Unstable Disk Galaxies. II. the Origin of Growing and Stationary Modes

I decompose the unstable growing modes of stellar disks to their Fourier components and present the physical mechanism of instabilities in the context of resonances. When the equilibrium distribution function is a non-uniform function of the orbital angular momentum, the capture of stars into the corotation resonance imbalances the disk angular momentum and triggers growing bar and spiral modes. The stellar disk can then recover its angular momentum balance through the response of non-resonant stars. I carry out a complete analysis of orbital structure corresponding to each Fourier component in the radial angle, and present a mathematical condition for the occurrence of van Kampen modes, which constitute a continuous family. I discuss on the discreteness and allowable pattern speeds of unstable modes and argue that the mode growth is saturated due to the resonance overlapping mechanism. An individually growing mode can also be suppressed if the corotation and inner Lindblad resonances coexist and compete to capture a group of stars. Based on this mechanism, I show that self-consistent scale-free disks with a sufficient distribution of non-circular orbits should be stable under perturbations of angular wavenumber $m>1$. I also derive a criterion for the stability of stellar disks against non-axisymmetric excitations.Comment: 15 Pages (emulateapj), 7 Figures, Accepted for Publication in The Astrophysical Journa

Self-gravitating warped discs around supermassive black holes

We consider warped equilibrium configurations for stellar and gaseous disks in the Keplerian force-field of a supermassive black hole, assuming that the self-gravity of the disk provides the only acting torques. Modeling the disk as a collection of concentric circular rings, and computing the torques in the non-linear regime, we show that stable, strongly warped precessing equilibria are possible. These solutions exist for a wide range of disk-to-black hole mass ratios $M_d/M_{bh}$, can span large warp angles of up to $\pm\sim 120\deg$, have inner and outer boundaries, and extend over a radial range of a factor of typically two to four. These equilibrium configurations obey a scaling relation such that in good approximation \phidot/\Omega\propto M_d/M_{bh} where \phidot is the (retrograde) precession frequency and $\Omega$ is a characteristic orbital frequency in the disk. Stability was determined using linear perturbation theory and, in a few cases, confirmed by numerical integration of the equations of motion. Most of the precessing equilibria are found to be stable, but some are unstable. The main result of this study is that highly warped disks near black holes can persist for long times without any persistent forcing other than by their self-gravity. The possible relevance of this to galactic nuclei is briefly discussed.Comment: 13 pages, 21 figures, published in MNRA

Tidal torques. A critical review of some techniques

We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This necessitates corrections in the theory of tidal despinning and libration damping. We prove that when the inclination is low and phase lags are linear in frequency, the Kaula series is equivalent to a corrected version of the MacDonald method. The correction to MacDonald's approach would be to set the phase lag of the integral bulge proportional to the instantaneous frequency. The equivalence of descriptions gets violated by a nonlinear frequency-dependence of the lag. We explain that both the MacDonald- and Darwin-torque-based derivations of the popular formula for the tidal despinning rate are limited to low inclinations and to the phase lags being linear in frequency. The Darwin-torque-based derivation, though, is general enough to accommodate both a finite inclination and the actual rheology. Although rheologies with Q scaling as the frequency to a positive power make the torque diverge at a zero frequency, this reveals not the impossible nature of the rheology, but a flaw in mathematics, i.e., a common misassumption that damping merely provides lags to the terms of the Fourier series for the tidal potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the magnitudes of the terms, too, get changed. Reinstating of this detail tames the infinities and rehabilitates the "impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial text overlap with arXiv:0712.105

The role of chaotic resonances in the solar system

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure

Morphological, physiological and behavioural evaluation of a ‘Mice in Space’ housing system

Environmental conditions likely affect physiology and behaviour of mice used for life sciences research on Earth or in Space. Here, we analysed the effects of cage confinement on the weightbearing musculoskeletal system, behaviour and stress of wild-type mice (C57BL/6JRj, 30 g b.wt., total n = 24) housed for 25 days in a prototypical ground-based and fully automated life support habitat device called “Mice in Space” (MIS). Compared with control housing (individually ventilated cages) the MIS mice revealed no significant changes in soleus muscle size and myofiber distribution (type I vs. II) and quality of bone (3-D microarchitecture and mineralisation of calvaria, spine and femur) determined by confocal and micro-computed tomography. Corticosterone metabolism measured non-invasively (faeces) monitored elevated adrenocortical activity at only start of the MIS cage confinement (day 1). Behavioural tests (i.e., grip strength, rotarod, L/D box, elevated plus-maze, open field, aggressiveness) performed subsequently revealed only minor changes in motor performance (MIS vs. controls). The MIS habitat will not, on its own, produce major effects that could confound interpretation of data induced by microgravity exposure during spaceflight. Our results may be even more helpful in developing multidisciplinary protocols with adequate scenarios addressing molecular to systems levels using mice of various genetic phenotypes in many laboratories

Habitable Zones in the Universe

Habitability varies dramatically with location and time in the universe. This was recognized centuries ago, but it was only in the last few decades that astronomers began to systematize the study of habitability. The introduction of the concept of the habitable zone was key to progress in this area. The habitable zone concept was first applied to the space around a star, now called the Circumstellar Habitable Zone. Recently, other, vastly broader, habitable zones have been proposed. We review the historical development of the concept of habitable zones and the present state of the research. We also suggest ways to make progress on each of the habitable zones and to unify them into a single concept encompassing the entire universe.Comment: 71 pages, 3 figures, 1 table; to be published in Origins of Life and Evolution of Biospheres; table slightly revise