The Collisional Evolution of Debris Disks

We explore the collisional decay of disk mass and infrared emission in debris disks. With models, we show that the rate of the decay varies throughout the evolution of the disks, increasing its rate up to a certain point, which is followed by a leveling off to a slower value. The total disk mass falls off ~ t^-0.35 at its fastest point (where t is time) for our reference model, while the dust mass and its proxy -- the infrared excess emission -- fades significantly faster (~ t^-0.8). These later level off to a decay rate of M_tot(t) ~ t^-0.08 and M_dust(t) or L_ir(t) ~ t^-0.6. This is slower than the ~ t^-1 decay given for all three system parameters by traditional analytic models. We also compile an extensive catalog of Spitzer and Herschel 24, 70, and 100 micron observations. Assuming a log-normal distribution of initial disk masses, we generate model population decay curves for the fraction of debris disk harboring stars observed at 24 micron and also model the distribution of measured excesses at the far-IR wavelengths (70-100 micron) at certain age regimes. We show general agreement at 24 micron between the decay of our numerical collisional population synthesis model and observations up to a Gyr. We associate offsets above a Gyr to stochastic events in a few select systems. We cannot fit the decay in the far infrared convincingly with grain strength properties appropriate for silicates, but those of water ice give fits more consistent with the observations.Comment: 32 pages, 16 figures, emulateapj format, Accepted for publication in Ap

On the mass-coupling relation of multi-scale quantum integrable models

We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of the perturbation of a projected product of minimal models. This representation enables us to identify conserved tensor currents on the UV side. These UV operators are then mapped via form factor perturbation theory to operators on the IR side, which are characterized by their form factors. The relation between the UV and IR operators is given in terms of the sought-for mass-coupling relation. By generalizing the $\Theta$ sum rule Ward identity we are able to derive differential equations for the mass-coupling relation, which we solve in terms of hypergeometric functions. We check these results against the data obtained by numerically solving the thermodynamic Bethe Ansatz equations, and find a complete agreement.Comment: 55 pages, 9 figures, reference added, minor changes, published versio

Search for signatures of dust in the Pluto-Charon system using Herschel/PACS observations

In this letter we explore the environment of Pluto and Charon in the far infrared with the main aim to identify the signs of any possible dust ring, should it exist in the system. Our study is based on observations performed at 70 um with the PACS instrument onboard the Herschel Space Observatory at 9 epochs between March 14 and 19, 2012. The far-infrared images of the Pluto-Charon system are compared to those of the point spread function (PSF) reference quasar 3C454.3. The deviation between the observed Pluto-Charon and reference PSFs are less then 1 sigma indicating that clear evidence for an extended dust ring around the system was not found. Our method is capable of detecting a hypothetical ring with a total flux of ~3.3 mJy at a distance of ~153 000 km (~8.2 Pluto-Charon distances) from the system barycentre. We place upper limits on the total disk mass and on the column density in a reasonable disk configuration and analyse the hazard during the flyby of NASAs New Horizons in July 2015. This realistic model configuration predicts a column density of 8.7x10^(-10) gcm^(-2) along the path of the probe and an impactor mass of 8.7x10^(-5) g.Comment: 10 pages, 4 figures, 2 table

Herschel-PACS photometry of faint stars

Our aims are to determine flux densities and their photometric accuracy for a set of seventeen stars that range in flux from intermediately bright (<2.5 Jy) to faint (>5 mJy) in the far-infrared (FIR). We also aim to derive signal-to-noise dependence with flux and time, and compare the results with predictions from the Herschel exposure-time calculation tool. The PACS faint star sample has allowed a comprehensive sensitivity assessment of the PACS photometer. Accurate photometry allows us to establish a set of five FIR primary standard candidates, namely alpha Ari, epsilon Lep, omega,Cap, HD41047 and 42Dra, which are 2 -- 20 times fainter than the faintest PACS fiducial standard (gamma Dra) with absolute accuracy of <6%. For three of these primary standard candidates, essential stellar parameters are known, meaning that a dedicated flux model code may be run.Comment: 42 pages, 12 figure

Terrestrial Zone Debris Disk Candidates in h and chi Persei

We analyze 8 sources with strong mid-infrared excesses in the 13 Myr-old double cluster h and chi Persei. New optical spectra and broadband SEDs (0.36-8 mu_m) are consistent with cluster membership. We show that material with T ~ 300-400 K and Ld/Lstar ~ 10^-4-10^-3 produces the excesses in these sources. Optically-thick blackbody disk models - including those with large inner holes - do not match the observed SEDs. The SEDs of optically-thin debris disks produced from terrestrial planet formation calculations match the observations well. Thus, some h and chi Persei stars may have debris from terrestrial zone planet formation.Comment: 5 pages, 3 figures, Matched to published version, Astrophysical Journal Letters, in press: 2007, ApJL, 663, 10

A Deep Spitzer Survey of Circumstellar Disks in the Young Double Cluster, h and chi Persei

We analyze very deep IRAC and MIPS photometry of $\sim$ 12,500 members of the 14 Myr old Double Cluster, h and $\chi$ Persei, building upon on our earlier, shallower Spitzer studies (Currie et al. 2007a, 2008a). Numerous likely members show infrared (IR) excesses at 8 {\mu}m and 24 $\mu$m indicative of circumstellar dust. The frequency of stars with 8 $\mu$m excess is at least 2% for our entire sample, slightly lower (higher) for B/A stars (later type, lower-mass stars). Optical spectroscopy also identifies gas in about 2% of systems but with no clear trend between the presence of dust and gas. Spectral energy distribution (SED) modeling of 18 sources with detections at optical wavelengths through MIPS 24 $\mu m$ reveals a diverse set of disk evolutionary states, including a high fraction of transitional disks, although similar data for all disk-bearing members would provide better constraints. We combine our results with those for other young clusters to study the global evolution of dust/gas disks. For nominal cluster ages, the e-folding times ($\tau_{o}$) for the frequency of warm dust and gas are 2.75 Myr and 1.75 Myr respectively. Assuming a revised set of ages for some clusters (e.g. Bell et al. 2013), these timescales increase to 5.75 and 3.75 Myr, respectively, implying a significantly longer typical protoplanetary disk lifetime. The transitional disk duration, averaged over multiple evolutionary pathways, is $\sim$ 1 Myr. Finally, 24 $\mu$m excess frequencies for 4-6 M$_{\odot}$ stars appear lower than for 1-2.5 M$_{\odot}$ stars in other 10-30 Myr old clusters.Comment: 35 pages, 6 tables, 21 figures; Accepted for publication in The Astrophysical Journa

Running coupling and non-perturbative corrections for O(N)(N) free energy and for disk capacitor

We reconsider the complete solution of the linear TBA equation describing the energy density of finite density states in the $O(N)$ nonlinear sigma models by the Wiener-Hopf method. We keep all perturbative and non-perturbative contributions and introduce a running coupling in terms of which all asymptotic series appearing in the problem can be represented as pure power series without logs. We work out the first non-perturbative contribution in the $O(3)$ case and show that (presumably because of the instanton corrections) resurgence theory fails in this example. Using the relation of the $O(3)$ problem to the coaxial disks capacitor problem we work out the leading non-perturbative terms for the latter and show that (at least to this order) resurgence theory, in particular the median resummation prescription, gives the correct answer. We demonstrate this by comparing the Wiener-Hopf results to the high precision numerical solution of the original integral equation.Comment: 56 pages, 4 figures, LaTeX. v3: discussion of resurgence clarified, 1 reference adde