arXiv subjects

Scott Tremaine

Publications and source records attributed to Scott Tremaine.

At least 109 records · Page 6Linked to original sources

arXiv2003

Planet finding prospects for the Space Interferometry Mission

The Space Interferometry Mission (SIM) will make precise astrometric measurements that can be used to detect planets around nearby stars. We have simulated SIM observations and estimated the ability of SIM to detect planets with given masses and orbital periods and measure their orbital elements. We combine these findings with an estimate of the mass and period distribution of planets determined from radial velocity surveys to predict the number and characteristics of planets SIM would likely find. Our predictions are based on extrapolating the mass distribution of known extrasolar planets by up to a factor of 100. This extrapolation provides the best prediction we can make of the actual number of planets that SIM will detect and characterize, but may substantially over- or underestimate the frequency of Earth-mass planets, especially if these form by a different mechanism than giant planets. We find that SIM is likely to detect 1-5 planets with masses less than 3 M_Earth (depending on mission parameters). SIM would measure masses and orbits with 30% accuracy for 0-2 of these planets, but is unlikely to measure orbits with 10% accuracy for more than one of them. SIM is likely to detect 5-25 planets with mass less than 20 M_Earth, measure masses and orbits with 30% accuracy for 2-12 of these, and measure masses and orbits with 10% accuracy for 2-8 such planets. SIM is likely to find 25-160 planets of all masses, depending on the observing strategy and mission lifetime.

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arXiv2002

On the origin of irregular structure in Saturn's rings

We suggest that the irregular structure in Saturn's B ring arises from the formation of shear-free ring-particle assemblies of up to ~100 km in radial extent. The characteristic scale of the irregular structure is set by the competition between tidal forces and the yield stress of these assemblies; the required tensile strength of ~10^5 dyn/cm^2 is consistent with the sticking forces observed in laboratory simulations of frosted ice particles. These assemblies could be the nonlinear outcome of a linear instability that occurs in a rotating fluid disk in which the shear stress is a decreasing function of the shear. We show that a simple model of an incompressible, non-Newtonian fluid in shear flow leads to the Cahn-Hilliard equation, which is widely used to model the formation of structure in binary alloys and other systems.

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arXiv2002

Axisymmetric Dynamical Models of the Central Regions of Galaxies

We present axisymmetric, orbit superposition models for 12 galaxies using data taken with the Hubble Space Telescope (HST) and ground-based observatories. In each galaxy, we detect a central black hole (BH) and measure its mass to accuracies ranging from 10% to 70%. We demonstrate that in most cases the BH detection requires both the HST and ground-based data. Using the ground-based data alone does provide an unbiased measure of the BH mass (provided they are fit with fully general models), but at a greatly reduced significance. The most significant correlation with host galaxy properties is the relation between the BH mass and the velocity dispersion of the host galaxy; we find no other equally strong correlation, and no second parameter that improves the quality of the mass-dispersion relation. We are also able to measure the stellar orbital properties from these general models. The most massive galaxies are strongly biased to tangential orbits near the BH, consistent with binary BH models, while lower-mass galaxies have a range of anisotropies, consistent with an adiabatic growth of the BH.

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arXiv2002

Galaxies with a Central Minimum in Stellar Luminosity Density

We used HST WFPC2 images to identify six early-type galaxies with surface- brightness profiles that decrease inward over a limited range of radii near their centers. The implied luminosity density profiles of these galaxies have local minima interior to their core break radii. NGC 3706 harbors a high surface brightness ring of starlight with radius ~20 pc. Its central structure may be related to that in the double-nucleus galaxies M31 and NGC 4486B. NGC 4406 and NGC 6876 have nearly flat cores that on close inspection are centrally depressed. Colors for both galaxies imply that this is not due to dust absorption. The surface brightness distributions of both galaxies are consistent with stellar tori that are more diffuse than the sharply defined system in NGC 3706. The remaining three galaxies are the brightest cluster galaxies in A260, A347, and A3574. Color information is not available for these objects, but they strongly resemble NGC 4406 and NGC 6876 in their cores. The thin ring in NGC 3706 may have formed dissipatively. The five other galaxies resemble the endpoints of some simulations of the merging of two gas-free stellar systems, each harboring a massive nuclear black hole. In one version of this scenario, diffuse stellar tori are produced when stars initially bound to one black hole are tidally stripped away by the second black hole. Alternatively, some inward-decreasing surface-brightness profiles may reflect the ejection of stars from a core during the hardening of the binary black hole created during the merger.

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arXiv2002

Observational constraints on growth of massive black holes

We study the observational constraints on the growth of massive black holes (BHs) in galactic nuclei. We use the velocity dispersions of early-type galaxies obtained by the SDSS and the relation between BH mass and velocity dispersion to estimate the local BH mass density to be 2.5x10^5 Msun/Mpc^3. We also use the QSO luminosity function from the 2dF Redshift Survey to estimate the BH mass density accreted during optically bright QSO phases. The local BH mass density is consistent with the density accreted during optically bright QSO phases if QSOs have an efficiency 0.1. By studying the continuity equation for the BH mass distribution, including the effect of BH mergers, we find relations between the local BH mass function and the QSO luminosity function. If the BH mass is assumed to be conserved during BH mergers, comparison of the predicted relations with the observations suggests that luminous QSOs (L_{bol}>10^{46} erg/s) have a high efficiency (e.g. 0.2), and the growth of high-mass BHs (>10^8 Msun) comes mainly from accretion during optically bright QSO phases, or that luminous QSOs have a super-Eddington luminosity. If luminous QSOs are not accreting with super-Eddington luminosities and the growth of low-mass BHs also occurs mainly during optically bright QSO phases, less luminous QSOs must accrete with a low efficiency <0.1; alternatively, they may accrete with high efficiency, but a significant fraction should be obscured. We estimate that the mean lifetime of luminous QSOs is (3-13)x10^7 yr, which is comparable to the Salpeter time. We also investigate the case in which total BH mass decreases during BH mergers due to gravitational radiation, and the observations again suggest that BHs in most luminous QSOs are Kerr BHs accreting with an efficiency >0.1.

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arXiv2002

The slope of the black-hole mass versus velocity dispersion correlation

Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object M and the velocity dispersion sigma of the host galaxy, of the form log(M/M_sun) = a + b*log(sigma/sigma_0); however, published estimates of the slope b span a wide range (3.75 to 5.3). Merritt & Ferrarese have argued that low slopes (<4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of systematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritt's extrapolation of central velocity dispersions to r_e/8 (r_e is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the measurements. A new determination of the slope using 31 galaxies yields b=4.02 +/- 0.32, a=8.13 +/- 0.06, for sigma_0=200 km/s. The M-sigma relation has an intrinsic dispersion in log M that is no larger than 0.3 dex. In an Appendix, we present a simple model for the velocity-dispersion profile of the Galactic bulge.

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arXiv2001

Maximum likelihood method for estimating the mass and period distributions of extra-solar planets

We investigate the distribution of mass M and orbital period P of extra-solar planets, taking account of selection effects due to the limited velocity precision and duration of existing surveys. We fit the data on 63 planets to a power-law distribution of the form dn=CM^{-alpha}P^{-beta}(dM/M)(dP/P), and find alpha=0.12+-0.10, beta=-0.26+-0.06 for M<10M_J, where M_J is the Jupiter mass. The correlation coefficient between these two exponents is -0.32, indicating that uncertainties in the two distributions are coupled. We estimate that 3% of solar-type stars have companions in the range 1M_J<M<10M_J, 2d<P<10yr.

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arXiv2000

Canonical elements for collision orbits

I derive a set of canonical elements that are useful for collision orbits (perihelion distance approaching zero at fixed semimajor axis). The coordinates are the mean anomaly and the two spherical polar angles at aphelion.

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arXiv2000

Slow modes in Keplerian disks

Low-mass disks orbiting a massive body can support "slow" normal modes, in which the eigenfrequency is much less than the orbital frequency. Slow modes are lopsided, i.e., the azimuthal wavenumber m=1. We investigate the properties of slow modes, using softened self-gravity as a simple model for collective effects in the disk. We employ both the WKB approximation and numerical solutions of the linear eigenvalue equation. We find that all slow modes are stable. Discrete slow modes can be divided into two types, which we label g-modes and p-modes. The g-modes involve long leading and long trailing waves, have properties determined by the self-gravity of the disk, and are only present in narrow rings or in disks where the precession rate is dominated by an external potential. In contrast, the properties of p-modes are determined by the interplay of self-gravity and other collective effects. P-modes involve both long and short waves, and in the WKB approximation appear in degenerate leading/trailing pairs. Disks support a finite number---sometimes zero---of discrete slow modes, and a continuum of singular modes.

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arXiv2000

Resonant capture by inward migrating planets

We investigate resonant capture of small bodies by planets that migrate inwards, using analytic arguments and three-body integrations. If the orbits of the planet and the small body are initially circular and coplanar, the small body is captured when it crosses the 2:1 resonance with the planet. As the orbit shrinks it becomes more eccentric, until by the time its semimajor axis has shrunk by a factor of four, its eccentricity reaches nearly unity (1-e<<10^{-4}). In typical planetary systems, bodies in this high-eccentricity phase are likely to be consumed by the central star. If they can avoid this fate, as migration continues the inclination flips from 0 to i=180 degrees; thereafter the eccentricity declines until the semimajor axis is a factor of nine smaller than at capture, at which point the small body is released from the 2:1 resonance on a nearly circular retrograde orbit. Small bodies captured into resonance from initially inclined or eccentric orbits can also be ejected from the system, or released from the resonance on highly eccentric polar orbits (i\simeq 90 degrees) that are stabilized by a secular resonance. We conclude that migration can drive much of the inner planetesimal disk into the star, and that post-migration multi-planet systems may not be coplanar.

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arXiv2000

Black Hole Mass Estimates from Reverberation Mapping and from Spatially Resolved Kinematics

Black hole (BH) masses that have been measured by reverberation mapping in active galaxies fall significantly below the correlation between bulge luminosity and BH mass determined from spatially resolved kinematics of nearby normal galaxies. This discrepancy has created concern that one or both techniques suffer from systematic errors. We show that BH masses from reverberation mapping are consistent with the recently discovered relationship between BH mass and galaxy velocity dispersion. Therefore the bulge luminosities are the probable source of the disagreement, not problems with either method of mass measurement. This result underscores the utility of the BH mass -- velocity dispersion relationship. Reverberation mapping can now be applied with increased confidence to galaxies whose active nuclei are too bright or whose distances are too large for BH searches based on spatially resolved kinematics.

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arXiv2000

A Relationship Between Nuclear Black Hole Mass and Galaxy Velocity Dispersion

We describe a correlation between the mass M_BH of a galaxy's central black hole and the luminosity-weighted line-of-sight velocity dispersion sigma_e within the half-light radius. The result is based on a sample of 26 galaxies, including 13 galaxies with new determinations of black hole masses from Hubble Space Telescope measurements of stellar kinematics. The best-fit correlation is M_BH = 1.2 (+-0.2) x 10^8 M_sun (sigma_e/200 km/s)^(3.75 (+-0.3))over almost three orders of magnitude in M_BH; the scatter in M_BH at fixed sigma_e is only 0.30 dex and most of this is due to observational errors. The M_BH-sigma_e relation is of interest not only for its strong predictive power but also because it implies that central black hole mass is constrained by and closely related to properties of the host galaxy's bulge.

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arXiv2000

Resonant capture, counter-rotating disks, and polar rings

We suggest that polar rings and/or counter-rotating disks in flattened galaxies can be formed from stars captured at the Binney resonance, where the rate of precession of the angular momentum vector of a disk star equals the pattern speed of a triaxial halo. If the halo pattern speed is initially retrograde and slowly decays to zero, stars can be trapped as the Binney resonance sweeps past them, and levitated into polar orbits. If the halo pattern speed is initially retrograde and slowly changes to prograde, trapped stars can evolve from prograde to retrograde disk orbits. The stellar components of polar rings formed by this process should consist of two equal, counter-rotating star streams.

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arXiv1999

Axisymmetric, 3-Integral Models of Galaxies: A Massive Black Hole in NGC3379

We fit axisymmetric 3-integral dynamical models to NGC3379 using the line-of-sight velocity distribution obtained from HST/FOS spectra of the galaxy center and ground-based long-slit spectroscopy along four position angles, with the light distribution constrained by WFPC2 and ground-based images. We have fitted models with inclinations from 29 (intrinsic galaxy type E5) to 90 degrees (intrinsic E1) and black hole masses from 0 to 1e9 M_solar. The best-fit black hole masses range from 6e7 to 2e8 M_solar, depending on inclination. The velocity ellipsoid of the best model is not consistent with either isotropy or a two-integral distribution function. Along the major axis, the velocity ellipsoid becomes tangential at the innermost bin, radial in the mid-range radii, and tangential again at the outermost bins. For the acceptable models, the radial to tangential dispersion in the mid-range radii ranges from 1.1 < sigma_r / sigma_t < 1.7. Compared with these 3-integral models, 2-integral isotropic models overestimate the black hole mass since they cannot provide adequate radial motion. However, the models presented in this paper still contain restrictive assumptions-namely assumptions of constant M/L and spheroidal symmetry-requiring yet more models to study black hole properties in complete generality.

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arXiv1999

A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems

Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive timestep control is added to a symplectic integrator. We describe an adaptive-timestep symplectic integrator that can be used if the Hamiltonian is the sum of kinetic and potential energy components and the required timestep depends only on the potential energy (e.g. test-particle integrations in fixed potentials). In particular, we describe an explicit, reversible, symplectic, leapfrog integrator for a test particle in a near-Keplerian potential; this integrator has timestep proportional to distance from the attracting mass and has the remarkable property of integrating orbits in an inverse-square force field with only "along-track" errors; i.e. the phase-space shape of a Keplerian orbit is reproduced exactly, but the orbital period is in error by O(1/N^2), where N is the number of steps per period.

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arXiv1999

Linear multistep methods for integrating reversible differential equations

This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem. It has previously been shown by Cano & Sanz-Serna that reversible linear multisteps for first-order differential equations are generally unstable. Here, we report on a subset of these methods -- the zero-growth methods -- that evade these instabilities. We provide an algorithm for identifying these rare methods. We find and study all zero-growth, reversible multisteps with six or fewer steps. This select group includes two well-known second-order multisteps (the trapezoidal and explicit midpoint methods), as well as three new fourth-order multisteps -- one of which is explicit. Variable timesteps can be readily implemented without spoiling the reversibility. Tests on Keplerian orbits show that these new reversible multisteps work well on orbits with low or moderate eccentricity, although at least 100 steps/radian are required for stability.

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arXiv1999

The dynamics of Plutinos

Plutinos are Kuiper-belt objects that share the 3:2 Neptune resonance with Pluto. The long-term stability of Plutino orbits depends on their eccentricity. Plutinos with eccentricities close to Pluto (fractional eccentricity difference |e-e_p|/e_p<=0.1) can be stable because the longitude difference librates, in a manner similar to the tadpole and horseshoe libration in coorbital satellites. Plutinos with |e-e_p|/e_p>=0.3 can also be stable; the longitude difference circulates and close encounters are possible, but the effects of Pluto are weak because the encounter velocity is high. Orbits with intermediate eccentricity differences are likely to be unstable over the age of the solar system, in the sense that encounters with Pluto drive them out of the 3:2 Neptune resonance and thus into close encounters with Neptune. This mechanism may be a source of Jupiter-family comets.

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arXiv1999

Rates of tidal disruption of stars by massive central black holes

There is strong evidence for some kind of massive dark object in the centres of many galaxy bulges. The detection of flares from tidally disrupted stars could confirm that these objects are black holes (BHs). Here we present calculations of the stellar disruption rates in detailed dynamical models of real galaxies, taking into account the refilling of the loss cone of stars on disruptable orbits by two-body relaxation and tidal forces in non-spherical galaxies. The highest disruption rates (one star per 10^4 yr) occur in faint (L>10^10 L_sun) galaxies, which have steep central density cusps. More luminous galaxies are less dense and have much longer relaxation times and more massive BHs. Dwarf stars in such galaxies are swallowed whole by the BH and hence do not emit flares; giant stars could produce flares as often as every 10^5 yr, although the rate depends sensitively on the shape of the stellar distribution function. We discuss the possibility of detecting disruption flares in current supernova searches. The total mass of stars consumed over the lifetime of the galaxy is of order 10^6 M_sun, independent of galaxy luminosity; thus disrupted stars may contribute significantly to the present BH mass in galaxies fainter than about 10^9 L_sun.

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