Binary mass ratios: system mass not primary mass

Binary properties are usually expressed (for good observational reasons) as a function of primary mass. It has been found that the distribution of companion masses – the mass ratio distribution – is different for different primary masses. We argue that system mass is the more fundamental physical parameter to use. We show that if system masses are drawn from a log-normal mass function, then the different observed mass ratio distributions as a function of primary mass, from M-dwarfs to A-stars, are all consistent with a universal, flat, system mass ratio distribution. We also show that the brown dwarf mass ratio distribution is not drawn from the same flat distribution, suggesting that the process which decides upon mass ratios is very different in brown dwarfs and stars

Comparisons between different techniques for measuring mass segregation

We examine the performance of four different methods which are used to measure mass segregation in star-forming regions: the radial variation of the mass function $\mathcal{M}_{\rm MF}$; the minimum spanning tree-based $\Lambda_{\rm MSR}$ method; the local surface density $\Sigma_{\rm LDR}$ method; and the $\Omega_{\rm GSR}$ technique, which isolates groups of stars and determines whether the most massive star in each group is more centrally concentrated than the average star. All four methods have been proposed in the literature as techniques for quantifying mass segregation, yet they routinely produce contradictory results as they do not all measure the same thing. We apply each method to synthetic star-forming regions to determine when and why they have shortcomings. When a star-forming region is smooth and centrally concentrated, all four methods correctly identify mass segregation when it is present. However, if the region is spatially substructured, the $\Omega_{\rm GSR}$ method fails because it arbitrarily defines groups in the hierarchical distribution, and usually discards positional information for many of the most massive stars in the region. We also show that the $\Lambda_{\rm MSR}$ and $\Sigma_{\rm LDR}$ methods can sometimes produce apparently contradictory results, because they use different definitions of mass segregation. We conclude that only $\Lambda_{\rm MSR}$ measures mass segregation in the classical sense (without the need for defining the centre of the region), although $\Sigma_{\rm LDR}$ does place limits on the amount of previous dynamical evolution in a star-forming region

Surviving gas expulsion with substructure

We investigate the reaction of clumpy stellar distributions to gas expulsion. We show that regions containing highly unbound substructures/subclusters after gas expulsion can produce a significant final bound cluster. The key quantity in determining if a region is able to form a bound cluster is the global virial ratio, and so regions must be looked at as a whole rather than by individual substructure/subclusters when determining if they might survive as a bound cluster

What does the IMF really tell us about star formation?

Obtaining accurate measurements of the initial mass function (IMF) is often considered to be the key to understanding star formation, and a universal IMF is often assumed to imply a universal star formation process. Here, we illustrate that different modes of star formation can result in the same IMF, and that, in order to truly understand star formation, a deeper understanding of the primordial binary population is necessary. Detailed knowledge on the binary fraction, mass ratio distribution, and other binary parameters, as a function of mass, is a requirement for recovering the star formation process from stellar population measurements

Mass segregation in star clusters is not energy equipartition

Mass segregation in star clusters is often thought to indicate the onset of energy equipartition, where the most massive stars impart kinetic energy to the lower-mass stars and brown dwarfs/free floating planets. The predicted net result of this is that the centrally concentrated massive stars should have significantly lower velocities than fast-moving low-mass objects on the periphery of the cluster. We search for energy equipartition in initially spatially and kinematically substructured N-body simulations of star clusters with N = 1500 stars, evolved for 100 Myr. In clusters that show significant mass segregation we find no differences in the proper motions or radial velocities as a function of mass. The kinetic energies of all stars decrease as the clusters relax, but the kinetic energies of the most massive stars do not decrease faster than those of lower-mass stars. These results suggest that dynamical mass segregation -- which is observed in many star clusters -- is not a signature of energy equipartition from two-body relaxation

Making top-heavy IMFs from canonical IMFs near the galactic centre

We show that dynamical evolution in a strong (Galactic Centre-like) tidal field can create clusters that would appear to have very top-heavy IMFs. The tidal disruption of single star forming events can leave several bound ‘clusters’ spread along 20 pc of the orbit within 1-2 Myr. These surviving (sub)clusters tend to contain an over-abundance of massive stars, with low-mass stars tending to be spread along the whole ‘tidal arm’. Therefore observing a cluster in a strong tidal field with a top-heavy IMF might well not mean the stars formed with a top-heavy IMF

How do binary clusters form?

Approximately 10 per cent of star clusters are found in pairs, known as binary clusters. We propose a mechanism for binary cluster formation; we use N-body simulations to show that velocity substructure in a single (even fairly smooth) region can cause binary clusters to form. This process is highly stochastic and it is not obvious from a region's initial conditions whether a binary will form and, if it does, which stars will end up in which cluster. We find the probability that a region will divide is mainly determined by its virial ratio, and a virial ratio above 'equilibrium' is generally necessary for binary formation. We also find that the mass ratio of the two clusters is strongly influenced by the initial degree of spatial substructure in the region

The Long-term Dynamical Evolution of Disk-fragmented Multiple Systems in the Solar Neighborhood

The origin of very low-mass hydrogen-burning stars, brown dwarfs (BDs), and planetary-mass objects (PMOs) at the low-mass end of the initial mass function is not yet fully understood. Gravitational fragmentation of circumstellar disks provides a possible mechanism for the formation of such low-mass objects. The kinematic and binary properties of very low-mass objects formed through disk fragmentation at early times (<10 Myr) were discussed in our previous paper. In this paper we extend the analysis by following the long-term evolution of diskfragmented systems up to an age of 10 Gyr, covering the ages of the stellar and substellar populations in the Galactic field. We find that the systems continue to decay, although the rates at which companions escape or collide with each other are substantially lower than during the first 10 Myr, and that dynamical evolution is limited beyond 1 Gyr. By t = 10 Gyr, about one third of the host stars are single, and more than half have only one companion left. Most of the other systems have two companions left that orbit their host star in widely separated orbits. A small fraction of companions have formed binaries that orbit the host star in a hierarchical triple configuration. The majority of such double-companion systems have internal orbits that are retrograde with respect to their orbits around their host stars. Our simulations allow a comparison between the predicted outcomes of disk fragmentation with the observed low-mass hydrogen-burning stars, BDs, and PMOs in the solar neighborhood. Imaging and radial velocity surveys for faint binary companions among nearby stars are necessary for verification or rejection of the formation mechanism proposed in this paper

The effect of the dynamical state of clusters on gas expulsion and infant mortality

The star formation efficiency (SFE) of a star cluster is thought to be the critical factor in determining if the cluster can survive for a significant (>50 Myr) time. There is an often quoted critical SFE of ~30 per cent for a cluster to survive gas expulsion. I reiterate that the SFE is not the critical factor, rather it is the dynamical state of the stars (as measured by their virial ratio) immediately before gas expulsion that is the critical factor. If the stars in a star cluster are born in an even slightly cold dynamical state then the survivability of a cluster can be greatly increased.Comment: 6 pages, 2 figures. Review talk given at the meeting on "Young massive star clusters - Initial conditions and environments", E. Perez, R. de Grijs, R. M. Gonzalez Delgado, eds., Granada (Spain), September 2007, Springer: Dordrecht. Replacement to correct mistake in a referenc

Finding binary star fractions in any distribution

Candidate visual binary systems are often found by identifying two stars that are closer together than would be expected by chance. However, in regions with non-trivial density distributions, the ‘random’ distances between stars varies because of the background distribution, as well as the presence of binaries. We show that when no binaries are present, the distribution of the ratios of the distances to the nearest and tenth nearest neighbours, d1/d10, is always well approximated by a Gaussian with mean 0.2–0.3 and variance 0.16–0.19 for any underlying density distribution. The introduction of binaries causes some (or all) nearest neighbours to become closer than expected by random chance, introducing a component to the distribution where d1/d10 is much lower than expected. We show how a simple single or double Gaussian fit to the distribution of d1/d10 can be used to find the binary fraction in any underlying density distribution quickly and simply