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Tremaine, Scott

Publications and source records attributed to Tremaine, Scott.

At least 19 records

Collisional Fragmentation Is Not a Barrier to Close-in Planet Formation

Collisional fragmentation is shown to not be a barrier to rocky planet formation at small distances from the host star. Simple analytic arguments demonstrate that rocky planet formation via collisions of homogeneous gravity-dominated bodies is possible down to distances of order the Roche radius ( r {sub Roche}). Extensive N -body simulations with initial bodies ≳1700 km that include plausible models for fragmentation and merging of gravity-dominated bodies confirm this conclusion and demonstrate that rocky planet formation is possible down to ∼1.1 r {sub Roche}. At smaller distances, tidal effects cause collisions to be too fragmenting to allow mass buildup to a final, dynamically stable planetary system. We argue that even differentiated bodies can accumulate to form planets at distances that are not much larger than r {sub Roche}.

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Isotropic–Nematic Phase Transitions in Gravitational Systems

We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different timescales. In particular, the orbital-plane orientations are typically driven into internal thermodynamic equilibrium by vector resonant relaxation before the orbital eccentricities or semimajor axes relax. We show that the statistical mechanics of such systems exhibit a striking resemblance to liquid crystals, with analogous ordered-nematic and disordered-isotropic phases. The ordered phase consists of bodies orbiting in a disk in both directions, with the disk thickness depending on temperature, while the disordered phase corresponds to a nearly isotropic distribution of the orbit normals. We show that below a critical value of the total angular momentum, the system undergoes a first-order phase transition between the ordered and disordered phases. At a critical point, the phase transition becomes second order, while for higher angular momenta there is a smooth crossover. We also find metastable equilibria containing two identical disks with mutual inclinations between 90° and 180°.

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Ultralight scalars as cosmological dark matter

Many aspects of the large-scale structure of the Universe can be described successfully using cosmological models in which 27 ± 1% of the critical mass-energy density consists of cold dark matter (CDM). However, few—if any—of the predictions of CDM models have been successful on scales of ~10 kpc or less. This lack of success is usually explained by the difficulty of modeling baryonic physics (star formation, supernova and black-hole feedback, etc.). An intriguing alternative to CDM is that the dark matter is an extremely light (m ~10 -22 eV) boson having a de Broglie wavelength λ ~1 kpc, often called fuzzy dark matter (FDM). Here 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 or subhalos smaller than about 10 7 (m/10 -22 eV) -3/2 M ⊙ do not form, and the abundance of halos smaller than a few times 10 10 (m/10 -22 eV) -4/3 M ⊙ is substantially smaller in FDM than in CDM. (ii) FDM halos are comprised of a central core that is a stationary, minimum-energy solution of the Schrödinger-Poisson equation, sometimes called a “soliton,” surrounded by an envelope that resembles a CDM halo. The soliton can produce a distinct signature in the rotation curves of FDM-dominated systems. (iii) The transition between soliton and envelope is determined by a relaxation process analogous to two-body relaxation in gravitating N-body systems, which proceeds as if the halo were composed of particles with mass ~ 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, but has negligible effect on disk thickening or globular cluster disruption near the solar radius. (v) Relaxation can produce FDM disks but a FDM disk in the solar neighborhood must have a half-thickness of at least ~300 (m/10 -22 eV) -2/3 pc and a midplane density less than 0.2(m/10 -22 eV) 2/3 times the baryonic disk density. (vi) Solitonic FDM subhalos evaporate by tunneling through the tidal radius and this limits the minimum subhalo mass inside ~30 kpc of the Milky Way to a few times 10 8 (m/10 - 22 eV) -3/2 M ⊙ . (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. (viii) FDM delays galaxy formation relative to CDM but its galaxy-formation history is consistent with current observations of high-redshift galaxies and the late reionization observed by Planck. If the dark matter is composed of FDM, most observations favor a particle mass ≳ 10 -22 eV and the most significant observational consequences occur if the mass is in the range 1 -10 × 10 - 22 eV. There is tension with observations of the Lyman-α forest, which favor m ≳10 - 20 × 10 -22 eV and we discuss whether more sophisticated models of reionization may resolve this tension.

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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 a mass comparable to the reduced mass of the binary and the companion orbit has a semimajor axis within a factor of ∼10 of the binary semimajor axis. Using a simple population-synthesis model and three-body simulations, we estimate the rate of mergers in triple black-hole systems in the field to be about six per Gpc{sup 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 km s{sup −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).

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Warm jupiters from secular planet-planet interactions

Most warm Jupiters (gas-giant planets with 0.1 au≲a≲1 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, but are typically observed at lower eccentricities. We show that in this model the steady-state eccentricity distribution of the warm Jupiters is approximately flat, which is consistent with the observed distribution if we restrict the sample to warm Jupiters with detected outer planetary companions. The eccentricity distribution of warm Jupiters without companions exhibits a peak at e≲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 (1) can account for ∼20% of the warm Jupiters and most of the warm Jupiters with e≳0.4; and (2) 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 ∼60% of hot Jupiters with projected obliquities ≲20{sup ∘}. Thus ∼20% of the warm Jupiters and ∼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.

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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{sup 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 (DF) if we assume that the initial DF 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{sup −1.3} (with a weak dependence on Sérsic index m), the line-of-sight velocity dispersion varies as R{sup −1/2}, and the velocity anisotropy is β≃−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 in spheroidal galaxies if they contain black holes.

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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.

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Relativistic redshifts in quasar broad lines

The broad emission lines commonly seen in quasar spectra have velocity widths of a few percent 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 Hβ line in the quasar rest frame (determined from the core component of the [O III] line) for over 20,000 quasars from the Sloan Digital Sky Survey Data Release 7 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°, consistent with simple active galactic nucleus 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.

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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 (of a few hundred to thousands of km s{sup –1}) 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-parsec (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 kinematically offset broad Hβ lines from the Sloan Digital Sky Survey (SDSS) Seventh Data Release 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 Hβ lines with a rest-frame baseline of a few years to nearly a decade. While previous work focused on objects with extreme velocity offset (>10{sup 3} km s{sup –1}), we explore the parameter space with smaller (a few hundred km s{sup –1}) yet significant offsets (99.7% confidence). Using cross-correlation analysis, we detect significant (99% confidence) radial accelerations in the broad Hβ lines in 24 of the 50 objects, of ∼10-200 km s{sup –1} yr{sup –1} with a median measurement uncertainty of ∼10 km s{sup –1} yr{sup –1}, implying a high fraction of variability of the broad-line velocity on multi-year timescales. 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 Hα 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.

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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 ≲ 0.1, i ≲ 0.1) 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.

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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 the 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{sub NSC}/M{sub ∗}≈0.0025 M{sub ∗,11}{sup −0.5}. Thus disrupted globular clusters could contribute most of the mass of NSCs in galaxies with stellar mass below 10{sup 11} M {sub ☉}. 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 ∼10{sup 5} M {sub ☉} within ≲ 1 Gyr of the beginning of globular cluster formation.

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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 (Y {sub V}), and dark matter halo profile. The best-fit model parameters with 1σ uncertainties are M=(6.0{sub −0.9}{sup +0.7})×10{sup 8} M{sub ⊙} and Υ{sub V}=6.0±0.2 M{sub ⊙} L{sub ⊙,V}{sup −1} at an assumed distance of 46 Mpc. The models are inconsistent with no black hole at a significance of Δχ{sup 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.

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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 Sloan Digital Sky Survey (SDSS) spectroscopy of the broad Hβ line. Our working model is that (1) one and only one of the two BHs in the binary is active; (2) the active BH dynamically dominates its own broad-line region (BLR) in the binary system, so that the mean velocity of the BLR reflects the mean velocity of its host BH; (3) the inactive companion BH is orbiting at a distance of a few R{sub BLR}, where R{sub 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 rest frame. Out of ∼700 pairs of spectra for which we have good measurements of the velocity shift between two epochs (1σ error ∼40 km s{sup –1}), we detect 28 systems with significant velocity shifts in broad Hβ, among which 7 are the best candidates for the hypothesized binaries, 4 are most likely due to broad-line variability in single BHs, and the rest are ambiguous. Continued spectroscopic observations of these candidates will easily strengthen or disprove these claims. 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 rest frame). 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. Future time-domain spectroscopic surveys of normal quasars can provide vital prior information on the structure function of stochastic velocity shifts induced by broad-line variability in single BHs. Such surveys with improved spectral quality, increased time baseline, and more epochs can greatly improve the statistical constraints of this method on the general binary population in broad-line quasars, further shrink the allowed binary parameter space, and detect true sub-parsec binaries.

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PLANETS NEAR MEAN-MOTION RESONANCES

The multiple-planet systems discovered by the Kepler mission exhibit the following feature: planet pairs near first-order mean-motion resonances prefer orbits just outside the nominal resonance, while avoiding those just inside the resonance. We explore an extremely simple dynamical model for planet formation, in which planets grow in mass at a prescribed rate without orbital migration or dissipation. We develop an analytic version of this model for two-planet systems in two limiting cases: the planet mass grows quickly or slowly relative to the characteristic resonant libration time. In both cases, the distribution of systems in period ratio develops a characteristic asymmetric peak-trough structure around the resonance, qualitatively similar to that observed in the Kepler sample. We verify this result with numerical integrations of the three-body problem. We show that for the 3 : 2 resonance, where the observed peak-trough structure is strongest, our simple model is consistent with the observations for a range of mean planet masses 20-100 M{sub Circled-Plus }. This predicted mass range is higher-by at least a factor of three-than the range expected from the few Kepler planets with measured masses, but part of this discrepancy could be due to oversimplifications in the dynamical model or uncertainties in the planetary mass-radius relation.

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ON THE LOCAL DARK MATTER DENSITY

An analysis of the kinematics of 412 stars at 1-4 kpc from the Galactic midplane by Moni Bidin et al. has claimed to derive a local density of dark matter that is an order of magnitude below standard expectations. We show that this result is incorrect and that it arises from the assumption that the mean azimuthal velocity of the stellar tracers is independent of Galactocentric radius at all heights. We substitute the assumption, supported by data, that the circular speed is independent of radius in the midplane. We demonstrate that the assumption of constant mean azimuthal velocity is implausible by showing that it requires the circular velocity to drop more steeply than allowed by any plausible mass model, with or without dark matter, at large heights above the midplane. Using the approximation that the circular-velocity curve is flat in the midplane, we find that the data imply a local dark matter density of 0.008 {+-} 0.003 M{sub Sun} pc{sup -3} = 0.3 {+-} 0.1 GeV cm{sup -3}, fully consistent with standard estimates of this quantity. This is the most robust direct measurement of the local dark matter density to date.

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SUPER-ECCENTRIC MIGRATING JUPITERS

An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e = 0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e > 0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is a-dot {proportional_to}a{sup 1/2} and consequently the number distribution satisfies dN/d log a{proportional_to}a{sup 1/2}. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.

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THE STATISTICS OF MULTI-PLANET SYSTEMS

We describe statistical methods for measuring the exoplanet multiplicity function (the fraction of host stars containing a given number of planets) and inclination distribution from transit and radial-velocity (RV) surveys. The analysis is based on the approximation of separability-that the distribution of planetary parameters in an n-planet system is the product of identical 1-planet distributions. We review the evidence that separability is a valid approximation for exoplanets and conclude that it captures many, but not all, of the known characteristics of multi-planet systems. We show how to relate the observable multiplicity function in surveys with similar host-star populations but different sensitivities. We also show how to correct for geometrical selection effects to derive the multiplicity function from transit surveys if the distribution of relative inclinations is known. Applying these tools to the Kepler transit survey and to RV surveys, we find that (1) the Kepler data alone do not constrain the mean inclination of multi-planet systems; even spherical distributions are allowed by the data but only if a small fraction of host stars contain large planet populations ({approx}> 30); (2) comparing the Kepler and RV surveys shows that the mean inclination of multi-planet systems is less than 5 Degree-Sign ; and (3) the multiplicity function of the Kepler planets is not well determined by the present data.

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Extrasolar Planet Inferometric Survey (EPIcS)

The discovery of the nature of the solar system was a crowning achievement of Renaissance science. The quest to evaluate the properties of extrasolar planetary systems is central to both the intellectual understanding of our origins and the cultural understanding of humanity's place in the Universe; thus it is appropriate that the goals and objectives of NASA's breakthrough Origins program emphasize the study of planetary systems, with a focus on the search for habitable planets. We propose an ambitious research program that will use SIM - the first major mission of the Origins program - to explore planetary systems in our Galactic neighborhood. Our program is a novel two-tiered SIM survey of nearby stars that exploits the capabilities of SIM to achieve two scientific objectives: (i) to identify Earth-like planets in habitable regions around nearby Sunlike stars: and (ii) to explore the nature and evolution of planetary systems in their full variety. The first of these objectives was recently recommended by the Astronomy and Astrophysics Survey Committee (the McKee-Taylor Committee) as a prerequisite for the development of the Terrestrial Planet Finder mission later in the decade. Our program combines this two-part survey with preparatory and contemporaneous research designed to maximize the scientific return from the limited and thus precious observing resources of SIM.

Shao, Michael↗