It takes a village to raise a tide: nonlinear multiple-mode coupling and mode identification in KOI-54

We explore the tidal excitation of stellar modes in binary systems using Kepler observations of the remarkable eccentric binary KOI-54 (HD 187091; KIC 8112039), which displays strong ellipsoidal variation as well as a variety of linear and nonlinear pulsations. We report the amplitude and phase of over 120 harmonic and anharmonic pulsations in the system. We use pulsation phases to determine that the two largest-amplitude pulsations, the 90th and 91st harmonics, most likely correspond to axisymmetric m=0 modes in both stars, and thus cannot be responsible for resonance locks as had been recently proposed. We find evidence that the amplitude of at least one of these two pulsations is decreasing with a characteristic timescale of ~100 yr. We also use the pulsations' phases to confirm the onset of the traveling wave regime for harmonic pulsations with frequencies <~50 Omega_orbit, in agreement with theoretical expectations. We present evidence that many pulsations that are not harmonics of the orbital frequency correspond to modes undergoing simultaneous nonlinear coupling to multiple linearly driven parent modes. Since coupling among multiple modes can lower the threshold for nonlinear interactions, nonlinear phenomena may be easier to observe in highly eccentric systems, where broader arrays of driving frequencies are available. This may help to explain why the observed amplitudes of the linear pulsations are much smaller than the theoretical threshold for decay via three-mode coupling.Comment: Accepted for publication in MNRAS. Only minor corrections. 16 Pages; 8 Figures; 3 Table

Modeling Algorithms in SystemC and ACL2

We describe the formal language MASC, based on a subset of SystemC and intended for modeling algorithms to be implemented in hardware. By means of a special-purpose parser, an algorithm coded in SystemC is converted to a MASC model for the purpose of documentation, which in turn is translated to ACL2 for formal verification. The parser also generates a SystemC variant that is suitable as input to a high-level synthesis tool. As an illustration of this methodology, we describe a proof of correctness of a simple 32-bit radix-4 multiplier.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Two paths of cluster evolution: global expansion versus core collapse

All gravitationally bound clusters expand, due to both gas loss from their most massive members and binary heating. All are eventually disrupted tidally, either by passing molecular clouds or the gravitational potential of their host galaxies. However, their interior evolution can follow two very different paths. Only clusters of sufficiently large initial population and size undergo the combined interior contraction and exterior expansion that leads eventually to core collapse. In all other systems, core collapse is frustrated by binary heating. These clusters globally expand for their entire lives, up to the point of tidal disruption. Using a suite of direct N-body calculations, we trace the "collapse line" in r_v-N space that separates these two paths. Here, r_v and N are the cluster's initial virial radius and population, respectively. For realistic starting radii, the dividing N-value is from 10^4 to over 10^5. We also show that there exists a minimum population, N_min, for core collapse. Clusters with N < N_min tidally disrupt before core collapse occurs. At the Sun's Galactocentric radius, R_G = 8.5 kpc, we find N_min >~ 300. The minimum population scales with Galactocentric radius as R_G^{-9/8}. The position of an observed cluster relative to the collapse line can be used to predict its future evolution. Using a small sample of open clusters, we find that most lie below the collapse line, and thus will never undergo core collapse. Most globular clusters, on the other hand, lie well above the line. In such a case, the cluster may or may not go through core collapse, depending on its initial size. We show how an accurate age determination can help settle this issue.Comment: Accepted for publication in MNRAS. 14 Pages, 9 Figures, 2 Table

Production of Hypervelocity Stars through Encounters with Stellar-Mass Black Holes in the Galactic Centre

Stars within 0.1 pc of the supermassive black hole Sgr A* at the Galactic centre are expected to encounter a cluster of stellar-mass black holes (BHs) that have segregated to that region. Some of these stars will scatter off an orbiting BH and be kicked out of the Galactic centre with velocities up to ~2000 km/s. We calculate the resulting ejection rate of hypervelocity stars (HVSs) by this process under a variety of assumptions, and find it to be comparable to the tidal disruption rate of binary stars by Sgr A*, first discussed by Hills (1988). Under some conditions, this novel process is sufficient to account for all of the hypervelocity B-stars observed in the halo, and may dominate the production rate of all HVSs with lifetimes much less than the relaxation time-scale at a distance ~2 pc from Sgr A* (>~ 2 Gyr). Since HVSs are produced by at least two unavoidable processes, the statistics of HVSs could reveal bimodal velocity and mass distributions, and can constrain the distribution of BHs and stars in the innermost 0.1 pc around Sgr A*.Comment: 8 pages, 3 figures. Accepted for publication in MNRAS. Some major changes to text, however conclusions remain the sam

Mergers of Stellar-Mass Black Holes in Nuclear Star Clusters

Mergers between stellar-mass black holes will be key sources of gravitational radiation for ground-based detectors. However, the rates of these events are highly uncertain, given that such systems are invisible. One formation scenario involves mergers in field binaries, where our lack of complete understanding of common envelopes and the distribution of supernova kicks has led to rate estimates that range over a factor of several hundred. A different, and highly promising, channel involves multiple encounters of binaries in globular clusters or young star clusters. However, we currently lack solid evidence for black holes in almost all such clusters, and their low escape speeds raise the possibility that most are ejected because of supernova recoil. Here we propose that a robust environment for mergers could be the nuclear star clusters found in the centers of small galaxies. These clusters have millions of stars, black hole relaxation times well under a Hubble time, and escape speeds that are several times those of globulars, hence they retain most of their black holes. We present simulations of the three-body dynamics of black holes in this environment and estimate that, if most nuclear star clusters do not have supermassive black holes that interfere with the mergers, at least several tens of events per year will be detectable with Advanced LIGO.Comment: 15 pages including one figure, submitted to The Astrophysical Journa