts of a large fraction of Galactic globular clusters. The differential rotation of pristine and polluted stars is identified as a unique kinematic signature that could allow us to distinguish between various scenarios, while other kinematic imprints are generally very similar from one scenario to the other.Comment: 22 pages, 16 figures + appendix. Accepted for publication 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

Massive binary stars and the kinematics of Young Massive Clusters

Located in the Large Magellanic Cloud, R136 is a rare example of a nearby young and dense massive star cluster in which individual stars can be resolved. Often suggested as a globular cluster in formation, its study is of great interest and promises to provide insights into the early dynamical evolution of massive star clusters. This is crucial to understand more extreme and distant starburst clusters, which contribute to a significant fraction of all current star formation in the Local Universe, in particular in interacting galaxies. The majority of this thesis is based on multi-epoch spectroscopic observations in and around R136 obtained as part of the VLT-FLAMES Tarantula Survey (VFTS), an ambitious programme which targeted nearly 1 000 massive stars in the intricate 30 Doradus star-forming region. The motivations and observing strategy of this survey, designed to address key questions about the evolution of massive stars and clusters, are first introduced. The data reduction procedures applied to VFTS data are described, with an emphasis on the tasks accomplished in the context of this thesis. The VFTS data are first used to perform a detailed kinematic study of R136, determine its dynamical state, and evaluate the importance of gas expulsion in the early evolution of massive star clusters. Orbital motions of binary stars are found to dominate the line- of-sight velocity dispersion of the cluster, illustrating the risk of interpreting velocity dispersion measurements for unresolved extragalactic young massive clusters. However, once the detected binaries are rejected and the contribution of undetected binaries is accounted for through Monte Carlo simulations, the true velocity dispersion of the cluster is found to be low and consistent with it being in virial equilibrium. This suggests that gas expulsion has not had a dramatic effect on the early dynamical evolution of R136. Using the velocity measurements of R136 as a test case, a maximum likelihood method that fits the velocity dispersion of a cluster from a single epoch of radial velocity data is then tested. The method must be applied with care given the high binary fraction of massive stars and the large uncertainties in their binary orbital parameter distributions, but for typical velocity dispersions of young massive clusters (& 4 kms−1), it is shown that the velocity dispersion can be measured with an accuracy of 40% or better. This offers an efficient way of constraining the dynamics of these systems. The radial velocity measurements of apparently single stars in R136 are also used to investigate the internal rotation of the cluster, a potentially important but largely unexplored characteristic of young clusters. Evidence is found, at the 95% confidence level, for rotation of the cluster as a whole. A simple maximum likelihood method is presented to fit rotation curves to the data, from which a typical rotational velocity of 3 kms−1 is found. When compared to the low velocity dispersion of R136, this suggests that star clusters may form with as much as 20% of their kinetic energy in rotation. Finally, a smaller-scale survey of massive stars in the Wing of the Small Magellanic Cloud is introduced. As an example of the particularly interesting massive binaries that can be revealed by the synergy between large optical spectroscopic surveys of young clusters and observations at other wavelengths, the discovery of a new Be/X-ray pulsar binary and associated supernova remnant is reported. With a long spin period of over 1 000 seconds and a young age of 104 years constrained by its association with the supernova remnant, the pulsar in this system is quickly emerging as a unique object that challenges our understanding of the spin evolution of accreting neutron stars

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