Binaries and the dynamical mass of star clusters

The total mass of a distant star cluster is often derived from the virial theorem, using line-of-sight velocity dispersion measurements and half-light radii, under the implicit assumption that all stars are single (although it is known that most stars form part of binary systems). The components of binary stars exhibit orbital motion, which increases the measured velocity dispersion, resulting in a dynamical mass overestimation. In this article we quantify the effect of neglecting the binary population on the derivation of the dynamical mass of a star cluster. We find that the presence of binaries plays an important role for clusters with total mass M < 10^5 Msun; the dynamical mass can be significantly overestimated (by a factor of two or more). For the more massive clusters, with Mcl > 10^5 Msun, binaries do not affect the dynamical mass estimation significantly, provided that the cluster is significantly compact (half-mass radius < 5 pc).Comment: Comments: 2 pages. Conference proceedings for IAUS246 'Dynamical Evolution of Dense Stellar Systems', ed. E. Vesperini (Chief Editor), M. Giersz, A. Sills, Capri, Sept. 200

The origin of very wide binary systems

The majority of stars in the Galactic field and halo are part of binary or multiple systems. A significant fraction of these systems have orbital separations in excess of thousands of astronomical units, and systems wider than a parsec have been identified in the Galactic halo. These binary systems cannot have formed through the 'normal' star-formation process, nor by capture processes in the Galactic field. We propose that these wide systems were formed during the dissolution phase of young star clusters. We test this hypothesis using N-body simulations of evolving star clusters and find wide binary fractions of 1-30%, depending on initial conditions. Moreover, given that most stars form as part of a binary system, our theory predicts that a large fraction of the known wide 'binaries' are, in fact, multiple systems.Comment: 4 pages, 1 figure, to appear in the proceedings of IAU Symposium 266, eds. R. de Grijs & J.R.D. Lepin

The dynamical fate of planetary systems in young star clusters

We carry out N-body simulations to examine the effects of dynamical interactions on planetary systems in young open star clusters. We explore how the planetary populations in these star clusters evolve, and how this evolution depends on the initial amount of substructure, the virial ratio, the cluster mass and density, and the initial semi-major axis of the planetary systems. The fraction of planetary systems that remains intact as a cluster member, fbps, is generally well-described by the functional form fbps=f0(1+[a/a0]^c)^-1, where (1-f0) is the fraction of stars that escapes from the cluster, a0 the critical semi-major axis for survival, and c a measure for the width of the transition region. The effect of the initial amount of substructure over time can be quantified as fbps=A(t)+B(D), where A(t) decreases nearly linearly with time, and B(D) decreases when the clusters are initially more substructured. Provided that the orbital separation of planetary systems is smaller than the critical value a0, those in clusters with a higher initial stellar density (but identical mass) have a larger probability of escaping the cluster intact. These results help us to obtain a better understanding of the difference between the observed fractions of exoplanets-hosting stars in star clusters and in the Galactic field. It also allows us to make predictions about the free-floating planet population over time in different stellar environments.Comment: 14 pages, 9 figures, accepted for publication in MNRA

The primordial binary population in the association Sco OB2

Observations over the last decade have indicated that a large fraction of the stars are part of a binary or multiple system. For our understanding of star formation it is therefore of crucial importance to characterise the outcome of the star forming process in terms of binary parameters. This thesis describes the recovery of the primordial binary population in the nearby OB association Sco OB2. The current binary population in Sco OB2 is first recovered using two adaptive optics surveys (ADONIS, NAOS-CONICA), a literature study, and a detailed analysis of the selection effects of visual, spectroscopic, and astrometric binary surveys. Our results indicate a binary fraction close to 100%. The mass ratio distribution (among A/B primaries) has the form f(q) = q^-0.4, while random pairing is excluded. The semi-major axis distribution has the form f(log a) = constant. Due to its youth and low stellar density, the current binary population of Sco OB2 is very similar to its primordial binary population. Our study further indicates a small brown dwarf companion frequency and a small substellar-to-stellar companion frequency among A and B type stars. These properties, often referred to as the brown dwarf desert, are a natural result of the mass ratio distribution in Sco OB2. The embryo ejection scenario is not necessary to explain observations. The brown dwarf desert may be ascribed to an excess of planetary companions, rather than by a lack of brown dwarf companions.Comment: PhD thesis, University of Amsterdam, 2006 (very low resolution). Full-resolution PDF available at http://dare.uva.nl/en/record/19564

The Link Between Ejected Stars, Hardening and Eccentricity Growth of Super Massive Black Holes in Galactic Nuclei

The hierarchical galaxy formation picture suggests that super massive black holes (MBHs) observed in galactic nuclei today have grown from coalescence of massive black hole binaries (MBHB) after galaxy merging. Once the components of a MBHB become gravitationally bound, strong three-body encounters between the MBHB and stars dominate its evolution in a "dry" gas free environment, and change the MBHB's energy and angular momentum (semi-major axis, eccentricity and orientation). Here we present high accuracy direct N-body simulations of spherical and axisymmetric (rotating) galactic nuclei with order a million stars and two massive black holes that are initially unbound. We analyze the properties of the ejected stars due to slingshot effects from three-body encounters with the MBHB in detail. Previous studies have investigated the eccentricity and energy changes of MBHs using approximate models or Monte-Carlo three body scatterings. We find general agreement with the average results of previous semi-analytic models for spherical galactic nuclei, but our results show a large statistical variation. Our new results show many more phase space details of how the process works, and also show the influence of stellar system rotation on the process. We detect that the angle between the orbital plane of the MBHBs and that of the stellar system (when it rotates) influences the phase-space properties of the ejected stars. We also find that massive MBHB tend to switch stars with counter-rotating orbits into co-rotating orbits during their interactions.Comment: 22 pages, 8 figures, accepted for publication in Ap

Clearing residual planetesimals by sweeping secular resonances in transitional disks: a lone-planet scenario for the wide gaps in debris disks around Vega and Fomalhaut

Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent `lone-planet' scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. During the depletion of the disk gas, the planet's secular resonance propagates inward and clears a wide gap over an extended region of the disk. Although some residual intermediate-size planetesimals may remain in the gap, their surface density is too low to either produce super-Earths or lead to sufficiently frequent disruptive collisions to generate any observable dusty signatures. The main advantage of this lone-planet sweeping-secular-resonance model over the previous multiple gas giant tidal truncation scenario is the relaxed requirement on the number of gas giants. The observationally inferred upper mass limit can also be satisfied provided the hypothetical planet has a significant eccentricity. A significant fraction of solar or more massive stars bear gas giant planets with significant eccentricities. If these planets acquired their present-day kinematic properties prior to the depletion of their natal disks, their sweeping secular resonance would effectively impede the retention of neighboring planets and planetesimals over a wide range of orbital semi-major axes.Comment: 20 pages, 12 figures. Accepted for publication in Ap

Close encounters involving free-floating planets in star clusters

Instabilities in planetary systems can result in the ejection of planets from their host system, resulting in free-floating planets (FFPs). If this occurs in a star cluster, the FFP may remain bound to the star cluster for some time and interact with the other cluster members until it is ejected. Here, we use $N$-body simulations to characterise close star-planet and planet-planet encounters and the dynamical fate of the FFP population in star clusters containing $500-2000$ single or binary star members. We find that FFPs ejected from their planetary system at low velocities typically leave the star cluster 40% earlier than their host stars, and experience tens of close ($<1000$ AU) encounters with other stars and planets before they escape. The fraction of FFPs that experiences a close encounter depends on both the stellar density and the initial velocity distribution of the FFPs. Approximately half of the close encounters occur within the first 30 Myr, and only 10% occur after 100 Myr. The periastron velocity distribution for all encounters is well-described by a modified Maxwell-Bolzmann distribution, and the periastron distance distribution is linear over almost the entire range of distances considered, and flattens off for very close encounters due to strong gravitational focusing. Close encounters with FFPs can perturb existing planetary systems and their debris structures, and they can result in re-capture of FFPs. In addition, these FFP populations may be observed in young star clusters in imaging surveys; a comparison between observations and dynamical predictions may provide clues to the early phases of stellar and planetary dynamics in star clusters.Comment: Accepted for publication in MNRAS; 18 pages, 12 figure

Stability of Multiplanetary Systems in Star Clusters

Most stars form in star clusters and stellar associated. To understand the roles of star cluster environments in shaping the dynamical evolution of planetary systems, we carry out direct $N$-body simulations of four planetary systems models in three different star cluster environments with respectively N=2k, 8k and 32k stars. In each cluster, an ensemble of initially identical planetary systems are assigned to solar-type stars with $\sim 1 M_{\odot}$ and evolved for 50~Myr. We found that following the depletion of protoplanetary disks, external perturbations and planet-planet interactions are two driving mechanisms responsible for the destabilization of planetary systems. The planet survival rate varies from $\sim 95\%$ in the N=2k cluster to $\sim 60\%$ in the N=32k cluster, which suggests that most planetary systems can indeed survive in low-mass clusters, except in the central regions. We also find that planet ejections through stellar encounters are cumulative processes, as only $\sim 3\%$ of encounters are strong enough to excite the eccentricity by $\Delta e \geq 0.5$. Short-period planets can be perturbed through orbit crossings with long-period planets. When taking into account planet-planet interactions, the planet ejection rate nearly doubles, and therefore multiplicity contributes to the vulnerability of planetary systems. In each ensemble, $\sim 0.2\%$ of planetary orbits become retrograde due to random directions of stellar encounters. Our results predict that young low-mass star clusters are promising sites for next-generation planet surveys, yet low planet detection rates are expected in dense globular clusters such as 47 Tuc. Nevertheless, planets in denser stellar environments are likely to have shorter orbital periods, which enhances their detectability.Comment: 19 pages, 13 figures, 4 tables, accepted for publication in MNRA