38 research outputs found
Polarimetry of Li-rich giants
Protoplanetary nebulae typically present non-spherical envelopes. The origin
of such geometry is still controversial. There are indications that it may be
carried over from an earlier phase of stellar evolution, such as the AGB phase.
But how early in the star's evolution does the non-spherical envelope appear?
Li-rich giants show dusty circumstellar envelopes that can help answer that
question. We study a sample of fourteen Li-rich giants using optical
polarimetry in order to detect non-spherical envelopes around them. We used the
IAGPOL imaging polarimeter to obtain optical linear polarization measurements
in V band. Foreground polarization was estimated using the field stars in each
CCD frame. After foreground polarization was removed, seven objects presented
low intrinsic polarization (0.19 - 0.34)% and two (V859 Aql and GCSS 557)
showed high intrinsic polarization values (0.87 - 1.16)%. This intrinsic
polarization suggests that Li-rich giants present a non-spherical distribution
of circumstellar dust. The intrinsic polarization level is probably related to
the viewing angle of the envelope, with higher levels indicating objects viewed
closer to edge-on. The correlation of the observed polarization with optical
color excess gives additional support to the circumstellar origin of the
intrinsic polarization in Li-rich giants. The intrinsic polarization correlates
even better with the IRAS 25 microns far infrared emission. Analysis of
spectral energy distributions for the sample show dust temperatures for the
envelopes tend to be between 190 and 260 K. We suggest that dust scattering is
indeed responsible for the optical intrinsic polarization in Li-rich giants.
Our findings indicate that non-spherical envelopes may appear as early as the
red giant phase of stellar evolution.Comment: to be published in A&A, 15 pages, 10 figures. Fig. 3 is available in
ftp://astroweb.iag.usp.br/pub/antonio/4270/4270.fig3.pd
A central limit theorem for the sojourn times of strongly ergodic Markov chains
Let Xn be an irreducible aperiodic recurrent Markov chain with countable state space I and with the mean recurrence times having second moments. There is proved a global central limit theorem for the properly normalized sojourn times. More precisely, if t(n)i=Σnk=1 Ãi(Xk), then the probability measures induced by {t(n)i/√n−√nÏ€i}iεI(Ï€i being the ergotic distribution) on the Hilbert-space of square summable I-sequences converge weakly in this space to a Gaussian measure determined by a certain weak potential operator
Gleason's theorem in a space with indefinite metric
An analog to the Gleason theorem for measures on logics of projections in indefinite metric spaces is proved