The evolution of the Sun's birth cluster and the search for the solar siblings with Gaia

We use self-consistent numerical simulations of the evolution and disruption of the Sun's birth cluster in the Milky Way potential to investigate the present-day phase space distribution of the Sun's siblings. The simulations include the gravitational N-body forces within the cluster and the effects of stellar evolution on the cluster population. In addition the gravitational forces due to the Milky Way potential are accounted for in a self-consistent manner. Our aim is to understand how the astrometric and radial velocity data from the Gaia mission can be used to pre-select solar sibling candidates. We vary the initial conditions of the Sun's birth cluster, as well as the parameters of the Galactic potential. We show that the disruption time-scales of the cluster are insensitive to the details of the non-axisymmetric components of the Milky Way model and we make predictions, averaged over the different simulated possibilities, about the number of solar siblings that should appear in surveys such as Gaia or GALAH. We find a large variety of present-day phase space distributions of solar siblings, which depend on the cluster initial conditions and the Milky Way model parameters. We show that nevertheless robust predictions can be made about the location of the solar siblings in the space of parallaxes ($\varpi$), proper motions ($\mu$) and radial velocities ($V_\mathrm{r}$). By calculating the ratio of the number of simulated solar siblings to that of the number of stars in a model Galactic disk, we find that this ratio is above 0.5 in the region given by: $\varpi \geq 5$mas, $4 \leq \mu \leq 6$masyr$^{-1}$, and $-2\leq V_\mathrm{r} \leq 0$kms$^{-1}$. Selecting stars from this region should increase the probability of success in identifying solar siblings through follow up observations [Abridged].Comment: 13 pages, 7 figures. Accepted for publication in MNRA

Face-on accretion onto a protoplanetary disc

Globular clusters (GCs) are known to harbor multiple stellar populations. To explain these observations Bastian et al. suggested a scenario in which a second population is formed by the accretion of enriched material onto the low-mass stars in the initial GC population. The idea is that the low-mass, pre-main sequence stars sweep up gas expelled by the massive stars of the same generation into their protoplanetary disc as they move through the GC core. We perform simulations with 2 different smoothed particle hydrodynamics codes to investigate if a low-mass star surrounded by a protoplanetary disc can accrete the amount of enriched material required in this scenario. We focus on the gas loading rate onto the disc and star as well as on the lifetime of the disc. We find that the gas loading rate is a factor of 2 smaller than the geometric rate, because the effective cross section of the disc is smaller than its surface area. The loading rate is consistent for both codes, irrespective of resolution. The disc gains mass in the high resolution runs, but loses angular momentum on a time scale of 10^4 yrs. Two effects determine the loss of (specific) angular momentum in our simulations: 1) continuous ram pressure stripping and 2) accretion of material with no azimuthal angular momentum. Our study and previous work suggest that the former, dominant process is mainly caused by numerical rather than physical effects, while the latter is not. The latter process causes the disc to become more compact, increasing the surface density profile at smaller radii. The disc size is determined in the first place by the ram pressure when the flow first hits the disc. Further evolution is governed by the decrease in the specific angular momentum of the disc. We conclude that the size and lifetime of the disc are probably not sufficient to accrete the amount of mass required in Bastian et al.'s scenario.Comment: Accepted for publication in A&A, 15 pages, 5 figures, 4 table

A note on polynomially growing C-0-semigroups

We characterize polynomial growth of a $C_0$-semigroup in terms of the first power of the resolvent of its generator. We do this for a class of semigroups which includes $C_0$-semigroups on Hilbert spaces and analytic semigroups on Banach spaces. Furthermore, we characterize polynomial growth for discrete semigroups

Demand for wool by grade

The aims of the project were to examine the relationships between auction prices of different types of wool, to identify categories of wool and to investigate substitution effects amongst wools. A modelling framework was developed which enabled these relationships to be analysed. While there are some clear avenues for further research, this study makes some useful first steps towards a conceptualisation of wool markets

Monte-Carlo Simulations of Globular Cluster Evolution - I. Method and Test Calculations

We present a new parallel supercomputer implementation of the Monte-Carlo method for simulating the dynamical evolution of globular star clusters. Our method is based on a modified version of Henon's Monte-Carlo algorithm for solving the Fokker-Planck equation. Our code allows us to follow the evolution of a cluster containing up to 5x10^5 stars to core collapse in < 40 hours of computing time. In this paper we present the results of test calculations for clusters with equal-mass stars, starting from both Plummer and King model initial conditions. We consider isolated as well as tidally truncated clusters. Our results are compared to those obtained from approximate, self-similar analytic solutions, from direct numerical integrations of the Fokker-Planck equation, and from direct N-body integrations performed on a GRAPE-4 special-purpose computer with N=16384. In all cases we find excellent agreement with other methods, establishing our new code as a robust tool for the numerical study of globular cluster dynamics using a realistic number of stars.Comment: 35 pages, including 8 figures, submitted to ApJ. Revised versio