Almost all conventional matter in the Universe is fluid, and fluid dynamics plays a crucial role in astrophysics. This graduate textbook, first published in 2007, provides a basic understanding of ...the fluid dynamical processes relevant to astrophysics. The mathematics used to describe these processes is simplified to bring out the underlying physics. The authors cover many topics, including wave propagation, shocks, spherical flows, stellar oscillations, the instabilities caused by effects such as magnetic fields, thermal driving, gravity, shear flows, and the basic concepts of compressible fluid dynamics and magnetohydrodynamics. The authors are Directors of the UK Astrophysical Fluids Facility (UKAFF) at the University of Leicester, and editors of the Cambridge Astrophysics Series. This book has been developed from a course in astrophysical fluid dynamics taught at the University of Cambridge. It is suitable for graduate students in astrophysics, physics and applied mathematics, and requires only a basic familiarity with fluid dynamics.
This paper explores how the stochastic accretion of planetesimals on to white dwarfs would be manifested in observations of their atmospheric pollution. Archival observations of pollution levels for ...unbiased samples of DA and non-DA white dwarfs are used to derive the distribution of inferred accretion rates, confirming that rates become systematically lower as sinking time (assumed here to be dominated by gravitational settling) is decreased, with no discernable dependence on cooling age. The accretion rates expected from planetesimals that are all the same mass (i.e., a mono-mass distribution) are explored both analytically and using a Monte Carlo model, quantifying how measured accretion rates inevitably depend on sinking time, since different sinking times probe different times since the last accretion event. However, that dependence is so dramatic that a mono-mass distribution can be excluded within the context of this model. Consideration of accretion from a broad distribution of planetesimal masses uncovers an important conceptual difference: accretion is continuous (rather than stochastic) for planetesimals below a certain mass, and the accretion of such planetesimals determines the rate typically inferred from observations; smaller planetesimals dominate the rates for shorter sinking times. A reasonable fit to the observationally inferred accretion rate distributions is found with model parameters consistent with a collisionally evolved mass distribution up to Pluto-mass, and an underlying accretion rate distribution consistent with that expected from descendants of debris discs of main-sequence A stars. With these parameters, while both DA and non-DA white dwarfs accrete from the same broad planetesimal distribution, this model predicts that the pollution seen in DAs is dominated by the continuous accretion of <35 km objects, and that in non-DAs by >35 km objects (though the dominant size varies between stars by around an order of magnitude from this reference value). Furthermore, observations that characterize the dependence of inferred accretion rates on sinking time and cooling age (including a consideration of the effect of thermohaline convection on models used to derive those rates), and the decadal variability of DA accretion signatures, will improve constraints on the mass distribution of accreted material and the lifetime of the disc through which it is accreted.
We investigate the evolution of the relative angle between the stellar rotation axis and the circumstellar disc axis of a star that forms in a stellar cluster from the collapse of a turbulent ...molecular cloud. This is an inherently chaotic environment with variable accretion, both in terms of rate and the angular momentum of the material, and dynamical interactions between stars. We find that the final stellar rotation axis and disc spin axis can be strongly misaligned, but this occurs primarily when the disc is truncated by a dynamical encounter so that the final disc rotation axis depends simply on what fell in last. This may lead to planetary systems with orbits that are misaligned with the stellar rotation axis, but only if the final disc contains enough mass to form planets. We also investigate the time variability of the inner-disc spin axis, which is likely to determine the direction of a protostellar jet. We find that the jet direction varies more strongly for lighter discs, such as those that have been truncated by dynamical interactions or have suffered a period of rapid accretion. Finally, we note that variability of the angular momentum of the material accreted by a star implies that the internal velocity field of such stars may be more complicated than that of aligned differential rotation.
We present a detailed study of the evolution of giant molecular clouds (GMCs) in a galactic disc simulation. We follow individual GMCs (defined in our simulations by a total column density ...criterion), including their level of star formation, from their formation to dispersal. We find the evolution of GMCs is highly complex, and GMCs cannot be considered as isolated objects. GMCs often form from a combination of smaller clouds and ambient interstellar medium (ISM), and similarly disperse by splitting into a number of smaller clouds and ambient ISM. However some clouds emerge as the result of the disruption of a more massive GMC, rather than from the assembly of smaller clouds. Likewise in some cases, clouds accrete on to more massive clouds rather than disperse. Because of the difficulty of determining a precursor or successor of a given GMC, determining GMC histories and lifetimes is highly non-trivial. Using a definition relating to the continuous evolution of a cloud, we obtain lifetimes typically of 4-25 Myr for >105 M GMCs, over which time the star formation efficiency is about 1 per cent. We also relate the lifetime of GMCs to their crossing time. We find that the crossing time is a reasonable measure of the actual lifetime of the cloud, although there is considerable scatter. The scatter is found to be unavoidable because of the complex and varied shapes and dynamics of the clouds. We study cloud dispersal in detail and find both stellar feedback and shear contribute to cloud disruption. We also demonstrate that GMCs do not behave as ridge clouds, rather massive spiral arm GMCs evolve into smaller clouds in interarm spurs.
Abstract
Supermassive black holes at the centre of galactic nuclei mostly grow in mass through gas accretion over cosmic time. This process also modifies the angular momentum (or spin) of black ...holes, both in magnitude and in orientation. Despite being often neglected in galaxy formation simulations, spin plays a crucial role in modulating accretion power, driving jet feedback, and determining recoil velocity of coalescing black hole binaries. We present a new accretion model for the moving-mesh code arepo that incorporates (i) mass accretion through a thin α-disc and (ii) spin evolution through the Bardeen–Petterson effect. We use a diverse suite of idealized simulations to explore the physical connection between spin evolution and larger scale environment. We find that black holes with mass ≲107 M⊙ experience quick alignment with the accretion disc. This favours prolonged phases of spin-up, and the spin direction evolves according to the gas inflow on time-scales as short as ≲100 Myr, which might explain the observed jet direction distribution in Seyfert galaxies. Heavier black holes (≳108 M⊙) are instead more sensitive to the local gas kinematic. Here, we find a wider distribution in spin magnitudes: spin-ups are favoured if gas inflow maintains a preferential direction, and spin-downs occur for nearly isotropic infall, while the spin direction does not change much over short time-scales ∼100 Myr. We therefore conclude that supermassive black holes with masses ≳5 × 108 M⊙ may be the ideal testbed to determine the main mode of black hole fuelling over cosmic time.
Accretion disc viscosity: how big is alpha? King, A. R.; Pringle, J. E.; Livio, M.
Monthly notices of the Royal Astronomical Society,
04/2007, Letnik:
376, Številka:
4
Journal Article
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Odprti dostop
We consider observational and theoretical estimates of the accretion disc viscosity parameter α. We find that in thin, fully ionized discs, the best observational evidence suggests a typical range α∼ ...0.1–0.4, whereas the relevant numerical simulations tend to derive estimates for α which are an order of magnitude smaller. We discuss possible reasons for this apparent discrepancy.
White dwarfs with surface magnetic fields in excess of 1 MG are found as isolated single stars and relatively more often in magnetic cataclysmic variables (CVs). Some 1253 white dwarfs with a ...detached low-mass main-sequence companion are identified in the Sloan Digital Sky Survey (SDSS) but none of these is observed to show evidence for Zeeman splitting of hydrogen lines associated with a magnetic field in excess of 1 MG. If such high magnetic fields on white dwarfs result from the isolated evolution of a single star, then there should be the same fraction of high field magnetic white dwarfs among this SDSS binary sample as among single stars. Thus, we deduce that the origin of such high magnetic fields must be intimately tied to the formation of CVs. The formation of a CV must involve orbital shrinkage from giant star to main-sequence star dimensions. It is believed that this shrinkage occurs as the low-mass companion and the white dwarf spiral together inside a common envelope. CVs emerge as very close but detached binary stars that are then brought together by magnetic braking or gravitational radiation. We propose that the smaller the orbital separation at the end of the common envelope phase, the stronger the magnetic field. The magnetic CVs originate from those common envelope systems that almost merge. We propose further that those common envelope systems that do merge are the progenitors of the single high field magnetic white dwarfs. Thus, all highly magnetic white dwarfs, be they single stars or the components of magnetic CVs, have a binary origin. This hypothesis also accounts for the relative dearth of single white dwarfs with fields of 104–106G. Such intermediate-field white dwarfs are found preferentially in CVs. In addition, the bias towards higher masses for highly magnetic white dwarfs is expected if a fraction of these form when two degenerate cores merge in a common envelope. Similar scenarios may account for very high field neutron stars. From the space density of single highly magnetic white dwarfs we estimate that about three times as many common envelope events lead to a merged core as to a CV.
Observations show that the central black hole in galaxies has a mass M of only ∼10−3 of the stellar bulge mass. Thus, whatever process grows the black hole also promotes star formation with far ...higher efficiency. We interpret this in terms of the generic tendency of active galactic nucleus (AGN) accretion discs to become self-gravitating outside some small radius Rsg∼ 0.01–0.1 pc from the black hole. We argue that mergers consist of sequences of such episodes, each limited by self-gravity to a mass ΔMepisode∼ 10−3M, with angular momentum characteristic of the small part of the accretion flow which formed it. In this picture, a major merger with ΔMmerger∼M gives rise to a long series of low-mass accretion disc episodes, all chaotically oriented with respect to one another. Thus, the angular momentum vector oscillates randomly during the accretion process, on mass-scales ∼ 103 times smaller than the total mass accreted in a major merger event. We show that for essentially all AGN parameters, the disc produced by any accretion episode of this type has lower angular momentum than the hole, allowing stable co- and counter-alignment of the discs through the Lense–Thirring effect. A sequence of randomly oriented accretion episodes as envisaged above then produces accretion discs stably co- or counter-aligned with the black hole spin with almost equal frequency. Accretion from these discs very rapidly adjusts the hole's spin parameter to average values (the precise range depending slightly on the disc vertical viscosity coefficient α2) from any initial conditions, but with significant fluctuations (Δa∼±0.2) about these. We conclude that (i) supermassive black holes (SMBH) should on average spin moderately, with the mean value decreasing slowly as the mass increases; (ii) SMBH coalescences leave little long-term effect on ; (iii) SMBH coalescence products in general have modest recoil velocities, so that there is little likelihood of their being ejected from the host galaxy; (iv) black holes can grow even from stellar masses to ∼5 × 109M⊙ at high redshift z∼ 6; and (v) jets produced in successive accretion episodes can have similar directions, but after several episodes the jet direction deviates significantly. Rare examples of massive holes with larger spin parameters could result from prograde coalescences with SMBHs of similar mass, and are most likely to be found in giant ellipticals. We compare these results with observation.
In this paper we explore numerically the evolution of a warped accretion disc. While previous analyses have concentrated on the case where the disc is thick enough that the warp propagates as a wave, ...we focus here on the opposite regime of a thin disc, where the warp evolves diffusively. By comparing the numerical results to a simple diffusion model, we are able to determine the diffusion coefficient of the warp, α2, as a function of the relevant disc parameters, such as its thickness and especially its viscosity. We find that while in general the disc behaviour is well reproduced by the diffusion model and for relatively large viscosities the warp diffusion is well described by the linear theory (in particular confirming that the warp diffusion coefficient is inversely proportional to viscosity), significant non‐linear effects are present as the viscosity becomes smaller, but still dominates over wave‐propagation effects. In particular, we find that the inverse dependence of the diffusion coefficient on viscosity breaks down at low viscosities, so that α2 never becomes larger than a saturation value αmax of the order of unity. This can have major consequences in the evolution of systems where a warped disc is present. In particular, it affects the location of the warp radius in the Bardeen–Petterson effect and therefore the spin‐up (or spin‐down) of supermassive black holes in the nuclei of galaxies. Additionally, we also find that while the rate of warp diffusion does not depend significantly on the detailed viscosity formulation, the rate of internal precession generated by the warp is strongly affected by it. Such effects should be considered with care when modelling the evolution of warped discs. This emphasizes the need to test the above results using different numerical schemes, and with higher resolution, in order to investigate the degree to which numerical simulations are able to provide accurate modelling of the complex fluid dynamics of warped discs.
Abstract
We consider the Blandford–Znajek (BZ) mechanism for extracting black hole spin energy to drive astrophysical jets. Analyses of the BZ mechanism generally take no account of any electric ...charge on the black hole. But, as noted by Wald and others, if the medium surrounding the black hole is an ionized plasma with mobile charges, then a spinning hole quickly acquires an electric charge. The effect of this charge is to nullify the electric field structures which drive the BZ mechanism. Since jets are now observed in a wide variety of classes of accreting objects, most of which do not contain a central black hole, it seems likely that the jet-driving mechanism in all astrophysical objects uses energy directly from the accretion disk, rather than black hole spin.
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