The observable effects of tidally induced warps in protostellar discs

We consider the response of a protostellar disc to a tidally induced warp and the resultant changes in the spectral energy distribution (SED). We argue that for typical protostellar disc parameters the warp is communicated through the disc in a wave-like fashion. We find that the main effects of the warp tend to be at large radii (greater than 30 AU) and, for sufficiently small viscosity, can be quite long-lived. This can result in non-uniform illumination of the disc at these radii and can induce significant changes to the SED at wavelengths greater than 100 microns.Comment: 7 pages, 9 figures. Accepted by MNRA

Rigidity of Frameworks Supported on Surfaces

A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in \bR^2. A more general theory is developed for frameworks in \bR^3 whose vertices are constrained to move on a two-dimensional smooth submanifold \M. Furthermore, when \M is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.Comment: Final version, 28 pages, with new figure

Retrograde Accretion and Merging Supermassive Black Holes

We investigate whether a circumbinary gas disc can coalesce a supermassive black hole binary system in the centre of a galaxy. This is known to be problematic for a prograde disc. We show that in contrast, interaction with a retrograde circumbinary disc is considerably more effective in shrinking the binary because there are no orbital resonances. The binary directly absorbs negative angular momentum from the circumbinary disc by capturing gas into a disc around the secondary black hole, or discs around both holes if the binary mass ratio is close to unity. In many cases the binary orbit becomes eccentric, shortening the pericentre distance as the eccentricity grows. In all cases the binary coalesces once it has absorbed the angular momentum of a gas mass comparable to that of the secondary black hole. Importantly, this conclusion is unaffected even if the gas inflow rate through the disc is formally super--Eddington for either hole. The coalescence timescale is therefore always $\sim M_2/\dot M$, where $M_2$ is the secondary black hole mass and $\dot M$ the inflow rate through the circumbinary disc.Comment: 8 pages, 4 figures. Accepted for publication in MNRAS. Movies of the simulations can be found at: http://www.astro.le.ac.uk/users/cjn12/RetroBinaryMovies.htm

Do stiffness and asymmetries predict change of direction performance?

Change of direction speed (CODS) underpins performance in a wide range of sports but little is known about how stiffness and asymmetries affect CODS. Eighteen healthy males performed unilateral drop jumps to determine vertical, ankle, knee and hip stiffness, and a CODS test to evaluate left and right leg cutting performance during which ground reaction force data were sampled. A step-wise regression analysis was performed to ascertain the determinants of CODS time. A two-variable regression model explained 63% (R-2 = 0.63; P = 0.001) of CODS performance. The model included the mean vertical stiffness and jump height asymmetry determined during the drop jump. Faster athletes (n = 9) exhibited greater vertical stiffness (F = 12.40; P = 0.001) and less asymmetry in drop jump height (F = 6.02; P = 0.026) than slower athletes (n = 9); effect sizes were both "large" in magnitude. Results suggest that overall vertical stiffness and drop jump height asymmetry are the strongest predictors of CODS in a healthy, non-athletic population

Modeling quasar accretion disc temperature profiles

Microlensing observations indicate that quasar accretion discs have half-light radii larger than expected from standard theoretical predictions based on quasar fluxes or black hole masses. Blackburne and colleagues have also found a very weak wavelength dependence of these half-light radii. We consider disc temperature profile models that might match these observations. Nixon and colleagues have suggested that misaligned accretion discs around spinning black holes will be disrupted at radii small enough for the Lense-Thirring torque to overcome the disc's viscous torque. Gas in precessing annuli torn off a disc will spread radially and intersect with the remaining disc, heating the disc at potentially large radii. However, if the intersection occurs at an angle of more than a degree or so, highly supersonic collisions will shock-heat the gas to a Compton temperature of T~10^7 K, and the spectral energy distributions (SEDs) of discs with such shock-heated regions are poor fits to observations of quasar SEDs. Torn discs where heating occurs in intermittent weak shocks that occur whenever the intersection angle reaches a tenth of a degree pose less of a conflict with observations, but do not have significantly larger half-light radii than standard discs. We also study two phenomenological disc temperature profile models. We find that discs with a temperature spike at relatively large radii and lowered temperatures at radii inside the spike yield improved and acceptable fits to microlensing sizes in most cases. Such temperature profiles could in principle occur in sub-Keplerian discs partially supported by magnetic pressure. However, such discs overpredict the fluxes from quasars studied with microlensing except in the limit of negligible continuum emission from radii inside the temperature spike.Comment: Submitted to MNRAS. Comments welcome. 20 pages, 5 figure

Methods of editing cloud and atmospheric layer affected pixels from satellite data

Subvisible cirrus clouds (SCi) were easily distinguished in mid-infrared (MIR) TIROS-N daytime data from south Texas and northeast Mexico. The MIR (3.55-3.93 micrometer) pixel digital count means of the SCi affected areas were more than 3.5 standard deviations on the cold side of the scene means. (These standard deviations were made free of the effects of unusual instrument error by factoring out the Ch 3 MIR noise on the basis of detailed examination of noisy and noise-free pixels). SCi affected areas in the IR Ch 4 (10.5-11.5 micrometer) appeared cooler than the general scene, but were not as prominent as in Ch 3, being less than 2 standard deviations from the scene mean. Ch 3 and 4 standard deviations and coefficients of variation are not reliable indicators, by themselves, of the presence of SCi because land features can have similar statistical properties

Methods of editing cloud and atmospheric layer affected pixels from satellite data

The location and migration of cloud, land and water features were examined in spectral space (reflective VIS vs. emissive IR). Daytime HCMM data showed two distinct types of cloud affected pixels in the south Texas test area. High altitude cirrus and/or cirrostratus and "subvisible cirrus" (SCi) reflected the same or only slightly more than land features. In the emissive band, the digital counts ranged from 1 to over 75 and overlapped land features. Pixels consisting of cumulus clouds, or of mixed cumulus and landscape, clustered in a different area of spectral space than the high altitude cloud pixels. Cumulus affected pixels were more reflective than land and water pixels. In August the high altitude clouds and SCi were more emissive than similar clouds were in July. Four-channel TIROS-N data were examined with the objective of developing a multispectral screening technique for removing SCi contaminated data