On invariant sets in Lagrangian graphs

In this exposition, we show that a Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are smooth enough. We also provide some counterexamples for the case that the Hamiltonians are not smooth enough.Comment: 4 page

Recovering Solar Toroidal Field Dynamics From Sunspot Location Patterns

We analyze both Kitt Peak magnetogram data and MDI continuum intensity sunspot data to search for the following solar toroidal band properties: width in latitude and the existence of a tipping instability (longitudinal m=1 mode) for any time during the solar cycle. To determine the extent which we can recover the toroidal field dynamics, we forward model artificially generated sunspot distributions from subsurface toroidal fields we assigned certain properties. We analyzed two sunspot distribution parameters using MDI and model data: the average latitudinal separation of sunspot pairs as a function of longitudinal separation, and the number of sunspot pairs creating a given angle with respect to the E-W direction. A toroidal band of 10 degrees width with a constant tipping of 5 degrees best fits MDI data early in the solar cycle. A toroidal band of 20 degrees width with a tipping amplitude decreasing in time from 5 to 0 degrees best fits MDI data late in the solar cycle. Model data generated by untipped toroidal bands cannot fit MDI high latitude data and can fit only one parameter at low latitudes. Tipped toroidal bands satisfy chi squared criteria at both high and low latitudes. We conclude this is evidence to reject the null hypothesis - that toroidal bands in the solar tachocline do not experience a tipping instability - in favor of the hypothesis that the toroidal band experiences an m=1 tipping instability. Our finding that the band widens from ~10 degrees early in the solar cycle to ~20 degrees late in the solar cycle may be explained in theory by magnetic drag spreading the toroidal band due to altered flow along the tipped field lines.Comment: This paper is accepted to Astrophysical Journal, September 2005 issu

Periodicities In The X-Ray Intensity Variations of TV Columbae: An Intermediate Polar

We present results from a temporal analysis of the longest and the most sensitive X-ray observations of TV Columbae--an intermediate polar. The observations were carried out with the RXTE PCA, ROSAT PSPC, and ASCA. Data were analyzed using a 1-dimensional CLEAN and Bayesian algorithms. The presence of a nearly sinusoidal modulation due to the spin of the white dwarf is seen clearly in all the data, confirming the previous reports based on the EXOSAT data. An improved period of 1909.7+/-2.5s is derived for the spin from the RXTE data.The binary period of 5.5hr is detected unambiguously in X-rays for the first time. Several side-bands due to the interaction of these periods are observed in the power spectra, thereby suggesting contributions from both the disk-fed and the stream-fed accretion for TV Col. The accretion disk could perhaps be precessing as side-bands due to the influence of 4 day period on the orbital period are seen. The presence of a significant power at certain side-bands of the spin frequency indicates that the emission poles are asymmetrically located. The strong power at the orbital side-bands seen in both the RXTE and ROSAT data gives an indication for an absorption site fixed in the orbital frame. Both the spin and the binary modulation are found to be energy-dependent. Increased hardness ratio during a broad dip in the intensity at binary phase of 0.75--1.0 confirms the presence of a strong attenuation due to additional absorbers probably from an impact site of the accretion stream with the disk or magnetosphere. Hardness ratio variations and the energy dependent modulation depth during the spin modulation can be explained by partially covered absorbers in the path of X-ray emission region in the accretion stream.Comment: 34 pages, including 12 figures, Accepted for publication in Astronomical Journal, scheduled for January 2004 issue (vol. 127

Meeting report: Thunderstorms

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