We use the functional renormalisation group to study the spectrum of three- and four-body states in bosonic systems around the unitary limit. Our effective action includes all energy-independent contact interactions in the four-atom sector and we int
roduce a running trimer field to eliminate couplings that involve the atom-atom-dimer channel. The results show qualitatively similar behaviour to those from exact approaches. The truncated action we use leads to overbinding of the two four-body states seen in those treatments. It also generates a third state, although only for a very narrow range of two-body scattering lengths.
We propose a new power counting for the effective field theory describing a near-threshold state with unstable constituents, such as the X(3872) meson. In this counting, the momenta of the heavy particles, the pion mass and the excitation energy of t
he unstable constituent -- the D* in the case of the X -- are treated as small scales, of order Q. The difference, delta, between the excitation energy of the D* and the pion mass is smaller than either by a factor ~20. We therefore assign delta an order Q^2 in our counting. This provides a consistent framework for a double expansion in both delta/m_pi and the ratio of m_pi to the high-energy scales in this system. It ensures that amplitudes have the correct behaviour at the three-body threshold. It allows us to derive, within an effective theory, various results which have previously been obtained using physically-motivated approximations.
I review the current state of determinations of the Hubble constant, which gives the length scale of the Universe by relating the expansion velocity of objects to their distance. There are two broad categories of measurements. The first uses individu
al astrophysical objects which have some property that allows their intrinsic luminosity or size to be determined, or allows the determination of their distance by geometric means. The second category comprises the use of all-sky cosmic microwave background, or correlations between large samples of galaxies, to determine information about the geometry of the Universe and hence the Hubble constant, typically in a combination with other cosmological parameters. Many, but not all, object-based measurements give $H_0$ values of around 72-74km/s/Mpc , with typical errors of 2-3km/s/Mpc. This is in mild discrepancy with CMB-based measurements, in particular those from the Planck satellite, which give values of 67-68km/s/Mpc and typical errors of 1-2km/s/Mpc. The size of the remaining systematics indicate that accuracy rather than precision is the remaining problem in a good determination of the Hubble constant. Whether a discrepancy exists, and whether new physics is needed to resolve it, depends on details of the systematics of the object-based methods, and also on the assumptions about other cosmological parameters and which datasets are combined in the case of the all-sky methods.
BINGO is a novel single-dish total-power telescope that will map the redshifted HI sky in a ~15 degree strip, at frequencies of 960-1260 MHz (z=0.12-0.48). BINGO will have the sensitivity to accurately measure the HI power spectrum and to detect Bary
on Acoustic Oscillations (BAOs) for the first time at radio wavelengths. This will provide complementary cosmological information to existing surveys and will measure the acoustic scale to ~2 % precision. We provide an update on BINGO including an improved two-mirror optical configuration, final site selection and foreground removal simulations.
Unified schemes of radio sources, which account for different types of radio AGN in terms of anisotropic radio and optical emission, together with different orientations of the ejection axis to the line of sight, have been invoked for many years. Rec
ently, large samples of optical quasars, mainly from the Sloan Digital Sky Survey, together with large radio samples, such as FIRST, have become available. These hold the promise of providing more stringent tests of unified schemes but, compared to previous samples, lack high resolution radio maps. Nevertheless they have been used to investigate unified schemes, in some cases yielding results which appear inconsistent with such theories. Here we investigate using simulations how the selection effects to which such investigations are subject can influence the conclusions drawn. In particular, we find that the effects of limited resolution do not allow core-dominated radio sources to be fully represented in the samples, that the effects of limited sensitivity systematically exclude some classes of sources and the lack of deep radio data make it difficult to decide to what extent closely separated radio sources are associated. Nevertheless, we conclude that relativistic unified schemes are entirely compatible with the current observational data. For a sample selected from SDSS and FIRST which includes weak-cored triples we find that the equivalent width of the [OIII] emission line decreases as core-dominance increases, as expected, and also that core-dominated quasars are optically brighter than weak-cored quasars.
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The dif
ference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.
Previous velocity images which reveal flows of ionized gas along the most prominent cometary tail (from Knot 38) in the Helix planetary nebula are compared with that taken at optical wavelengths with the Hubble Space Telescope and with an image in th
e emission from molecular hydrogen. The flows from the second most prominent tail from Knot 14 are also considered. The kinematics of the tail from the more complex Knot 32, shown here for the first time, also reveals an acceleration away from the central star. All of the tails are explained as accelerating ionized flows of ablated material driven by the previous, mildly supersonic, AGB wind from the central star. The longest tail of ionized gas, even though formed by this mechanism in a very clumpy medium, as revealed by the emission from molecular hydrogen, appears to be a coherent outflowing feature.
Recent research of the author has given an explicit geometric description of free (two-sided) adequate semigroups and monoids, as sets of labelled directed trees under a natural combinatorial multiplication. In this paper we show that there are natur
al embeddings of each free right adequate and free left adequate semigroup or monoid into the corresponding free adequate semigroup or monoid. The corresponding classes of trees are easily described and the resulting geometric representation of free left adequate and free right adequate semigroups is even easier to understand than that in the two-sided case. We use it to establish some basic structural properties of free left and right adequate semigroups and monoids.
In 1996, Sakurais object (V4334 Sgr) suddenly brightened in the centre of a faint Planetary Nebula (PN). This very rare event was interpreted as the reignition of a hot white dwarf that caused a rapid evolution back to the cool giant phase. From 1998
on, a copious amount of dust has formed continuously, screening out the star which has remained embedded in this expanding high optical depth envelope. The new observations, reported here, are used to study the morphology of the circumstellar dust in order to investigate the hypothesis that Sakurais Object is surrounded by a thick spherical envelope of dust. We have obtained unprecedented, high-angular resolution spectro-interferometric observations, taken with the mid-IR interferometer MIDI/VLTI, which resolve the dust envelope of Sakurais object. We report the discovery of a unexpectedly compact (30 x 40 milliarcsec, 105 x 140 AU assuming a distance of 3.5 kpc), highly inclined, dust disk. We used Monte Carlo radiative-transfer simulations of a stratified disk to constrain its geometric and physical parameters, although such a model is only a rough approximation of the rapidly evolving dust structure. Even though the fits are not fully satisfactory, some useful and robust constraints can be inferred. The disk inclination is estimated to be 75+/-3 degree with a large scale height of 47+/-7 AU. The dust mass of the disk is estimated to be 6 10^{-5} solar mass. The major axis of the disk (132+/-3 degree) is aligned with an asymmetry seen in the old PN that was re-investigated as part of this study. This implies that the mechanism responsible for shaping the dust envelope surrounding Sakurais object was already at work when the old PN formed.
The driving mechanism of the AGB superwind has become controversial in recent years. The efficacy of dust-driven mass loss has been queried. Spitzer observation of AGB stars in Local Group Galaxies show the surprising result that at low metallicity,
AGB mass loss occurs at low luminosity, possibly lower than in the Galaxy, but only for carbon-rich stars. Oxygen-rich stars in the Galaxy and in lower metallicity galaxies have similar mass-loss rates only at high luminosities. To explain this dichotomy, we propose that the superwind has a dual trigger. The superwind starts either when sufficient excess carbon builds up for efficient formation of carbonaceous dust (which we propose occurs when $X_{rm CO} = rm (C - O)/ O_odot = 0.1$), or when the luminosity reaches a value sufficient for a silicate-dust-driven wind (proposed at $L = 10^4 Z^{-4/3} rm L_odot)$. We show that this dual trigger fits the current observational constraints: the luminosity at which the superwind begins, and the predominance of carbon superwind star at low metallicity. We use stellar evolution models to check the consistency of our explanations and present detailed predictions of the luminosities at which the superwind is triggered for different metallicities and initial stellar masses.
