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In this chapter, we begin by writing out the full reaction rate matrix accounting for the radiative and collisional processes presented in Chapter 34. The radiation field is assumed to originate externally and is thus not in equilibrium with the gas. We then derive the closed-form equilibrium solution for a pure hydrogen gas. Important to achieving equilibrium are the photoionization and recombination timescales. The industry standard ionization code is Cloudy; we describe how one uses this code to create model clouds. Important concepts such as the ionization parameter, cloud ionization structure, and shelf shielding of ionizing photons are discussed in detail. The building of grids of models is explained and example grids showing predictions of ionic column densities and ionization corrections are presented for commonly observed ions. Non-equilibrium collisional ionization models are described, and grids are presented. Sensitivities of the models to variations in the ionizing spectrum are explored. Finally, homology relationships useful for scaling cloud models to infer cloud densities, sizes, masses, and cloud stability are derived.
In this chapter, we apply the formalism of hydrogenic and multi-electron atoms and build the periodic table of ground-state elements. Examination of the table shows that all elements in a given column share the same Russell-Saunders state symbol; they have identical orbital and total angular momentum states and valence electron multiplicities. These columns are formally grouped, and we show how each group shares the same spectral characteristics (the transition energies differ, but the relationships between transitions are identical from one element to another in a group). We then introduce the idea of iso-electronic sequences, which neatly explain the many lithium-like and sodium-like ions (CIV, NV, OVI, NeVIII, MgII, etc.) that have hydrogenic-like spectral series, including zero-volt resonant fine-structure doublets. We then provide accurate tables of ionization potentials and describe the physical reasons for the ion-to-ion trends in these potentials. We conclude the chapter with a complete suite of Grotrian diagrams (visual representations of the energy states and allowed electron transitions) for ions commonly studied using quasar absorption lines.
In the 1950s, Lyman Spitzer predicted that a hot gaseous medium surrounded the Milky Way in a halo/corona and that this gas should be detectable in strong absorption from highly ionized oxygen and nitrogen. It was confirmed in the 1970s using the Copernicus satellite. In the early 1990s, the first hydrodynamic cosmological simulations predicted that a warm-hot intergalactic medium (WHIM) was pervasive and extended out to the mildly overdense regions in the Universe. At low redshifts, the WHIM was predicted to harbor most of the baryons in the Universe. This was a bold prediction in which five-, six-, and seven-times oxygen (OVI, OVII, and OVIII) was predicted to trace this gas in absorption. The latter two require the X-ray spectroscopy, which has its challenges. The WHIM is also believed to be the source of the so-called broad Ly α absorbers (BLAs) in the Ly α forest and can be probed using fast radio bursts. In this chapter, we describe the discovery and confirmation of the WHIM and its characteristic properties. This includes a review of cooling flows, astrophysical plasmas, shocks, and interfaces.
The fundamental quantity of the expansion dynamics of the Universe is the time-dependent scale factor. However, neither time nor the scale factor is a measurable quantity. The measurable quantity due to universal expansion is the cosmological redshift of observed radiation. This redshift gives the ratio by which the Universe has expanded relative to the present epoch. In this chapter, we rewrite the expands dynamics in terms of redshift and define proper and co-moving coordinates. Using the radial and transverse components of the Robertson-Walker metric, we derive relations for cosmic time and multiple useful distance measures as a function of redshift. These include the radial and transverse proper and co-moving distances, the angular diameter distance, the luminosity distance, and the “absorption” distance. We also derive the equations for the redshift dependence of the line-of-sight separations of gravitationally lensed quasars. The redshift path density is derived. Finally, the redshift dependence of line-of-sight peculiar velocities and cosmological recessional velocities are derived from the metric.
The energy structures and transition energies of single-electron atoms and ions are presented. Five Nobel Prizes in Physics were awarded for the theories discussed in this chapter. We first review the Bohr model, which was based on quantized angular momentum and classical circular orbits. The wave model of Schrödinger followed, in which spherical boundary conditions quantized polar and azimuthal standing waves. The energies were identical to Bohr’s, but transition selection rules dictated the change in angular momentum of the system during absorption and emission. Dirac incorporated electron spin and relativistic energies, resulting in energy shifts and fine structure splitting of the energy levels for non-zero angular momentum states. Feynman and Swinger incorporated quantization of the electric vector potential. This physics broke energy degeneracies in the Dirac model and correctly predicted the famous Lamb shift. In this chapter, each of these models are described in detail. The final full characterization of the energy levels and transitions are presented. The chapter ends with a discussion on isotope shifting and transitions to the continuum (ionization/recombination).
'Quasar Absorption Lines' is a comprehensive, detailed exposition on the science and analysis of quasar spectra in two volumes, for both aspiring and seasoned astronomers. This Volume 2: 'Astrophysics, Analysis, and Modeling' describes atomic transitions of hydrogenic and multi-electron ions, the theoretical foundation and practical application of the ΛCDM cosmological model, and radiative transfer from cosmological sources. The theory of spectrographs and the mathematical formalism and quantitative analysis of spectral absorption lines and ionization breaks are treated in detail, including column density measurements, line deblending, and Voigt profile fitting. The philosophies, methods, and techniques of large absorption line surveys are presented, including methods for correcting incompleteness and for measuring accurate absorber population statistics. Gas physics, heating/cooling, and ionization are also covered, followed by detailed methods for undertaking multi-component, multiphase chemical-ionization modeling.
We search data from the GLEAM-X survey, obtained with the Murchison Widefield Array (MWA) in 2020, for the presence of radio frequency interference from distant Earth-orbiting satellites, in the form of unintended emissions similar to those recently seen from objects in Low Earth Orbits (LEO). Using the GLEAM-X $\delta=1.6^{\circ}$ pointing, which is stationary in azimuth (on the local Meridian) and elevation (near the celestial Equator), the very wide field of view of the MWA maintains custody of a large number of satellites in geostationary and geosynchronous (GEO) orbits in this direction for long periods of time. We use one night of GLEAM-X data in the 72–231 MHz frequency range to form stacked images at the predicted coordinates of up to 162 such satellites, in order to search for unintended radio emission. In the majority of cases, we reach 4$\sigma$ upper limits of better than 1 mW Equivalent Isotropic Radiated Power (EIRP) in a 30.72 MHz bandwidth (dual polarisation), with the best limits below 10 $\unicode{x03BC}$W. No convincing evidence for unintended emissions at these detection thresholds was found. This study builds on recent work showing an increasing prevalence of unintended emissions from satellites in LEO. Any such emission from objects in GEO could be a significant contributor to radio frequency interference experienced by the low frequency Square Kilometre Array and warrants monitoring. The current study forms a baseline for comparisons to future monitoring.
A coronal mass ejection (CME) was detected crossing the radio signals transmitted by the Mars Express (MEX) and Tianwen-1 (TIW) spacecraft at a solar elongation of $4.4^{\circ}$. The impact of the CME was clearly identifiable in the spacecraft signal SNR, Doppler noise, and phase residuals observed at the University of Tasmania’s Very Long Baseline Interferometry (VLBI) antenna in Ceduna, South Australia. The residual phases observed from the spacecraft were highly correlated with each other during the transit of the CME across the radio ray-path despite the spacecraft signals having substantially different Doppler trends. We analyse the auto- and cross-correlations between the spacecraft phase residuals, finding time-lags ranging between 3.18 and 14.43 seconds depending on whether the imprinted fluctuations were stronger on the uplink or the downlink radio ray-paths. We also examine the temporal evolution of the phase fluctuations to probe the finer structure of the CME and demonstrate that there was a clear difference in the turbulence regime of the CME leading edge and the background solar wind conditions several hours prior to the CME radio occultation. Finally, autocorrelation of the MEX two-way radio Doppler noise data from Ceduna and closed-loop Doppler data from ESA’s New Norcia ground station antenna were used to constrain the location of the CME impact along the radio ray-path to a region 0.2 AU from the Sun, at a heliospheric longitude consistent with CME origin at the Sun. The results presented demonstrate the potential of the multi-spacecraft-in-beam technique for studying CME structures in great detail and providing measurements that complement the capabilities of future solar monitoring instruments.
'Quasar Absorption Lines' is a comprehensive, detailed exposition on the science and analysis of quasar spectra in two volumes, for both aspiring and seasoned astronomers. This Volume 1: 'Introduction, Discoveries, and Methods' covers the evolution of the field of quasar spectroscopy over the six decades since quasars were discovered, including the development and application of observational methods and the knowledge gained from them. The broad treatment includes studies of the Ly α forest, Lyman limit systems, damped Ly α absorbers, deuterium (D/H), 21-cm absorbers, HI and HeII reionization, the warm/hot intergalactic medium, and the multiple ionization phases of metal lines. The connections between these absorbers and galaxies (the circumgalactic medium), galaxy groups (the intragroup medium), and clusters of galaxies (the intracluster medium) are treated in depth. Also covered are the taxonomy and classifications of AGN/quasar spectra, black hole accretion, broad and narrow associated absorption lines, and the quasar circumgalactic medium.
Common envelope (CE) evolution is largely governed by the drag torque applied on the in-spiralling stellar components by the envelope. Previous work has shown that idealized models of the torque based on a single body moving in rectilinear motion through an unperturbed atmosphere can be highly inaccurate. Progress requires new models for the torque that account for binarity. Towards this end, we perform a new 3D global hydrodynamic CE simulation with the mass of the companion point particle set equal to the mass of the asymptotic giant branch star core particle to maximize symmetry and facilitate interpretation. First, we find that a region around the particles of a scale comparable to their separation contributes essentially all of the torque. Second, the density pattern of the torque-dominating gas and, to an extent, this gas itself, is roughly in corotation with the binary. Third, approximating the spatial distribution of the torquing gas as a uniform-density prolate spheroid whose major axis resides in the orbital plane and lags the line joining the binary components by a constant phase angle reproduces the torque evolution remarkably well, analogous to studies of binary supermassive black holes. Fourth, we compare the torque measured in the simulation with the predictions of a model that assumes two weak point-mass perturbers undergoing circular motion in a uniform background without gas self-gravity and find remarkable agreement with our results if the background density is taken to be equal to a fixed fraction ($\approx0.44$) of the density at the spheroid surface. Overall, this work makes progress towards developing simple time-dependent models of the CE phase, for example by informing the development of drag force prescriptions for 1D spherically symmetric CE simulations, which could be used to explore the parameter space of luminous red novae or in binary population synthesis studies.
Astronomical objects that change rapidly give us insight into extreme environments, allowing us to identify new phenomena, test fundamental physics, and probe the Universe on all scales. Transient and variable radio sources range from the cosmological, such as gamma-ray bursts, to much more local events, such as massive flares from stars in our Galactic neighbourhood. The capability to observe the sky repeatedly, over many frequencies and timescales, has allowed us to explore and understand dynamic phenomena in a way that has not been previously possible. In the past decade, there have been great strides forward as we prepared for the revolution in time domain radio astronomy that is being enabled by the SKA Observatory telescopes, the SKAO pathfinders and precursors, and other ‘next generation’ radio telescopes. Hence, it is timely to review the current status of the field and summarise the developments that have happened to get to our current point. This review focuses on image domain (or ‘slow’) transients, on timescales of seconds to years. We discuss the physical mechanisms that cause radio variability and the classes of radio transients that result. We then outline what an ideal image domain radio transients survey would look like and summarise the history of the field, from targeted observations to surveys with existing radio telescopes. We discuss methods and approaches for transient discovery and classification and identify some of the challenges in scaling up current methods for future telescopes. Finally, we present our current understanding of the dynamic radio sky, in terms of source populations and transient rates, and look at what we can expect from surveys on future radio telescopes.
High-sensitivity observations of PSR J1919+1745 were conducted using the Five-hundred-metre Aperture Spherical Radio Telescope (FAST) at a central frequency of 1 250 MHz, enabling a detailed investigation of its single-pulse behaviour. Our research indicates that this pulsar is a normal pulsar, exhibiting null behaviour, subpulse drifting, and occasional bright pulses. Moreover, we observed that the null events tend to be of short duration, with an estimated overall null fraction of approximately $29.5\pm1.1\% $. Through Sliding Fluctuation Spectrum analysis, the modulation period of subpulse drifting is determined to be $P_3=(6.1 \pm 0.7)P_1$ (where $P_1$ denotes the pulsar rotation period), and a non-drifting behaviour is also observed besides this. Analysis using the Harmonic-Resolved Fourier Spectrum indicates that a combination of amplitude modulation and phase modulation causes the subpulse drifting behaviour of this pulsar. Furthermore, the value $P_2$, derived from phase modulation, is approximately $360^\circ / 21 = 17.1^\circ$. polarisation analysis shows a moderate degree of linear polarisation ($37.22\pm0.59\% $), an S-shaped swing in the polarisation position angle, and an approximate $90^\circ$ orthogonal polarisation jump. The radiation characteristics of PSR J1919+1745 will expand the sample of pulsars with pulse null and subpulse drifting, thus contributing to future systematic studies on the physical origins of pulse null and subpulse drifting phenomena.
We report the first observations in a rare family of class II methanol maser transitions in both CH$_3$OH and $^{13}$CH$_3$OH towards three southern high-mass star formation regions, along with the first maser detected in the $^{13}$CH$_3$OH line. The $8_2 \rightarrow 9_1 A^{-}$ methanol transition was observed in both CH$_3$OH and $^{13}$CH$_3$OH (at 28.9 GHz and 41.9 GHz, respectively) towards three sources; G358.93-0.03, NGC6334I, and G345.01+1.79, all of which are star formation regions with recent maser flaring events. We report the first maser detection of the 41.9 GHz line in $^{13}$CH$_3$OH towards G358.93-0.03 and the first confirmed maser detection of the 28.9 GHz line in CH$_3$OH towards NGC6334I. Additionally, we report a maser detection of the 28.9 GHz line in CH$_3$OH towards G358.93-0.03, meaning that with our detection of the 41.9 GHz line, this is the first isotopic detection of these lines towards G358.93-0.03. The newly detected maser transitions are associated with the primary millimetre continuum sources (MM1) in both G358.93-0.03 and NGC6334I, within the varying positional uncertainties.
Bars are ubiquitous morphological features in the observed distribution of galaxies. There are similarly many methods for classifying these features and, without a strict theoretical definition or common standard practice, this is often left to circumstance. So, we were concerned whether astronomers even agree on the bar which they perceive in a given galaxy and whether this could impact perceived scientific results. As an elementary test, we twenty-one astronomers with varied experience in studying resolved galaxies and circumstances, have each assessed 200 galaxy images, spanning the early phase of bar evolution in two different barred galaxy simulations. We find variations exist within the classification of all the standard bar parameters assessed: bar length, axis-ratio, pitch-angle and even whether a bar is present at all. If this is indicative of the wider community, it has implications for interpreting morphological trends, such as bar-end effects. Furthermore, we find that it is surprisingly not expertise but gender, followed by career stage, which gives rise to the largest discrepancies in the reported bar parameters. Currently, automation does not seem to be a viable solution, with bar classifications from two automated bar-finding algorithms tested and failing to find bars in snapshots where most astronomers agree a bar must exist. Increasing dependence on machine learning or crowdsourcing with a training dataset can only serve to obfuscate any existing biases if these originate from the specific astronomer producing the training material. On the strength of this small sample, we encourage an interim best practice to reduce the impact of any possible classification bias and set goals for the community to resolve the issue in the future.
Post-asymptotic giant branch (post-AGB) binary stars are evolved systems that host circumbinary discs formed through mass loss during late stage binary interactions. Their structural, morphological, kinematic, and chemical similarities to planet-forming discs suggest that these systems may act as sites of ‘second-generation’ planet formation. In this study, we assess whether the disc instability mechanism – a proposed pathway for rapid, giant planet formation in some protoplanetary discs - can operate in post-AGB discs; motivated by their short lifetimes ($10^{4-5}$ yr). Using the Toomre criterion under well motivated assumptions for disc structure and size, mass, and thermal properties, we assess the conditions for gravitational instability. We first benchmark our analytical framework using well studied protoplanetary disc systems (including HL Tauri, Elias 2-27, GQ Lupi) before applying the same analysis to observed post-AGB discs. We find that post-AGB discs are generally gravitationally stable at present, due primarily to their low masses. Using viscous disc theory, we find that the discs were stable against collapse even in the past, when their masses were potentially higher. In contrast, several protoplanetary discs analysed in the same way show that they likely experienced gravitationally unstable phases early on. We also find that higher viscosity parameters ($\alpha \sim 10^{-2}$) are better aligned with expected post-AGB disc lifetimes. Finally, we revisit the planet formation scenario proposed for the post-common envelope system NN Ser, first carried out by Schleicher and Dreizler, and we show that gravitational instability could be feasible under specific, high disc mass assumptions. Overall, our results provide the first systematic theoretical assessment of gravitational instability in post-AGB discs, demonstrating that this mechanism is unlikely to dominate second-generation planet formation in these systems and underscoring the need to explore alternative pathways – such as core accretion – in future studies.
With the growing number of gravitational wave detections, achieving a competitive measurement of $H_0$ with dark sirens is becoming increasingly feasible. The expansion of the LIGO-Virgo-KAGRA Collaboration into a four detector network will reduce both the localisation area and the luminosity distance uncertainty associated with each gravitational wave event. It is therefore essential to identify and mitigate other major sources of error that could increase the uncertainty in $H_0$. In this work, we explore three scenarios relevant to the dark siren method in future observing runs. First, we demonstrate that there is a precision gain offered by a catalogue of spectroscopic-like redshifts compared to photometric-like redshifts, with the greatest improvements observed in smaller localisation areas. Second, we show that redshift outliers (as occur in realistic photometric redshift catalogues), do not introduce bias into the measurement of $H_0$. Finally, we find that uniformly sub-sampling spectroscopic-like redshift catalogues increases the uncertainty in $H_0$ as the completeness fraction is decreased; at a completeness of 50% the benefit of spectroscopic redshift precision is outweighed by the degradation from incompleteness. In all three scenarios, we obtain unbiased estimates of $H_0$. We conclude that a competitive measurement of $H_0$ using the dark siren method will require a hybrid catalogue of both photometric and spectroscopic redshifts, at least until highly complete spectroscopic catalogues become available. This, however, will come at the cost of a more complex selection function.