Are the majority of Sun-like stars single?

It has recently been suggested that, in the field, $\sim\!\!56\%$ of Sun-like stars ($0.8\,{\rm M}_{_\odot}\lesssim M_\star\lesssim 1.2\,{\rm M}_{_\odot}$) are single. We argue here that this suggestion may be incorrect, since it appears to be based on the multiplicity frequency of systems with Sun-like primaries, and therefore takes no account of Sun-like stars that are secondary (or higher-order) components in multiple systems. When these components are included in the reckoning, it seems likely that only $\sim\!46\%$ of Sun-like stars are single. This estimate is based on a model in which the system mass function has the form proposed by Chabrier, with a power-law Salpeter extension to high masses; there is a flat distribution of mass ratios; and the probability that a system of mass $M$ is a binary is $\,0.50 + 0.46\log_{_{10}}\!\left(M/{\rm M}_{_\odot}\right)\,$ for $\,0.08\,{\rm M}_{_\odot}\leq M\leq 12.5\,{\rm M}_{_\odot}$, $\,0\,$ for $\,M<0.08\,{\rm M}_{_\odot}$, and $\,1\,$ for $\,M>12.5\,{\rm M}_{_\odot}$. The constants in this last relation are chosen so that the model also reproduces the observed variation of multiplicity frequency with primary mass. However, the more qualitative conclusion, that a minority of Sun-like stars are single, holds up for virtually all reasonable values of the model parameters. Parenthetically, it is still likely that the majority of {\it all} stars in the field are single, but that is because most M Dwarfs probably are single.Comment: 6 pages. Accepted by MNRA

The intrinsic shapes of starless cores in Ophiuchus

Using observations of cores to infer their intrinsic properties requires the solution of several poorly constrained inverse problems. Here we address one of these problems, namely to deduce from the projected aspect ratios of the cores in Ophiuchus their intrinsic three-dimensional shapes. Four models are proposed, all based on the standard assumption that cores are randomly orientated ellipsoids, and on the further assumption that a core's shape is not correlated with its absolute size. The first and simplest model, M1, has a single free parameter, and assumes that the relative axes of a core are drawn randomly from a log-normal distribution with zero mean and standard deviation \sigma o. The second model, M2a, has two free parameters, and assumes that the log-normal distribution (with standard deviation \sigma o) has a finite mean, \mu o, defined so that \mu o<0 means elongated (prolate) cores are favoured, whereas \mu o>0 means flattened (oblate) cores are favoured. Details of the third model (M2b, two free parameters) and the fourth model (M4, four free parameters) are given in the text. Markov chain Monte Carlo sampling and Bayesian analysis are used to map out the posterior probability density functions of the model parameters, and the relative merits of the models are compared using Bayes factors. We show that M1 provides an acceptable fit to the Ophiuchus data with \sigma o ~ 0.57+/-0.06; and that, although the other models sometimes provide an improved fit, there is no strong justification for the introduction of their additional parameters.Comment: 10 pages, 8 figures. Accepted by MNRA

Q+\mathcal{Q}^{+}: Characterising the structure of young star clusters

Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of sub-structure. We suggest that, even at the simplest level, the internal structure of a fractal cluster requires the specification of three parameters. (i) The 3D fractal dimension, $\mathcal{D}$, measures the extent to which the clusters on one level of the nested hierarchy fill the volume of their parent cluster. (ii) The number of levels, $\mathcal{L}$, reflects the finite ratio between the linear size of the large root-cluster at the top of the hierarchy, and the smallest leaf-clusters at the bottom of the hierarchy. (iii) The volume-density scaling exponent, $\mathcal{C}=-\textrm{d}\ln[\delta n]/\textrm{d}\ln[L]$ measures the factor by which the excess density, $\delta n$, in a structure of scale $L$, exceeds that of the background formed by larger structures; it is similar, but not exactly equivalent, to the exponent in Larson's scaling relation between density and size for molecular clouds. We describe an algorithm which can be used to constrain the values of $({\cal D},{\cal L},{\cal C})$ and apply this method to artificial and observed clusters. We show that this algorithm is able to reliably describe the three dimensional structure of an artificial star cluster from the two dimensional projection, and quantify the varied structures observed in real and simulated clusters.Comment: Accepted by MNRA

On the effects of solenoidal and compressive turbulence in prestellar cores

We present the results of an ensemble of SPH simulations that follow the evolution of prestellar cores for $0.2\,{\rm Myr}$. All the cores have the same mass, and start with the same radius, density profile, thermal and turbulent energy. Our purpose is to explore the consequences of varying the fraction of turbulent energy, $\delta_\mathrm{sol}$, that is solenoidal, as opposed to compressive; specifically we consider $\delta_\mathrm{sol}=1,\,2/3,\,1/3,\,1/9\;{\rm and}\;0$. For each value of $\delta_\mathrm{sol}$, we follow ten different realisations of the turbulent velocity field, in order also to have a measure of the stochastic variance blurring any systematic trends. With low $\delta_\mathrm{sol}(<\!1/3)$ filament fragmentation dominates and delivers relatively high mass stars. Conversely, with high values of $\delta_\mathrm{sol}(>\!1/3)$ disc fragmentation dominates and delivers relatively low mass stars. There are no discernible systematic trends in the multiplicity statistics obtained with different $\delta_\mathrm{sol}$.Comment: 9 pages. Accepted by MNRA

Ravenstein Revisited: The Analysis of Migration, Then and Now

In 1876, 1885 and 1889, Ernst Ravenstein, an Anglo-German geographer, published papers on internal and international migration in Britain, Europe and North America. He generalized his findings as “laws of migration”, which have informed subsequent migration research. This paper aims to compare Ravenstein’s approach to investigating migration with how researchers have studied the phenomenon more recently. Ravenstein used lifetime migrant tables for counties from the 1871 and 1881 censuses of the British Isles. Data on lifetime migrants are still routinely collected but, because of the indeterminate time interval, they are rarely used to study internal migration. Today, internal migration measures from alternative sources are used to measure internal migration: fixed interval migrant data from censuses and surveys, continuous records of migrations from registers, and “big data” from telecommunications and internet companies. Ravenstein described and mapped county-level lifetime migration patterns, using the concepts of “absorption” and “dispersion”, using migration rates and net balances. Recently, researchers have used lifetime migrant stocks from consecutive censuses to estimate country to country flows for the world. In the last decade, an Australian-led team has built an international database of internal migration flow data and summary measures. Methods were developed to investigate the modifiable areal unit problem (MAUP), in order to design summary internal migration measures comparable across countries. Indicators of internal migration were produced for countries covering 80 percent of the world’s population. Ravenstein observed that most migrants moved only short distances, anticipating the development of “gravity” models of migration. Recent studies calibrated the relationship between migration and distance, using gravity models. For mid-19th century Britain, Ravenstein found the dominant direction of internal migration to be towards the “centres of commerce and industry”. Urbanization is still the dominant flow direction in most countries, though, late in the process, suburbanization, counter-urbanization and re-urbanization can occur. Ravenstein focussed on place-specific migration, whereas today researchers describe migration flows using area typologies, seeking spatial generality. Ravenstein said little about migrant attributes except that women migrated more than men. In recent decades, the behaviour of migrants by age, sex, education, ethnicity, social class and partnership status have been studied intensively, using microdata from censuses and surveys. Knowledge about processes influencing internal and international migration has rarely been built into demographic projections. Scenarios that link migration with sub-national or national inequalities and with climate or environmental change are influencing the design of policies to reduce inequalities or slow global warming

Sub-national projection methods for Scotland and Scottish areas: a review and recommendations

This report responds to a request for advice by National Records of Scotland (NRS) on how to adapt and improve the methodology used for the Scotland Sub-National Population Projections (SNPP). The 2014- based Scotland SNPP are currently being prepared