On invariant Schreier structures

Schreier graphs, which possess both a graph structure and a Schreier structure (an edge-labeling by the generators of a group), are objects of fundamental importance in group theory and geometry. We study the Schreier structures with which unlabeled graphs may be endowed, with emphasis on structures which are invariant in some sense (e.g. conjugation-invariant, or sofic). We give proofs of a number of "folklore" results, such as that every regular graph of even degree admits a Schreier structure, and show that, under mild assumptions, the space of invariant Schreier structures over a given invariant graph structure is very large, in that it contains uncountably many ergodic measures. Our work is directly connected to the theory of invariant random subgroups, a field which has recently attracted a great deal of attention.Comment: 16 pages, added references and figure, to appear in L'Enseignement Mathematiqu

The boundary action of a sofic random subgroup of the free group

We prove that the boundary action of a sofic random subgroup of a finitely generated free group is conservative. This addresses a question asked by Grigorchuk, Kaimanovich, and Nagnibeda, who studied the boundary actions of individual subgroups of the free group. Following their work, we also investigate the cogrowth and various limit sets associated to sofic random subgroups. We make heavy use of the correspondence between subgroups and their Schreier graphs, and central to our approach is an investigation of the asymptotic density of a given set inside of large neighborhoods of the root of a sofic random Schreier graph.Comment: 21 pages, 2 figures, made minor corrections, to appear in Groups, Geometry, and Dynamic

The Shape of Long Outbursts in U Gem Type Dwarf Novae from AAVSO Data

We search the American Association of Variable Star Observers (AAVSO) archives of the two best studied dwarf novae in an attempt to find light curves for long outbursts that are extremely well-characterized. The systems are U Gem and SS Cyg. Our goal is to search for embedded precursors such as those that have been found recently in the high fidelity Kepler data for superoutbursts of some members of the SU UMa subclass of dwarf novae. For the vast majority of AAVSO data, the combination of low data cadence and large errors associated with individual measurements precludes one from making any strong statement about the shape of the long outbursts. However, for a small number of outbursts, extensive long term monitoring with digital photometry yields high fidelity light curves. We report the discovery of embedded precursors in two of three candidate long outbursts. This is the first time that such embedded precursors have been found in dwarf novae above the period gap, and reinforces van Paradijs' finding that long outbursts in dwarf novae above the period gap and superoutbursts in systems below the period gap constitute a unified class. The thermal-tidal instability to account for superoutbursts in the SU UMa stars predicts embedded precursors only for short orbital period dwarf novae, therefore the presence of embedded precursors in long orbital period systems - U Gem and SS Cyg - argues for a more general mechanism to explain long outbursts.Comment: 4 pages, 5 figures; accepted into the Astrophysical Journa

The Kepler Light Curve of V344 Lyrae: Constraining the Thermal-Viscous Limit Cycle Instability

We present time dependent modeling based on the accretion disk limit cycle model for a 270 d light curve of the short period SU UMa-type dwarf nova V344 Lyr taken by Kepler. The unprecedented precision and cadence (1 minute) far surpass that generally available for long term light curves. The data encompass two superoutbursts and 17 normal (i.e., short) outbursts. The main decay of the superoutbursts is nearly perfectly exponential, decaying at a rate ~12 d/mag, while the much more rapid decays of the normal outbursts exhibit a faster-than-exponential shape. Our modeling using the basic accretion disk limit cycle can produce the main features of the V344 Lyr light curve, including the peak outburst brightness. Nevertheless there are obvious deficiencies in our model light curves: (1) The rise times we calculate, both for the normal and superoutbursts, are too fast. (2) The superoutbursts are too short. (3) The shoulders on the rise to superoutburst have more structure than the shoulder in the observed superoutburst and are too slow, comprising about a third to half of the total viscous plateau, rather than the ~10% observed. However, one of the alpha_{cold} -> alpha_{hot} interpolation schemes we investigate (one that is physically motivated) does yield longer superoutbursts with suitably short, less structured shoulders.Comment: 39 pages, 9 figures, accepted in the Astrophysical Journa

Kepler Observations of V447 Lyr: An Eclipsing U Gem Cataclysmic Variable

We present the results of an analysis of data covering 1.5 years of the dwarf nova V447 Lyr. We detect eclipses of the accretion disk by the mass donating secondary star every 3.74 hrs which is the binary orbital period. V447 Lyr is therefore the first dwarf nova in the Kepler field to show eclipses. We also detect five long outbursts and six short outbursts showing V447 Lyr is a U Gem type dwarf nova. We show that the orbital phase of the mid-eclipse occurs earlier during outbursts compared to quiescence and that the width of the eclipse is greater during outburst. This suggests that the bright spot is more prominent during quiescence and that the disk is larger during outburst than quiescence. This is consistent with an expansion of the outer disk radius due to the presence of high viscosity material associated with the outburst, followed by a contraction in quiescence due to the accretion of low angular momentum material. We note that the long outbursts appear to be triggered by a short outburst, which is also observed in the super-outbursts of SU UMa dwarf novae as observed using Kepler.Comment: Accepted by MNRA

The Fall and the Rise of X-rays from Dwarf Novae in Outburst: RXTE Observations of VW Hydri and WW Ceti

In a dwarf nova, the accretion disk around the white dwarf is a source of ultraviolet, optical, and infrared photons, but is never hot enough to emit X-rays. Observed X-rays instead originate from the boundary layer between the disk and the white dwarf. As the disk switches between quiescence and outburst states, the 2-10 keV X-ray flux is usually seen to be anti-correlated with the optical brightness. Here we present RXTE monitoring observations of two dwarf novae, VW Hyi and WW Cet, confirming the optical/X-ray anti-correlation in these two systems. However, we do not detect any episodes of increased hard X-ray flux on the rise (out of two possible chances for WW Cet) or the decline (two for WW Cet and one for VW Hyi) from outburst, attributes that are clearly established in SS Cyg. The addition of these data to the existing literature establishes the fact that the behavior of SS Cyg is the exception, rather than the archetype as is often assumed. We speculate on the origin of the diversity of behaviors exhibited by dwarf novae, focusing on the role played by the white dwarf mass.Comment: PASP, in press (18 pages including 3 figures

Application of the Hilbert-Huang Transform to the Search for Gravitational Waves

We present the application of a novel method of time-series analysis, the Hilbert-Huang Transform, to the search for gravitational waves. This algorithm is adaptive and does not impose a basis set on the data, and thus the time-frequency decomposition it provides is not limited by time-frequency uncertainty spreading. Because of its high time-frequency resolution it has important applications to both signal detection and instrumental characterization. Applications to the data analysis of the ground and space based gravitational wave detectors, LIGO and LISA, are described