32 research outputs found
The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables
The Hamiltonian theory of Earth rotation, known as the Kinoshita-Souchay
theory, operates with nonosculating Andoyer elements. This situation parallels
a similar phenomenon that often happens (but seldom gets noticed) in orbital
dynamics, when the standard Lagrange-type or Delaunay-type planetary equations
unexpectedly render nonosculating orbital elements. In orbital mechanics,
osculation loss happens when a velocity-dependent perturbation is plugged into
the standard planetary equations. In attitude mechanics, osculation is lost
when an angular-velocity-dependent disturbance is plugged in the standard
dynamical equations for the Andoyer elements. We encounter exactly this
situation in the theory of Earth rotation, because this theory contains an
angular-velocity-dependent perturbation (the switch from an inertial frame to
that associated with the precessing ecliptic of date).
While the osculation loss does not influence the predictions for the figure
axis of the planet, it considerably alters the predictions for the
instantaneous spin-axis' orientation. We explore this issue in great detail
Anisotropic distribution functions for spherical galaxies
A method is presented for finding anisotropic distribution functions for
stellar systems with known, spherically symmetric, densities, which depends
only on the two classical integrals of the energy and the magnitude of the
angular momentum. It requires the density to be expressed as a sum of products
of functions of the potential and of the radial coordinate. The solution
corresponding to this type of density is in turn a sum of products of functions
of the energy and of the magnitude of the angular momentum. The products of the
density and its radial and transverse velocity dispersions can be also
expressed as a sum of products of functions of the potential and of the radial
coordinate. Several examples are given, including some of new anisotropic
distribution functions. This device can be extended further to the related
problem of finding two-integral distribution functions for axisymmetric
galaxies.Comment: 5 figure
Indirect Dark Matter Detection from Dwarf Satellites: Joint Expectations from Astrophysics and Supersymmetry
We present a general methodology for determining the gamma-ray flux from
annihilation of dark matter particles in Milky Way satellite galaxies, focusing
on two promising satellites as examples: Segue 1 and Draco. We use the
SuperBayeS code to explore the best-fitting regions of the Constrained Minimal
Supersymmetric Standard Model (CMSSM) parameter space, and an independent MCMC
analysis of the dark matter halo properties of the satellites using published
radial velocities. We present a formalism for determining the boost from halo
substructure in these galaxies and show that its value depends strongly on the
extrapolation of the concentration-mass (c(M)) relation for CDM subhalos down
to the minimum possible mass. We show that the preferred region for this
minimum halo mass within the CMSSM with neutralino dark matter is ~10^-9-10^-6
solar masses. For the boost model where the observed power-law c(M) relation is
extrapolated down to the minimum halo mass we find average boosts of about 20,
while the Bullock et al (2001) c(M) model results in boosts of order unity. We
estimate that for the power-law c(M) boost model and photon energies greater
than a GeV, the Fermi space-telescope has about 20% chance of detecting a dark
matter annihilation signal from Draco with signal-to-noise greater than 3 after
about 5 years of observation
N-body simulations of gravitational dynamics
We describe the astrophysical and numerical basis of N-body simulations, both
of collisional stellar systems (dense star clusters and galactic centres) and
collisionless stellar dynamics (galaxies and large-scale structure). We explain
and discuss the state-of-the-art algorithms used for these quite different
regimes, attempt to give a fair critique, and point out possible directions of
future improvement and development. We briefly touch upon the history of N-body
simulations and their most important results.Comment: invited review (28 pages), to appear in European Physics Journal Plu
Dense Stellar Populations: Initial Conditions
This chapter is based on four lectures given at the Cambridge N-body school
"Cambody". The material covered includes the IMF, the 6D structure of dense
clusters, residual gas expulsion and the initial binary population. It is aimed
at those needing to initialise stellar populations for a variety of purposes
(N-body experiments, stellar population synthesis).Comment: 85 pages. To appear in The Cambridge N-body Lectures, Sverre Aarseth,
Christopher Tout, Rosemary Mardling (eds), Lecture Notes in Physics Series,
Springer Verla
The Physics of Star Cluster Formation and Evolution
© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00689-4.Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and effectively channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work.Peer reviewe
Multiple Solutions in Preliminary Orbit Determination from Three Observations
SUMMARY Charlier's theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace's method of preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized theory works for both Laplace's and Gauss' methods. We also provide a geometric definition of a curve that generalizes Charlier's limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier's: they may change according to the value of a parameter that depends on the observations
A model-based approach to climate reconstruction using tree-ring data
Quantifying long-term historical climate is fundamental to understanding recent climate change. Most instrumentally recorded climate data are only available for the past 200 years, s o proxy observations from natural archives are often considered. We describe a model-based approach to reconstructing climate defined in terms of raw tree-ring measurement data that simultaneously accounts for non-climatic and climatic variability. In this approach we specify a joint model for the tree-ring data and climate variable that we fit using Bayesian inference. We consider a range of prior densities and compare the modeling approach to current methodology using an example case of Scots pine from Torneträsk, Sweden to reconstruct growing season temperature. We describe how current approaches translate into particular model assumptions. We explore how changes to various components in the model-based approach affect the resulting reconstruction. We show that minor changes in model specification can have little effect on model fit but lead to large changes in the predictions. In particular, the periods of relatively warmer and cooler temperatures are robust between models, but the magnitude of the resulting temperatures are highly model dependent. Such sensitivity may not be apparent with traditional approaches because the underlying statistical model is often hidden or poorly described
Comparative compositions of metabolites and dietary fibre components in doughs and breads produced from bread wheat, emmer and spelt and using yeast and sourdough processes
Wholemeal flours from blends of bread wheat, emmer and spelt were processed into bread using yeast-based and sourdough fermentation. The bread wheat flour contained significantly higher concentrations of total dietary fibre and fructans than the spelt and emmer flours, the latter having the lowest contents. Breadmaking using sourdough and yeast systems resulted in changes in composition from flour to dough to bread including increases in organic acids and mannitol in the sourdough system and increases in amino acids and sugars (released by hydrolysis of proteins and starch, respectively) in both processing systems. The concentrations of fructans and raffinose (the major endogenous FODMAPs) were reduced by yeast and sourdough fermentation, with yeast having the greater effect. Both systems resulted in greater increases in sugars and glycerol in emmer than in bread wheat and spelt, but the significance of these differences for human health has not been established