How to play a disc brake

We consider a gyroscopic system under the action of small dissipative and non-conservative positional forces, which has its origin in the models of rotating bodies of revolution being in frictional contact. The spectrum of the unperturbed gyroscopic system forms a "spectral mesh" in the plane "frequency -gyroscopic parameter" with double semi-simple purely imaginary eigenvalues at zero value of the gyroscopic parameter. It is shown that dissipative forces lead to the splitting of the semi-simple eigenvalue with the creation of the so-called "bubble of instability" - a ring in the three-dimensional space of the gyroscopic parameter and real and imaginary parts of eigenvalues, which corresponds to complex eigenvalues. In case of full dissipation with a positive-definite damping matrix the eigenvalues of the ring have negative real parts making the bubble a latent source of instability because it can "emerge" to the region of eigenvalues with positive real parts due to action of both indefinite damping and non-conservative positional forces. In the paper, the instability mechanism is analytically described with the use of the perturbation theory of multiple eigenvalues. As an example stability of a rotating circular string constrained by a stationary load system is studied in detail. The theory developed seems to give a first clear explanation of the mechanism of self-excited vibrations in the rotating structures in frictional contact, that is responsible for such well-known phenomena of acoustics of friction as the squealing disc brake and the singing wine glass.Comment: 25 pages, 9 figures, Presented at BIRS 07w5068 Workshop "Geometric Mechanics: Continuous and discrete, finite and infinite dimensional", August 12-17, 2007, Banff, Canad

Exocometary gas structure, origin and physical properties around β Pictoris through ALMA CO multitransition observations

Recent ALMA observations unveiled the structure of CO gas in the 23 Myr-old $\beta$ Pictoris planetary system, a component that has been discovered in many similarly young debris disks. We here present ALMA CO J=2-1 observations, at an improved spectro-spatial resolution and sensitivity compared to previous CO J=3-2 observations. We find that 1) the CO clump is radially broad, favouring the resonant migration over the giant impact scenario for its dynamical origin, 2) the CO disk is vertically tilted compared to the main dust disk, at an angle consistent with the scattered light warp. We then use position-velocity diagrams to trace Keplerian radii in the orbital plane of the disk. Assuming a perfectly edge-on geometry, this shows a CO scale height increasing with radius as $R^{0.75}$, and an electron density (derived from CO line ratios through NLTE analysis) in agreement with thermodynamical models. Furthermore, we show how observations of optically thin line ratios can solve the primordial versus secondary origin dichotomy in gas-bearing debris disks. As shown for $\beta$ Pictoris, subthermal (NLTE) CO excitation is symptomatic of H$_2$ densities that are insufficient to shield CO from photodissociation over the system's lifetime. This means that replenishment from exocometary volatiles must be taking place, proving the secondary origin of the disk. In this scenario, assuming steady state production/destruction of CO gas, we derive the CO+CO$_2$ ice abundance by mass in $\beta$ Pic's exocomets to be at most $\sim$6%, consistent with comets in our own Solar System and in the coeval HD181327 system.LM acknowledges support by STFC and ESO through graduate studentships and, together with MCW and QK, by the European Union through ERC grant number 279973. Work of OP is funded by the Royal Society Dorothy Hodgkin Fellowship, and AMH gratefully acknowledges support from NSF grant AST-1412647.This is the final version of the article. It first appeared from Oxford University Press via https://doi.org/10.1093/mnras/stw241

Gas and dust around A-type stars at tens of Myr: signatures of cometary breakup

Discs of dusty debris around main-sequence stars indicate fragmentation of orbiting planetesimals, and for a few A-type stars, a gas component is also seen that may come from collisionally released volatiles. Here we find the sixth example of a CO-hosting disc, around the ∼30 Myr-old A0-star HD 32997. Two more of these CO-hosting stars, HD 21997 and 49 Cet, have also been imaged in dust with SCUBA-2 within the SCUBA-2 Survey of Nearby Stars project. A census of 27 A-type debris hosts within 125 pc now shows 7/16 detections of carbon-bearing gas within the 5–50 Myr epoch, with no detections in 11 older systems. Such a prolonged period of high fragmentation rates corresponds quite well to the epoch when most of the Earth was assembled from planetesimal collisions. Recent models propose that collisional products can be spatially asymmetric if they originate at one location in the disc, with CO particularly exhibiting this behaviour as it can photodissociate in less than an orbital period. Of the six CO-hosting systems, only β Pic is in clear support of this hypothesis. However, radiative transfer modelling with the ProDiMo code shows that the CO is also hard to explain in a proto-planetary disc context.JSG and PW thank the ERC for funding for project DiscAnalysis, under the grant FP7-SPACE-2011 collaborative project 284405. JPM is supported by a UNSW Vice-Chancellor's postdoctoral fellowship. MCW and LM acknowledge the support of the European Union through ERC grant 279973. The JCMT is operated by the East Asian Observatory on behalf of The National Astronomical Observatory of Japan, Academia Sinica Institute of Astronomy and Astrophysics, the Korea Astronomy and Space Science Institute, the National Astronomical Observatories of China and the Chinese Academy of Sciences (Grant No. XDB09000000), with additional funding support from the Science and Technology Facilities Council of the United Kingdom and participating universities in the United Kingdom and Canada. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ

PedGenie: meta genetic association testing in mixed family and case-control designs

<p>Abstract</p> <p>Background-</p> <p>PedGenie software, introduced in 2006, includes genetic association testing of cases and controls that may be independent or related (nuclear families or extended pedigrees) or mixtures thereof using Monte Carlo significance testing. Our aim is to demonstrate that PedGenie, a unique and flexible analysis tool freely available in Genie 2.4 software, is significantly enhanced by incorporating meta statistics for detecting genetic association with disease using data across multiple study groups.</p> <p>Methods-</p> <p>Meta statistics (chi-squared tests, odds ratios, and confidence intervals) were calculated using formal Cochran-Mantel-Haenszel techniques. Simulated data from unrelated individuals and individuals in families were used to illustrate meta tests and their empirically-derived p-values and confidence intervals are accurate, precise, and for independent designs match those provided by standard statistical software.</p> <p>Results-</p> <p>PedGenie yields accurate Monte Carlo p-values for meta analysis of data across multiple studies, based on validation testing using pedigree, nuclear family, and case-control data simulated under both the null and alternative hypotheses of a genotype-phenotype association.</p> <p>Conclusion-</p> <p>PedGenie allows valid combined analysis of data from mixtures of pedigree-based and case-control resources. Added meta capabilities provide new avenues for association analysis, including pedigree resources from large consortia and multi-center studies.</p

ALMA observations of the η Corvi debris disc: Inward scattering of CO-rich exocomets by a chain of 3-30 M⊕ planets?

While most of the known debris discs present cold dust at tens of astronomical unit (au), a few young systems exhibit hot dust analogous to the Zodiacal dust. η Corvi is particularly interesting as it is old and it has both, with its hot dust significantly exceeding the maximum luminosity of an in situ collisional cascade. Previous work suggested that this system could be undergoing an event similar to the Late Heavy Bombardment (LHB) soon after or during a dynamical instability. Here, we present ALMA observations of η Corvi with a resolution of 1.2 arcsec (~22 au) to study its outer belt. The continuum emission is consistent with an axisymmetric belt, with a mean radius of 152 au and radial full width at half-maximum of 46 au, which is too narrow compared to models of inward scattering of an LHB-like scenario. Instead, the hot dust could be explained as material passed inwards in a rather stable planetary configuration. We also report a 4σ detection of CO at ~20 au. CO could be released in situ from icy planetesimals being passed in when crossing the H2O or CO2 ice lines. Finally, we place constraints on hidden planets in the disc. If a planet is sculpting the disc's inner edge, this should be orbiting at 75-100 au, with a mass of 3-30M⊕ and an eccentricity < 0.08. Such a planet would be able to clear its chaotic zone on a time-scale shorter than the age of the system and scatter material inwards from the outer belt to the inner regions, thus feeding the hot dust.ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. MCW, LM, AB and QK acknowledge the support of the European Union through ERC grant number 279973. LM also acknowledges support by STFC through a graduate studentship. The work of OP is supported by the Royal Society Dorothy Hodgkin Fellowship. GMK is supported by the Royal Society as a Royal Society University Research Fellow

Circumstellar discs: What will be next?

This prospective chapter gives our view on the evolution of the study of circumstellar discs within the next 20 years from both observational and theoretical sides. We first present the expected improvements in our knowledge of protoplanetary discs as for their masses, sizes, chemistry, the presence of planets as well as the evolutionary processes shaping these discs. We then explore the older debris disc stage and explain what will be learnt concerning their birth, the intrinsic links between these discs and planets, the hot dust and the gas detected around main sequence stars as well as discs around white dwarfs.Comment: invited review; comments welcome (32 pages

A planetary system as the origin of structure in Fomalhaut's dust belt

The Sun and >15 percent of nearby stars are surrounded by dusty debris disks that must be collisionally replenished by asteroids and comets, as the dust would otherwise be depleted on <10 Myr timescales (ref. 1). Theoretical studies show that disk structure can be modified by the gravitational influence of planets (ref. 2-4), but the observational evidence is incomplete, at least in part because maps of the thermal infrared emission from disks have low linear resolution (35 AU in the best case; ref. 5). Optical images provide higher resolution, but the closest examples (AU Mic and Beta Pic) are edge-on (ref. 6,7), preventing the direct measurement of azimuthal and radial disk structure that is required for fitting theoretical models of planetary perturbations. Here we report the detection of optical light reflected from the dust grains orbiting Fomalhaut (HD 216956). The system is inclined 24 degrees away from edge-on, enabling the measurement of disk structure around its entire circumference, at a linear resolution of 0.5 AU. The dust is distributed in a belt 25 AU wide, with a very sharp inner edge at a radial distance of 133 AU, and we measure an offset of 15 AU between the belt's geometric centre and Fomalhaut. Taken together, the sharp inner edge and offset demonstrate the presence of planet-mass objects orbiting Fomalhaut.Comment: 8 pages, 3 figures, 1 tabl

The Northern Arc of ε Eridani’s Debris Ring as Seen by ALMA

We present the first Atacama Large Millimeter/submillimeter Array (ALMA) observations of the closest known extrasolar debris disc. This disc orbits the star ε Eri, a K-type star just 3.2 pc away. Due to the proximity of the star, the entire disc cannot fit within the ALMA field of view. Therefore, the observations have been centred 18" North of the star, providing us with a clear detection of the Northern arc of the ring, at a wavelength of 1.3 mm. The observed disc emission is found to be narrow with a width of just 11–13 AU. The fractional disc width we find is comparable to that of the Solar system’s Kuiper Belt and makes this one of the narrowest debris discs known. If the inner and outer edges are due to resonances with a planet then this planet likely has a semi-major axis of 48 AU. We find tentative evidence for clumps in the ring, although there is a strong chance that at least one is a background galaxy. We confirm, at much higher significance, the previous detection of an unresolved emission at the star that is above the level of the photosphere and attribute this excess to stellar chromospheric emission.MB acknowledges support from a FONDECYT Postdoctoral Fellowship, project no. 3140479 and the Deutsche Forschungsgemeinschaft (DFG) through project no. Kr 2164/15-1. AJ and SC acknowledge financial support from the Millennium Nucleus RC130007 (Chilean Ministry of Economy). AJ acknowledges support from FONDECYT project no. 1130857, BASAL CATA PFB-06 and the Ministry for the Economy, Development, and Tourism’s Programa Iniciativa Cient´ıfica Milenio through grant no. IC 120009, awarded to the Millennium Institute of Astrophysics (MAS). MCW acknowledges the support of the European Union through ERC grant no. 279973. GMK is supported by the Royal Society as a Royal Society University Research Fellow. JCA acknowledges support from PNP/CNES. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00645.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research made use of Astropy, a community-developed core PYTHON package for Astronomy (Astropy Collaboration et al. 2013)

Herschel images of Fomalhaut An extrasolar Kuiper belt at the height of its dynamical activity

Context. Fomalhaut is a young (2 ± 1 × 108 years), nearby (7.7 pc), 2 M⊙ star that is suspected to harbor an infant planetary system, interspersed with one or more belts of dusty debris. Aims. We present far-infrared images obtained with the Herschel Space Observatory with an angular resolution between 5.7′′ and 36.7′′ at wavelengths between 70 μm and 500 μm. The images show the main debris belt in great detail. Even at high spatial resolution, the belt appears smooth. The region in between the belt and the central star is not devoid of material; thermal emission is observed here as well. Also at the location of the star, excess emission is detected. We aim to construct a consistent image of the Fomalhaut system. Methods. We use a dynamical model together with radiative-transfer tools to derive the parameters of the debris disk. We include detailed models of the interaction of the dust grains with radiation, for both the radiation pressure and the temperature determination. Comparing these models to the spatially resolved temperature information contained in the images allows us to place strong constraints on the presence of grains that will be blown out of the system by radiation pressure. We use this to derive the dynamical parameters of the system. Results. The appearance of the belt points toward a remarkably active system in which dust grains are produced at a very high rate by a collisional cascade in a narrow region filled with dynamically excited planetesimals. Dust particles with sizes below the blow-out size are abundantly present. The equivalent of 2000 one-km-sized comets are destroyed every day, out of a cometary reservoir amounting to 110 Earth masses. From comparison of their scattering and thermal properties, we find evidence that the dust grains are fluffy aggregates, which indicates a cometary origin. The excess emission at the location of the star may be produced by hot dust with a range of temperatures, but may also be due to gaseous free-free emission from a stellar wind