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Analytic Expressions for the Inner-rim Structure of Passively Heated Protoplanetary Disks

We analytically derive the expressions for the structure of the inner region of protoplanetary disks based on the results from the recent hydrodynamical simulations. The inner part of a disk can be divided into four regions: a dust-free region with a gas temperature in the optically thin limit, an optically thin dust halo, an optically thick condensation front, and the classical, optically thick region, in order from the innermost to the outermost. We derive the dust-to-gas mass ratio profile in the dust halo using the fact that partial dust condensation regulates the temperature relative to the dust evaporation temperature. Beyond the dust halo, there is an optically thick condensation front where all the available silicate gas condenses out. The curvature of the condensation surface is determined by the condition that the surface temperature must be nearly equal to the characteristic temperature ∼1200 K. We derive the midplane temperature in the outer two regions using the two-layer approximation, with the additional heating by the condensation front for the outermost region. As a result, the overall temperature profile is step-like, with steep gradients at the borders between the outer three regions. The borders might act as planet traps where the inward migration of planets due to gravitational interaction with the gas disk stops. The temperature at the border between the two outermost regions coincides with the temperature needed to activate magnetorotational instability, suggesting that the inner edge of the dead zone must lie at this border. The radius of the dead zone inner edge predicted from our solution is ∼2–3 times larger than that expected from the classical optically thick temperature.

79 ASTRONOMY AND ASTROPHYSICS↗

Two transiting earth-size planets near resonance orbiting a nearby cool star

Discoveries from the prime Kepler mission demonstrated that small planets (<3 R{sub ⊕}) are common outcomes of planet formation. While Kepler detected many such planets, all but a handful orbit faint, distant stars and are not amenable to precise follow up measurements. Here, we report the discovery of two small planets transiting K2-21, a bright (K = 9.4) M0 dwarf located 65±6 pc from Earth. We detected the transiting planets in photometry collected during Campaign 3 of NASA’s K2 mission. Analysis of transit light curves reveals that the planets have small radii compared to their host star, R{sub P}/R{sub ⋆} = 2.60±0.14% and 3.15±0.20%, respectively. We obtained follow up NIR spectroscopy of K2-21 to constrain host star properties, which imply planet sizes of 1.59 ± 0.43 R{sub ⊕} and 1.92 ± 0.53 R{sub ⊕}, respectively, straddling the boundary between high-density, rocky planets and low-density planets with thick gaseous envelopes. The planets have orbital periods of 9.32414 days and 15.50120 days, respectively, and a period ratio P{sub c}/P{sub b} = 1.6624, very near to the 5:3 mean motion resonance, which may be a record of the system’s formation history. Transit timing variations due to gravitational interactions between the planets may be detectable using ground-based telescopes. Finally, this system offers a convenient laboratory for studying the bulk composition and atmospheric properties of small planets with low equilibrium temperatures.

79 ASTRONOMY AND ASTROPHYSICS↗

DIFFICULTY IN THE FORMATION OF COUNTER-ORBITING HOT JUPITERS FROM NEAR-COPLANAR HIERARCHICAL TRIPLE SYSTEMS: A SUB-STELLAR PERTURBER

Among 100 transiting planets with a measured projected spin–orbit angle λ, several systems are suggested to be counter-orbiting. While these cases may be due to the projection effect, the mechanism that produces a counter-orbiting planet has not been established. A promising scenario for counter-orbiting planets is the extreme eccentricity evolution in near-coplanar hierarchical triple systems with eccentric inner and outer orbits. We examine this scenario in detail by performing a series of systematic numerical simulations, and consider the possibility of forming hot Jupiters (HJs), especially a counter-orbiting one under this mechanism with a distant sub-stellar perturber. We incorporate quadrupole and octupole secular gravitational interaction between the two orbits, and also short-range forces (correction for general relativity, star and inner planetary tide, and rotational distortion) simultaneously. We find that most systems are tidally disrupted and that a small fraction of the surviving planets turn out to be prograde. The formation of counter-orbiting HJs in this scenario is possible only in a very restricted parameter region, and thus is very unlikely in practice.

79 ASTRONOMY AND ASTROPHYSICS↗

A gap with a deficit of large grains in the protoplanetary disk around TW Hya

We report ∼3 au resolution imaging observations of the protoplanetary disk around TW Hya at 145 and 233 GHz with the Atacama Large Millimeter/submillimeter Array. Our observations revealed two deep gaps (∼25%–50%) at 22 and 37 au and shallower gaps (a few percent) at 6, 28, and 44 au, as recently reported by Andrews et al. The central hole with a radius of ∼3 au was also marginally resolved. The most remarkable finding is that the spectral index α(R) between bands 4 and 6 peaks at the 22 au gap. The derived power-law index of the dust opacity β(R) is ∼1.7 at the 22 au gap and decreases toward the disk center to ∼0. The most prominent gap at 22 au could be caused by the gravitational interaction between the disk and an unseen planet with a mass of ≲1.5 M {sub Neptune}, although other origins may be possible. The planet-induced gap is supported by the fact that β(R) is enhanced at the 22 au gap, indicating a deficit of ∼millimeter-sized grains within the gap due to dust filtration by a planet.

79 ASTRONOMY AND ASTROPHYSICS↗

The JCMT BISTRO Survey: The Magnetic Field Strength in the Orion A Filament

We determine the magnetic field strength in the OMC 1 region of the Orion A filament via a new implementation of the Chandrasekhar–Fermi method using observations performed as part of the James Clerk Maxwell Telescope (JCMT) B-Fields In Star-forming Region Observations (BISTRO) survey with the POL-2 instrument. We combine BISTRO data with archival SCUBA-2 and HARP observations to find a plane-of-sky magnetic field strength in OMC 1 of B{sub pos}=6.6±4.7 mG, where δB{sub pos}=4.7 mG represents a predominantly systematic uncertainty. We develop a new method for measuring angular dispersion, analogous to unsharp masking. We find a magnetic energy density of ∼1.7×10{sup −7} J m{sup −3} in OMC 1, comparable both to the gravitational potential energy density of OMC 1 (∼10{sup −7} J m{sup −3}) and to the energy density in the Orion BN/KL outflow (∼10{sup −7} J m{sup −3}). We find that neither the Alfvén velocity in OMC 1 nor the velocity of the super-Alfvénic outflow ejecta is sufficiently large for the BN/KL outflow to have caused large-scale distortion of the local magnetic field in the ∼500 yr lifetime of the outflow. Hence, we propose that the hourglass field morphology in OMC 1 is caused by the distortion of a primordial cylindrically symmetric magnetic field by the gravitational fragmentation of the filament and/or the gravitational interaction of the BN/KL and S clumps. We find that OMC 1 is currently in or near magnetically supported equilibrium, and that the current large-scale morphology of the BN/KL outflow is regulated by the geometry of the magnetic field in OMC 1, and not vice versa.

79 ASTRONOMY AND ASTROPHYSICS↗

CHARACTERIZING THE STAR FORMATION OF THE LOW-MASS SHIELD GALAXIES FROM HUBBLE SPACE TELESCOPE IMAGING

The Survey of Hi in Extremely Low-mass Dwarfs is an on-going multi-wavelength program to characterize the gas, star formation, and evolution in gas-rich, very low-mass galaxies that populate the faint end of the galaxy luminosity function. The galaxies were selected from the first ∼10% of the Hi Arecibo Legacy Fast ALFA survey based on their low Hi mass and low baryonic mass. Here, we measure the star formation properties from optically resolved stellar populations for 12 galaxies using a color–magnitude diagram fitting technique. We derive lifetime average star formation rates (SFRs), recent SFRs, stellar masses, and gas fractions. Overall, the recent SFRs are comparable to the lifetime SFRs with mean birthrate parameter of 1.4, with a surprisingly narrow standard deviation of 0.7. Two galaxies are classified as dwarf transition galaxies (dTrans). These dTrans systems have star formation and gas properties consistent with the rest of the sample, in agreement with previous results that some dTrans galaxies may simply be low-luminosity dwarf irregulars. We do not find a correlation between the recent star formation activity and the distance to the nearest neighboring galaxy, suggesting that the star formation process is not driven by gravitational interactions, but regulated internally. Further, we find a broadening in the star formation and gas properties (i.e., specific SFRs, stellar masses, and gas fractions) compared to the generally tight correlation found in more massive galaxies. Overall, the star formation and gas properties indicate these very low-mass galaxies host a fluctuating, non-deterministic, and inefficient star formation process.

79 ASTRONOMY AND ASTROPHYSICS↗

Quantisation of the holographic Ricci dark energy model

While general relativity is an extremely robust theory to describe the gravitational interaction in our Universe, it is expected to fail close to singularities like the cosmological ones. On the other hand, it is well known that some dark energy models might induce future singularities; this can be the case for example within the setup of the Holographic Ricci Dark Energy model (HRDE). On this work, we perform a cosmological quantisation of the HRDE model and obtain under which conditions a cosmic doomsday can be avoided within the quantum realm. We show as well that this quantum model not only avoid future singularities but also the past Big Bang.

79 ASTRONOMY AND ASTROPHYSICS↗

Transit timing variations for planets co-orbiting in the horseshoe regime

Although not yet detected, pairs of exoplanets in 1:1 mean motion resonance probably exist. Low eccentricity, near-planar orbits, which in the comoving frame follow horseshoe trajectories, are one of the possible stable configurations. Here we study transit timing variations (TTVs) produced by mutual gravitational interaction of planets in this orbital architecture, with the goal to develop methods that can be used to recognize this case in observational data. In particular, we use a semi-analytic model to derive parametric constraints that should facilitate data analysis. We show that characteristic traits of the TTVs can directly constrain the (1) ratio of planetary masses and (2) their total mass (divided by that of the central star) as a function of the minimum angular separation as seen from the star. In an ideal case, when transits of both planets are observed and well characterized, the minimum angular separation can also be inferred from the data. As a result, parameters derived from the observed transit timing series alone can directly provide both planetary masses scaled to the central star mass.

79 ASTRONOMY AND ASTROPHYSICS↗

Potential Themis-family Asteroid Contribution to the Jupiter-family Comet Population

Recent dynamical analyses suggest that some Jupiter family comets (JFCs) may originate in the main asteroid belt instead of the outer solar system. This possibility is particularly interesting given evidence that icy main-belt objects are known to be present in the Themis asteroid family. We report results from dynamical analyses specifically investigating the possibility that icy Themis family members could contribute to the observed population of JFCs. Numerical integrations show that such dynamical evolution is indeed possible via a combination of eccentricity excitation apparently driven by the nearby 2:1 mean-motion resonance with Jupiter, gravitational interactions with planets other than Jupiter, and the Yarkovsky effect. We estimate that, at any given time, there may be tens of objects from the Themis family on JFC-like orbits with the potential to mimic active JFCs from the outer solar system, although not all, or even any, may necessarily be observably active. We find that dynamically evolved Themis family objects on JFC-like orbits have semimajor axes between 3.15 and 3.40 au for the vast majority of their time on such orbits, consistent with the strong role that the 2:1 mean-motion resonance with Jupiter likely plays in their dynamical evolution. We conclude that a contribution from the Themis family to the active JFC population is plausible, although further work is needed to better characterize this contribution.

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DYNAMICS AND TRANSIT VARIATIONS OF RESONANT EXOPLANETS

Transit timing variations (TTVs) are deviations of the measured midtransit times from the exact periodicity. One of the most interesting causes of TTVs is the gravitational interaction between planets. Here we consider a case of two planets in a mean motion resonance (orbital periods in a ratio of small integers). This case is important because the resonant interaction can amplify the TTV effect and allow planets to be detected more easily. We develop an analytic model of the resonant dynamics valid for small orbital eccentricities and use it to derive the principal TTV terms. We find that a resonant system should show TTV terms with two basic periods (and their harmonics). The resonant TTV period is proportional ( m / M {sub *}){sup −2/3}, where m and M {sub *} are the planetary and stellar masses. For m = 10{sup −4} M {sub *}, for example, the TTV period exceeds the orbital period by about two orders of magnitude. The amplitude of the resonant TTV terms scales linearly with the libration amplitude. The ratio of the TTV amplitudes of two resonant planets is inversely proportional to the ratio of their masses. These and other relationships discussed in the main text can be used to aid the interpretation of TTV observations.

79 ASTRONOMY AND ASTROPHYSICS↗

FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS

We consider Earth satellite orbits in the range of semimajor axes where the perturbing effects of Earth’s oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of primary importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.

79 ASTRONOMY AND ASTROPHYSICS↗

Orbital Modification of the Himalia Family during an Early Solar System Dynamical Instability

Among the irregular satellites orbiting Jupiter, the Himalia family is characterized by a high velocity dispersion δv of several hundred m s{sup −1} among its members, inconsistent with a collisional origin. Efforts to account for this through internecine gravitational interactions do not readily reproduce this feature. Here, we revisit the problem in the context of recent cosmogonical models, where the giant planets migrated significantly through interaction with a planetesimal disk and suffered encounters with planetesimals and planet-sized objects. Our starting assumption is that family formation either predated this phase or occurred soon after its onset. We simulate numerically the diffusive effect of three distinct populations of perturbers on a set of test particles representing the family: Moon-sized (MPT) and Pluto-sized (PPT) planetesimals, and planetary-mass objects (PMO) with masses typical of ice-giant planets. We find that PPT flybys are inefficient, but encounters with MPTs raise the δv of ∼60% of our test particles to >200 m s{sup −1} with respect to Himalia, in agreement with observations. As MPTs may not have been abundant in the disk, we simulate encounters between Jupiter and PMOs. We find that too few encounters generate less dispersion than MPTs while too many essentially destroy the family. For PMO masses in the range 5--20 m{sub ⊕}, the family orbital distribution is reproduced by a few tens of encounters.

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Linear growth of structure in massive bigravity

The ghost-free theory of massive gravity with two dynamical metrics has been shown to produce viable cosmological expansion, where the late-time acceleration of the Universe is due to the finite range of the gravitational interaction rather than a nonzero cosmological constant. Here the cosmological perturbations are studied in this theory. The full perturbation equations are presented in a general gauge and analyzed, focusing on subhorizon scales in the quasistatic limit during the matter-dominated era. An evolution equation for the matter inhomogeneities and the parameters quantifying the deviations from general relativistic structure formation are expressed in terms of five functions whose forms are determined directly by the coupling parameters in the theory. The evolution equation has a similar structure to Horndeski-type scalar-tensor theories, exhibiting a modified growth rate and scale-dependence at intermediate wavenumbers. Predictions of the theory are confronted with observational data on both background expansion and large-scale structure, although care must be taken to ensure a model is stable. It is found that while the stable models fit the data well, they feature deviations from the standard cosmology that could be detected or ruled out by near-future experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

SUPERMASSIVE BLACK HOLES IN A STAR-FORMING GASEOUS CIRCUMNUCLEAR DISK

Using N-body/smoothed particle hydrodynamics simulations we study the evolution of the separation of a pair of supermassive black holes (SMBHs) embedded in a star-forming circumnuclear disk (CND). This type of disk is expected to be formed in the central kiloparsec of the remnant of gas-rich galaxy mergers. Our simulations indicate that orbital decay of the SMBHs occurs more quickly when the mean density of the CND is higher, due to increased dynamical friction. However, in simulations where the CND is fragmented in high-density gaseous clumps (clumpy CND), the orbits of the SMBHs are erratically perturbed by the gravitational interaction with these clumps, delaying, in some cases, the orbital decay of the SMBHs. The densities of these gaseous clumps in our simulations and in recent studies of clumpy CNDs are two orders of magnitude higher than the observed density of molecular clouds in isolated galaxies or ultraluminous infrared galaxies (ULIRGs), thus, we expect that SMBH orbits are perturbed less in real CNDs than in the simulated CNDs of this study and other recent studies. We also find that the migration timescale has a weak dependence on the star formation rate of the CND. Furthermore, the migration timescale of an SMBH pair in a star-forming clumpy CND is at most a factor of three longer than the migration timescale of a pair of SMBHs in a CND modeled with more simple gas physics. Therefore, we estimate that the migration timescale of the SMBHs in a clumpy CND is on the order of 10{sup 7} years.

79 ASTRONOMY AND ASTROPHYSICS↗

Primordial perturbations from dilaton-induced gauge fields

We study the primordial scalar and tensor perturbations in inflation scenario involving a spectator dilaton field. In our setup, the rolling spectator dilaton causes a tachyonic instability of gauge fields, leading to a copious production of gauge fields in the superhorizon regime, which generates additional scalar and tensor perturbations through gravitational interactions. Our prime concern is the possibility to enhance the tensor-to-scalar ratio r relative to the standard result, while satisfying the observational constraints. To this end, we allow the dilaton field to be stabilized before the end of inflation, but after the CMB scales exit the horizon. We show that for the inflaton slow roll parameter ε ∼> 10{sup −3}, the tensor-to-scalar ratio in our setup can be enhanced only by a factor of O(1) compared to the standard result. On the other hand, for smaller ε corresponding to a lower inflation energy scale, a much bigger enhancement can be achieved, so that our setup can give rise to an observably large r∼> 10{sup −2} even when ε|| 10{sup −3}. The tensor perturbation sourced by the spectator dilaton can have a strong scale dependence, and is generically red-tilted. We also discuss a specific model to realize our scenario, and identify the parameter region giving an observably large r for relatively low inflation energy scales.

79 ASTRONOMY AND ASTROPHYSICS↗

Do the most massive black holes at z = 2 grow via major mergers?

The most frequently proposed model for the origin of quasars holds that the high accretion rates seen in luminous active galactic nuclei (AGN) are primarily triggered during major mergers between gas-rich galaxies. While plausible for decades, this model has only begun to be tested with statistical rigor in the past few years. Here, we report on a Hubble Space Telescope study to test this hypothesis for z = 2 quasars with high supermassive black hole masses (M{sub BH}=10{sup 9}--10{sup 10} M{sub ⊙} ), which dominate cosmic black hole growth at this redshift. We compare Wide Field Camera 3 F160W (rest-frame V-band) imaging of 19 point source-subtracted quasar hosts to a matched sample of 84 inactive galaxies, testing whether the quasar hosts have greater evidence for strong gravitational interactions. Using an expert ranking procedure, we find that the quasar hosts are uniformly distributed within the merger sequence of inactive galaxies, with no preference for quasars in high-distortion hosts. Using a merger/non-merger cutoff approach, we recover distortion fractions of f{sub m,qso}=0.39±0.11 for quasar hosts and f{sub m,gal}=0.30±0.05 for inactive galaxies (distribution modes, 68% confidence intervals), with both measurements subjected to the same observational conditions and limitations. The slight enhancement in distorted fraction for quasar hosts over inactive galaxies is not significant, with a probability that the quasar fraction is higher P(f{sub m,qso}>f{sub m,gal})=0.78 (0.78σ), in line with results for lower mass and lower z AGN. We find no evidence that major mergers are the primary triggering mechanism for the massive quasars that dominate accretion at the peak of cosmic quasar activity.

79 ASTRONOMY AND ASTROPHYSICS↗

Review of the fermionic dark matter model applied to galactic structures

Baryonic components (e.g. bulge and disk) of galactic structures are assumed to be embedded in an isothermal dark matter halo of fermionic nature. Besides the Pauli principle only gravitational interaction is considered. Using the underlying Fermi-Dirac phase space distribution, typical of collisionless relaxation processes, it yields an one-parameter family of scaled solutions which reproduces the observed flat rotation curves in galaxies, and additionally predicts a degenerate core through their centers. In order to provide the right DM halo properties of galaxies a set of four parameters (particle mass, degeneracy parameter at the galactic center, central density and the velocity dispersion) is necessary. The more general density profile shows three regimes depending on radius: an almost uniform very dense quantum core followed by a steep fall, a plateau in the diluted regime and a Boltzmannian tail representing the halo. In contrast to purely Boltzmannian configurations the fermionic DM model containing a quantum core allows to determine the particle mass. We show that the quantum core can be well approximated by a polytrope of index n = 3/2, while the halo can be perfectly described by an isothermal sphere with a halo scale length radius equal to approximately 3/4 of the King-radius.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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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