18,890 research outputs found
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
- …