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At least 1,171 records · Page 65

ANALYSIS OF A FRAGMENTING SUNSPOT USING HINODE OBSERVATIONS

We employ high-resolution filtergrams and polarimetric measurements from Hinode to follow the evolution of a sunspot for eight days starting on 2007 June 28. The imaging data were corrected for intensity gradients, projection effects, and instrumental stray light prior to the analysis. The observations show the formation of a light bridge at one corner of the sunspot by a slow intrusion of neighboring penumbral filaments. This divided the umbra into two individual umbral cores. During the light bridge formation, there was a steep increase in its intensity from 0.28 to 0.7 I{sub QS} in nearly 4 hr, followed by a gradual increase to quiet-Sun (QS) values in 13 hr. This increase in intensity was accompanied by a large reduction in the field strength from 1800 G to 300 G. The smaller umbral core gradually broke away from the parent sunspot nearly two days after the formation of the light bridge, rendering the parent spot without a penumbra at the location of fragmentation. The penumbra in the fragment disappeared first within 34 hr, followed by the fragment whose area decayed exponentially with a time constant of 22 hr. In comparison, the parent sunspot area followed a linear decay rate of 0.94 Mm{sup 2} hr{sup -1}. The depleted penumbra in the parent sunspot regenerated when the inclination of the magnetic field at the penumbra-QS boundary became within 40 Degree-Sign from being completely horizontal and this occurred near the end of the fragment's lifetime. After the disappearance of the fragment, another light bridge formed in the parent which had similar properties as the fragmenting one, but did not divide the sunspot. The significant weakening in field strength in the light bridge along with the presence of granulation is suggestive of strong convection in the sunspot, which might have triggered the expulsion and fragmentation of the smaller spot. Although the presence of QS photospheric conditions in sunspot umbrae could be a necessary condition for fragmentation, it is not a sufficient one.

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NEAR-INFRARED VARIABILITY IN YOUNG STARS IN CYGNUS OB7

We present the first results from a 124 night J, H, K near-infrared monitoring campaign of the dark cloud L 1003 in Cygnus OB7, an active star-forming region. Using three seasons of UKIRT observations spanning 1.5 years, we obtained high-quality photometry on 9200 stars down to J = 17 mag, with photometric uncertainty better than 0.04 mag. On the basis of near-infrared excesses from disks, we identify 30 pre-main-sequence stars, including 24 which are newly discovered. We analyze those stars and find that the NIR excesses are significantly variable. All 9200 stars were monitored for photometric variability; among the field star population, {approx}160 exhibited near-infrared variability (1.7% of the sample). Of the 30 young stellar objects (YSOs), 28 of them (93%) are variable at a significant level. Of the 30 YSOs, twenty-five have near-infrared excess consistent with simple disk-plus-star classical T Tauri models. Nine of these (36%) drift in color space over the course of these observations and/or since Two Micron All Sky Survey observations such that they cross the boundary defining the NIR excess criteria; effectively, they have a transient near-infrared excess. Thus, time-series JHK observations can be used to obtain a more complete sample of disk-bearing stars than single-epoch JHK observations. About half of the YSOs have color-space variations parallel to either the classical T Tauri star locus or a hybrid track which includes the dust reddening trajectory. This indicates that the NIR variability in YSOs that possess accretion disks arises from a combination of variable extinction and changes in the inner accretion disk: either in accretion rate, central hole size, and/or the inclination of the inner disk. While some variability may be due to stellar rotation, the level of variability on the individual stars can exceed a magnitude. This is a strong empirical suggestion that protoplanetary disks are quite dynamic and exhibit more complex activity on short timescales than is attributable to rotation alone or captured in static disk models.

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Spatial structure of sunspot oscillations observed with SDO/AIA

The spatial structure of sunspot oscillations and its variation with frequency and height have been studied using data from SDO/AIA for two well-developed sunspots observed in 2010. Computation of potential magnetic fields together with line-of-sight and vector magnetograms from SDO/HMI allowed us to interpret discovered features of spatial structure. Namely, we have found that (1) expansion of the magnetic field lines above the sunspot causes a gradual broadening of the area occupied by the 3 minute oscillations with height, and (2) variation of magnetic field inclination across the sunspot causes a decrease in the pulsation frequency with distance from the center of the umbra. We have shown that the transformation from 3 minute umbral oscillations to 5 minute penumbral waves can be explained by variation of the acoustic cutoff frequency across the sunspot.

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RAPID FORMATION OF SATURN AFTER JUPITER COMPLETION

We have investigated Saturn's core formation at a radial pressure maximum in a protoplanetary disk, which is created by gap opening by Jupiter. A core formed via planetesimal accretion induces the fragmentation of surrounding planetesimals, which generally inhibits further growth of the core by removal of the resulting fragments due to radial drift caused by gas drag. However, the emergence of the pressure maximum halts the drift of the fragments, while their orbital eccentricities and inclinations are efficiently damped by gas drag. As a result, the core of Saturn rapidly grows via accretion of the fragments near the pressure maximum. We have found that in the minimum-mass solar nebula, kilometer-sized planetesimals can produce a core exceeding 10 Earth masses within two million years. Since Jupiter may not have undergone significant type II inward migration, it is likely that Jupiter's formation was completed when the local disk mass has already decayed to a value comparable to or less than Jovian mass. The expected rapid growth of Saturn's core on a timescale comparable to or shorter than the observationally inferred disk lifetime enables Saturn to acquire the current amount of envelope gas before the disk gas is completely depleted. The high heat energy release rate onto the core surface due to the rapid accretion of the fragments delays onset of runaway gas accretion until the core mass becomes somewhat larger than that of Jupiter, which is consistent with the estimate based on interior modeling. Therefore, the rapid formation of Saturn induced by gap opening of Jupiter can account for the formation of multiple gas giants (Jupiter and Saturn) without significant inward migration and larger core mass of Saturn than that of Jupiter.

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DYNAMICAL EVOLUTION OF VISCOUS DISKS AROUND Be STARS. I. PHOTOMETRY

Be stars possess gaseous circumstellar disks that modify in many ways the spectrum of the central B star. Furthermore, they exhibit variability at several timescales and for a large number of observables. Putting the pieces together of this dynamical behavior is not an easy task and requires a detailed understanding of the physical processes that control the temporal evolution of the observables. There is an increasing body of evidence that suggests that Be disks are well described by standard {alpha}-disk theory. This paper is the first of a series that aims at studying the possibility of inferring several disk and stellar parameters through the follow-up of various observables. Here we study the temporal evolution of the disk density for different dynamical scenarios, including the disk build-up as a result of a long and steady mass injection from the star, the disk dissipation that occurs after mass injection is turned off, as well as scenarios in which active periods are followed by periods of quiescence. For those scenarios, we investigate the temporal evolution of continuum photometric observables using a three-dimensional non-LTE radiative transfer code. We show that light curves for different wavelengths are specific of a mass loss history, inclination angle, and {alpha} viscosity parameter. The diagnostic potential of those light curves is also discussed.

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OPTICAL MONITORING OF THE BROAD-LINE RADIO GALAXY 3C 390.3

We have undertaken a new ground-based monitoring campaign on the broad-line radio galaxy 3C 390.3 to improve the measurement of the size of the broad emission-line region and to estimate the black hole mass. Optical spectra and g-band images were observed in late 2005 for three months using the 2.4 m telescope at MDM Observatory. Integrated emission-line flux variations were measured for the hydrogen Balmer lines H{alpha}, H{beta}, H{gamma}, and for the helium line He II{lambda}4686, as well as g-band fluxes and the optical active galactic nucleus (AGN) continuum at {lambda} = 5100 A. The g-band fluxes and the optical AGN continuum vary simultaneously within the uncertainties, {tau}{sub cent} (0.2 {+-} 1.1) days. We find that the emission-line variations are delayed with respect to the variable g-band continuum by {tau}(H{alpha}) 56.3{sup +2.4}{sub -6.6} days, {tau}(H{beta}) = 44.3{sup +3.0}{sub -3.3} days, {tau}(H{gamma}) = 58.1{sup +4.3}{sub -6.1} days, and {tau}(He II 4686) = 22.3{sup +6.5}{sub -3.8} days. The blue and red peaks in the double-peaked line profiles, as well as the blue and red outer profile wings, vary simultaneously within {+-}3 days. This provides strong support for gravitationally bound orbital motion of the dominant part of the line-emitting gas. Combining the time delay of the strong Balmer emission lines of H{alpha} and H{beta} and the separation of the blue and red peaks in the broad double-peaked profiles in their rms spectra, we determine M {sup vir}{sub bh} = 1.77{sup +0.29}{sub -0.31} Multiplication-Sign 10{sup 8} M{sub Sun} and using {sigma}{sub line} of the rms spectra M {sup vir}{sub bh} 2.60{sup +0.23}{sub -0.31} Multiplication-Sign 10{sup 8} M{sub Sun} for the central black hole of 3C 390.3, respectively. Using the inclination angle of the line-emitting region which is measured from superluminal motion detected in the radio range, accretion disk models to fit the optical double-peaked emission-line profiles, and X-ray observations, the mass of the black hole amounts to M{sub bh} = 0.86{sup +0.19}{sub -0.18} Multiplication-Sign 10{sup 9} M{sub Sun} (peak separation) and M{sub bh} 1.26{sup +0.21}{sub -0.16} Multiplication-Sign 10{sup 9} M{sub Sun} ({sigma}{sub line}), respectively. This result is consistent with the black hole masses indicated by simple accretion disk models to describe the observed double-peaked profiles, derived from the stellar dynamics of 3C 390.3, and with the AGN radius-luminosity relation. Thus, 3C 390.3 as a radio-loud AGN with a low Eddington ratio, L{sub edd}/L{sub bol} = 0.02, follows the same AGN radius-luminosity relation as radio-quiet AGNs.

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TWO MILLISECOND PULSARS DISCOVERED BY THE PALFA SURVEY AND A SHAPIRO DELAY MEASUREMENT

We present two millisecond pulsar discoveries from the PALFA survey of the Galactic plane with the Arecibo telescope. PSR J1955+2527 is an isolated pulsar with a period of 4.87 ms, and PSR J1949+3106 has a period of 13.14 ms and is in a 1.9 day binary system with a massive companion. Their timing solutions, based on 4 years of timing measurements with the Arecibo, Green Bank, Nancay, and Jodrell Bank telescopes, allow precise determination of spin and astrometric parameters, including precise determinations of their proper motions. For PSR J1949+3106, we can clearly detect the Shapiro delay. From this we measure the pulsar mass to be 1.47{sup +0.43}{sub -0.31} M{sub Sun }, the companion mass to be 0.85{sup +0.14}{sub -0.11} M{sub Sun }, and the orbital inclination to be i = 79.9{sup -1.9}{sub +1.6} deg, where uncertainties correspond to {+-}1{sigma} confidence levels. With continued timing, we expect to also be able to detect the advance of periastron for the J1949+3106 system. This effect, combined with the Shapiro delay, will eventually provide very precise mass measurements for this system and a test of general relativity.

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ASTROMETRIC REVERBERATION MAPPING

Spatially extended emission regions of active galactic nuclei respond to continuum variations, if such emission regions are powered by energy reprocessing of the continuum. The response from different parts of the reverberating region arrives at different times lagging behind the continuum variation. The lags can be used to map the geometry and kinematics of the emission region (i.e., reverberation mapping, RM). If the extended emission region is not spherically symmetric in configuration and velocity space, reverberation may produce astrometric offsets in the emission region photocenter as a function of time delay and velocity, detectable with future {mu}as to tens of {mu}as astrometry. Such astrometric responses provide independent constraints on the geometric and kinematic structure of the extended emission region, complementary to traditional RM. In addition, astrometric RM is more sensitive to infer the inclination of a flattened geometry and the rotation angle of the extended emission region.

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THE EPOCH OF DISK SETTLING: z {approx} 1 TO NOW

We present evidence from a sample of 544 galaxies from the DEEP2 Survey for evolution of the internal kinematics of blue galaxies with stellar masses ranging 8.0 < log M {sub *}(M {sub Sun }) < 10.7 over 0.2 < z < 1.2. DEEP2 provides galaxy spectra and Hubble imaging from which we measure emission-line kinematics and galaxy inclinations, respectively. Our large sample allows us to overcome scatter intrinsic to galaxy properties in order to examine trends in kinematics. We find that at a fixed stellar mass, galaxies systematically decrease in disordered motions and increase in rotation velocity and potential well depth with time. Massive galaxies are the most well ordered at all times examined, with higher rotation velocities and less disordered motions than less massive galaxies. We quantify disordered motions with an integrated gas velocity dispersion corrected for beam smearing ({sigma} {sub g}). It is unlike the typical pressure-supported velocity dispersion measured for early type galaxies and galaxy bulges. Because both seeing and the width of our spectral slits comprise a significant fraction of the galaxy sizes, {sigma} {sub g} integrates over velocity gradients on large scales which can correspond to non-ordered gas kinematics. We compile measurements of galaxy kinematics from the literature over 1.2 < z < 3.8 and do not find any trends with redshift, likely for the most part, because these data sets are biased toward the most highly star-forming systems. In summary, over the last {approx}8 billion years since z = 1.2, blue galaxies evolve from disordered to ordered systems as they settle to become the rotation-dominated disk galaxies observed in the universe today, with the most massive galaxies being the most evolved at any time.

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THE WIRED SURVEY. III. AN INFRARED EXCESS AROUND THE ECLIPSING POST-COMMON ENVELOPE BINARY SDSS J030308.35+005443.7

We present the discovery with WISE of a significant infrared excess associated with the eclipsing post-common envelope binary SDSS J030308.35+005443.7, the first excess discovered around a non-interacting white dwarf+main-sequence M dwarf binary. The spectral energy distribution of the white dwarf+M dwarf companion shows significant excess longward of 3 {mu}m. A T {sub eff} of 8940 K for the white dwarf is consistent with a cooling age >2 Gyr, implying that the excess may be due to a recently formed circumbinary dust disk of material that extends from the tidal truncation radius of the binary at 1.96 R {sub Sun} out to <0.8 AU, with a total mass of {approx}10{sup 20} g. We also construct WISE and follow-up ground-based near-infrared light curves of the system and find variability in the K band that appears to be in phase with ellipsoidal variations observed in the visible. The presence of dust might be due to (1) material being generated by the destruction of small rocky bodies that are being perturbed by an unseen planetary system or (2) dust condensing from the companion's wind. The high inclination of this system and the presence of dust make it an attractive target for M dwarf transit surveys and long-term photometric monitoring.

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A THEORETICAL COLOR-VELOCITY CORRELATION FOR SUPERNOVAE ASSOCIATED WITH GAMMA-RAY BURSTS

We carry out the first multi-dimensional radiative transfer calculations to simultaneously compute synthetic spectra and light curves for models of supernovae driven by fast bipolar outflows. These allow us to make self-consistent predictions for the orientation dependence of both color evolution and spectral features. We compare models with different degrees of asphericity and metallicity and find significant observable consequences of both. In aspherical models, we find spectral and light curve features that vary systematically with observer orientation. In particular, we find that the early-phase light curves are brighter and bluer when viewed close to the polar axis but that the peak flux is highest for equatorial (off-axis) inclinations. Spectral line features also depend systematically on observer orientation, including the velocity of the Si II 6355 A line. Consequently, our models predict a correlation between line velocity and color that could assist the identification of supernovae associated with off-axis jet-driven explosions. The amplitude and range of this correlation depends on the degree of asphericity, the metallicity, and the epoch of observation but we find that it is always present and acts in the same direction.

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A DISK-BASED DYNAMICAL MASS ESTIMATE FOR THE YOUNG BINARY V4046 Sgr

We present sensitive, arcsecond-resolution Submillimeter Array observations of the {sup 12}CO J = 2-1 line emission from the circumstellar disk orbiting the double-lined spectroscopic binary star V4046 Sgr. Based on a simple model of the disk structure, we use a novel Monte Carlo Markov Chain technique to extract the Keplerian velocity field of the disk from these data and estimate the total mass of the central binary. Assuming the distance inferred from kinematic parallax measurements in the literature (d Almost-Equal-To 73 pc), we determine a total stellar mass M {sub *} = 1.75{sup +0.09} {sub -0.06} M {sub Sun} and a disk inclination i{sub d} = 33.{sup 0}5{sup +0.7} {sub -1.4} from face-on. These measurements are in excellent agreement with independent dynamical constraints made from multi-epoch monitoring of the stellar radial velocities, confirming the absolute accuracy of this precise ({approx}few percent uncertainties) disk-based method for estimating stellar masses and reaffirming previous assertions that the disk and binary orbital planes are well aligned (with |i{sub d} - i {sub *}| Almost-Equal-To 0.{sup 0}1 {+-} 1 Degree-Sign ). Using these results as a reference, we demonstrate that various pre-main-sequence evolution models make consistent and accurate predictions for the masses of the individual components of the binary, and uniformly imply an advanced age of {approx}5-30 Myr. Taken together, these results verify that V4046 Sgr is one of the precious few nearby and relatively evolved pre-main-sequence systems that still hosts a gas-rich accretion disk.

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HANLE EFFECT FOR STELLAR DIPOLES AND QUADRUPOLES

We derive exact expressions for the degree of lineal polarization over a resolved or integrated stellar disc due to resonance scattering and the Hanle effect from a dipolar or quadrupolar distribution of magnetic fields. We apply the theory of scattering polarization within the formalism of the spherical tensors representation for the density matrix and radiation field. The distribution of linear polarization over the stellar disk for different configurations of the magnetic field is studied and its topology discussed. For an unresolved dipole, the resulting polarization can be expressed in terms of just three functions (of the inclination angle and effective dipole strength) that are calculated numerically and their behavior discussed. Dipolar and (aligned) quadrupoles are considered in some detail, but the techniques here-in particular, the extensive use of the spherical tensor formalism for polarization-can easily be applied to more general field configurations.

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MULTIPOLAR PLANETARY NEBULAE: NOT AS GEOMETRICALLY DIVERSIFIED AS THOUGHT

Planetary nebulae (PNe) have diverse morphological shapes, including point-symmetric and multipolar structures. Many PNe also have complicated internal structures such as tori, lobes, knots, and ansae. A complete accounting of all the morphological structures through physical models is difficult. A first step toward such an understanding is to derive the true three-dimensional structure of the nebulae. In this paper, we show that a multipolar nebula with three pairs of lobes can explain many such features, if orientation and sensitivity effects are taken into account. Using only six parameters-the inclination and position angles of each pair-we are able to simulate the observed images of 20 PNe with complex structures. We suggest that multipolar structure is an intrinsic structure of PNe and the statistics of multipolar PNe have been severely underestimated in the past.

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THE SINS/zC-SINF SURVEY of z {approx} 2 GALAXY KINEMATICS: OUTFLOW PROPERTIES

Using SINFONI H{alpha}, [N II], and [S II] AO data of 27 z {approx} 2 star-forming galaxies (SFGs) from the SINS and zC-SINF surveys, we explore the dependence of outflow strength (via the broad flux fraction) on various galaxy parameters. For galaxies that have evidence for strong outflows, we find that the broad emission is spatially extended to at least the half-light radius ({approx}a few kpc). Decomposition of the [S II] doublet into broad and narrow components suggests that this outflowing gas probably has a density of {approx}10-100 cm{sup -3}, less than that of the star-forming gas (600 cm{sup -3}). There is a strong correlation of the H{alpha} broad flux fraction with the star formation surface density of the galaxy, with an apparent threshold for strong outflows occurring at 1 M{sub Sun} yr{sup -1} kpc{sup -2}. Above this threshold, we find that SFGs with log m{sub *} > 10 have similar or perhaps greater wind mass-loading factors ({eta} = M-dot{sub out}/SFR) and faster outflow velocities than lower mass SFGs, suggesting that the majority of outflowing gas at z {approx} 2 may derive from high-mass SFGs. The mass-loading factor is also correlated with the star formation rate (SFR), galaxy size, and inclination, such that smaller, more star-forming, and face-on galaxies launch more powerful outflows. We propose that the observed threshold for strong outflows and the observed mass loading of these winds can be explained by a simple model wherein break-out of winds is governed by pressure balance in the disk.

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ON THE ORIGIN OF THE HIGH COLUMN DENSITY TURNOVER IN THE H I COLUMN DENSITY DISTRIBUTION

We study the high column density regime of the H I column density distribution function and argue that there are two distinct features: a turnover at N{sub H{sub I}} Almost-Equal-To 10{sup 21} cm{sup -2}, which is present at both z = 0 and z Almost-Equal-To 3, and a lack of systems above N{sub H{sub I}} Almost-Equal-To 10{sup 22} cm{sup -2} at z = 0. Using observations of the column density distribution, we argue that the H I-H{sub 2} transition does not cause the turnover at N{sub H{sub I}} Almost-Equal-To 10{sup 21} cm{sup -2} but can plausibly explain the turnover at N{sub H{sub I}} {approx}> 10{sup 22} cm{sup -2}. We compute the H I column density distribution of individual galaxies in the THINGS sample and show that the turnover column density depends only weakly on metallicity. Furthermore, we show that the column density distribution of galaxies, corrected for inclination, is insensitive to the resolution of the H I map or to averaging in radial shells. Our results indicate that the similarity of H I column density distributions at z = 3 and 0 is due to the similarity of the maximum H I surface densities of high-z and low-z disks, set presumably by universal processes that shape properties of the gaseous disks of galaxies. Using fully cosmological simulations, we explore other candidate physical mechanisms that could produce a turnover in the column density distribution. We show that while turbulence within giant molecular clouds cannot affect the damped Ly{alpha} column density distribution, stellar feedback can affect it significantly if the feedback is sufficiently effective in removing gas from the central 2-3 kpc of high-redshift galaxies. Finally, we argue that it is meaningful to compare column densities averaged over {approx} kpc scales with those estimated from quasar spectra that probe sub-pc scales due to the steep power spectrum of H I column density fluctuations observed in nearby galaxies.

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MEASURING THE ABUNDANCE OF SUB-KILOMETER-SIZED KUIPER BELT OBJECTS USING STELLAR OCCULTATIONS

We present here the analysis of about 19,500 new star hours of low ecliptic latitude observations (|b| {<=} 20 Degree-Sign ) obtained by the Hubble Space Telescope's Fine Guidance Sensors over a time span of more than nine years, which is in addition to the {approx}12, 000 star hours previously analyzed by Schlichting et al. Our search for stellar occultations by small Kuiper Belt Objects (KBOs) yielded one new candidate event corresponding to a body with a 530 {+-} 70 m radius at a distance of about 40 AU. Using bootstrap simulations, we estimate a probability of Almost-Equal-To 5% that this event is due to random statistical fluctuations within the new data set. Combining this new event with the single KBO occultation reported by Schlichting et al. we arrive at the following results: (1) the ecliptic latitudes of 6. Degree-Sign 6 and 14. Degree-Sign 4 of the two events are consistent with the observed inclination distribution of larger, 100-km-sized KBOs. (2) Assuming that small, sub-kilometer-sized KBOs have the same ecliptic latitude distribution as their larger counterparts, we find an ecliptic surface density of KBOs with radii larger than 250 m of N(r > 250 m) = 1.1{sup +1.5}{sub -0.7} Multiplication-Sign 10{sup 7} deg{sup -2}; if sub-kilometer-sized KBOs have instead a uniform ecliptic latitude distribution for -20 Degree-Sign < b < 20 Degree-Sign then N(r > 250 m) = 4.4{sup +5.8}{sub -2.8} Multiplication-Sign 10{sup 6} deg{sup -2}. This is the best measurement of the surface density of sub-kilometer-sized KBOs to date. (3) Assuming the KBO size distribution can be well described by a single power law given by N(> r){proportional_to}r{sup 1-q}, where N(> r) is the number of KBOs with radii greater than r, and q is the power-law index, we find q = 3.8 {+-} 0.2 and q = 3.6 {+-} 0.2 for a KBO ecliptic latitude distribution that follows the observed distribution for larger, 100-km-sized KBOs and a uniform KBO ecliptic latitude distribution for -20 Degree-Sign < b < 20 Degree-Sign , respectively. (4) Regardless of the exact power law, our results suggest that small KBOs are numerous enough to satisfy the required supply rate for the Jupiter family comets. (5) We can rule out a single power law below the break with q > 4.0 at 2{sigma}, confirming a strong deficit of sub-kilometer-sized KBOs compared to a population extrapolated from objects with r > 45 km. This suggests that small KBOs are undergoing collisional erosion and that the Kuiper Belt is a true analog to the dust producing debris disks observed around other stars.

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RESONANCES REQUIRED: DYNAMICAL ANALYSIS OF THE 24 Sex AND HD 200964 PLANETARY SYSTEMS

We perform several suites of highly detailed dynamical simulations to investigate the architectures of the 24 Sextantis and HD 200964 planetary systems. The best-fit orbital solution for the two planets in the 24 Sex system places them on orbits with periods that lie very close to 2:1 commensurability, while that for the HD 200964 system places the two planets therein in orbits whose periods lie close to a 4:3 commensurability. In both cases, the proposed best-fit orbits are mutually crossing-a scenario that is only dynamically feasible if the planets are protected from close encounters by the effects of mutual mean-motion resonance (MMR). Our simulations reveal that the best-fit orbits for both systems lie within narrow islands of dynamical stability, and are surrounded by much larger regions of extreme instability. As such, we show that the planets are only feasible if they are currently trapped in mutual MMR-the 2:1 resonance in the case of 24 Sex b and c, and the 4:3 resonance in the case of HD 200964 b and c. In both cases, the region of stability is strongest and most pronounced when the planetary orbits are mutually coplanar. As the inclination of planet c with respect to planet b is increased, the stability of both systems rapidly collapses.

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