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Newton's Universal Law of Gravitation is compared and contrasted to Coulomb’s Law and the differences highlighted. Tides are discussed, and the Equivalence Principle and how it leads to the notion of curved space-times is explained.
Investigating rare and new objects have always been an important direction in astronomy. Cataclysmic variables (CVs) are ideal and natural celestial bodies for studying the accretion process of semi-detached binaries with accretion processes. However, the sample size of CVs must increase because a lager gap exists between the observational and the theoretical expanding CVs. Astronomy has entered the big data era and can provide massive images containing CV candidates. CVs as a type of faint celestial objects, are highly challenging to be identified directly from images using automatic manners. Deep learning has rapidly developed in intelligent image processing and has been widely applied in some astronomical fields with excellent detection results. YOLOX, as the latest YOLO framework, is advantageous in detecting small and dark targets. This work proposes an improved YOLOX-based framework according to the characteristics of CVs and Sloan Digital Sky Survey (SDSS) photometric images to train and verify the model to realise CV detection. We use the Convolutional Block Attention Module to increase the number of output features with the feature extraction network and adjust the feature fusion network to obtain fused features. Accordingly, the loss function is modified. Experimental results demonstrate that the improved model produces satisfactory results, with average accuracy (mean average Precision at 0.5) of 92.0%, Precision of 92.9%, Recall of 94.3%, and $F1-score$ of 93.6% on the test set. The proposed method can efficiently achieve the identification of CVs in test samples and search for CV candidates in unlabeled images. The image data vastly outnumber the spectra in the SDSS-released data. With supplementary follow-up observations or spectra, the proposed model can help astronomers in seeking and detecting CVs in a new manner to ensure that a more extensive CV catalog can be built. The proposed model may also be applied to the detection of other kinds of celestial objects.
Einsteins field equations are derived and discussed. It is argued that the Einstein tensor is proportional to the energy-momentum tensor and the constant of proportionality is derived by demanding that Newton’s Universal Law of gravitation be recovered in the non-relativistic limit. The modification of Einstein's equations when a cosmological constant is introduced is also presented.
In this chapter some empty space solutions of Einstein's are presented. The form of the Ricci tensor for a general spherical spherically symmetric static metric is given, from which the Schwarzschild solution is derived. Gravitational waves are presented as a solution of Einstein’s equations in empty space in a linear approximation.
The mathematics required to analyse higher dimensional curved spaces and space-times is developed in this chapter. General coordinate transformations, tangent spaces, vectors and tensors are described. Lie derivatives and covariant derivatives are motivated and defined. The concepts of parallel transport and a connection is introduced and the relation between the Levi-Civita connection and geodesics is elucidated. Christoffel symbols the Riemann tensor are defined as well as the Ricci tensor, the Ricci scalar and the Einstein tensor, and their algebraic and differential properties are described (though technical details of the derivationa of the Rimeann tensor are let to an appendix).
The concept to the metric is introduced. Various geometries, both flat and curved, are described including Euclidean space; Minkowski space-time; spheres; hyperbolic planes and expanding space-times. Lorentz transformations and relativistic time dilation in flat space-time is discussed as well as gravitational red-shift and the Global Positioning System. Hubble expansion and the cosmological red-shift are also explained.
Gamma-ray bursts (GRBs) and double neutron star merger gravitational-wave events are followed by afterglows that shine from X-rays to radio, and these broadband transients are generally interpreted using analytical models. Such models are relatively fast to execute, and thus easily allow estimates of the energy and geometry parameters of the blast wave, through many trial-and-error model calculations. One problem, however, is that such analytical models do not capture the underlying physical processes as well as more realistic relativistic numerical hydrodynamic (RHD) simulations do. Ideally, those simulations are used for parameter estimation instead, but their computational cost makes this intractable. To this end, we present DeepGlow, a highly efficient neural network architecture trained to emulate a computationally costly RHD-based model of GRB afterglows, to within a few percent accuracy. As a first scientific application, we compare both the emulator and a different analytical model calibrated to RHD simulations, to estimate the parameters of a broadband GRB afterglow. We find consistent results between these two models, and also give further evidence for a stellar wind progenitor environment around this GRB source. DeepGlow fuses simulations that are otherwise too complex to execute over all parameters, to real broadband data of current and future GRB afterglows.
The International VLBI Service for Geodesy and Astrometry (IVS) regularly provides high-quality data to produce Earth Orientation Parameters (EOP), and for the maintenance and realisation of the International Terrestrial and Celestial Reference Frames, ITRF and ICRF. The first iteration of the celestial reference frame (CRF) at radio wavelengths, the ICRF1, was adopted by the International Astronomical Union (IAU) in 1997 to replace the FK5 optical frame. Soon after, the IVS began official operations and in 2009 there was a significant increase in data sufficient to warrant a second iteration of the CRF, ICRF2. The most recent ICRF3, was adopted by the IAU in 2018. However, due to the geographic distribution of observing stations being concentrated in the Northern hemisphere, CRFs are generally weaker in the South due to there being fewer Southern Hemisphere observations. To increase the Southern Hemisphere observations, and the density, precision of the sources, a series of deep South observing sessions was initiated in 1995. This initiative in 2004 became the IVS Celestial Reference Frame Deep South (IVS-CRDS) observing programme. This paper covers the evolution of the CRDS observing programme for the period 1995–2021, details the data products and results, and concludes with a summary of upcoming improvements to this ongoing project.
Einstein's general theory of relativity can be a notoriously difficult subject for students approaching it for the first time, with arcane mathematical concepts such as connection coefficients and tensors adorned with a forest of indices. This book is an elementary introduction to Einstein's theory and the physics of curved space-times that avoids these complications as much as possible. Its first half describes the physics of black holes, gravitational waves and the expanding Universe, without using tensors. Only in the second half are Einstein's field equations derived and used to explain the dynamical evolution of the early Universe and the creation of the first elements. Each chapter concludes with problem sets and technical mathematical details are given in the appendices. This short text is intended for undergraduate physics students who have taken courses in special relativity and advanced mechanics.
We present a comparison between the performance of a selection of source finders (SFs) using a new software tool called Hydra. The companion paper, Paper I, introduced the Hydra tool and demonstrated its performance using simulated data. Here we apply Hydra to assess the performance of different source finders by analysing real observational data taken from the Evolutionary Map of the Universe (EMU) Pilot Survey. EMU is a wide-field radio continuum survey whose primary goal is to make a deep ($20\mu$Jy/beam RMS noise), intermediate angular resolution ($15^{\prime\prime}$), 1 GHz survey of the entire sky south of $+30^{\circ}$ declination, and expecting to detect and catalogue up to 40 million sources. With the main EMU survey it is highly desirable to understand the performance of radio image SF software and to identify an approach that optimises source detection capabilities. Hydra has been developed to refine this process, as well as to deliver a range of metrics and source finding data products from multiple SFs. We present the performance of the five SFs tested here in terms of their completeness and reliability statistics, their flux density and source size measurements, and an exploration of case studies to highlight finder-specific limitations.
We investigate the diversity in the sizes and average surface densities of the neutral atomic hydrogen (H i) gas discs in $\sim$280 nearby galaxies detected by the Widefield ASKAP L-band Legacy All-sky Blind Survey (WALLABY). We combine the uniformly observed, interferometric H i data from pilot observations of the Hydra cluster and NGC 4636 group fields with photometry measured from ultraviolet, optical, and near-infrared imaging surveys to investigate the interplay between stellar structure, star formation, and H i structural parameters. We quantify the H i structure by the size of the H i relative to the optical disc and the average H i surface density measured using effective and isodensity radii. For galaxies resolved by $>$$1.3$ beams, we find that galaxies with higher stellar masses and stellar surface densities tend to have less extended H i discs and lower H i surface densities: the isodensity H i structural parameters show a weak negative dependence on stellar mass and stellar mass surface density. These trends strengthen when we limit our sample to galaxies resolved by $>$2 beams. We find that galaxies with higher H i surface densities and more extended H i discs tend to be more star forming: the isodensity H i structural parameters have stronger correlations with star formation. Normalising the H i disc size by the optical effective radius (instead of the isophotal radius) produces positive correlations with stellar masses and stellar surface densities and removes the correlations with star formation. This is due to the effective and isodensity H i radii increasing with mass at similar rates while, in the optical, the effective radius increases slower than the isophotal radius. Our results are in qualitative agreement with previous studies and demonstrate that with WALLABY we can begin to bridge the gap between small galaxy samples with high spatial resolution H i data and large, statistical studies using spatially unresolved, single-dish data.