arXiv subjects
Publications and source records attributed to Katharine C. Walker.
In this paper, we study fundamental groups of strata of the moduli space of quadratic differentials. We use certain properties of the Abel-Jacobi map, combined with local surgeries on quadratic differentials, to construct quotient groups of the fundamental groups for a particular family of strata.
In this paper, we study connected components of strata of the space of quadratic differentials lying over $\T_g$. We use certain general properties of sections of line bundles to put a upper bound on the number of connected components, and a generalized version of the Gauss map as an invariant to put a lower bound on the number of such components. For strata with sufficiently many zeroes of the same order we can state precisely the number of components.
We have performed searches for isolated flares and for steady flickering in Gamma Ray Burst light curves on the microsecond to millisecond time scales. Two bursts out of our sample of 20 revealed four isolated flares with time scales from $256 μs$ to $2048 μs$. A wavelet analysis for our sample showed low level flickering for all bursts on time scales from $256 μs$ to 33 ms, with the majority of bursts containing rise times faster than four milliseconds and 30% having rise times faster than one millisecond. These results show that millisecond variability is common in classical bursts and not some exceptional activity by a possibly separate class of bursts. These fast rise times can be used to place severe limits on burst models: (1) The characteristic thickness of the energy generation region must be less than 1200 km along the line of sight. (2) The angular size of the gamma ray emission region as subtended from the central source must be less than 42 arc-seconds. (3) The expanding ejecta must have a range of Lorentz factors along a radius line with a dispersion of less than roughly 2%. (4) Within the external shock scenario, the characteristic dimension of the impacted cloud must be smaller than 16 Astronomical Units on average. (5) Within the collimated jet scenario, the collimation angle must be smaller than 42 arc-seconds.
The Gamma Ray Burst GRB920229 has four extreme and unprecedented properties; a rise in brightness with an e-folding time scale of $220 \pm 30 μs$, a fall in brightness with an e-folding time scale of $400 \pm 100 μs$, a large change in spectral shape over a time of $768 μs$, and a sharp spectral cutoff to high energies with $ΔE/E = 18 %$. The rapid changes occur during a spike in the light curve which was seen 0.164 s after the start of the burst. The spectrum has a peak $νF_ν$ at 200 keV with no significant flux above 239 keV, although the cutoff energy shifts to less than 100 keV during the decay of the spike. These numbers can be used to place severe limits on fireball models of bursts. The thickness of the energy production region must be smaller than $\sim 66 km$, ejected shells must have a dispersion of the Lorentz factor of less than roughly 1% along a particular radius, and the angular size of the radiation emission region is of order 1 arc-minute as viewed from the burst center. The physical mechanism that caused the sharp spectral cutoff has not been determined.