Bubbling with L2L^2-almost constant mean curvature and an Alexandrov-type theorem for crystals

A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main applications of the compactness theorem are discussed. First, we obtain a description of critical points/local minimizers of elliptic energies interacting with a confinement potential. Second, we prove an Alexandrov-type theorem for crystalline isoperimetric problems

Triaxial orbit-based modelling of the Milky Way Nuclear Star Cluster

We construct triaxial dynamical models for the Milky Way nuclear star cluster using Schwarzschild's orbit superposition technique. We fit the stellar kinematic maps presented in Feldmeier et al. (2014). The models are used to constrain the supermassive black hole mass M_BH, dynamical mass-to-light ratio M/L, and the intrinsic shape of the cluster. Our best-fitting model has M_BH = (3.0 +1.1 -1.3)x10^6 M_sun, M/L = (0.90 +0.76 -0.08) M_sun/L_{sun,4.5micron}, and a compression of the cluster along the line-of-sight. Our results are in agreement with the direct measurement of the supermassive black hole mass using the motion of stars on Keplerian orbits. The mass-to-light ratio is consistent with stellar population studies of other galaxies in the mid-infrared. It is possible that we underestimate M_BH and overestimate the cluster's triaxiality due to observational effects. The spatially semi-resolved kinematic data and extinction within the nuclear star cluster bias the observations to the near side of the cluster, and may appear as a compression of the nuclear star cluster along the line-of-sight. We derive a total dynamical mass for the Milky Way nuclear star cluster of M_MWNSC = (2.1 +-0.7)x10^7 M_sun within a sphere with radius r = 2 x r_eff = 8.4 pc. The best-fitting model is tangentially anisotropic in the central r = 0.5-2 pc of the nuclear star cluster, but close to isotropic at larger radii. Our triaxial models are able to recover complex kinematic substructures in the velocity map.Comment: 14 pages, 10 figures. Accepted for publication in MNRA

An Upper Limit on the Mass of a Central Black Hole in the Large Magellanic Cloud from the Stellar Rotation Field

We constrain the possible presence of a central black hole (BH) in the center of the Large Magellanic Cloud (LMC). This requires spectroscopic measurements over an area of order a square degree, due to the poorly known position of the kinematic center. Such measurements are now possible with the impressive field of view of the Multi Unit Spectroscopic Explorer (MUSE) on the ESO Very Large Telescope. We used the Calcium Triplet (~850nm) spectral lines in many short-exposure MUSE pointings to create a two-dimensional integrated-light line-of-sight velocity map from the ~$10^8$ individual spectra, taking care to identify and remove Galactic foreground populations. The data reveal a clear velocity gradient at an unprecedented spatial resolution of 1 arcmin$^{2}$. We fit kinematic models to arrive at a $3\sigma$ upper-mass-limit of $10^{7.1}$ M$_{Sun}$ for any central BH - consistent with the known scaling relations for supermassive black holes and their host systems. This adds to the growing body of knowledge on the presence of BHs in low-mass and dwarf galaxies, and their scaling relations with host-galaxy properties, which can shed light on theories of BH growth and host system interaction.Comment: 12 pages, 11 figures, 1 table, ApJ - in pres

KMOS view of the Galactic Centre - II. Metallicity distribution of late-type stars

Knowing the metallicity distribution of stars in the Galactic Centre has important implications for the formation history of the Milky Way nuclear star cluster. However, this distribution is not well known, and is currently based on a small sample of fewer than 100 stars. We obtained near-infrared K-band spectra of more than 700 late-type stars in the central 4 pc^2 of the Milky Way nuclear star cluster with the integral-field spectrograph KMOS (VLT). We analyse the medium-resolution spectra using a full-spectral fitting method employing the G\"ottingen Spectral library of synthetic PHOENIX spectra. The derived stellar metallicities range from metal-rich [M/H]>+0.3 dex to metal-poor [M/H]<-1.0 dex, with a fraction of 5.2(^{+6.0}+{-3.1}) per cent metal-poor ([M/H]<-0.5 dex) stars. The metal-poor stars are distributed over the entire observed field. The origin of metal-poor stars remains unclear. They could originate from infalling globular clusters. For the metal-rich stellar population ([M/H]>0 dex) a globular cluster origin can be ruled out. As there is only a very low fraction of metal-poor stars in the central 4 pc^2 of the Galactic Centre, we believe that our data can discard a scenario in which the Milky Way nuclear star cluster is purely formed from infalling globular clusters.Comment: 18 pages, 9 Figures, accepted for publication in MNRA

Large scale kinematics and dynamical modelling of the Milky Way nuclear star cluster

Within the central 10pc of our Galaxy lies a dense nuclear star cluster (NSC), and similar NSCs are found in most nearby galaxies. Studying the structure and kinematics of NSCs reveals the history of mass accretion of galaxy nuclei. Because the Milky Way (MW) NSC is at a distance of only 8kpc, we can spatially resolve the MWNSC on sub-pc scales. This makes the MWNSC a reference object for understanding the formation of all NSCs. We have used the NIR long-slit spectrograph ISAAC (VLT) in a drift-scan to construct an integral-field spectroscopic map of the central 9.5 x 8pc of our Galaxy. We use this data set to extract stellar kinematics both of individual stars and from the unresolved integrated light spectrum. We present a velocity and dispersion map from the integrated light and model these kinematics using kinemetry and axisymmetric Jeans models. We also measure CO bandhead strengths of 1,375 spectra from individual stars. We find kinematic complexity in the NSCs radial velocity map including a misalignment of the kinematic position angle by 9 degree counterclockwise relative to the Galactic plane, and indications for a rotating substructure perpendicular to the Galactic plane at a radius of 20" or 0.8pc. We determine the mass of the NSC within r = 4.2pc to 1.4 x 10^7 Msun. We also show that our kinematic data results in a significant underestimation of the supermassive black hole (SMBH) mass. The kinematic substructure and position angle misalignment may hint at distinct accretion events. This indicates that the MWNSC grew at least partly by the mergers of massive star clusters. Compared to other NSCs, the MWNSC is on the compact side of the r_eff - M_NSC relation. The underestimation of the SMBH mass might be caused by the kinematic misalignment and a stellar population gradient. But it is also possible that there is a bias in SMBH mass measurements obtained with integrated light.Comment: 20 pages, 19 Figures, Accepted for publication in A&

Recruitment to publicly funded trials - are surgical trials really different?

Good recruitment is integral to the conduct of a high-quality randomised controlled trial. It has been suggested that recruitment is particularly difficult for evaluations of surgical interventions, a field in which there is a dearth of evidence from randomised comparisons. While there is anecdotal speculation to support the inference that recruitment to surgical trials is more challenging than for medical trials we are unaware of any formal assessment of this. In this paper, we compare recruitment to surgical and medical trials using a cohort of publicly funded trials. Data: Overall recruitment to trials was assessed using of a cohort of publicly funded trials (n = 114). Comparisons were made by using the Recruitment Index, a simple measure of recruitment activity for multicentre randomised controlled trials. Recruitment at the centre level was also investigated through three example surgical trials. Results: The Recruitment Index was found to be higher, though not statistically significantly, in the surgical group (n = 18, median = 38.0 IQR (10.7, 77.4)) versus (n = 81, median = 34.8 IQR (11.7, 98.0)) days per recruit for the medical group (median difference 1.7 (− 19.2, 25.1); p = 0.828). For the trials where the comparison was between a surgical and a medical intervention, the Recruitment Index was substantially higher (n = 6, 68.3 (23.5, 294.8)) versus (n = 93, 34.6 (11.7, 90.0); median difference 25.9 (− 35.5, 221.8); p = 0.291) for the other trials. Conclusions: There was no clear evidence that surgical trials differ from medical trials in terms of recruitment activity. There was, however, support for the inference that medical versus surgical trials are more difficult to recruit to. Formal exploration of the recruitment data through a modelling approach may go some way to tease out where important differences exist.The first author was supported by a Medical Research Council UK Fellowship.Peer reviewedAuthor versio

VLT Diffraction Limited Imaging and Spectroscopy in the NIR: Weighing the black hole in Centaurus A with NACO

We present high spatial resolution near-infrared spectra and images of the nucleus of Centaurus A (NGC 5128) obtained with NAOS-CONICA at the VLT. The adaptive optics corrected data have a spatial resolution of 0.06" (FWHM) in K- and 0.11" in H-band, four times higher than previous studies. The observed gas motions suggest a kinematically hot disk which is orbiting a central object and is oriented nearly perpendicular to the nuclear jet. We model the central rotation and velocity dispersion curves of the [FeII] gas orbiting in the combined potential of the stellar mass and the (dominant) black hole. Our physically most plausible model, a dynamically hot and geometrically thin gas disk, yields a black hole mass of M_bh = (6.1 +0.6/-0.8) 10^7 M_sun. As the physical state of the gas is not well understood, we also consider two limiting cases: first a cold disk model, which completely neglects the velocity dispersion; it yields an M_bh estimate that is almost two times lower. The other extreme case is to model a spherical gas distribution in hydrostatic equilibrium through Jeans equation. Compared to the hot disk model the best-fit black hole mass increases by a factor of 1.5. This wide mass range spanned by the limiting cases shows how important the gas physics is even for high resolution data. Our overall best-fitting black hole mass is a factor of 2-4 lower than previous measurements. With our revised M_bh estimate, Cen A's offset from the M_bh-sigma relation is significantly reduced; it falls above this relation by a factor of ~2, which is close to the intrinsic scatter of this relation. (Abridged)Comment: 12 pages, 14 figures, including minor changes following the referee report; accepted for publication in The Astrophysical Journa

KMOS view of the Galactic Centre I. Young stars are centrally concentrated

The Galactic centre hosts a crowded, dense nuclear star cluster with a half-light radius of 4 pc. Most of the stars in the Galactic centre are cool late-type stars, but there are also >100 hot early-type stars in the central parsec of the Milky Way. These stars are only 3-8 Myr old. Our knowledge of the number and distribution of early-type stars in the Galactic centre is incomplete. Only a few spectroscopic observations have been made beyond a projected distance of 0.5 pc of the Galactic centre. The distribution and kinematics of early-type stars are essential to understand the formation and growth of the nuclear star cluster. We cover the central >4pc^2 of the Galactic centre using the integral-field spectrograph KMOS. We extracted more than 1,000 spectra from individual stars and identified early-type stars based on their spectra. Our data set contains 114 bright early-type stars: 6 have narrow emission lines, 23 are Wolf-Rayet stars, 9 stars have featureless spectra, and 76 are O/B type stars. Our wide-field spectroscopic data confirm that the distribution of young stars is compact, with 90% of the young stars identified within 0.5 pc of the nucleus. We identify 24 new O/B stars primarily at large radii. We estimate photometric masses of the O/B stars and show that the total mass in the young population is >12,000M_sun. The O/B stars all appear to be bound to the Milky Way nuclear star cluster, while less than 30% belong to the clockwise rotating disk. The central concentration of the early-type stars is a strong argument that they have formed in situ. A large part of the young O/B stars is not on the disk, which either means that the early-type stars did not all form on the same disk or that the disk is dissolving rapidly. [abridged]Comment: 27 pages, 17 figures, matches journal version: Corrected typos, corrected Notes in Table B.