K2 Ultracool Dwarfs Survey II: The White Light Flare Rate of Young Brown Dwarfs

We use Kepler K2 Campaign 4 short-cadence (one-minute) photometry to measure white light flares in the young, moving group brown dwarfs 2MASS J03350208+2342356 (2M0335+23) and 2MASS J03552337+1133437 (2M0355+11), and report on long-cadence (thirty-minute) photometry of a superflare in the Pleiades M8 brown dwarf CFHT-PL-17. The rotation period (5.24 hr) and projected rotational velocity ($45$ km s$^{-1}$) confirm 2M0335+23 is inflated ($R \ge 0.20 R_\odot$) as predicted for a $0.06M_\odot$, 26-Myr old brown dwarf $\beta$Pic moving group member. We detect 22 white light flares on 2M0335+23. The flare frequency distribution follows a power-law distribution with slope $-\alpha = -1.8 \pm 0.2$ over the range $10^{31}$ to $10^{33}$ erg. This slope is similar to that observed in the Sun and warmer flare stars, and is consistent with lower energy flares in previous work on M6-M8 very-low-mass stars; taken the two datasets together, the flare frequency distribution for ultracool dwarfs is a power law over 4.3 orders of magnitude. The superflare ($2.6\times10^{34}$ erg) on CFHT-PL-17 shows higher energy flares are possible. We detect no flares down to a limit of $2 \times 10^{30}$ erg in the nearby L$5\gamma$ AB Dor Moving Group brown dwarf 2M0355+11, consistent with the view that fast magnetic reconnection is suppressed in cool atmospheres. We discuss two multi-peaked flares observed in 2M0335+23, and argue that these complex flares can be understood as sympathetic flares, in which a fast-mode MHD waves similar to EUV waves in the Sun trigger magnetic reconnection in different active regions.Comment: Accepted version, The Astrophysical Journa

Stable manifolds and homoclinic points near resonances in the restricted three-body problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers $p$ and $q$, if its period around the heavier primary is approximately $2\pi p/q$, and by its approximate eccentricity $e$. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with $q/p$ equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any $\mu$ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for $\mu$ small enough in the unaveraged restricted three-body problem

Men and talk about legal abortion in South Africa: equality, support and rights discourses undermining reproductive ‘choice’

Discursive constructions of abortion are embedded in the social and gendered power relations of a particular socio-historical space. As part of research on public discourses concerning abortion in South Africa where there has been a radical liberalisation of abortion legislation, we collected data from male group discussions about a vignette concerning abortion, and newspaper articles written by men about abortion. Our analysis revealed how discourses of equality, support and rights may be used by men to subtly undermine women’s reproductive right to ‘choose’ an abortion. Within an Equal Partnership discourse, abortion, paired with the assumption of foetal personhood, was equated with violating an equal heterosexual partnership and a man’s patriarchal duty to protect a child. A New Man discourse, which positions men as supportive of women, was paired with the assumption of men as rational and women as irrational in decision-making, to allow for the possibility of men dissuading women from terminating a pregnancy. A Rights discourse was invoked to suggest that abortion violates men’s paternal rights

Deep 10 and 18 micron Imaging of the HR 4796A Circumstellar Disk: Transient Dust Particles & Tentative Evidence for a Brightness Asymmetry

We present new 10.8 and 18.2 micron images of HR 4796A, a young A0V star that was recently discovered to have a spectacular, nearly edge-on, circumstellar disk prominent at ~20 microns (Jayawardhana et al. 1998; Koerner et al. 1998). These new images, obtained with OSCIR at Keck II, show that the disk's size at 10 microns is comparable to its size at 18 microns. Therefore, the 18 micron-emitting dust may also emit some, or all, of the 10 micron radiation. Using these multi-wavelength images, we determine a "characteristic" diameter of 2-3 microns for the mid-infrared-emitting dust particles if they are spherical and composed of astronomical silicates. Particles this small are expected to be blown out of the system by radiation pressure in a few hundred years, and therefore these particles are unlikely to be primordial. Dynamical modeling of the disk (Wyatt et al. 2000) indicates that the disk surface density is relatively sharply peaked near 70 AU, which agrees with the mean annular radius deduced by Schneider et al. (1999) from their NICMOS images. We present evidence (~1.8 sigma significance) for a brightness asymmetry that may result from the presence of the hole and the gravitational perturbation of the disk particle orbits by the low-mass stellar companion or a planet. This "pericenter glow," which must still be confirmed, results from a very small (a few AU) shift of the disk's center of symmetry relative to the central star HR 4796A; one side of the inner boundary of the annulus is shifted towards HR 4796A, thereby becoming warmer and more infrared-emitting. The possible detection of pericenter glow implies that the detection of even complex dynamical effects of planets on disks is within reach.Comment: 18 pages. 9 GIF images. Total size ~800 kB. High resolution images available upon request. Accepted for publication in the Astrophysical Journal (scheduled for January 10, 2000

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

Signatures of recent asteroid disruptions in the formation and evolution of solar system dust bands

We have performed detailed dynamical modeling of the structure of a faint dust band observed in coadded InfraRed Astronomical Satellite data at an ecliptic latitude of 17 degrees that convincingly demonstrates that it is the result of a relatively recent (significantly less than 1Ma) disruption of an asteroid and is still in the process of forming. We show here that young dust bands retain information on the size distribution and cross-sectional area of dust released in the original asteroid disruption, before it is lost to orbital and collisional decay. We find that the Emilkowalski cluster is the source of this partial band and that the dust released in the disruption would correspond to a regolith layer similar to 3 m deep on the similar to 10 km diameter source body's surface. The dust in this band is described by a cumulative size-distribution inverse power-law index with a lower bound of 2.1 (implying domination of cross-sectional area by small particles) for dust particles with diameters ranging from a few mu m up to a few cm. The coadded observations show that the thermal emission of the dust band structure is dominated by large (mm-cm size) particles. We find that dust particle ejection velocities need to be a few times the escape velocity of the Emilkowalski cluster source body to provide a good fit to the inclination dispersion of the observations. We discuss the implications that such a significant release of material during a disruption has for the temporal evolution of the structure, composition, and magnitude of the zodiacal cloud

Debris disk size distributions: steady state collisional evolution with P-R drag and other loss processes

We present a new scheme for determining the shape of the size distribution, and its evolution, for collisional cascades of planetesimals undergoing destructive collisions and loss processes like Poynting-Robertson drag. The scheme treats the steady state portion of the cascade by equating mass loss and gain in each size bin; the smallest particles are expected to reach steady state on their collision timescale, while larger particles retain their primordial distribution. For collision-dominated disks, steady state means that mass loss rates in logarithmic size bins are independent of size. This prescription reproduces the expected two phase size distribution, with ripples above the blow-out size, and above the transition to gravity-dominated planetesimal strength. The scheme also reproduces the expected evolution of disk mass, and of dust mass, but is computationally much faster than evolving distributions forward in time. For low-mass disks, P-R drag causes a turnover at small sizes to a size distribution that is set by the redistribution function (the mass distribution of fragments produced in collisions). Thus information about the redistribution function may be recovered by measuring the size distribution of particles undergoing loss by P-R drag, such as that traced by particles accreted onto Earth. Although cross-sectional area drops with 1/age^2 in the PR-dominated regime, dust mass falls as 1/age^2.8, underlining the importance of understanding which particle sizes contribute to an observation when considering how disk detectability evolves. Other loss processes are readily incorporated; we also discuss generalised power law loss rates, dynamical depletion, realistic radiation forces and stellar wind drag.Comment: Accepted for publication by Celestial Mechanics and Dynamical Astronomy (special issue on EXOPLANETS

Multi-Epoch Observations of HD69830: High Resolution Spectroscopy and Limits to Variability

The main-sequence solar-type star HD69830 has an unusually large amount of dusty debris orbiting close to three planets found via the radial velocity technique. In order to explore the dynamical interaction between the dust and planets, we have performed multi-epoch photometry and spectroscopy of the system over several orbits of the outer dust. We find no evidence for changes in either the dust amount or its composition, with upper limits of 5-7% (1 $\sigma$ per spectral element) on the variability of the {\it dust spectrum} over 1 year, 3.3% (1 $\sigma$) on the broad-band disk emission over 4 years, and 33% (1 $\sigma$) on the broad-band disk emission over 24 years. Detailed modeling of the spectrum of the emitting dust indicates that the dust is located outside of the orbits of the three planets and has a composition similar to main-belt, C-type asteroids asteroids in our solar system. Additionally, we find no evidence for a wide variety of gas species associated with the dust. Our new higher SNR spectra do not confirm our previously claimed detection of H$_2$O ice leading to a firm conclusion that the debris can be associated with the break-up of one or more C-type asteroids formed in the dry, inner regions of the protoplanetary disk of the HD69830 system. The modeling of the spectral energy distribution and high spatial resolution observations in the mid-infrared are consistent with a $\sim$ 1 AU location for the emitting material

Avoiding degenerate coframes in an affine gauge approach to quantum gravity

In quantum models of gravity, it is surmized that configurations with degenerate coframes could occur during topology change of the underlying spacetime structure. However, the coframe is not the true Yang--Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden" piece within the framework of the affine gauge approach to gravity, one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. This is an important advantage for quantization.Comment: 14 pages, Preprint Cologne-thp-1993-H