Dust production in debris discs: constraints on the smallest grains

The surface energy constraint puts a limit on the smallest fragment $s_{surf}$ that can be produced after a collision. Based on analytical considerations, this mechanism has been recently identified as been potentially able to prevent the production of small dust grains in debris discs and cut off their size distribution at sizes larger than the blow-out size. We numerically investigate the importance of this effect to find under which conditions it can leave a signature in the small-size end of a disc's particle size distribution (PSD). An important part of this work is to map out, in a disc at steady-state, what is the most likely collisional origin for micron-sized grains, in terms of the sizes of their collisional progenitors. We implement, for the first time, the surface energy constraint into a collisional evolution code. We consider a debris disc extending from 50 to 100AU and 2 different stellar types. We also consider two levels of stirring in the disc: dynamically "hot" (e=0.075) and "cold" (e=0.01). For all cases, we derive $s_{surf}$ maps as a function of target and projectile sizes, $s_t$ and $s_p$, and compare them to equivalent maps for the dust-production rate. We then compute disc-integrated PSDs and estimate the imprint of the surface energy constraint. We find that the ($s_p$,$s_t$) regions of high $s_{surf}$ values do not coincide with those of high dust production rate. As a consequence, the surface energy constraint has generally a weak effect on the system's PSD. The maximum $s_{surf}$-induced depletion of $\mu$m-sized grains is $\sim 30$% and is obtained for a sun-like star and a dynamically hot case. For the e=0.01 cases, the surface energy effect is negligible compared to the massive small grain depletion induced by another mechanism: the natural imbalance between dust production and destruction rates in low-stirring discs identified by Thebault&Wu(2008).Comment: Accepted for Publication in A&A (abstract truncated for astroph) (v3 and v4 corrected from minor language errors and typos

Schrodinger Evolution for the Universe: Reparametrization

Starting from a generalized Hamilton-Jacobi formalism, we develop a new framework for constructing observables and their evolution in theories invariant under global time reparametrizations. Our proposal relaxes the usual Dirac prescription for the observables of a totally constrained system (`perennials') and allows one to recover the influential partial and complete observables approach in a particular limit. Difficulties such as the non-unitary evolution of the complete observables in terms of certain partial observables are explained as a breakdown of this limit. Identification of our observables (`mutables') relies upon a physical distinction between gauge symmetries that exist at the level of histories and states (`Type 1'), and those that exist at the level of histories and not states (`Type 2'). This distinction resolves a tension in the literature concerning the physical interpretation of the partial observables and allows for a richer class of observables in the quantum theory. There is the potential for the application of our proposal to the quantization of gravity when understood in terms of the Shape Dynamics formalism.Comment: 25 pages (including title page and references), 1 figur

Symplectic reduction and the problem of time in nonrelativistic mechanics

The deep connection between the interpretation of theories invariant under local symmetry transformations (i.e. gauge theories) and the philosophy of space and time can be illustrated nonrelativistically via the investigation of reparameterisation invariant reformulations of Newtonian mechanics, such as Jacobi's theory. Like general relativity, the canonical formulation of such theories feature Hamiltonian constraints; and like general relativity, the interpretation of these constraints along conventional Dirac lines is highly problematic in that it leads to a nonrelativistic variant of the infamous problem of time. I argue that, nonrelativistically at least, the source of the problem can be found precisely within the symplectic reduction that goes along with strict adherence to the Dirac view. Avoiding reduction, two viable alternative strategies for dealing with Hamiltonian constraints are available. Each is found to lead us to a novel and interesting re-conception of time and change within nonrelativistic mechanics. Both these strategies and the failure of reduction have important implications for the debate concerning the relational or absolute status of time within physical theory

Transient events in bright debris discs: Collisional avalanches revisited

A collisional avalanche is set off by the breakup of a large planetesimal, releasing small unbound grains that enter a debris disc located further away from the star, triggering there a collisional chain reaction that can potentially create detectable transient structures. We explore this mechanism, using for the first time a code coupling dynamical and collisional evolutions, and investigate if avalanches could explain the short-term luminosity variations observed in some extremely bright discs. We consider two set-ups: a cold disc case, with a dust release at 10au and an outer disc extending from 50 to 120au, and a warm disc case with the release at 1au and a 5-12au outer disc. We find that avalanches could leave detectable structures on resolved images, for both cold and warm disc cases, in discs with optical depth $\tau$ of a few $10^{-3}$, provided that large dust masses ($\gtrsim$10$^{20}$-5$\times$10$^{22}$g) are initially released. The integrated photometric excess due to an avalanche is limited, less than 10% for these released dust masses, peaking in the mid-IR and becoming insignificant beyond $\sim$40-50$\mu$m. Contrary to earlier studies, we do not obtain stronger avalanches when increasing $\tau$ to higher values. Likewise, we do not observe a significant luminosity deficit, as compared to the pre-avalanche level, after the passage of the avalanche. These two results concur to make avalanches an unlikely explanation for the sharp luminosity drops observed in some extremely bright debris discs. The ideal configuration for observing an avalanche would be a two-belt structure, with an inner belt of fractional luminosity >10$^{-4}$ where breakups of massive planetesimals occur, and a more massive outer belt, with $\tau$ of a few $10^{-3}$, into which the avalanche chain reaction develops and propagates.Comment: Accepted for publication in Astronomy & Astrophysics (abstract drastically shortened to meet astro-ph requirements

Planet Signatures in Collisionally Active Debris Discs: scattered light images

Planet perturbations are often invoked as a potential explanation for many spatial structures that have been imaged in debris discs. So far this issue has been mostly investigated with collisionless N-body numerical models. We numerically investigate how the coupled effect of collisions and radiation pressure can affect the formation and survival of radial and azimutal structures in a disc perturbed by a planet. We consider two set-ups: a planet embedded within an extended disc and a planet exterior to an inner debris ring. We use the DyCoSS code of Thebault(2012) and derive synthetic images of the system in scattered light. The planet's mass and orbit, as well as the disc's collisional activity are explored as free parameters. We find that collisions always significantly damp planet-induced structures. For the case of an embedded planet, the planet's signature, mostly a density gap around its radial position, should remain detectable in head-on images if M_planet > M_Saturn. If the system is seen edge-on, however, inferring the presence of the planet is much more difficult, although some planet-induced signatures might be observable under favourable conditions. For the inner-ring/external-planet case, planetary perturbations cannot prevent collision-produced small fragments from populating the regions beyond the ring: The radial luminosity profile exterior to the ring is close to the one it should have in the absence of the planet. However, a Jovian planet on a circular orbit leaves precessing azimutal structures that can be used to indirectly infer its presence. For a planet on an eccentric orbit, the ring is elliptic and the pericentre glow effect is visible despite of collisions and radiation pressure, but detecting such features in real discs is not an unambiguous indicator of the presence of an outer planet.Comment: Accepted for Publication in A&A (NOTE: Abridged abstract and (very)LowRes Figures. Better version, with High Res figures and full abstract can be found at http://lesia.obspm.fr/perso/philippe-thebault/planpapph.pdf

Scattering of small bodies by planets: a potential origin for exozodiacal dust ?

High levels of exozodiacal dust are observed around a growing number of main sequence stars. The origin of such dust is not clear, given that it has a short lifetime against both collisions and radiative forces. Even a collisional cascade with km-sized parent bodies, as suggested to explain outer debris discs, cannot survive sufficiently long. In this work we investigate whether the observed exozodiacal dust could originate from an outer planetesimal belt. We investigate the scattering processes in stable planetary systems in order to determine whether sufficient material could be scattered inwards in order to retain the exozodiacal dust at its currently observed levels. We use N-body simulations to investigate the efficiency of this scattering and its dependence on the architecture of the planetary system. The results of these simulations can be used to assess the ability of hypothetical chains of planets to produce exozodi in observed systems. We find that for older (>100Myr) stars with exozodiacal dust, a massive, large radii (>20AU) outer belt and a chain of tightly packed, low-mass planets would be required in order to retain the dust at its currently observed levels. This brings into question how many, if any, real systems possess such a contrived architecture and are therefore capable of scattering at sufficiently high rates to retain exozodi dust on long timescales