Fun for Two

We performed populations synthesis calculations of single stars and binaries and show that binary evolution is extremely important for Galactic astronomy. We review several binary evolution models and conclude that they give quite different results. These differences can be understood from the assumptions related to how mass is transfered in the binary systems. Most important are 1) the fraction of mass that is accreted by the companion star during mass transfer, 2) the amount of specific angular momentum which is carried away with the mass that leaves the binary system.Comment: 7 pages, 0 figures to appear in the proceeding of the IAU Symposium 200, "The Formation of Binary Stars" eds. H. Zinnecker and R. Mathie

Black hole mergers in the universe

Mergers of black-hole binaries are expected to release large amounts of energy in the form of gravitational radiation. However, binary evolution models predict merger rates too low to be of observational interest. In this paper we explore the possibility that black holes become members of close binaries via dynamical interactions with other stars in dense stellar systems. In star clusters, black holes become the most massive objects within a few tens of millions of years; dynamical relaxation then causes them to sink to the cluster core, where they form binaries. These black-hole binaries become more tightly bound by superelastic encounters with other cluster members, and are ultimately ejected from the cluster. The majority of escaping black-hole binaries have orbital periods short enough and eccentricities high enough that the emission of gravitational radiation causes them to coalesce within a few billion years. We predict a black-hole merger rate of about $1.6 \times 10^{-7}$ per year per cubic megaparsec, implying gravity wave detection rates substantially greater than the corresponding rates from neutron star mergers. For the first generation Laser Interferometer Gravitational-Wave Observatory (LIGO-I), we expect about one detection during the first two years of operation. For its successor LIGO-II, the rate rises to roughly one detection per day. The uncertainties in these numbers are large. Event rates may drop by about an order of magnitude if the most massive clusters eject their black hole binaries early in their evolution.Comment: 12 pages, ApJL in pres

On the Interpretation of the Age Distribution of Star Clusters in the Small Magellanic Cloud

We re-analyze the age distribution (dN/dt) of star clusters in the Small Magellanic Cloud (SMC) using age determinations based on the Magellanic Cloud Photometric Survey. For ages younger than 3x10^9 yr the dN/dt distribution can be approximated by a power-law distribution, dN/dt propto t^-beta, with -beta=-0.70+/-0.05 or -beta=-0.84+/-0.04, depending on the model used to derive the ages. Predictions for a cluster population without dissolution limited by a V-band detection result in a power-law dN/dt distribution with an index of ~-0.7. This is because the limiting cluster mass increases with age, due to evolutionary fading of clusters, reducing the number of observed clusters at old ages. When a mass cut well above the limiting cluster mass is applied, the dN/dt distribution is flat up to 1 Gyr. We conclude that cluster dissolution is of small importance in shaping the dN/dt distribution and incompleteness causes dN/dt to decline. The reason that no (mass independent) infant mortality of star clusters in the first ~10-20 Myr is found is explained by a detection bias towards clusters without nebular emission, i.e. cluster that have survived the infant mortality phase. The reason we find no evidence for tidal (mass dependent) cluster dissolution in the first Gyr is explained by the weak tidal field of the SMC. Our results are in sharp contrast to the interpretation of Chandar et al. (2006), who interpret the declining dN/dt distribution as rapid cluster dissolution. This is due to their erroneous assumption that the sample is limited by cluster mass, rather than luminosity.Comment: 8 pages, 4 figures, accepted for publication in Ap

Star cluster ecology IVa: Dissection of an open star cluster---photometry

The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries are taken self-consistently into account. Initial conditions are chosen to represent relatively young Galactic open clusters, such as the Pleiades, Praesepe and the Hyades. The calculations include a realistic mass function, primordial binaries and the external potential of the parent Galaxy. Our model clusters are generally significantly flattened in the Galactic tidal field, and dissolve before deep core collapse occurs. The binary fraction decreases initially due to the destruction of soft binaries, but increases later because lower mass single stars escape more easily than the more massive binaries. At late times, the cluster core is quite rich in giants and white dwarfs. There is no evidence for preferential evaporation of old white dwarfs, on the contrary the formed white dwarfs are likely to remain in the cluster. Stars tend to escape from the cluster through the first and second Lagrange points, in the direction of and away from the Galactic center. Mass segregation manifests itself in our models well within an initial relaxation time. As expected, giants and white dwarfs are much more strongly affected by mass segregation than main-sequence stars. Open clusters are dynamically rather inactive. However, the combined effect of stellar mass loss and evaporation of stars from the cluster potential drives its dissolution on a much shorter timescale than if these effects are neglected. The often-used argument that a star cluster is barely older than its relaxation time and therefore cannot be dynamically evolved is clearly in error for the majority of star clusters.Comment: reduced abstract, 33 pages (three separate color .jpg figures), submitted to MNRA

The gravitational wave signal from the Galactic disk population of binaries containing two compact objects

We review the properties of Galactic binaries containing two compact objects, as derived by means of population synthesis. Using this information we calculate the gravitational wave signal of these binaries. At frequencies below f ~< 2 mHz the double white dwarf population forms an unresolved background for the low-frequency gravitational wave detector LISA. Above this limit some few thousand double white dwarfs and few tens of binaries containing neutron stars will be resolved. Of the resolved double white dwarfs ~500 have a total mass above the Chandrasekhar limit. About ~95 of these have a measurable frequency change allowing a determination of their chirp mass. We discuss the properties of the resolved systems.Comment: Accepted for publication in A&

Weakly admissible H-calculus on reflexive Banach spaces

AbstractWe show that, given a reflexive Banach space and a generator of an exponentially stable C0-semigroup, a weakly admissible operator g(A) can be defined for any g bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. The construction uses a Toeplitz operator and is motivated by system theory. In separable Hilbert spaces, we even get admissibility. Furthermore, it is investigated when a bounded calculus can be guaranteed. For this we introduce the new notion of exact observability by direction