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

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

Debris Disks: Probing Planet Formation

Debris disks are the dust disks found around ~20% of nearby main sequence stars in far-IR surveys. They can be considered as descendants of protoplanetary disks or components of planetary systems, providing valuable information on circumstellar disk evolution and the outcome of planet formation. The debris disk population can be explained by the steady collisional erosion of planetesimal belts; population models constrain where (10-100au) and in what quantity (>1Mearth) planetesimals (>10km in size) typically form in protoplanetary disks. Gas is now seen long into the debris disk phase. Some of this is secondary implying planetesimals have a Solar System comet-like composition, but some systems may retain primordial gas. Ongoing planet formation processes are invoked for some debris disks, such as the continued growth of dwarf planets in an unstirred disk, or the growth of terrestrial planets through giant impacts. Planets imprint structure on debris disks in many ways; images of gaps, clumps, warps, eccentricities and other disk asymmetries, are readily explained by planets at >>5au. Hot dust in the region planets are commonly found (<5au) is seen for a growing number of stars. This dust usually originates in an outer belt (e.g., from exocomets), although an asteroid belt or recent collision is sometimes inferred.Comment: Invited review, accepted for publication in the 'Handbook of Exoplanets', eds. H.J. Deeg and J.A. Belmonte, Springer (2018

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

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

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)

ALMA long baseline phase calibration using phase referencing

© 2016 SPIE.The Atacama Large Millimeter/submillimeter Array (ALMA) is the world's largest millimeter/submillimeter telescope and provides unprecedented sensitivities and spatial resolutions. To achieve the highest imaging capa- bilities, interferometric phase calibration for the long baselines is one of the most important subjects: The longer the baselines, the worse the phase stability becomes because of turbulent motions of the Earth's atmosphere, es- pecially, the water vapor in the troposphere. To overcome this subject, ALMA adopts a phase correction scheme using a Water Vapor Radiometer (WVR) to estimate the amount of water vapor content along the antenna line of sight. An additional technique is phase referencing, in which a science target and a nearby calibrator are observed by turn by quickly changing the antenna pointing. We conducted feasibility studies of the hybrid technique with the WVR phase correction and the antenna Fast Switching (FS) phase referencing (WVR+FS phase correction) for the ALMA 16 km longest baselines in cases that (1) the same observing frequency both for a target and calibrator is used, and (2) higher and lower frequencies for a target and calibrator, respectively, with a typical switching cycle time of 20 s. It was found that the phase correction performance of the hybrid technique is promising where a nearby calibrator is located within roughly 3? from a science target, and that the phase correction with 20 s switching cycle time significantly improves the performance with the above separation angle criterion comparing to the 120 s switching cycle time. The currently trial phase calibration method shows the same performance independent of the observing frequencies. This result is especially important for the higher frequency observations because it becomes difficult to find a bright calibrator close to an arbitrary sky position. In the series of our experiments, it is also found that phase errors affecting the image quality come from not only the water vapor content in the lower troposphere but also a large structure of the atmosphere with a typical cell scale of a few tens of kilometers

ALMA long baseline phase calibration using phase referencing

© 2016 SPIE.The Atacama Large Millimeter/submillimeter Array (ALMA) is the world's largest millimeter/submillimeter telescope and provides unprecedented sensitivities and spatial resolutions. To achieve the highest imaging capa- bilities, interferometric phase calibration for the long baselines is one of the most important subjects: The longer the baselines, the worse the phase stability becomes because of turbulent motions of the Earth's atmosphere, es- pecially, the water vapor in the troposphere. To overcome this subject, ALMA adopts a phase correction scheme using a Water Vapor Radiometer (WVR) to estimate the amount of water vapor content along the antenna line of sight. An additional technique is phase referencing, in which a science target and a nearby calibrator are observed by turn by quickly changing the antenna pointing. We conducted feasibility studies of the hybrid technique with the WVR phase correction and the antenna Fast Switching (FS) phase referencing (WVR+FS phase correction) for the ALMA 16 km longest baselines in cases that (1) the same observing frequency both for a target and calibrator is used, and (2) higher and lower frequencies for a target and calibrator, respectively, with a typical switching cycle time of 20 s. It was found that the phase correction performance of the hybrid technique is promising where a nearby calibrator is located within roughly 3? from a science target, and that the phase correction with 20 s switching cycle time significantly improves the performance with the above separation angle criterion comparing to the 120 s switching cycle time. The currently trial phase calibration method shows the same performance independent of the observing frequencies. This result is especially important for the higher frequency observations because it becomes difficult to find a bright calibrator close to an arbitrary sky position. In the series of our experiments, it is also found that phase errors affecting the image quality come from not only the water vapor content in the lower troposphere but also a large structure of the atmosphere with a typical cell scale of a few tens of kilometers

Exocometary gas in the HD 181327 debris ring

An increasing number of observations have shown that gaseous debris discs are not an exception. However, until now, we only knew of cases around A stars. Here we present the first detection of 12CO (2-1) disc emission around an F star, HD 181327, obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) observations at 1.3 mm. The continuum and CO emission are resolved into an axisymmetric disc with ring-like morphology. Using a Markov chain Monte Carlo method coupled with radiative transfer calculations, we study the dust and CO mass distribution. We find the dust is distributed in a ring with a radius of 86.0 ± 0.4 au and a radial width of 23.2 ± 1.0 au. At this frequency, the ring radius is smaller than in the optical, revealing grain size segregation expected due to radiation pressure. We also report on the detection of low-level continuum emission beyond the main ring out to ~200 au. We model the CO emission in the non-local thermodynamic equilibrium regime and we find that the CO is co-located with the dust, with a total CO gas mass ranging between 1.2 × 10-6 M⊕ and 2.9 × 10-6 M⊕, depending on the gas kinetic temperature and collisional partners densities. The CO densities and location suggest a secondary origin, i.e. released from icy planetesimals in the ring. We derive a CO+CO2 cometary composition that is consistent with Solar system comets. Due to the low gas densities, it is unlikely that the gas is shaping the dust distribution.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. This work was supported by the European Union through ERC grant number 279973. SM, SC, SP acknowledge financial support from Millennium Nucleus RC130007 (Chilean Ministry of Economy), and additionally by FONDECYT grants 1130949 and 3140601. GMK is supported by the Royal Society as a Royal Society University Research Fellow