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Scott Tremaine

Publications and source records attributed to Scott Tremaine.

At least 55 records · Page 3Linked to original sources
arXiv2017

Ultralight scalars as cosmological dark matter

An intriguing alternative to cold dark matter (CDM) is that the dark matter is a light ( $m \sim 10^{-22}$ eV) boson having a de Broglie wavelength $λ\sim 1$ kpc, often called fuzzy dark matter (FDM). We describe the arguments from particle physics that motivate FDM, review previous work on its astrophysical signatures, and analyze several unexplored aspects of its behavior. In particular, (i) FDM halos smaller than about $10^7 (m/10^{-22} {\rm eV})^{-3/2} M_\odot$ do not form. (ii) FDM halos are comprised of a core that is a stationary, minimum-energy configuration called a "soliton", surrounded by an envelope that resembles a CDM halo. (iii) The transition between soliton and envelope is determined by a relaxation process analogous to two-body relaxation in gravitating systems, which proceeds as if the halo were composed of particles with mass $\sim ρλ^3$ where $ρ$ is the halo density. (iv) Relaxation may have substantial effects on the stellar disk and bulge in the inner parts of disk galaxies. (v) Relaxation can produce FDM disks but an FDM disk in the solar neighborhood must have a half-thickness of at least $300 (m/10^{-22} {\rm eV})^{-2/3}$ pc. (vi) Solitonic FDM sub-halos evaporate by tunneling through the tidal radius and this limits the minimum sub-halo mass inside 30 kpc of the Milky Way to roughly $10^8 (m/10^{-22} {\rm eV})^{-3/2} M_\odot$. (vii) If the dark matter in the Fornax dwarf galaxy is composed of CDM, most of the globular clusters observed in that galaxy should have long ago spiraled to its center, and this problem is resolved if the dark matter is FDM.

astro-ph.CO↗
arXiv2017

Lidov-Kozai Cycles with Gravitational Radiation: Merging Black Holes in Isolated Triple Systems

We show that a black-hole binary with an external companion can undergo Lidov-Kozai cycles that cause a close pericenter passage, leading to a rapid merger due to gravitational-wave emission. This scenario occurs most often for systems in which the companion has mass comparable to the reduced mass of the binary and the companion orbit has semi-major axis within a factor of $\sim 10$ of the binary semi-major axis. Using a simple population-synthesis model and 3-body simulations, we estimate the rate of mergers in triple black hole systems in the field to be about six per Gpc$^3$ per year in the absence of natal kicks during black hole formation. This value is within the low end of the 90\% credible interval for the total black-hole black-hole merger rate inferred from the current LIGO results. There are many uncertainties in these calculations, the largest of which is the unknown distribution of natal kicks. Even modest natal kicks of $40\mbox{km s}^{-1}$ will reduce the merger rate by a factor of 40. A few percent of these systems will have eccentricity greater than 0.999 when they first enter the frequency band detectable by aLIGO (above 10 Hz).

astro-ph.HE↗
arXiv2016

Modeling the Nearly Isotropic Comet Population in Anticipation of LSST Observations

We run simulations to determine the expected distribution of orbital elements of nearly isotropic comets (NICs) in the outer solar system, assuming that these comets originate in the Oort Cloud at thousands of AU and are perturbed into the planetary region by the Galactic tide. We show that the Large Synoptic Survey Telescope (LSST) should detect and characterize the orbits of hundreds to thousands of NICs with perihelion distance outside 5 AU. Observing NICs in the outer solar system is our only way of directly detecting comets from the inner Oort Cloud, as these comets are dynamically excluded from the inner solar system by the giant planets. Thus the distribution of orbital elements constrains the spatial distribution of comets in the Oort cloud and the environment in which the solar system formed. Additionally, comet orbits can be characterized more precisely when they are seen far from the Sun as they have not been affected by non-gravitational forces.

astro-ph.EP↗
arXiv2016

Warm Jupiters from secular planet-planet interactions

Most warm Jupiters (gas-giant planets with $0.1~{\rm AU}\lesssim a \lesssim1$ AU) have pericenter distances that are too large for significant orbital migration by tidal friction. We study the possibility that the warm Jupiters are undergoing secular eccentricity oscillations excited by an outer companion (a planet or star) in an eccentric and/or mutually inclined orbit. In this model the warm Jupiters migrate periodically, in the high-eccentricity phase of the oscillation when the pericenter distance is small, but are typically observed at much lower eccentricities. We show that the steady-state eccentricity distribution of the warm Jupiters migrating by this mechanism is approximately flat, which is consistent with the observed distribution if and only if we restrict the sample to warm Jupiters that have outer companions detected by radial-velocity surveys. The eccentricity distribution of warm Jupiters without companions exhibits a peak at low eccentricities ($e\lesssim 0.2$) that must be explained by a different formation mechanism. Based on a population-synthesis study we find that high-eccentricity migration excited by an outer planetary companion (i) can account for $\sim20\%$ of the warm Jupiters and most of the warm Jupiters with $e\gtrsim 0.4$, a fraction that is consistent with the observed population of warm Jupiters with outer companions; (ii) can produce most of the observed population of hot Jupiters, with a semimajor axis distribution that matches the observations, but fails to account adequately for $\sim 60\%$ of hot Jupiters with projected obliquities $\lesssim 20^\circ$. Thus $\sim 20\%$ of the warm Jupiters and $\sim 60\%$ of the hot Jupiters can be produced by high-eccentricity migration. We also provide predictions for the expected mutual inclinations and spin-orbit angles of the planetary systems with hot and warm Jupiters produced by high-eccentricity migration.

astro-ph.EP↗
arXiv2015

Adiabatic black hole growth in Sérsic models of elliptical galaxies

We have examined the effect of slow growth of a central black hole on spherical galaxies that obey Sérsic or $R^{1/m}$ surface-brightness profiles. During such growth the actions of each stellar orbit are conserved, which allows us to compute the final distribution function if we assume that the initial distribution function is isotropic. We find that black-hole growth leads to a central cusp or ``excess light', in which the surface brightness varies with radius as $R^{-1.3}$ (with a weak dependence on Sérsic index $m$), the line-of-sight velocity dispersion varies as $R^{-1/2}$, and the velocity anisotropy is $β\simeq -0.24$ to $-0.28$ depending on $m$. The excess stellar mass in the cusp scales approximately linearly with the black-hole mass, and is typically 0.5--0.85 times the black-hole mass. This process may strongly influence the structure of nuclear star clusters if they contain black holes.

astro-ph.GA↗
arXiv2015

The statistical mechanics of planet orbits

The final "giant-impact" phase of terrestrial planet formation is believed to begin with a large number of planetary "embryos" on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits cross and they collide and merge; through this process the number of surviving bodies declines until the system contains a small number of planets on well-separated, stable orbits. In this paper we explore a simple statistical model for the orbit distribution of planets formed by this process, based on the sheared-sheet approximation and the ansatz that the planets explore uniformly all of the stable region of phase space. The model provides analytic predictions for the distribution of eccentricities and semimajor axis differences, correlations between orbital elements of nearby planets, and the complete N-planet distribution function, in terms of a single parameter, the "dynamical temperature", that is determined by the planetary masses. The predicted properties are generally consistent with N-body simulations of the giant-impact phase and with the distribution of semimajor axis differences in the Kepler catalog of extrasolar planets. A similar model may apply to the orbits of giant planets if these orbits are determined mainly by dynamical evolution after the planets have formed and the gas disk has disappeared.

astro-ph.EP↗
arXiv2015

A numerical study of vector resonant relaxation

Stars bound to a supermassive black hole interact gravitationally. Persistent torques acting between stellar orbits lead to the rapid resonant relaxation of the orbital orientation vectors ("vector" resonant relaxation) and slower relaxation of the eccentricities ("scalar" resonant relaxation), both at rates much faster than two-body or non-resonant relaxation. We describe a new parallel symplectic integrator, N-ring, which follows the dynamical evolution of a cluster of N stars through vector resonant relaxation, by averaging the pairwise interactions over the orbital period and periapsis-precession timescale. We use N-ring to follow the evolution of clusters containing over 10^4 stars for tens of relaxation times. Among other results, we find that the evolution is dominated by torques among stars with radially overlapping orbits, and that resonant relaxation can be modelled as a random walk of the orbit normals on the sphere, with angular step size ranging from 0.5-1 radian. The relaxation rate in a cluster with a fixed number of stars is proportional to the RMS mass of the stars. The RMS torque generated by the cluster stars is reduced below the torque between Kepler orbits due to apsidal precession and declines weakly with the eccentricity of the perturbed orbit. However since the angular momentum of an orbit also decreases with eccentricity, the relaxation rate is approximately eccentricity-independent for e<0.7 and grows rapidly with eccentricity for e>0.8. We quantify the relaxation using the autocorrelation function of the spherical multipole moments; this decays exponentially and the e-folding time may be identified with the vector resonant relaxation timescale.

astro-ph.GA↗
arXiv2014

The statistical mechanics of self-gravitating Keplerian disks

We describe the dynamics and thermodynamics of collisionless particle disks orbiting a massive central body, in the case where the disk mass is small compared to the central mass, the self-gravity of the disk dominates the non-Keplerian force, and the spread in semi-major axes is small. We show that with plausible approximations such disks have logarithmic two-body interactions and a compact phase space, and therefore exhibit thermodynamics that are simpler than most other gravitating systems, which require a confining box and artificial softening of the potential at small scales to be thermodynamically well-behaved. We solve for the microcanonical axisymmetric thermal equilibria and demonstrate the existence of a symmetry-breaking bifurcation into lopsided equilibria. We discuss the relation between thermal and dynamical instability in these systems and draw connections to astrophysical settings, as well as to the wider subject of the statistical mechanics of particles with logarithmic long-range interactions, such as point vortices in two-dimensional fluids.

astro-ph.GA↗
arXiv2014

Advances in exoplanet science from Kepler

Numerous telescopes and techniques have been used to find and study extrasolar planets, but none has been more successful than NASA's Kepler Space Telescope. Kepler has discovered the majority of known exoplanets, the smallest planets to orbit normal stars, and the worlds most likely to be similar to our home planet. Most importantly, Kepler has provided our first look at typical characteristics of planets and planetary systems for planets with sizes as small as and orbits as large as those of the Earth.

astro-ph.EP↗
arXiv2014

The odd couple: quasars and black holes

Quasars emit more energy than any other objects in the universe, yet are not much bigger than the solar system. We are almost certain that quasars are powered by giant black holes of up to $10^{10}$ times the mass of the Sun, and that black holes of between $10^6$ and $10^{10}$ solar masses---dead quasars---are present at the centers of most galaxies. Our own galaxy contains a black hole of $4.3\times10^6$ solar masses. The mass of the central black hole appears to be closely related to other properties of its host galaxy, such as the total mass in stars, but the origin of this relation and the role that black holes play in the formation of galaxies are still mysteries.

astro-ph.GA↗
arXiv2014

Constraining Sub-Parsec Binary Supermassive Black Holes in Quasars with Multi-Epoch Spectroscopy. II. The Population with Kinematically Offset Broad Balmer Emission Lines

A small fraction of quasars have long been known to show bulk velocity offsets in the broad Balmer lines with respect to the systemic redshift of the host galaxy. Models to explain these offsets usually invoke broad-line region gas kinematics/asymmetry around single black holes (BHs), orbital motion of massive (~sub-pc) binary black holes (BBHs), or recoil BHs, but single-epoch spectra are unable to distinguish between these scenarios. The line-of-sight (LOS) radial velocity (RV) shifts from long-term spectroscopic monitoring can be used to test the BBH hypothesis. We have selected a sample of 399 quasars with offset broad H-beta lines from the SDSS DR7 quasar catalog, and have conducted second-epoch optical spectroscopy for 50 of them. Combined with the existing SDSS spectra, the new observations enable us to constrain the LOS RV shifts of broad H-beta lines with a rest-frame baseline of a few years to nearly a decade. Using cross-correlation analysis, we detect significant (99% confidence) radial accelerations in the broad H-beta lines in 24 of the 50 objects. We suggest that 9 of the 24 detections are sub-pc BBH candidates, which show consistent velocity shifts independently measured from a second broad line (either H-alpha or Mg II) without significant changes in the broad-line profiles. Combining the results on the general quasar population studied in Paper I, we find a tentative anti-correlation between the velocity offset in the first-epoch spectrum and the average acceleration between two epochs, which could be explained by orbital phase modulation when the time separation between two epochs is a non-negligible fraction of the orbital period of the motion causing the line displacement. We discuss the implications of our results for the identification of sub-pc BBH candidates in offset-line quasars and for the constraints on their frequency and orbital parameters. [Abridged]

astro-ph.CO↗
arXiv2014

Relativistic redshifts in quasar broad lines

The broad emission lines commonly seen in quasar spectra have velocity widths of a few per cent of the speed of light, so special- and general-relativistic effects have a significant influence on the line profile. We have determined the redshift of the broad H-beta line in the quasar rest frame (determined from the core component of the [OIII] line) for over 20,000 quasars from the Sloan Digital Sky Survey DR7 quasar catalog. The mean redshift as a function of line width is approximately consistent with the relativistic redshift that is expected if the line originates in a randomly oriented Keplerian disk that is obscured when the inclination of the disk to the line of sight exceeds ~30-45 degrees, consistent with simple AGN unification schemes. This result also implies that the net line-of-sight inflow/outflow velocities in the broad-line region are much less than the Keplerian velocity when averaged over a large sample of quasars with a given line width.

astro-ph.GA↗
arXiv2014

Scattering outcomes of close-in planets: constraints on planet migration

Many exoplanets in close-in orbits are observed to have relatively high eccentricities and large stellar obliquities. We explore the possibility that these result from planet-planet scattering by studying the dynamical outcomes from a large number of orbit integrations in systems with two and three gas-giant planets in close-in orbits (0.05 AU < a < 0.15 AU). We find that at these orbital separations, unstable systems starting with low eccentricities and mutual inclinations ($e\lesssim0.1$, $i\lesssim0.1$) generally lead to planet-planet collisions in which the collision product is a planet on a low-eccentricity, low-inclination orbit. This result is inconsistent with the observations. We conclude that eccentricity and inclination excitation from planet-planet scattering must precede migration of planets into short-period orbits. This result constrains theories of planet migration: the semi-major axis must shrink by 1-2 orders of magnitude without damping the eccentricity and inclination.

astro-ph.EP↗
arXiv2014

Co-Evolution of Galactic Nuclei and Globular Cluster Systems

We revisit the hypothesis that dense galactic nuclei are formed from inspiraling globular clusters. Recent advances in understanding of the continuous formation of globular clusters over cosmic time and the concurrent evolution of the galaxy stellar distribution allow us to construct a simple model that matches the observed spatial and mass distributions of clusters in the Galaxy and the giant elliptical galaxy M87. In order to compare with observations, we model the effects of dynamical friction and dynamical evolution, including stellar mass loss, tidal stripping of stars, and tidal disruption of clusters by the growing galactic nucleus. We find that inspiraling globular clusters form a dense central structure, with mass and radius comparable to the typical values in observed nuclear star clusters (NSCs) in late-type and low-mass early-type galaxies. The density contrast associated with the NSC is less pronounced in giant elliptical galaxies. Our results indicate that the NSC mass as a fraction of mass of the galaxy stellar spheroid scales as M_NSC/M_* = 0.0025 M_{*,11}^{-0.5}. Thus disrupted globular clusters could contribute most of the mass of NSCs in galaxies with stellar mass below 10^{11} Msun. The inner part of the accumulated cluster may seed the growth of a central black hole via stellar dynamical core collapse, thereby relieving the problem of how to form luminous quasars at high redshift. The seed black hole may reach about 10^5 Msun within 1 Gyr of the beginning of globular cluster formation.

astro-ph.CO↗
arXiv2013

The Black Hole Mass and the Stellar Ring in NGC 3706

We determine the mass of the nuclear black hole ($M$) in NGC 3706, an early type galaxy with a central surface brightness minimum arising from an apparent stellar ring, which is misaligned with respect to the galaxy's major axis at larger radii. We fit new HST/STIS and archival data with axisymmetric orbit models to determine $M$, mass-to-light ratio ($Υ_V$), and dark matter halo profile. The best-fit model parameters with 1$σ$ uncertainties are $M = (6.0^{+0.7}_{-0.9}) \times 10^8\ M_{\scriptscriptstyle \odot}$ and $Υ_V = 6.0 \pm 0.2\ M_{\scriptscriptstyle \odot}\ L_{{\scriptscriptstyle \odot},V}^{-1}$ at an assumed distance of 46 Mpc. The models are inconsistent with no black hole at a significance of $Δχ^2 = 15.4$ and require a dark matter halo to adequately fit the kinematic data, but the fits are consistent with a large range of plausible dark matter halo parameters. The ring is inconsistent with a population of co-rotating stars on circular orbits, which would produce a narrow line-of-sight velocity distribution (LOSVD). Instead, the ring's LOSVD has a small value of $|V|/σ$, the ratio of mean velocity to velocity dispersion. Based on the observed low $|V|/σ$, our orbit modeling, and a kinematic decomposition of the ring from the bulge, we conclude that the stellar ring contains stars that orbit in both directions. We consider potential origins for this unique feature, including multiple tidal disruptions of stellar clusters, a change in the gravitational potential from triaxial to axisymmetric, resonant capture and inclining of orbits by a binary black hole, and multiple mergers leading to gas being funneled to the center of the galaxy.

astro-ph.GA↗
arXiv2013

Why do Earth satellites stay up?

Satellites in low Earth orbits must accurately conserve their orbital eccentricity, since a decrease in perigee of only 5-10% would cause them to crash. However, these satellites are subject to gravitational perturbations from the Earth's multipole moments, the Moon, and the Sun that are not spherically symmetric and hence do not conserve angular momentum, especially over the tens of thousands of orbits made by a typical satellite. Why then do satellites not crash? We describe a vector-based analysis of the long-term behavior of satellite orbits and apply this to several toy systems containing a single non-Keplerian perturbing potential. If only the quadrupole potential from the Earth's equatorial bulge is present, all near-circular orbits are stable. If only the octupole potential is present, all such orbits are unstable. If only the lunar or solar potential is present, all near-circular orbits with inclinations to the ecliptic exceeding 39 degrees are unstable. We describe the behavior of satellites in the simultaneous presence of all of these perturbations and show that almost all low Earth orbits are stable because of an accidental property of the dominant quadrupole potential. We also relate these results to the phenomenon of Lidov-Kozai oscillations.

astro-ph.EP↗
arXiv2013

Constraining sub-Parsec Binary Supermassive Black Holes in Quasars with Multi-Epoch Spectroscopy. I. The General Quasar Population

We perform a systematic search for sub-parsec binary supermassive black holes (BHs) in normal broad line quasars at z<0.8, using multi-epoch SDSS spectroscopy of the broad Hbeta line. Our working model is that: only one of the two BHs in the binary is active, and dynamically dominates its own broad line region (BLR); the inactive companion BH is orbiting at a distance of a few R_BLR, where R_BLR~0.01-0.1 pc is the BLR size. We search for the expected line-of-sight acceleration of the broad line velocity from binary orbital motion by cross-correlating SDSS spectra from two epochs separated by up to several years in the quasar restframe. Out of ~700 pairs of spectra for which we have good measurements of the velocity shift between two epochs (1-sigma error~40 km/s), we detect 28 systems with significant velocity shifts in broad Hbeta, among which seven are the best candidates for the hypothesized binaries. We use the distribution of the observed accelerations (mostly non-detections) to place constraints on the abundance of such binary systems among the general quasar population. Excess variance in the velocity shift is inferred for observations separated by longer than 0.4 yr (quasar restframe). Attributing all the excess to binary motion would imply that most of the quasars in this sample must be in binaries; that the inactive BH must be on average more massive than the active one; and that the binary separation is at most a few times the size of the BLR. However, if this excess variance is partly or largely due to long-term broad line variability, the requirement of a large population of close binaries is much weakened or even disfavored for massive companions. [Abridged]

astro-ph.CO↗