41 research outputs found
On Predicting the Solar Cycle using Mean-Field Models
We discuss the difficulties of predicting the solar cycle using mean-field
models. Here we argue that these difficulties arise owing to the significant
modulation of the solar activity cycle, and that this modulation arises owing
to either stochastic or deterministic processes. We analyse the implications
for predictability in both of these situations by considering two separate
solar dynamo models. The first model represents a stochastically-perturbed flux
transport dynamo. Here even very weak stochastic perturbations can give rise to
significant modulation in the activity cycle. This modulation leads to a loss
of predictability. In the second model, we neglect stochastic effects and
assume that generation of magnetic field in the Sun can be described by a fully
deterministic nonlinear mean-field model -- this is a best case scenario for
prediction. We designate the output from this deterministic model (with
parameters chosen to produce chaotically modulated cycles) as a target
timeseries that subsequent deterministic mean-field models are required to
predict. Long-term prediction is impossible even if a model that is correct in
all details is utilised in the prediction. Furthermore, we show that even
short-term prediction is impossible if there is a small discrepancy in the
input parameters from the fiducial model. This is the case even if the
predicting model has been tuned to reproduce the output of previous cycles.
Given the inherent uncertainties in determining the transport coefficients and
nonlinear responses for mean-field models, we argue that this makes predicting
the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap
In--out intermittency in PDE and ODE models
We find concrete evidence for a recently discovered form of intermittency,
referred to as in--out intermittency, in both PDE and ODE models of mean field
dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in
systems with invariant submanifolds and, as opposed to on--off intermittency
which can also occur in skew product systems, it requires an absence of skew
product structure. By this we mean that the dynamics on the attractor
intermittent to the invariant manifold cannot be expressed simply as the
dynamics on the invariant subspace forcing the transverse dynamics; the
transverse dynamics will alter that tangential to the invariant subspace when
one is far enough away from the invariant manifold.
Since general systems with invariant submanifolds are not likely to have skew
product structure, this type of behaviour may be of physical relevance in a
variety of dynamical settings.
The models employed here to demonstrate in--out intermittency are
axisymmetric mean--field dynamo models which are often used to study the
observed large scale magnetic variability in the Sun and solar-type stars. The
occurrence of this type of intermittency in such models may be of interest in
understanding some aspects of such variabilities.Comment: To be published in Chaos, June 2001, also available at
http://www.eurico.web.co
Generalized Boltzmann Equation for Lattice Gas Automata
In this paper, for the first time a theory is formulated that predicts
velocity and spatial correlations between occupation numbers that occur in
lattice gas automata violating semi-detailed balance. Starting from a coupled
BBGKY hierarchy for the -particle distribution functions, cluster expansion
techniques are used to derive approximate kinetic equations. In zeroth
approximation the standard nonlinear Boltzmann equation is obtained; the next
approximation yields the ring kinetic equation, similar to that for hard sphere
systems, describing the time evolution of pair correlations. As a quantitative
test we calculate equal time correlation functions in equilibrium for two
models that violate semi-detailed balance. One is a model of interacting random
walkers on a line, the other one is a two-dimensional fluid type model on a
triangular lattice. The numerical predictions agree very well with computer
simulations.Comment: 31 pages LaTeX, 12 uuencoded tar-compressed Encapsulated PostScript
figures (`psfig' macro), hardcopies available on request, 78kb + 52k
The Differential Rotation of Kappa1 Ceti as Observed by MOST
We first reported evidence for differential rotation of Kappa1 Ceti in Paper
I. In this paper we demonstrate that the differential rotation pattern closely
matches that for the Sun. This result is based on additional MOST
(Microvariability & Oscillations of STars) observations in 2004 and 2005, to
complement the 2003 observations discussed in Paper I. Using StarSpotz, a
program developed specifically to analyze MOST photometry, we have solved for
k, the differential rotation coefficient, and P_{EQ}, the equatorial rotation
period using the light curves from all three years. The spots range in latitude
from 10 to 75 degrees and k = 0.090^{+0.006}_{-0.005} -- less than the solar
value but consistent with the younger age of the star. k is also well
constrained by the independent spectroscopic estimate of vsini. We demonstrate
independently that the pattern of differential rotation with latitude in fact
conforms to solar.
Details are given of the parallel tempering formalism used in finding the
most robust solution which gives P_{EQ} = 8.77^{+0.03}_{-0.04} days -- smaller
than that usually adopted, implying an age < 750 My. Our values of P_{EQ} and k
can explain the range of rotation periods determined by others by spots or
activity at a variety of latitudes. Historically, Ca II activity seems to occur
consistently between latitudes 50 and 60 degrees which might indicate a
permanent magnetic feature. Knowledge of k and P_{EQ} are key to understanding
the dynamo mechanism and rotation structure in the convective zone as well
assessing age for solar-type stars. We recently published values of k and
P_{EQ} for epsilon Eri based on MOST photometry and expect to analyze MOST
light curves for several more spotted, solar-type stars.Comment: 16 pages, 7 Figures, published in Ap
MOST detects variability on tau Bootis possibly induced by its planetary companion
(abridged) There is considerable interest in the possible interaction between
parent stars and giant planetary companions in 51 Peg-type systems. We
demonstrate from MOST satellite photometry and Ca II K line emission that there
has been a persistent, variable region on the surface of tau Boo A which
tracked its giant planetary companion for some 440 planetary revolutions and
lies ~68deg (phi=0.8) in advance of the sub-planetary point. The light curves
are folded on a range of periods centered on the planetary orbital period and
phase dependent variability is quantified by Fourier methods and by the mean
absolute deviation (MAD) of the folded data for both the photometry and the Ca
II K line reversals. The region varies in brightness on the time scale of a
rotation by ~1 mmag. In 2004 it resembled a dark spot of variable depth, while
in 2005 it varied between bright and dark. Over the 123 planetary orbits
spanned by the photometry the variable region detected in 2004 and in 2005 are
synchronised to the planetary orbital period within 0.0015 d. The Ca II K line
in 2001, 2002 and 2003 also shows enhanced K-line variability centered on
phi=0.8, extending coverage to some 440 planetary revolutions. The apparently
constant rotation period of the variable region and its rapid variation make an
explanation in terms of conventional star spots unlikely. The lack of
complementary variability at phi=0.3 and the detection of the variable region
so far in advance of the sub-planetary point excludes tidal excitation, but the
combined photometric and Ca II K line reversal results make a good case for an
active region induced magnetically on the surface of tau Boo A by its planetary
companion.Comment: 7 pages, 7 figures; accepted for publication in A&
The case for a distributed solar dynamo shaped by near-surface shear
Arguments for and against the widely accepted picture of a solar dynamo being
seated in the tachocline are reviewed and alternative ideas concerning dynamos
operating in the bulk of the convection zone, or perhaps even in the
near-surface shear layer, are discussed. Based on the angular velocities of
magnetic tracers it is argued that the observations are compatible with a
distributed dynamo that may be strongly shaped by the near-surface shear layer.
Direct simulations of dynamo action in a slab with turbulence and shear are
presented to discuss filling factor and tilt angles of bipolar regions in such
a model.Comment: 10 pages, 6 figures, Astrophys. J. 625 (scheduled for the 1 June 2005
issue
The Origin of T Tauri X-ray Emission: New Insights from the Chandra Orion Ultradeep Project
We use the data of the Chandra Orion Ultradeep Project (COUP) to study the
nearly 600 X-ray sources that can be reliably identified with optically well
characterized T Tauri stars (TTS) in the Orion Nebula Cluster. We detect X-ray
emission from more than 97% of the optically visible late-type (spectral types
F to M) cluster stars. This proofs that there is no ``X-ray quiet'' population
of late-type stars with suppressed magnetic activity. All TTS with known
rotation periods lie in the saturated or super-saturated regime of the relation
between activity and Rossby numbers seen for main-sequence (MS) stars, but the
TTS show a much larger scatter in X-ray activity than seen for the MS stars.
Strong near-linear relations between X-ray luminosities, bolometric
luminosities and mass are present. We also find that the fractional X-ray
luminosity rises slowly with mass over the 0.1 - 2 M_sun range. The plasma
temperatures determined from the X-ray spectra of the TTS are much hotter than
in MS stars, but seem to follow a general solar-stellar correlation between
plasma temperature and activity level. The large scatter about the relations
between X-ray activity and stellar parameters seems to be related to the
influence of accretion on the X-ray emission. While the X-ray activity of the
non-accreting TTS is consistent with that of rapidly rotating MS stars, the
accreting stars are less X-ray active (by a factor of ~2-3 on average) and
produce much less well defined correlations than the non-accretors. We discuss
possible reasons for the suppression of X-ray emission by accretion and the
implications of our findings on long-standing questions related to the origin
of the X-ray emission from young stars.Comment: accepted for ApJS, COUP Special Issu
Feint Lines: Notes on the Creation of a Skateboard Choreography
Magnetic fields on a range of scales play a large role in the ecosystems of
galaxies, both in the galactic disk and in the extended layers of gas away from
the plane. Observing magnetic field strength, structure and orientation is
complex, and necessarily indirect. Observational data of magnetic fields in the
halo of the Milky Way are scarce, and non-conclusive about the large-scale
structure of the field. In external galaxies, various large-scale
configurations of magnetic fields are measured, but many uncertainties about
exact configurations and their origin remain. There is a strong interaction
between magnetic fields and other components in the interstellar medium such as
ionized and neutral gas and cosmic rays. The energy densities of these
components are comparable on large scales, indicating that magnetic fields are
not passive tracers but that magnetic field feedback on the other interstellar
medium components needs to be taken into account.Comment: 13 pages, 7 figures. Accepted in Space Science Review