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This Chapter describes, in concise manner, aspects of differential geometry that are necessary to follow the developments of this book. We give several definitions of the concept of the manifold, illustrated by a number of examples. We then define differential forms, which are viewed as the most primitive objects one can put on a manifold. We define their wedge product and the operation of exterior differentiation. We then define the notions necessary to define the integration of differential forms. After this we define vector fields, their Lie bracket, interior product, then tensors. We then describe the Lie derivative. We briefly talk about distributions and their integrability conditions. Define metrics and isometries. Then define Lie groups, discuss their action on manifolds, then define Lie algebras. Describe main Cartan's isomoprhisms. Define fibre bundles and the Ehresmann connections. Define principal bundles and connections in them. Describe the Hopf fibration. Define vector bundles and give some canonical examples of the latter. Describe covariant differentiation. Briefly reivew Riemannian geometry and the affine connection. We end this Chapter with a description of spinors and their relation to differential forms.
This monograph describes the different formulations of Einstein's General Theory of Relativity. Unlike traditional treatments, Cartan's geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. The book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.
Gravitational waves from coalescing neutron stars encode information about nuclear matter at extreme densities, inaccessible by laboratory experiments. The late inspiral is influenced by the presence of tides, which depend on the neutron star equation of state. Neutron star mergers are expected to often produce rapidly rotating remnant neutron stars that emit gravitational waves. These will provide clues to the extremely hot post-merger environment. This signature of nuclear matter in gravitational waves contains most information in the 2–4 kHz frequency band, which is outside of the most sensitive band of current detectors. We present the design concept and science case for a Neutron Star Extreme Matter Observatory (NEMO): a gravitational-wave interferometer optimised to study nuclear physics with merging neutron stars. The concept uses high-circulating laser power, quantum squeezing, and a detector topology specifically designed to achieve the high-frequency sensitivity necessary to probe nuclear matter using gravitational waves. Above 1 kHz, the proposed strain sensitivity is comparable to full third-generation detectors at a fraction of the cost. Such sensitivity changes expected event rates for detection of post-merger remnants from approximately one per few decades with two A+ detectors to a few per year and potentially allow for the first gravitational-wave observations of supernovae, isolated neutron stars, and other exotica.
Precise instrumental calibration is of crucial importance to 21-cm cosmology experiments. The Murchison Widefield Array’s (MWA) Phase II compact configuration offers us opportunities for both redundant calibration and sky-based calibration algorithms; using the two in tandem is a potential approach to mitigate calibration errors caused by inaccurate sky models. The MWA Epoch of Reionization (EoR) experiment targets three patches of the sky (dubbed EoR0, EoR1, and EoR2) with deep observations. Previous work in Li et al. (2018) and (2019) studied the effect of tandem calibration on the EoR0 field and found that it yielded no significant improvement in the power spectrum (PS) over sky-based calibration alone. In this work, we apply similar techniques to the EoR1 field and find a distinct result: the improvements in the PS from tandem calibration are significant. To understand this result, we analyse both the calibration solutions themselves and the effects on the PS over three nights of EoR1 observations. We conclude that the presence of the bright radio galaxy Fornax A in EoR1 degrades the performance of sky-based calibration, which in turn enables redundant calibration to have a larger impact. These results suggest that redundant calibration can indeed mitigate some level of model incompleteness error.
We have used Hubble Space Telescope and ground-based photometry to determine total V-band magnitudes and mass-to-light ratios of more than 150 Galactic globular clusters. We do this by summing up the magnitudes of their individual member stars, using colour-magnitude information, Gaia DR2 proper motions, and radial velocities to distinguish cluster stars from background stars. Our new magnitudes confirm literature estimates for bright clusters with $V<8$, but can deviate by up to two magnitudes from literature values for fainter clusters. They lead to absolute mass-to-light ratios that are confined to the narrow range $1.4<M/L_V<2.5$, significantly smaller than what was found before. We also find a correlation between a cluster’s $M/L_V$ value and its age, in agreement with theoretical predictions. The $M/L_V$ ratios of globular clusters are also in good agreement with those predicted by stellar isochrones, arguing against a significant amount of dark matter inside globular clusters. We finally find that, in agreement with what has been seen in M 31, the magnitude distribution of outer halo globular clusters has a tail towards faint clusters that is absent in the inner parts of the Milky Way.
In the Galactic center, there are many massive stars blowing strong stellar winds, which will strongly influence the surrounding environment and even the Galactic feedback. The Galactic center is quiescent at present, so the unique continuous energy input source is the massive star, consequently giving rise to many special features, such as the radio bubbles, the X-ray chimneys, the non-thermal filaments and high-metallicity abundance. However, it is difficult to quantify their contributions due to the complex environment in this region, and the past supernovae and Sgr A* activity are also important factors shaping these features. In this work, we discuss some structures possibly related to the stellar winds and perform preliminary simulations to study their evolution. We conclude the stellar winds can obviously influence a large scale ∼ 100 pc, and can possibly influence a larger scale environment indirectly.
Most stars with birth masses larger than that of our Sun belong to binary or higher order multiple systems. Similarly, most stars have stellar winds. Radiation pressure and multiplicity create outflows of material that remove mass from the primary star and inject it into the interstellar medium or transfer it to a companion. Both have strong impact on the subsequent evolution of the stars, yet they are often studied separately. In this short review, I will sketch part of the landscape of the interplay between stellar winds and binarity. I will present several examples where binarity shapes the stellar outflows, providing new opportunities to understand and measure mass loss properties. Stellar winds spectral signatures often help clearly identifying key stages of stellar evolution. The multiplicity properties of these stages then shed a new light onto evolutionary connections between the different categories of evolved stars.
One of the big challenges for 21st century stellar astrophysics is the impact of binary interactions on stellar evolution. Such interactions are believed to play a key role in the death throes of 1-8 M⊙ stars, as they evolve from the AGB stars into Planetary Nebulae. X-ray surveys of UV-emitting AGB stars show that ∼40% of objects with FUV emission and GALEX FUV/NUV flux ratios ≳0.2 have variable X-ray emission characterized by very high temperatures (Tx∼35-160 MK) and luminosities (Lx∼0.002-0.2L⊙). We hypothesize that such AGB stars have accretion and (accretion-powered) outflows associated with a close binary companion. UV spectroscopy with HST/STIS of our brightest object (Y Gem) shows the presence of infalling and outflowing gas, providing direct kinematic confirmation of this hypothesis. However, the UV-emitting AGB star population is dominated by objects with little or no FUV emission, and we do not know whether the UV emission from these is intrinsic to the AGB star or extrinsic (i.e., due to binarity). Here we present the first results from a large grid of simple chromospheric models to help discriminate between the intrinsic and extrinsic mechanisms of UV emission for AGB stars.
S-type AGB stars, with C/O ratios close to 1, are expected to have a mixed circumstellar chemistry as they transition from being oxygen-rich stars to carbon-rich stars. Recently, several different carbonaceous molecules, thought to be more characteristic of carbon stars, have been found in the circumstellar envelope of the S-type AGB star W Aql. We have obtained new high spatial resolution ALMA images of some of these molecules, specifically HC3N, SiC2 and SiC, and SiN, which we present here. We report diverse behaviour for these molecules, with SiC2 being seen with a symmetric spatial distribution around the star, SiN and SiC being asymmetrically distributed to the north-east of the star, and HC3N being seen in a broken shell to the south-west. These differing distributions point to complex dynamics in the circumstellar envelope of W Aql.
The origin of chemically peculiar stars and nonzero eccentricity in evolved close binaries have been long-standing problems in binary stellar evolution. Answers to these questions may trace back to an intense mass transfer during the asymptotic-giant-branch (AGB) binary phase. We use AstroBEAR to solve the 3D radiation hydrodynamic equations and calculate the mass transfer rate in AGB binaries that undergo the wind-Roche-lobe overflow or Bondi-Hoyle-Lyttleton (BHL) accretion. One of the goals of this work is to illustrate the transition from the wind- Roche-lobe overflow to BHL accretion. Both circumbinary disks and spiral structure outflows can appear in the simulations. As a result of enhanced mass transfer and angular momentum transfer, some AGB binaries may undergo orbit shrinkage, and some will expand. The high mass transfer efficiency is closely related to the presence of the circumbinary disks.
Binary interaction with a stellar or planetary companion has been proposed to be the driving mechanism behind large-scale asymmetries, such as spirals and disks, observed within AGB outflows. We developed the first chemical kinetics model that takes the effect of a stellar companions’s UV radiation into account. The presence of a stellar companion can initiate a rich photochemistry in the inner wind. Its impact is determined by the intensity of the UV radiation and the extinction the radiation experiences. The outcome of the inner wind photochemistry depends on the balance between two-body reactions and photoreactions. If photoreactions dominate, the outflow can appear molecule-poor. If two-body reactions dominate, chemical complexity within the outflow can increase, yielding daughter species with a large inner wind abundance. A comprehensive view on the molecular content of the outflow, especially combined with abundance profiles, can point towards the presence of a stellar companion.
From November 2019 to April 2020, the prototypical red supergiant Betelgeuse experienced an unexpected and historic dimming. This event was observed worldwide by astrophysicists, and also by the general public with the naked eye. We present here the results of our observing campaign with ESO’s VLT and VLTI in the visible and infrared domains. The observations with VLT/SPHERE-ZIMPOL, VLT/SPHERE-IRDIS, VLTI/GRAVITY and VLTI/MATISSE provide spatially resolved diagnostics of this event. Using PHOENIX atmosphere models and RADMC3D dust radiative transfer simulations, we built a consistent model reproducing the images and the photometry.
We have conducted a near-infrared monitoring campaign at the UK InfraRed Telescope (UKIRT), of the Local Group spiral galaxy M 33 (Triangulum). In this paper, we present the dust and gas mass-loss rates by the pulsating Asymptotic Giant Branch (AGB) stars and red supergiants (RSGs) across the stellar disc of M 33.
Thanks to the long-term collaborations between nuclear and astrophysics, we have good understanding on the origin of elements in the universe, except for the elements around Ti and some neutron-capture elements. From the comparison between observations of nearby stars and Galactic chemical evolution models, a rapid neutron-capture process associated with core-collapse supernovae is required. The production of C, N, F and some minor isotopes depends on the rotation of massive stars, and the observations of distant galaxies with ALMA indicate rapid cosmic enrichment. It might be hard to find very metal-poor or Population III (and dust-free) galaxies at very high redshifts even with JWST.
Because they lose tremendous amounts of mass, cool evolved stars are major sources of dust and molecules for the interstellar medium. Spectro-imaging of the dust-driven winds around these stars has enabled us to identify recurring nonspherical patterns (e.g. spirals, arcs, compressed wind). We use radiative-hydrodynamic simulations of dust-driven winds to study the imprints left in the wind by an orbiting stellar or sub-stellar companion. We designed 3D numerical setup to solve the wind dynamics beyond the dust condensation radius and follow the flow up to several hundreds of stellar radii. Non-uniform grids enable us to capture small scale features such as shocks or disks forming around the orbiting object. Depending on its mass and orbital parameters, we reproduced typical non-spherical features such as arcs, spirals, petals and orbital density enhancements, and identified patterns associated to eccentric orbits.
Progenitors of Type Ib and Ic supernovae (SNe) are stripped envelope stars and provide important clues on the mass-loss history of massive stars. Direct observations of the progenitors before the supernova explosion would provide strong constraints on the exact nature of SN Ib/Ic progenitors. Given that stripped envelope massive stars can have an optically thick wind as in the case of Wolf-Rayet stars, the influence of the wind on the observational properties needs to be properly considered to correctly infer progenitor properties from pre-SN observations. Non-LTE stellar atmosphere models indicate that the optical brightness could be greatly enhanced with an optically thick wind because of lifting-up of the photosphere from the stellar surface to the wind matter, and line and free-free emissions. So far, only a limited number of SN Ib/Ic progenitor candidates have been reported, including iPTF13bvn, SN 2017ein and SN 2019yvr. We argue that these three candidates are a biased sample, being unusually bright in the optical compared to what is expected from typical SN Ib/Ic progenitors, and that mass-loss enhancement during the final evolutionary stage can explain their optical properties.
We run numerical simulations of massive colliding wind binaries, and quantify the accretion onto the secondary under different conditions. We set 3D simulation of a LBV–WR system and vary the LBV mass loss rate to obtain different values of wind momentum ratio η. We show that the mean accretion rate for stationary systems fits a power law Macc∝ η–1.6 for a wide range of η, until for extremely small η saturation in the accretion is reached. We find that the stronger the primary wind, the smaller the opening angle of the colliding wind structure (CWS), and compare it with previous analytical estimates. We demonstrate the efficiency of clumpy wind in penetrating the CWS and inducing smaller scale clumps that can be accreted. We propose that simulations of colliding winds can reveal more relations as the ones we found, and can be used to constrain stellar parameters.
Close binary evolution is widely invoked to explain the formation of axisymmetric planetary nebulae, after a brief common envelope phase. The evolution of the primary would be interrupted abruptly, its still quite massive envelope being fully ejected to form the PN, which should be more massive than a planetary nebula coming from the same star, were it single. We test this hypothesis by investigating the ionised and molecular masses of a sample consisting of 21 post-common-envelope planetary nebulae, roughly one fifth of their known total population, and comparing them to a large sample of regular planetary nebulae (not known to host close-binaries). We find that post-common-envelope planetary nebulae arising from single-degenerate systems are, on average, neither more nor less massive than regular planetary nebulae, whereas post-common-envelope planetary nebulae arising from double-degenerate systems are considerably more massive, and show substantially larger linear momenta and kinetic energy than the rest. Reconstruction of the common envelope of four objects further suggests that the mass of single-degenerate nebulae actually amounts to a very small fraction of the envelope of their progenitor stars. This leads to the uncomfortable question of where the rest of the envelope is, raising serious doubts on our understanding of these intriguing objects.
Carbon-rich dust is known to form in the atmosphere of the semiregular variable star R Sculptoris. Such stardust, as well as the molecules and gas produced during the lifetime of the star, will be spread into the Galaxy via the mass-loss process. Probing this process is crucial to understand the chemical enrichment of the Galaxy. R Scl was observed using the ESO/VLTI MATISSE instrument in December 2018. Here we show the first images of the star between 3 and 10 R*. Using the complementary MIRA 3D image reconstruction and the RHAPSODY 1D intensity profile reconstruction code, we reveal the location of molecules and dust in the close environment of the star. Indeed, the C2H2 and HCN molecules are spatially located between 1 and 3.4 R* which is much closer to the star than the location of the dust. The R Scl spectrum is fitted by molecules and a dust mixture of 90% of amorphous carbon and 10% of silicone carbide. The inner boundary of the dust envelope is estimated by DUSTY at about 4.6 R*. We derive a mass-loss rate of 1.2 ± 0.4 × 10−6M⊙ yr−1however no clear SiC forming region has been detected in the MATISSE data.