We present a novel method for sampling iso-likelihood contours in nested sampling using a type of machine learning algorithm known as normalising flows and incorporate it into our sampler nessai. Nessai is designed for problems where computing the li
kelihood is computationally expensive and therefore the cost of training a normalising flow is offset by the overall reduction in the number of likelihood evaluations. We validate our sampler on 128 simulated gravitational wave signals from compact binary coalescence and show that it produces unbiased estimates of the system parameters. Subsequently, we compare our results to those obtained with dynesty and find good agreement between the computed log-evidences whilst requiring 2.07 times fewer likelihood evaluations. We also highlight how the likelihood evaluation can be parallelised in nessai without any modifications to the algorithm. Finally, we outline diagnostics included in nessai and how these can be used to tune the samplers settings.
We determine central values and radial trends in the stellar populations of the bulges of a sample of 28 edge-on S0-Sb disk galaxies, 22 of which are boxy/peanut-shaped (and therefore barred). Our principal findings are the following. (1) At a given
velocity dispersion, the central stellar populations of galaxies with boxy/peanut-shaped bulges are indistinguishable from those of early-type (elliptical and S0) galaxies. Either secular evolution affects stellar populations no differently to monolithic collapse or mergers, or secular evolution is not important in the central regions of these galaxies, despite the fact that they are barred. (2) The radial metallicity gradients of boxy/peanut-shaped bulges are uncorrelated with velocity dispersion and are, on average, shallower than those of unbarred early-type galaxies. This is qualitatively consistent with chemodynamical models of bar formation, in which radial inflow and outflow smears out pre-existing gradients.
Boxy and peanut-shaped bulges are seen in about half of edge-on disc galaxies. Comparisons of the photometry and major-axis gas and stellar kinematics of these bulges to simulations of bar formation and evolution indicate that they are bars viewed in
projection. If the properties of boxy bulges can be entirely explained by assuming they are bars, then this may imply that their hosts are pure disc galaxies with no classical bulge. A handful of these bulges, including that of the Milky Way, have been observed to rotate cylindrically, i.e. with a mean stellar velocity independent of height above the disc. In order to assess whether such behaviour is ubiquitous in boxy bulges, and whether a pure disc interpretation is consistent with their stellar populations, we have analysed the stellar kinematics and populations of the boxy or peanut-shaped bulges in a sample of five edge-on galaxies. We placed slits along the major axis of each galaxy and at three offset but parallel positions to build up spatial coverage. The boxy bulge of NGC3390 rotates perfectly cylindrically within the spatial extent and uncertainties of the data. This is consistent with the metallicity and alpha-element enhancement of the bulge, which are the same as in the disk. This galaxy is thus a pure disc galaxy. The boxy bulge of ESO311-G012 also rotates very close to cylindrically. The boxy bulge of NGC1381 is neither clearly cylindrically nor non-cylindrically rotating, but it has a negative vertical metallicity gradient and is alpha-enhanced with respect to its disc, suggesting a composite bulge comprised of a classical bulge and bar (and possibly a discy pseudobulge) [abridged] Even this relatively small sample is sufficient to demonstrate that boxy bulges display a range of rotational and population properties, indicating that they do not form a homogeneous class of object.
We demonstrate that the comparison of Tully-Fisher relations (TFRs) derived from global HI line widths to TFRs derived from the circular velocity profiles of dynamical models (or stellar kinematic observations corrected for asymmetric drift) is vulne
rable to systematic and uncertain biases introduced by the different measures of rotation used. We therefore argue that to constrain the relative locations of the TFRs of spiral and S0 galaxies, the same tracer and measure must be used for both samples. Using detailed near-infrared imaging and the circular velocities of axisymmetric Jeans models of 14 nearby edge-on Sa-Sb spirals and 14 nearby edge-on S0s drawn from a range of environments, we find that S0s lie on a TFR with the same slope as the spirals, but are on average 0.53+/-0.15 mag fainter at Ks-band at a given rotational velocity. This is a significantly smaller offset than that measured in earlier studies of the S0 TFR, which we attribute to our elimination of the bias associated with using different rotation measures and our use of earlier type spirals as a reference. Since our measurement of the offset avoids systematic biases, it should be preferred to previous estimates. A spiral stellar population in which star formation is truncated would take ~1 Gyr to fade by 0.53 mag at Ks-band. If S0s are the products of a simple truncation of star formation in spirals, then this finding is difficult to reconcile with the observed evolution of the spiral/S0 fraction with redshift. Recent star formation could explain the observed lack of fading in S0s, but the offset of the S0 TFR persists as a function of both stellar and dynamical mass. We show that the offset of the S0 TFR could therefore be explained by a systematic difference between the total mass distributions of S0s and spirals, in the sense that S0s need to be smaller or more concentrated than spirals.
We construct mass models of 28 S0-Sb galaxies. The models have an axisymmetric stellar component and a NFW dark halo and are constrained by observed Ks-band photometry and stellar kinematics. The median dark halo virial mass is 10^12.8 Msun, and the
median dark/total mass fraction is 20% within a sphere of radius r_1/2, the intrinsic half-light radius, and 50% within R_25. We compare the Tully-Fisher relations of the spirals and S0s in the sample and find that S0s are 0.5 mag fainter than spirals at Ks-band and 0.2 dex less massive for a given rotational velocity. We use this result to rule out scenarios in which spirals are transformed into S0s by processes which truncate star formation without affecting galaxy dynamics or structure, and raise the possibility of a break in homology between spirals and S0s.
(Abridged) We present mass models of a sample of 14 spiral and 14 S0 galaxies that constrain their stellar and dark matter content. For each galaxy we derive the stellar mass distribution from near-infrared photometry under the assumptions of axisymm
etry and a constant Ks-band stellar mass-to-light ratio, (M/L)_Ks. To this we add a dark halo assumed to follow a spherically symmetric NFW profile and a correlation between concentration and dark mass within the virial radius, M_DM. We solve the Jeans equations for the corresponding potential under the assumption of constant anisotropy in the meridional plane, beta_z. By comparing the predicted second velocity moment to observed long-slit stellar kinematics, we determine the three best-fitting parameters of the model: (M/L)_Ks, M_DM and beta_z. These simple axisymmetric Jeans models are able to accurately reproduce the wide range of observed stellar kinematics, which typically extend to ~2-3 Re or, equivalently, ~0.5-1 R_25. We find a median stellar mass-to-light ratio at Ks-band of 1.09 (solar units) with an rms scatter of 0.31. We present preliminary comparisons between this large sample of dynamically determined stellar mass-to-light ratios and the predictions of stellar population models. The stellar population models predict slightly lower mass-to-light ratios than we measure. The mass models contain a median of 15 per cent dark matter by mass within an effective radius Re, and 49 per cent within the optical radius R_25. Dark and stellar matter contribute equally to the mass within a sphere of radius 4.1 Re or 1.0 R_25. There is no evidence of any significant difference in the dark matter content of the spirals and S0s in our sample.
It is shown that if the exterior of a link L in the three sphere admits a genus 2 Heegaard splitting, then L has Generalized Property R.
A knot k in a closed orientable 3-manifold is called nonsimple if the exterior of k possesses a properly embedded essential surface of nonnegative Euler characteristic. We show that if k is a nonsimple prime tunnel number one knot in a lens space M (
where M does not contain any embedded Klein bottles), then k is a (1,1) knot. Elements of the proof include handle addition and Dehn filling results/techniques of Jaco, Eudave-Munoz and Gordon as well as structure results of Schultens on the Heegaard splittings of graph manifolds.
We measure the Tully-Fisher relations of 14 lenticular galaxies (S0s) and 14 spirals. We use two measures of rotational velocity. One is derived directly from observed spatially-resolved stellar kinematics and the other from the circular velocities o
f mass models that include a dark halo and whose parameters are constrained by detailed kinematic modelling. Contrary to the naive expectations of theories of S0 formation, we find no significant difference between the Tully-Fisher relations of the two samples when plotted as functions of both brightness and stellar mass.
We examine a sample of 30 edge-on spiral and S0 galaxies that have boxy and peanut-shaped bulges. We compute model stellar kinematics by solving the Jeans equations for axisymmetric mass distributions derived from K-band images. These simple models h
ave only one free parameter: the dynamical mass-to-light ratio, which we assume is independent of radius. Given the simplicity of the modelling procedure, the model second velocity moments are strikingly good fits to the observed stellar kinematics within the extent of our kinematic data, which typically reach ~ 0.5-1 R25 (where R25 is the optical radius), or equivalently 2-3 Re (where Re is the effective or half-light radius). We therefore find no evidence for a dominant dark matter component within the optical disk of spiral galaxies. This is equally true of the S0s in our sample, which significantly extends previous observational constraints on dark matter in these galaxies. The predicted kinematics do deviate slightly but systematically from the observations in the bulge region of most galaxies, but we argue that this is consistent with the claim that boxy and peanut-shaped bulges are bars viewed edge-on.
