How Observations of Circumstellar Disk Asymmetries Can Reveal Hidden Planets: Pericenter Glow and its Application to the HR 4796 Disk

Recent images of the disks of dust around the young stars HR 4796A and Fomalhaut show, in each case, a double-lobed feature that may be asymmetric (one lobe may be brighter than the other). A symmetric double-lobed structure is that expected from a disk of dust with a central hole that is observed nearly edge-on (i.e., close to the plane of the disk). This paper shows how the gravitational influence of a second body in the system with an eccentric orbit would cause a brightness asymmetry in such a disk by imposing a "forced eccentricity" on the orbits of the constituent dust particles, thus shifting the center of symmetry of the disk away from the star and causing the dust near the forced pericenter of the perturbed disk to glow. Dynamic modeling of the HR 4796 disk shows that its 5% brightness asymmetry could be the result of a forced eccentricity as small as 0.02 imposed on the disk by either the binary companion HR 4796B, or by an unseen planet close to the inner edge of the disk. Since it is likely that a forced eccentricity of 0.01 or higher would be imposed on a disk in a system in which there are planets, but no binary companion, the corresponding asymmetry in the disk's structure could serve as a sensitive indicator of these planets that might otherwise remain undetected.Comment: 61 pages, 10 figures, accepted for publication in the Astrophysical Journal (scheduled for January 10, 2000

Accretion in the Early Kuiper Belt II. Fragmentation

We describe new planetesimal accretion calculations in the Kuiper Belt that include fragmentation and velocity evolution. All models produce two power law cumulative size distributions, N_C propto r^{-q}, with q = 2.5 for radii less than 0.3-3 km and q = 3 for radii exceeding 1-3 km. The power law indices are nearly independent of the initial mass in the annulus, the initial eccentricity of the planetesimal swarm, and the initial size distribution of the planetesimal swarm. The transition between the two power laws moves to larger radii as the initial eccentricity increases. The maximum size of objects depends on their intrinsic tensile strength; Pluto formation requires a strength exceeding 300 erg per gram. Our models yield formation timescales for Pluto-sized objects of 30-40 Myr for a minimum mass solar nebula. The production of several `Plutos' and more than 10^5 50 km radius Kuiper Belt objects leaves most of the initial mass in 0.1-10 km radius objects that can be collisionally depleted over the age of the solar system. These results resolve the puzzle of large Kuiper Belt objects in a small mass Kuiper Belt.Comment: to appear in the Astronomical Journal (July 1999); 54 pages including 7 tables and 13 figure

P/2010 A2 LINEAR II: dynamical dust modelling

P/2010 A2 is an object on an asteroidal orbit that was observed to have an extended tail or debris trail in January 2010. In this work, we fit the outburst of P/2010 A2 with a conical burst model, and verify previous suspicions that this was a one--time collisional event rather than an sustained cometary outburst, implying that P/2010 A2 is not a new Main Belt Comet driven by ice sublimation. We find that the best--fit cone opening angle is about 40 to 50 degrees, in agreement with numerical and laboratory simulations of cratering events. Mapping debris orbits to sky positions suggests that the distinctive arc features in the debris correspond to the same debris cone inferred from the extended dust. From the velocity of the debris, and from the presence of a velocity maximum at around 15 cm/s, we infer that the surface of A2 probably has a very low strength (<1 kPa), comparable to lunar regolith.Comment: 14 pages, 25 figures; accepted by Astronomy and Astrophysic

Steady-state evolution of debris disks around A stars

In this paper a simple analytical model for the steady-state evolution of debris disks due to collisions is confronted with Spitzer observations of main sequence A stars. All stars are assumed to have planetesimal belts with a distribution of initial masses and radii. In the model disk mass is constant until the largest planetesimals reach collisional equilibrium whereupon the mass falls off oc 1/t. We find that the detection statistics and trends seen at both 24 and 70um can be fitted well by the model. While there is no need to invoke stochastic evolution or delayed stirring to explain the statistics, a moderate rate of stochastic events is not ruled out. Potentially anomalous systems are identified by a high dust luminosity compared with the maximum permissible in the model (HD3003, HD38678, HD115892, HD172555). Their planetesimals may have unusual properties (high strength or low eccentricity) or this dust could be transient. While transient phenomena are also favored for a few systems in the literature, the overall success of our model, which assumes planetesimals in all belts have the same strength, eccentricity and maximum size, suggests a large degree of uniformity in the outcome of planet formation. The distribution of planetesimal belt radii, once corrected for detection bias, follows N(r) oc r^{-0.8+-0.3} for 3-120AU. Since the inner edge is often attributed to an unseen planet, this provides a unique constraint on the planetary systems of A stars. It is also shown that P-R drag may sculpt the inner edges of A star disks close to the Spitzer detection threshold (HD2262, HD19356, HD106591, HD115892). This model can be readily applied to the interpretation of future surveys, and predictions are made for the upcoming SCUBA-2 survey, including that >17% of A stars should be detectable at 850um.Comment: Accepted by Ap

IRS Spectra of Solar-Type Stars: \break A Search for Asteroid Belt Analogs

We report the results of a spectroscopic search for debris disks surrounding 41 nearby solar type stars, including 8 planet-bearing stars, using the {\it Spitzer Space Telescope}. With accurate relative photometry using the Infrared Spectrometer (IRS) between 7-34 \micron we are able to look for excesses as small as $\sim$2% of photospheric levels with particular sensitivity to weak spectral features. For stars with no excess, the $3\sigma$ upper limit in a band at 30-34 $\mu$m corresponds to $\sim$ 75 times the brightness of our zodiacal dust cloud. Comparable limits at 8.5-13 $\mu$m correspond to $\sim$ 1,400 times the brightness of our zodiacal dust cloud. These limits correspond to material located within the $<$1 to $\sim$5 AU region that, in our solar system, originates from debris associated with the asteroid belt. We find excess emission longward of $\sim$25 $\mu$m from five stars of which four also show excess emission at 70 $\mu$m. This emitting dust must be located around 5-10 AU. One star has 70 micron emission but no IRS excess. In this case, the emitting region must begin outside 10 AU; this star has a known radial velocity planet. Only two stars of the five show emission shortward of 25 \micron where spectral features reveal the presence of a population of small, hot dust grains emitting in the 7-20 $\mu$m band. The data presented here strengthen the results of previous studies to show that excesses at 25 \micron and shorter are rare: only 1 star out of 40 stars older than 1 Gyr or $\sim 2.5$% shows an excess. Asteroid belts 10-30 times more massive than our own appear are rare among mature, solar-type stars

Collisional Cascades in Planetesimal Disks I. Stellar Flybys

We use a new multiannulus planetesimal accretion code to investigate the evolution of a planetesimal disk following a moderately close encounter with a passing star. The calculations include fragmentation, gas and Poynting-Robertson drag, and velocity evolution from dynamical friction and viscous stirring. We assume that the stellar encounter increases planetesimal velocities to the shattering velocity, initiating a collisional cascade in the disk. During the early stages of our calculations, erosive collisions damp particle velocities and produce substantial amounts of dust. For a wide range of initial conditions and input parameters, the time evolution of the dust luminosity follows a simple relation, L_d/L_{\star} = L_0 / [alpha + (t/t_d)^{beta}]. The maximum dust luminosity L_0 and the damping time t_d depend on the disk mass, with L_0 proportional to M_d and t_d proportional to M_d^{-1}. For disks with dust masses of 1% to 100% of the `minimum mass solar nebula' (1--100 earth masses at 30--150 AU), our calculations yield t_d approx 1--10 Myr, alpha approx 1--2, beta = 1, and dust luminosities similar to the range observed in known `debris disk' systems, L_0 approx 10^{-3} to 10^{-5}. Less massive disks produce smaller dust luminosities and damp on longer timescales. Because encounters with field stars are rare, these results imply that moderately close stellar flybys cannot explain collisional cascades in debris disk systems with stellar ages of 100 Myr or longer.Comment: 33 pages of text, 12 figures, and an animation. The paper will appear in the March 2002 issue of the Astronmomical Journal. The animation and a copy of the paper with full resolution figures are at S. Kenyon's planet formation website: http://cfa-www.harvard.edu/~kenyon/p

The Vega Debris Disk -- A Surprise from Spitzer

We present high spatial resolution mid- and far-infrared images of the Vega debris disk obtained with the Multiband Imaging Photometer for Spitzer (MIPS). The disk is well resolved and its angular size is much larger than found previously. The radius of the disk is at least 43" (330 AU), 70"(543 AU), and 105" (815 AU) in extent at 24, 70 and 160 um, respectively. The disk images are circular, smooth and without clumpiness at all three wavelengths. The radial surface brightness profiles imply an inner boundary at a radius of 11"+/-2" (86 AU). Assuming an amalgam of amorphous silicate and carbonaceous grains, the disk can be modeled as an axially symmetric and geometrically thin disk, viewed face-on, with the surface particle number density following an r^-1 power law. The disk radiometric properties are consistent with a range of models using grains of sizes ~1 to ~50 um. We find that a ring, containing grains larger than 180 um and at radii of 86-200 AU from the star, can reproduce the observed 850 um flux, while its emission does not violate the observed MIPS profiles. This ring could be associated with a population of larger asteroidal bodies analogous to our own Kuiper Belt. Cascades of collisions starting with encounters amongthese large bodies in the ring produce the small debris that is blown outward by radiation pressure to much larger distances where we detect its thermal emission. The dust production rate is >~10^15 g/s based on the MIPS results. This rate would require a very massive asteroidal reservoir for the dust to be produced in a steady state throughout Vega's life. Instead, we suggest that the disk we imaged is ephemeral and that we are witnessing the aftermath of a large and relatively recent collisional event, and subsequent collisional cascade.Comment: 13 pages, 17 figures, accepted for publication in ApJ. (Figures 2, 3a, 3b and 4 have been degraded to lower resolutions.

Debris disks in main sequence binary systems

We observed 69 A3-F8 main sequence binary star systems using the Multiband Imaging Photometer for Spitzer onboard the Spitzer Space Telescope. We find emission significantly in excess of predicted photospheric flux levels for 9(+4/-3)% and 40(+7/-6)% of these systems at 24 and 70 microns, respectively. Twenty two systems total have excess emission, including four systems that show excess emission at both wavelengths. A very large fraction (nearly 60%) of observed binary systems with small (<3 AU) separations have excess thermal mission. We interpret the observed infrared excesses as thermal emission from dust produced by collisions in planetesimal belts. The incidence of debris disks around main sequence A3-F8 binaries is marginally higher than that for single old AFGK stars. Whatever combination of nature (birth conditions of binary systems) and nurture (interactions between the two stars) drives the evolution of debris disks in binary systems, it is clear that planetesimal formation is not inhibited to any great degree. We model these dust disks through fitting the spectral energy distributions and derive typical dust temperatures in the range 100--200 K and typical fractional luminosities around 10^-5, with both parameters similar to other Spitzer-discovered debris disks. Our calculated dust temperatures suggest that about half the excesses we observe are derived from circumbinary planetesimal belts and around one third of the excesses clearly suggest circumstellar material. Three systems with excesses have dust in dynamically unstable regions, and we discuss possible scenarios for the origin of this short-lived dust.Comment: ApJ, in press. 57 pages, including 7 figures (one of which is in color

Searching for Saturn's Dust Swarm: Limits on the size distribution of Irregular Satellites from km to micron sizes

We describe a search for dust created in collisions between the Saturnian irregular satellites using archival \emph{Spitzer} MIPS observations. Although we detected a degree scale Saturn-centric excess that might be attributed to an irregular satellite dust cloud, we attribute it to the far-field wings of the PSF due to nearby Saturn. The Spitzer PSF is poorly characterised at such radial distances, and we expect PSF characterisation to be the main issue for future observations that aim to detect such dust. The observations place an upper limit on the level of dust in the outer reaches of the Saturnian system, and constrain how the size distribution extrapolates from the smallest known (few km) size irregulars down to micron-size dust. Because the size distribution is indicative of the strength properties of irregulars, we show how our derived upper limit implies irregular satellite strengths more akin to comets than asteroids. This conclusion is consistent with their presumed capture from the outer regions of the Solar System.Comment: accepted to MNRA

Spitzer/MIPS 24 micron Detection of Photoevaporating Protoplanetary Disks

We present 24 micron images of three protoplanetary disks being photoevaporated around high mass O type stars. These objects have ``cometary'' structure where the dust pulled away from the disk by the photoevaporating flow is forced away from the O star by photon pressure on the dust and heating and ionization of the gas. Models of the 24 micron and 8 micron brightness profiles agree with this hypothesis. These models show that the mass-loss rate needed to sustain such a configuration is in agreement with or somewhat less than the theoretical predictions for the photoevaporation process.Comment: 4 pages 4 figures. Accepted for publication in The Astrophysical Journal Letter