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

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

An electromyographic evaluation of dual role breathing and upper body muscles in response to front crawl swimming

The upper body trunk musculature is key in supporting breathing, propulsion, and stabilization during front crawl swimming. The aim of this study was to determine if the latissimus dorsi, pectoralis major, and serratus anterior contributed to the development of inspiratory muscle fatigue observed following front crawl swimming. Fourteen trained swimmers completed a 200-m front crawl swim at 90% of race pace. Maximal inspiratory and expiratory mouth pressures (PImax and PEmax) were assessed before (baseline) and after each swim, and electromyography was recorded from the three muscles. Post-swim PImax fell by 11% (P < 0.001, d = 0.57) and the median frequency (MDF: a measure of fatigue) of the latissimus dorsi, pectoralis major, and serratus anterior fell to 90% (P = 0.001, d = 1.57), 87% (P = 0.001, r = −0.60) and 89% (P = 0.018, d = 1.04) of baseline, respectively. The fall in serratus anterior MDF was correlated with breathing frequency (r = 0.675, P = 0.008) and stroke rate (r = 0.639, P = 0.014). The results suggest that the occurrence of inspiratory muscle fatigue was partly caused by fatigue of these muscles, and that breathing frequency and stroke rate particularly affect the serratus anterior

Modelling the structure of star clusters with fractional Brownian motion

The degree of fractal substructure in molecular clouds can be quantified by comparing them with Fractional Brownian Motion (FBM) surfaces or volumes. These fields are self-similar over all length scales and characterised by a drift exponent $H$, which describes the structural roughness. Given that the structure of molecular clouds and the initial structure of star clusters are almost certainly linked, it would be advantageous to also apply this analysis to clusters. Currently, the structure of star clusters is often quantified by applying $\mathcal{Q}$ analysis. $\mathcal{Q}$ values from observed targets are interpreted by comparing them with those from artificial clusters. These are typically generated using a Box-Fractal (BF) or Radial Density Profile (RDP) model. We present a single cluster model, based on FBM, as an alternative to these models. Here, the structure is parameterised by $H$, and the standard deviation of the log-surface/volume density $\sigma$. The FBM model is able to reproduce both centrally concentrated and substructured clusters, and is able to provide a much better match to observations than the BF model. We show that $\mathcal{Q}$ analysis is unable to estimate FBM parameters. Therefore, we develop and train a machine learning algorithm which can estimate values of $H$ and $\sigma$, with uncertainties. This provides us with a powerful method for quantifying the structure of star clusters in terms which relate to the structure of molecular clouds. We use the algorithm to estimate the $H$ and $\sigma$ for several young star clusters, some of which have no measurable BF or RDP analogue.Comment: 11 Pages, accepted by MNRA

Temperature as a third dimension in column-density mapping of dusty astrophysical structures associated with star formation

We present point process mapping (PPMAP), a Bayesian procedure that uses images of dust continuum emission at multiple wavelengths to produce resolution-enhanced image cubes of differential column density as a function of dust temperature and position. PPMAP is based on the generic ‘point process formalism, whereby the system of interest (in this case, a dusty astrophysical structure such as a filament or pre-stellar core) is represented by a collection of points in a suitably defined state space. It can be applied to a variety of observational data, such as Herschel images, provided only that the image intensity is delivered by optically thin dust in thermal equilibrium. PPMAP takes full account of the instrumental point-spread functions and does not require all images to be degraded to the same resolution. We present the results of testing using simulated data for a pre-stellar core and a fractal turbulent cloud, and demonstrate its performance with real data from the Herschel infrared Galactic Plane Survey (Hi-GAL). Specifically, we analyse observations of a large filamentary structure in the CMa OB1 giant molecular cloud. Histograms of differential column density indicate that the warm material (T ≳ 13 K) is distributed lognormally, consistent with turbulence, but the column densities of the cooler material are distributed as a high-density tail, consistent with the effects of self-gravity. The results illustrate the potential of PPMAP to aid in distinguishing between different physical components along the line of sight in star-forming clouds, and aid the interpretation of the associated Probability distribution functions (PDFs) of column density