The Formation of Solar System Analogs in Young Star Clusters

The Solar system was once rich in the short-lived radionuclide (SLR) $^{26}$Al\, but deprived in $^{60}$Fe. Several models have been proposed to explain these anomalous abundances in SLRs, but none has been set within a self-consistent framework of the evolution of the Solar system and its birth environment. The anomalous abundance in $^{26}$Al may have originated from the accreted material in the wind of a massive \apgt 20\,$M_\odot$ Wolf-Rayet star, but the star could also have been a member of the parental star-cluster instead of an interloper or an older generation that enriched the proto-solar nebula. The protoplanetary disk at that time was already truncated around the Kuiper-cliff (at $45$ au) by encounters with another cluster members before it was enriched by the wind of the nearby Wolf-Rayet star. The supernova explosion of a nearby star, possibly but not necessarily the exploding Wolf-Rayet star, heated the disk to \apgt 1500K, melting small dust grains and causing the encapsulation and preservation of $^{26}$Al into vitreous droplets. This supernova, and possibly several others, caused a further abrasion of the disk and led to its observed tilt of $5.6\pm1.2^\circ$ with respect to the Sun's equatorial plane. The abundance of $^{60}$Fe originates from a supernova shell, but its preservation results from a subsequent supernova. At least two supernovae are needed (one to deliver $^{60}$Fe\, and one to preserve it in the disk) to explain the observed characteristics of the Solar system. The most probable birth cluster then has $N = 2500\pm300$ stars and a radius of $r_{\rm vir} = 0.75\pm0.25$ pc. We conclude that Solar systems equivalent systems form in the Milky Way Galaxy at a rate of about 30 per Myr, in which case approximately 36,000 Solar system analogues roam the Milky Way.Comment: Submitted to A&

Stellar disk destruction by dynamical interactions in the Orion Trapezium star cluster

We compare the observed size distribution of circum stellar disks in the Orion Trapezium cluster with the results of $N$-body simulations in which we incorporated an heuristic prescription for the evolution of these disks. In our simulations, the sizes of stellar disks are affected by close encounters with other stars (with disks). We find that the observed distribution of disk sizes in the Orion Trapezium cluster is excellently reproduced by truncation due to dynamical encounters alone. The observed distribution appears to be a sensitive measure of the past dynamical history of the cluster, and therewith on the conditions of the cluster at birth. The best comparison between the observed disk size distribution and the simulated distribution is realized with a cluster of $N = 2500\pm500$ stars with a half-mass radius of about 0.5\,pc in virial equilibrium (with a virial ratio of $Q = 0.5$, or somewhat colder $Q \simeq 0.3$), and with a density structure according to a fractal dimension of $F \simeq 1.6$. Simulations with these parameters reproduce the observed distribution of circum stellar disks in about 0.2--0.5\,Myr.Comment: submitted to MNRA

The origin of the two populations of blue stragglers in M30

We analyze the position of the two populations of blue stragglers in the globular cluster M30 in the Hertzsprung-Russell diagram. Both populations of blue stragglers are brighter than the cluster's turn-off, but one population (the blue blue-stragglers) align along the zero-age main-sequence whereas the (red) population is elevated in brightness (or colour) by $\sim 0.75$ mag. Based on stellar evolution and merger simulations we argue that the red population, which composes about 40\% of the blue stragglers in M 30, is formed at a constant rate of $\sim 2.8$ blue stragglers per Gyr over the last $\sim 10$ Gyr. The blue population is formed in a burst that started $\sim 3.2$ Gyr ago at a peak rate of $30$ blue stragglers per Gyr$^{-1}$ with an e-folding time scale of $0.93$ Gyr. We speculate that the burst resulted from the core collapse of the cluster at an age of about 9.8 Gyr, whereas the constantly formed population is the result of mass transfer and mergers through binary evolution. In that case about half the binaries in the cluster effectively result in a blue straggler.Comment: Accepted for publication as Letter in A&

The formation and dynamical evolution of young star clusters

Recent observations have revealed a variety of young star clusters, including embedded systems, young massive clusters, and associations. We study the formation and dynamical evolution of these clusters using a combination of simulations and theoretical models. Our simulations start with a turbulent molecular cloud that collapses under its own gravity. The stars are assumed to form in the densest regions in the collapsing cloud after an initial free-fall times of the molecular cloud. The dynamical evolution of these stellar distributions are continued by means of direct $N$-body simulations. The molecular clouds typical for the Milky Way Galaxy tend to form embedded clusters which evolve to resemble open clusters. The associations were initially considerably more clumpy, but lost their irregularity in about a dynamical time scale due to the relaxation process. The densest molecular clouds, which are absent in the Milky Way but are typical in starburst galaxies, form massive young star clusters. They indeed are rare in the Milky Way. Our models indicate a distinct evolutionary path from molecular clouds to open clusters and associations or to massive star clusters. The mass-radius relation for both types of evolutionary tracks excellently matches the observations. According to our calculations the time evolution of the half-mass radius for open clusters and associations follows $r_{\rm h}/{\rm pc}=2.7(t_{\rm age}/{\rm pc})^{2/3}$, whereas for massive star clusters $r_{\rm h}/{\rm pc}=0.34(t_{\rm age}/{\rm Myr})^{2/3}$. Both trends are consistent with the observed age-mass-radius relation for clusters in the Milky Way.Comment: 16 pages, 9 figures, accepted for publication in Ap

A debris disk under the influence of a wide planetary mass companion: The system of HD106906

The 13 Myr old star HD106906 is orbited by a debris disk of at least 0.067 M_Moon with an inner and outer radius of 20 AU and 120 AU, respectively, and by a planet at a distance of 650 AU. We use this curious combination of a close low-mass disk and a wide planet to motivate our simulations of this system. We study the parameter space of the initial conditions to quantify the mass loss from the debris disk and its lifetime under the influence of the planet. We find that when the planet orbits closer to the star than about 50 AU and with low inclination relative to the disk (less than about 10 degrees), more disk material is perturbed outside than inside the region constrained by observations on timescales shorter than 1 Myr. Considering the age of the system, such a short lifetime of the disk is incompatible with the timescale for planet--planet scattering which is one of the scenarios suggested to explain the wide separation of the planet. For some configurations when the planet's orbit is inclined with respect to the disk, the latter will start to wobble. We argue that this wobbling is caused by a mechanism similar to the Kozai--Lidov oscillations. We also observe various resonant structures (such as rings and spiral arms) induced in the disk by the planet.Comment: 10 pages, 9 figures, accepted for publication in MNRA