Shaping the Kuiper belt size spectrum by shattering large but strengthless bodies

The observed size distribution of Kuiper belt objects (KBOs)--small icy and rocky solar system bodies orbiting beyond Neptune--is well described by a power law at large KBO sizes. However, recent work by Bernstein et al. (2003) indicates that the size spectrum breaks and becomes shallower for KBOs smaller than about 70 km in size. Here we show that we expect such a break at KBO radius ~40 km since destructive collisions are frequent for smaller KBOs. Specifically, we assume that KBOs are rubble piles with low material strength rather than solid monoliths. This gives a power-law slope q~3 where the number N(r) of KBOs larger than a size r is given by $N(r) \propto r^{1-q}$; the break location follows from this slope through a self-consistent calculation. The existence of this break, the break's location, and the power-law slope we expect below the break are consistent with the findings of Bernstein et al. (2003). The agreement with observations indicates that KBOs are effectively strengthless rubble piles.Comment: 11 pages, 2 figures; submitted to Icaru

The Plane of the Kuiper Belt

We present a robust method for measuring the effective plane of the Kuiper belt. The derived plane has an inclination with respect to the ecliptic of 1º.86 and an ascending node of 81º.6, with a 1 σ error in pole position of the plane of 0º.37. The plane of the Kuiper belt is inconsistent with the invariable plane, the plane of Jupiter, and the plane of Neptune at the greater than 3 σ level. Using linear secular perturbation theory, we show that the plane of the Kuiper belt is expected to oscillate about the position of the invariable plane with a period of 1.9 million years and an amplitude of 1º.2. The present predicted position of the plane of the Kuiper belt has an inclination with respect to the ecliptic of 1º.74 and an ascending node of 86º.7, within 0º.20 of our measured position

Self-consistent size and velocity distributions of collisional cascades

The standard theoretical treatment of collisional cascades derives a steady-state size distribution assuming a single constant velocity dispersion for all bodies regardless of size. Here we relax this assumption and solve self-consistently for the bodies' steady-state size and size-dependent velocity distributions. Specifically, we account for viscous stirring, dynamical friction, and collisional damping of the bodies' random velocities in addition to the mass conservation requirement typically applied to find the size distribution in a steady-state cascade. The resulting size distributions are significantly steeper than those derived without velocity evolution. For example, accounting self-consistently for the velocities can change the standard q=3.5 power-law index of the Dohnanyi (1969) differential size spectrum to an index as large as q=4. Similarly, for bodies held together by their own gravity, the corresponding power-law index range 2.88<q<3.14 of Pan & Sari (2005) can steepen to values as large as q=3.26. Our velocity results allow quantitative predictions of the bodies' scale heights as a function of size. Together with our predictions, observations of the scale heights for different sized bodies for the Kuiper belt, the asteroid belt, and extrasolar debris disks may constrain the mass and number of large bodies stirring the cascade as well as the colliding bodies' internal strengths.Comment: 23 pages, 3 figures, 1 table; submitted to Ap

Care and feeding of frogs

"Propellers" are features in Saturn's A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion (Tiscareno 2010); the longitude residuals of the best-observed propeller, "Bl\'eriot," appear consistent with a sinusoid of period ~4 years. Pan and Chiang (2010) proposed that propeller moonlets librate in "frog resonances" with co-orbiting ring material. By analogy with the restricted three-body problem, they treated the co-orbital material as stationary in the rotating frame and neglected non-co-orbital material. Here we use simple numerical experiments to extend the frog model, including feedback due to the gap's motion, and drag associated with the Lindblad disk torques that cause Type I migration. Because the moonlet creates the gap, we expect the gap centroid to track the moonlet, but only after a time delay t_diff, the time for a ring particle to travel from conjunction with the moonlet to the end of the gap. We find that frog librations can persist only if t_diff exceeds the frog libration period P_lib, and if damping from Lindblad torques balances driving from co-orbital torques. If t_diff << P_lib, then the libration amplitude damps to zero. In the case of Bl\'eriot, the frog resonance model can reproduce the observed libration period P_lib ~ 4 yr. However, our simple feedback prescription suggests that Bl\'eriot's t_diff ~ 0.01P_lib, which is inconsistent with the observed libration amplitude of 260 km. We urge more accurate treatments of feedback to test the assumptions of our toy models.Comment: 15 pages, 4 figures; AJ in prin

Apocenter glow in eccentric debris disks: implications for Fomalhaut and epsilon Eridani

Debris disks often take the form of eccentric rings with azimuthal asymmetries in surface brightness. Such disks are often described as showing "pericenter glow", an enhancement of the disk brightness in regions nearest the central star. At long wavelengths, however, the disk apocenters should appear brighter than their pericenters: in the long wavelength limit, we find the apocenter/pericenter flux ratio scales as 1+e for disk eccentricity e. We produce new models of this "apocenter glow" to explore its causes and wavelength dependence and study its potential as a probe of dust grain properties. Based on our models, we argue that several far-infrared and (sub)millimeter images of the Fomalhaut and epsilon Eridani debris rings obtained with Herschel, JCMT, SHARC II, ALMA, and ATCA should be reinterpreted as suggestions or examples of apocenter glow. This reinterpretation yields new constraints on the disks' dust grain properties and size distributions.Comment: 20 pages, 7 figures; accepted to Ap

Disseminated Nocardia cyriacigeorgia causing pancreatitis in a haploidentical stem cell transplant recipient.

We report the first published case of acute pancreatitis secondary to disseminated nocardiosis in a hematopoietic stem cell transplant (HSCT) recipient on chronic immunosuppression for graft-versus-host disease (GVHD). Nocardiosis in the HSCT population is relatively rare, and has not yet been described in haploidentical HSCT recipients. Our patient is a 28-year-old male with a history of haploidentical HSCT and GVHD of the skin and lung who was admitted to the hospital with acute pancreatitis. The workup for the etiology of his pancreatitis was initially unrevealing. He subsequently developed worsening sepsis and respiratory failure despite broad spectrum antimicrobials. After multiple bronchoscopies and pancreatic fluid sampling, he was found to have disseminated nocardiosis with Nocardia cyriacigeorgia

Composite self-similar solutions for relativistic shocks: the transition to cold fluid temperatures

The flow resulting from a strong ultrarelativistic shock moving through a stellar envelope with a polytrope-like density profile has been studied analytically and numerically at early times while the fluid temperature is relativistic--that is, just before and just after the shock breaks out of the star. Such a flow should expand and accelerate as its internal energy is converted to bulk kinetic energy; at late enough times, the assumption of relativistic temperatures becomes invalid. Here we present a new self-similar solution for the post-breakout flow when the accelerating fluid has bulk kinetic Lorentz factors much larger than unity but is cooling through $p/n$ of order unity to subrelativistic temperatures. This solution gives a relation between a fluid element's terminal Lorentz factor and that element's Lorentz factor just after it is shocked. Our numerical integrations agree well with the solution. While our solution assumes a planar flow, we show that corrections due to spherical geometry are important only for extremely fast ejecta originating in a region very close to the stellar surface. This region grows if the shock becomes relativistic deeper in the star.Comment: 25 pages, 8 figures; submitted to Physics of Fluid