Friction Timescale Research Articles

Modeling the dynamical friction timescale of a sinking satellite

When a satellite galaxy falls into a massive dark matter halo, it suffers from the dynamical friction force which drags it into the halo's center, where it finally merges with the central galaxy. The time interval between entry and merger is called the dynamical friction timescale (Tdf). Many studies have been dedicated to deriving Tdf using analytical models or N-body simulations. These studies have obtained qualitative agreements on how Tdf depends on the orbital parameters, and the mass ratio between the satellite and the host's halo. However, there are still disagreements on deriving an accurate form for Tdf. We present a semi-analytical model to predict Tdf and we focus on interpreting the discrepancies among different studies. We find that the treatment of mass loss from the satellite by tidal stripping dominates the behavior of Tdf. We also identify other model parameters which affect the predicted Tdf.

Relative velocity of inertial particles in turbulent flows

We present a model for the relative velocity of inertial particles in turbulent flows that provides new physical insight into this problem. Our general formulation shows that the relative velocity has contributions from two terms, referred to as the ‘generalized acceleration’ and ‘generalized shear’, because they reduce to the well-known acceleration and shear terms in the Saffman–Turner limit. The generalized shear term represents particles' memory of the flow velocity difference along their trajectories and depends on the inertial particle pair dispersion backward in time. The importance of this backward dispersion in determining the particle relative velocity is emphasized. We find that our model with a two-phase separation behaviour, an early ballistic phase and a later tracer-like phase, as found by recent simulations for the forward (in time) dispersion of inertial particle pairs, gives good fits to the measured relative speeds from simulations at low Reynolds numbers. In the monodisperse case with identical particles, the generalized acceleration term vanishes and the relative velocity is determined by the generalized shear term. At large Reynolds numbers, our model gives a St1/2-dependence of the relative velocity on the Stokes number St in the inertial range for both the ballistic behaviour and the Richardson separation law. This leads to the same inertial-range scaling for the two-phase separation that well fits the simulation results. Our calculations for the bidisperse case show that, with the friction timescale of one particle fixed, the relative speed as a function of the other particle's friction time has a dip when the two timescales are similar. This indicates that similar-size particles tend to have stronger velocity correlation than different ones. We find that the primary contribution at the dip, i.e. for similar particles, is from the generalized shear term, while the generalized acceleration term is dominant for particles of very different sizes. Future numerical studies are motivated to check the accuracy of the assumptions made in our model and to investigate the backward-in-time dispersion of inertial particle pairs in turbulent flows.

Dynamics and circulation regimes of terrestrial planets

By the study of simple analogues, either in the form of simplified numerical models or laboratory experiments, considerable insights may be gained as to the likely roles of planetary size, rotation, thermal stratification and other factors in determining the principal length scales, styles of global circulation and dominant waves and instability processes active in the respective climate systems of Earth, Mars, Venus and Titan. In this review, we explore aspects of these analogues and demonstrate the importance of a number of key dimensionless parameters, most notably thermal Rossby and Rhines numbers and a measure of the dominant frictional or radiative timescale, in defining the type of circulation regime to be expected in a prototype planetary atmosphere subject to axisymmetric driving. These considerations help to place Mars, Venus, Titan and Earth into an appropriate context, and may also lay the foundations for predicting and understanding the climate and circulation regimes of (as yet undiscovered) Earth-like extra-solar planets. However, as recent discoveries of ‘super-Earth’ planets around some nearby stars are beginning to reveal, the parameter space determined from axisymmetrically forced prototype atmospheres may be incomplete and other factors, such as the possibility of tidally locked rotation and tidal forcing, may also need to be taken into account for some classes of extra-solar planet.

PAIRING OF SUPERMASSIVE BLACK HOLES IN UNEQUAL-MASS GALAXY MERGERS

We examine the pairing process of supermassive black holes (SMBHs) down to scales of 20-100 pc using a set of N-body/SPH simulations of binary mergers of disk galaxies with mass ratios of 1:4 and 1:10. Our numerical experiments are designed to represent merger events occurring at various cosmic epochs. The initial conditions of the encounters are consistent with the LambdaCDM paradigm of structure formation, and the simulations include the effects of radiative cooling, star formation, and supernovae feedback. We find that the pairing of SMBHs depends sensitively on the amount of baryonic mass preserved in the center of the companion galaxies during the last phases of the merger. In particular, due to the combination of gasdynamics and star formation, we find that a pair of SMBHs can form in 1:10 minor mergers provided that galaxies are relatively gas-rich (gas fractions of 30% of the disk mass) and that the mergers occur at relatively high redshift (z~3), when dynamical friction timescales are shorter. Since 1:10 mergers are most common events during the assembly of galaxies, and mergers are more frequent at high redshift when galaxies are also more gas-rich, our results have positive implications for future gravitational wave experiments such as the Laser Interferometer Space Antenna.

DOUBLE QUASARS: PROBES OF BLACK HOLE SCALING RELATIONSHIPS AND MERGER SCENARIOS

We analyze the available sample of double quasars, and investigate their physical properties. Our sample comprises 85 pairs, selected from the Sloan Digital Sky Survey (SDSS). We derive physical parameters for the engine and the host, and model the dynamical evolution of the pair. First, we compare different scaling relationships between massive black holes and their hosts (bulge mass, velocity dispersion, and their possible redshift dependences), and discuss their consistency. We then compute dynamical friction timescales for the double quasar systems to investigate their frequency and their agreement with scenarios for quasar triggering. Comparing typical merging timescales to expected quasar lifetimes, the fraction of double quasars should be roughly a factor of 10 larger than observed. Additionally, we find that, depending on the correlations between black holes and their hosts, the occurrence of double quasars could be redshift-dependent. Comparison of our models to the SDSS quasar catalog suggests that double quasars should be more common at high redshift. We compare the typical separations at which double quasars are observed to the predictions of merger simulations. We find that the distribution of physical separations peaks at ~30 kpc, with a tail at larger separations (~100-200 kpc). These large separation pairs are instead consistent with unequal mass mergers where gas is dynamically perturbed during the first pericentric passage, but the gas reaches the black hole only at the next apocenter, where the pair is observed.

The three-dimensional structure of an electromagnetically generated dipolar vortex in a shallow fluid layer

Many experiments have been performed in electromagnetically driven shallow fluid layers to study quasi-two-dimensional (Q2D) turbulence, the shallowness of the layer commonly is assumed to ensure Q2D dynamics. In this paper, however, we demonstrate that shallow fluid flows exhibit complex three-dimensional (3D) structures. For this purpose we study one of the elementary vortex structures in Q2D turbulence, the dipolar vortex, in a shallow fluid layer. The flow evolution is studied both experimentally and by numerical simulations. Experimentally, stereoscopic particle image velocimetry is used to measure instantaneously all three components of the velocity field in a horizontal plane, and 3D numerical simulations provide the full 3D velocity and vorticity fields over the entire flow domain. It is found that significant and complex 3D structures and vertical motions occur throughout the flow evolution, i.e., during and after the forcing phase. We conclude that the bottom friction is not the main mechanism leading to three-dimensionality of the flow but rather the impermeability of the boundaries. It is further shown that free-surface deformations, i.e., gravity waves, are of minor importance too as a mechanism to generate 3D motion. Furthermore, it is demonstrated that the observations are not due to three-dimensionality introduced by the forcing mechanism but intrinsically due to the flow dynamics itself. The flow evolution is analyzed with respect to its quasi-two-dimensionality by adopting the ratio of “horizontal” to “vertical” kinetic energies, the normalized horizontal divergence, and a measure of the relaxation to a Poiseuille-like profile. An important observation is that, although the relative magnitude of the vertical velocity as compared to the horizontal flow components decreases for decreasing fluid depth, the vertical profile of the horizontal flow relaxes rather slowly to a Poiseuille-like profile, i.e., not faster than the bottom friction time scale.

Effects of AGN feedback on ΛCDM galaxies

We study the effects of Active Galactic Nuclei (AGN) feedback on the formation and evolution of galaxies in a semi-analytic model of galaxy formation. This model is an improved version of the one described by Cora (2006), which now considers the growth of black holes (BHs) as driven by (i) gas accretion during merger-driven starbursts and mergers with other BHs, (ii) accretion during starbursts triggered by disc instabilities, and (iii) accretion of gas cooled from quasi-hydrostatic hot gas haloes. It is assumed that feedback from AGN operates in the later case. The model has been calibrated in order to reproduce observational correlations between BH mass and mass, velocity dispersion, and absolute magnitudes of the galaxy bulge. AGN feedback has a strong impact on reducing or even suppressing gas cooling, an effect that becomes important at lower redshifts. This phenomenon helps to reproduce the observed galaxy luminosity function (LF) in the optical and near IR bands at z=0, and the cosmic star formation rate and stellar mass functions over a wide redshift range (0 1, which are mostly early-type and have older and redder stellar populations than lower mass galaxies, reproducing the observed bimodality in the galaxy colour distribution, and the morphological fractions. The evolution of the optical QSO LF is also reproduced, provided that the presence of a significant fraction of obscured QSOs is assumed. We explore the effects of AGN feedback during starbursts and new recent prescriptions for dynamical friction time-scales. (ABRIDGED)

Dynamical friction in modified Newtonian dynamics

We have tested a previous analytical estimate of the dynamical friction time-scale in modified Newtonian dynamics (MOND) with fully non-linear N-body simulations. The simulations confirm that the dynamical friction time-scale is significantly shorter in MOND than in equivalent Newtonian systems, i.e. systems with the same phase-space distribution of baryons and additional dark matter. An apparent conflict between this result and the long time-scales determined for bars to slow and mergers to be completed in previous N-body simulations of MOND systems is explained. The confirmation of the short dynamical-friction time-scale in MOND underlines the challenge that the Fornax dwarf spheroidal poses to the viability of MOND.

A Model for Dark Matter Halos

A halo model is presented which possesses a constant phase space density (Q) core followed by a radial CDM-like power law decrease in Q. The motivation for the core is the allowance for a possible primordial phase space density limit such as the Tremaine-Gunn upper bound. The space density profile derived from this model has a constant density core and falls off rapidly beyond. The new model is shown to improve the fits to the observations of LSB galaxy rotation curves, naturally provides a model which has been shown to result in a lengthened dynamical friction time scale for the Fornax dwarf spheroidal galaxy and predicts a flattening of the density profile within the Einstein radius of galaxy clusters. A constant gas entropy floor is predicted whose adiabatic constant provides a lower limit in accord with observed galaxy cluster values. While `observable-sized' cores are not seen in standard cold dark matter (CDM) simulations, phase space considerations suggest that they could appear in warm dark matter (WDM) cosmological simulations and in certain hierarchically consistent SuperWIMP scenarios.

Dynamical friction and galaxy merging time-scales

The timescale for galaxies within merging dark matter halos to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging timescales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies, and the statistical properties of satellite galaxies within dark matter halos. In this paper, we study the merging timescales of extended dark matter halos using N-body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging timescales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for $M_sat/M_host \approx 0.1$ and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of $\sim 3.3$ for $M_sat/M_host\approx 0.01$. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the timescale for an extended satellite to sink from the virial radius of a host halo down to the halo's center for a wide range of $M_sat/M_host$ and orbits. Including a central bulge in each galaxy changes the merging timescale by $\la 10%$. To highlight one concrete application of our results, we show that merging timescales often used in the literature overestimate the growth of stellar mass by satellite accretion by $\approx 40 %$, with the extra mass gained in low mass ratio mergers.

Satellite galaxies and fossil groups in the Millennium Simulation

We use a semianalytic galaxy catalogue constructed from the Millennium Simulation(MS) to study the satellites of isolated galaxies in theCDM cosmogony. The large volume surveyed by the MS (500 3 h 3 Mpc 3 ), together with its unprecedented numerical resolution, e nable the compilation of a large sample of � 80,000 bright (Mr < 20.5) primaries, surrounded by � 178,000 satellites down to the faint magnitude limit (Mr = 17) of our catalogue. This sample allows the characterization, with minimal statistical uncertainty, of the dynam- ical properties of satellite/primary galaxy systems in aCDM universe. The details of this characterization are sensitive to the details of the modeli ng, such as its assumptions on galaxy merging and dynamical friction timescales, but many of its general predictions should be ap- plicable to hierarchical formation models such asCDM. We find that, overall, the satellite population traces the dark matter rather well: its spatial d istribution and kinematics may be approximated by an NFW profile with a mildly anisotropic velo city distribution. Their spatial distribution is also mildly anisotropic, with a well-define d anti-Holmberg effect that reflects the misalignment between the major axis and angular momentum of the host halo. Our anal- ysis also highlights a number of difficulties afflicting stud ies that rely on satellite velocities to constrain the primary halo mass. These arise from variations in the star formation efficiency and assembly history of isolated galaxies, which result in a scatter of up to � 2 decades in halo mass at fixed primary luminosity. Our isolation criteri on (primaries may only have com- panions at least 2 mag fainter within 1 h 1 Mpc) contributes somewhat to the scatter, since it picks not only galaxies in sparse environments, but also a number of primaries at the centre of fossil groups. We find that the abundance and luminosity fu nction of these unusual systems are in reasonable agreement with the few available observational constraints. Much tighter halo mass-luminosity relations are found when splitting the sample by colour: red primaries inhabit halos more than twice as massive as those surrounding blue primaries, a difference that vanishes, however, when considering stellar mass instead of luminosity. The large scat- ter in the halo mass-luminosity relation hinders the interp retation of the velocity dispersion of satellites stacked according to the luminosity of the pri mary. We find L / σ 3 (the natu- ral scaling expected forCDM) for truly-isolated primaries, i.e., systems where the central galaxy contributes more than 85% of the total luminosity within its virial radius. Less stric t primary selection, however, leads to substantial modificat ion of the scaling relation: blindly stacking satellites of all primaries results in a much shall ower L-σ relation that is only poorly approximated by a power law.

The ACS Virgo Cluster Survey. XII. The Luminosity Function of Globular Clusters in Early‐Type Galaxies

We analyze the luminosity function of the globular clusters (GCs) belonging to the early-type galaxies observed in the ACS Virgo Cluster Survey. We have obtained estimates for a Gaussian representation of the GC luminosity function (GCLF) for 89 galaxies. We have also fit the GCLFs with an Schechter function, which is meant to reflect the preferential depletion of low-mass GCs, primarily by evaporation due to two-body relaxation, from an initial Schechter mass function similar to that of young massive clusters. We find a significant trend of the GCLF dispersion with galaxy luminosity, in the sense that smaller galaxies have narrower GCLFs. We show that this narrowing of the GCLF in a Gaussian description is driven by a steepening of the GC mass function above the turnover mass, as one moves to smaller host galaxies. We argue that this behavior at the high-mass end of the GC mass function is most likely a consequence of systematic variations of the initial cluster mass function. The GCLF turnover mass M_TO is roughly constant, at ~ 2.2 x 10^5 M_sun in bright galaxies, but it decreases slightly in dwarfs with M_B >~ -18. We show that part of the variation could arise from the shorter dynamical friction timescales in smaller galaxies. We probe the variation of the GCLF to projected galactocentric radii of 20-35 kpc in the Virgo giants M49 and M87, finding that M_TO is essentially constant over these spatial scales. Our fits of evolved Schechter functions imply average dynamical mass losses (Delta) over a Hubble time that fall in the range 2 x 10^5 <~ (Delta/M_sun) < 10^6 per GC. We agree with previous suggestions that if the full GCLF is to be understood in more detail GCLF models will have to include self-consistent treatments of dynamical evolution inside time-dependent galaxy potentials. (Abridged)

Photometry of the Globular Cluster NGC 5466: Red Giants and Blue Stragglers

We present wide-field BVI photometry for about 11,500 stars in the low-metallicity cluster NGC 5466. We have detected the red giant branch bump for the first time, although it is at least 0.2 mag fainter than expected relative to the turnoff. The number of red giants (relative to main sequence turnoff stars) is in excellent agreement with stellar models from the Yonsei-Yale and Teramo groups, and slightly high compared to Victoria-Regina models. This adds to evidence that an abnormally large ratio of red giant to main-sequence stars is not correlated with cluster metallicity. We discuss theoretical predictions from different research groups and find that the inclusion or exclusion of helium diffusion and strong limit Coulomb interactions may be partly responsible. We also examine indicators of dynamical history: the mass function exponent and the blue straggler frequency. NGC 5466 has a very shallow mass function, consistent with large mass loss and recently-discovered tidal tails. The blue straggler sample is significantly more centrally concentrated than the HB or RGB stars. We see no evidence of an upturn in the blue straggler frequency at large distances from the center. Dynamical friction timescales indicate that the stragglers should be more concentrated if the cluster's present density structure has existed for most of its history. NGC 5466 also has an unusually low central density compared to clusters of similar luminosity. In spite of this, the specific frequency of blue stragglers that puts it right on the frequency -- cluster M_V relation observed for other clusters.

Ejection of High‐Velocity Stars from the Galactic Center by an Inspiraling Intermediate‐Mass Black Hole

The presence of young stars in the immediate vicinity and strong tidal field of SgrA* remains unexplained. One currently popular idea for their origin posits that the stars were bused in by an Intermediate-Mass Black Hole (IMBH) which has inspiraled into the Galactic Center a few million years ago. Yu and Tremaine (2003) have argued that in this case some of the old stars in the SgrA* cusp would be ejected by hard gravitational collisions with the IMBH. Here we derive a general expression for the phase-space distribution of the ejected high-velocity stars, given the distribution function of the stars in the cusp. We compute it explicitly for the Peebles-Young distribution function of the cusp, and make a detailed model for the time-dependent ejection of stars during the IMBH inspiral. We find that (1) the stars are ejected in a burst lasting a few dynamical friction timescales; if the ejected stars are detected by Gaia they are likely to be produced by a single inspiral event, (2) if the inspiral is circular than in the beginning of the burst the velocity vectors of the ejected stars cluster around the inspiral plane, but rapidly isotropise as the burst proceeds, (3) if the inspiral is eccentric, then the stars are ejected in a broad jet roughly perpendicular to the Runge-Lenz vector of the IMBH orbit. In a typical cusp the orbit will precess with a period of \sim 10^5 years, and the rate of ejection into our part of the Galaxy (as defined by e.g. the Gaia visibility domain) will be modulated periodically. Gaia, together with the ground-based follow-up observations, will be able to clock many high-velocity stars back to their ejection from the Galactic Center, thus measuring some of the above phenomena. This would provide a clear signature of the IMBH inspiral in the past 10--20 Myr.

Acceleration of a Stratified Current over a Sloping Bottom, Driven by an Alongshelf Pressure Gradient*

Abstract An idealized theoretical model is developed for the acceleration of a two-dimensional, stratified current over a uniformly sloping bottom, driven by an imposed alongshelf pressure gradient and taking into account the effects of buoyancy advection in the bottom boundary layer. Both downwelling and upwelling pressure gradients are considered. For a specified pressure gradient, the model response depends primarily on the Burger number S = Nα/f, where N is the initial buoyancy frequency, α is the bottom slope, and f is the Coriolis parameter. Without stratification (S = 0), buoyancy advection is absent, and the alongshelf flow accelerates until bottom stress balances the imposed pressure gradient. The e-folding time scale to reach this steady state is the friction time, h/r, where h is the water depth and r is a linear bottom friction coefficient. With stratification (S ≠ 0), buoyancy advection in the bottom boundary layer produces vertical shear, which prevents the bottom stress from becoming large enough to balance the imposed pressure gradient for many friction time scales. Thus, the alongshelf flow continues to accelerate, potentially producing large velocities. The acceleration increases rapidly with increasing S, such that even relatively weak stratification (S &amp;gt; 0.2) has a major impact. These results are supported by numerical model calculations.

Wind‐forced setup of upwelling, geographical origins, and numerical models: The role of bottom drag

An analysis is made to determine the properties and scales for the setup of upwelling driven by an impulsively started, steady, uniform wind of semi‐infinite fetch. The backward edge of the wind field acts as a geographical origin for the generation of coastal‐trapped waves (CTWs). A perturbation analysis is used to show that prior to the arrival of the nth mode CTW, the alongshore velocity is shown to asymptote to a constant value, (set by bottom drag) and over a timescale Tn. As this viscous limit is achieved, the upwelling becomes increasingly confined to the bottom boundary layer and bottom stress balances wind stress: Interior upwelling is shut down. The viscous limit may not be achieved, since after the arrival of the nth CTW mode, a gradient in the alongshore velocity is set up and its divergence acts to feed the offshore Ekman transport and shut the upwelling down. Numerical results are used to show that the frictional length and timescales predicted by the perturbation analysis are unrealistically small due to an underestimation of thermal wind shear. Moreover, the theory underpredicts the importance of the first CTW mode, which is shown to largely determine the setup and shutdown of upwelling. A simple first‐mode model for upwelling is developed and used to evaluate the validity of a numerical, open boundary condition in determining the correct degree of upwelling. A case study for the Chilean shelf is presented.

Early Reionization by Miniquasars

Motivated by the recent detection by the Wilkinson Microwave Anisotropy Probe of a large optical depth to Thomson scattering, implying a very early reionization epoch, we assess a scenario where the universe was reionized by powered by intermediate-mass black holes (IMBHs), the remnants of the first generation of massive stars. Pregalactic IMBHs form within minihalos above the cosmological Jeans mass collapsing at z > 20, get incorporated through mergers into larger and larger systems, sink to the center as a result of dynamical friction, and accrete cold material. The merger history of dark halos and associated IMBHs is followed by Monte Carlo realizations of the merger hierarchy in a ΛCDM cosmology. Our model is based on the assumptions that quasar activity is driven by major mergers and nuclear IMBHs accrete at the Eddington rate a fraction of the gas in the merger remnant. The long dynamical frictional timescales leave many IMBHs wandering in galaxy halos after a minor merger. While seed IMBHs that are as rare as the 3.5 σ peaks of the primordial density field evolve largely in isolation, a significant number of BH binary systems will form if IMBHs populate the more numerous 3 σ peaks instead. In the case of rapid binary coalescence a fraction of IMBHs will be displaced from galaxy centers and ejected into the intergalactic medium (IGM) by the gravitational rocket effect, rather than accrete and shine as miniquasars. We show that, under a number of plausible assumptions for the amount of gas accreted onto IMBHs and their emission spectrum, miniquasars powered by IMBHs, and not their stellar progenitors, may be responsible for cosmological reionization at z ~ 15. Reionization by miniquasars with a hard spectrum may be more economical than stellar reionization, as soft X-rays escape more easily from the dense sites of star formation and travel farther than EUV radiation. Energetic photons will permeate the universe more uniformly, make the low-density diffuse IGM warm and weakly ionized prior to the epoch of reionization breakthrough, set an entropy floor, and reduce gas clumping. Future 21 cm observations may detect a preheated, weakly ionized IGM in emission against the cosmic microwave background.

The efficiency of the spiral-in of a black hole to the Galactic Centre

We study the efficiency at which a black hole or dense star cluster spirals in to the Galactic Centre. This process takes place on a dynamical friction time-scale, which depends on the value of the Coulomb logarithm (In Λ). We determine the accurate value of this parameter using the direct N-body method, a tree algorithm and a particle-mesh technique with up to two million plus one particles. The three different techniques are in excellent agreement. Our measurement for the Coulomb logarithm appears to be independent of the number of particles. We conclude that In A = 6.6 ′ 0.6 for a massive point particle in the inner few parsec of the Galactic bulge. For an extended object, such as a dense star cluster, In A is smaller, with a value of the logarithm argument A inversely proportional to the object size.

Evolution of massive binary black holes

Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). The evolution of BBHs depends on BH mass ratio and host galaxy type. BBHs with very low mass ratios (say, ≲0.001) are hardly ever formed by mergers of galaxies because the dynamical friction timescale is too long for the smaller BH to sink into the galactic centre within a Hubble time. BBHs with moderate mass ratios are most likely to form and survive in spherical or nearly spherical galaxies and in high-luminosity or high-dispersion galaxies; they are most likely to have merged in low-dispersion galaxies (line-of-sight velocity dispersion ≲90 km s−1) or in highly flattened or triaxial galaxies. The semimajor axes of surviving BBHs are generally in the range 10−3–10 pc. The upper limit of this range is close to the HST resolution for the typical nearby galaxies (i.e., galaxies of the Virgo cluster). The absence of double nuclei in the centres of nearby galaxies does not necessarily mean that they have no BBHs. If all galaxies are highly triaxial, there will be no surviving BBHs. Possible observational characteristics of surviving BBHs are also discussed.

Ocean currents at Axial Volcano, a northeastern Pacific seamount

Axial Volcano is a magmatically active seamount that straddles the Juan de Fuca Ridge (JdFR). With a summit depth of ∼1400 m, the volcano intercepts deep ocean flows at a height well above that of the linear ridge adjoining it to the north and south. Multiyear, yearlong observations of currents at Axial show that mean flow circles the seamount in an anticyclonic sense, consistent with dynamical constraints, with means as large as 6.6 cm s−1. Spectra of currents indicate prominent tidal, inertial, and in some cases weather‐band period (3‐ to 7‐day) peaks, as has been seen elsewhere along the JdFR ridge. For K1, O1, and S2 tidal currents at the seamount, amplitudes are several times larger than the corresponding background amplitudes and rotation around the tidal current ellipses is anticyclonic. M2 tidal currents show none of the same properties. Energy at the inertial frequency decreases by more than an order of magnitude from 100 m above to 400 m below the volcano's summit. In contrast, weather‐band (WB) period energy increases tenfold over the same depth range, with WB energy all but unobservable at summit depth. The presence of WB oscillations makes Axial unlike other seamounts where long observations have been made. The current meter observations also provide a picture of seasonal trends. As expected, during the period Summer 1996 to Spring 1997, largest amounts of WB energy are found during autumn and winter; in contrast, WB motion at Axial Volcano during Winter 2000 was summer‐like in intensity. A linear, baroclinic model of forced damped azimuthal mode‐one oscillatory flow around an idealized axisymmetric seamount shows that amplification of diurnal flow should occur principally at the seamount summit while amplification of the WB should occur, as the observations show, on the seamount flanks. Model and measured phase relationships for temperature and current time series pairs circumscribing Axial support the view that azimuthal mode‐one oscillations are prominent. Over the 0.8‐ to 6‐day range for forcing period (TC) the model indicates that the principal topographic resonance, as indicated by kinetic energy (KE) amplification, occurs for a TC greater than 1 and less than 2 days with only mild dependence in that range on background stratification and seamount shape. Additional but weaker topographic resonances can occur at longer periods in model results, but as TC becomes slightly larger than the frictional timescale, topographic resonances no longer appear. High dissipation and thus short frictional timescales reported by others in regions of rough, sloping topography make topographic resonances at Axial at periods greater than a few days somewhat unlikely. The relatively broad WB spectral peaks at some Axial sites are consequently more likely the result of spectral peaks in forcing than of topographic resonance.