We report the discovery of WASP-8b, a transiting planet of 2.25 ± 0.08 MJup on a strongly inclined eccentric 8.15-day orbit, moving in a retrograde direction to the rotation of its late-G host star. Evidence is found that the star is in a multiple stellar system with two other companions. The dynamical complexity of the system indicates that it may have experienced secular interactions such as the Kozai mechanism or a formation that differs from the “classical” disc-migration theory.
Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This method is implemented in the parallel N-body code, PKDGRAV, and tested on some simple orbits. The method demonstrates a lack of secular changes in orbital elements, making it a very useful technique for integrating Hill's equations over many dynamical times. Furthermore, the method allows for efficient collision searching using linear extrapolation of particle positions.
Duration and period of transits in extrasolar planetary systems can exhibit long-term variations for a variety of reasons. Here we investigate how systemic proper motion, which steadily re-orients planetary orbit with respect to our line of sight, affects the timing of transits. We find that in a typical system with a period of several days, proper motion at the level of 100 mas yr–1 makes transit duration vary at a rate ~10-100 ms yr–1. In some isolated systems this variation is at the measurable level (can be as high as 0.6 s yr–1 for GJ436) and may exceed all other transit-timing contributions (due to the general relativity, stellar quadrupole, etc.). In addition, proper motion causes evolution of the observed period between transits P obs via the Shklovskii effect at a rate 
10 µs yr–1 for the nearby transiting systems (0.26 ms yr–1 in GJ436), which in some cases exceeds all other contributions to 
. Earth's motion around the Sun gives rise to additional periodic timing signal (even for systems with zero intrinsic proper motion) allowing a full determination of the spatial orientation of the planetary orbit. Unlike most other timing effects, the proper motion signatures persist even in systems with zero eccentricity and get stronger as the planetary period increases. They should be the dominant cause of transit-timing variations in isolated wide-separation (periods of months) systems that will be sought by Kepler.
We present the results of a comprehensive assessment of companions to solar-type stars. A sample of 454 stars, including the Sun, was selected from the Hipparcos catalog with π>40 mas, σπ/π < 0.05, 0.5 <= B - V <= 1.0 (~F6-K3), and constrained by absolute magnitude and color to exclude evolved stars. These criteria are equivalent to selecting all dwarf and subdwarf stars within 25 pc with V-band flux between 0.1 and 10 times that of the Sun, giving us a physical basis for the term "solar-type." New observational aspects of this work include surveys for (1) very close companions with long-baseline interferometry at the Center for High Angular Resolution Astronomy Array, (2) close companions with speckle interferometry, and (3) wide proper-motion companions identified by blinking multi-epoch archival images. In addition, we include the results from extensive radial-velocity monitoring programs and evaluate companion information from various catalogs covering many different techniques. The results presented here include four new common proper-motion companions discovered by blinking archival images. Additionally, the spectroscopic data searched reveal five new stellar companions. Our synthesis of results from many methods and sources results in a thorough evaluation of stellar and brown dwarf companions to nearby Sun-like stars. The overall observed fractions of single, double, triple, and higher-order systems are 56% ± 2%, 33% ± 2%, 8% ± 1%, and 3% ± 1%, respectively, counting all confirmed stellar and brown dwarf companions. If all candidate, i.e., unconfirmed, companions identified are found to be real, the percentages would change to 54% ± 2%, 34% ± 2%, 9% ± 2%, and 3% ± 1%, respectively. Our completeness analysis indicates that only a few undiscovered companions remain in this well-studied sample, implying that the majority (54% ± 2%) of solar-type stars are single, in contrast to the results of prior multiplicity studies. Our sample is large enough to enable a check of the multiplicity dependence on various physical parameters by analyzing appropriate subsamples. Bluer, more massive stars are seen as more likely to have companions than redder, less massive ones, consistent with the trend seen over the entire spectral range. Systems with larger interaction cross sections, i.e., those with more than two components or long orbital periods, are preferentially younger, suggesting that companions may be stripped over time by dynamical interactions. We confirm the planet-metallicity correlation (i.e., higher metallicity stars are more likely to host planets), but are unable to check it for brown dwarfs due to the paucity of such companions, implying that the brown dwarf desert extends over all separation regimes. We find no correlation between stellar companions and metallicity for B - V < 0.625, but among the redder subset, metal-poor stars ([Fe/H] <-0.3) are more likely to have companions with a 2.4σ significance. The orbital-period distribution of companions is unimodal and roughly log normal with a peak and median of about 300 years. The period-eccentricity relation shows the expected circularization for periods below 12 days, caused by tidal forces over the age of the Galaxy, followed by a roughly flat distribution. The mass-ratio distribution shows a preference for like-mass pairs, which occur more frequently in relatively close pairs. The fraction of planet hosts among single, binary, and multiple systems are statistically indistinguishable, suggesting that planets are as likely to form around single stars as they are around components of binary or multiple systems with sufficiently wide separations. This, along with the preference of long orbital periods among stellar systems, increases the space around stars conducive for planet formation, and perhaps life.
We perform a survey whether higher dimensional Schwarzschild space-time is compatible with some of the solar system phenomena. As a test we examine four well known solar system effects, viz., (1) Perihelion shift, (2) Bending of light, (3) Gravitational redshift, and (4) Gravitational time delay. It is shown, under a N-dimensional solutions of Schwarzschild type very narrow class of metrics, that the results related to all these physical phenomena are mostly incompatible with the higher dimensional version of general relativity. We compare all these restricted results with the available data in the literature.
We develop an idealized dynamical model to predict the typical properties of outer extrasolar planetary systems, at radii comparable to the Jupiter-to-Neptune region of the solar system. The model is based upon the hypothesis that dynamical evolution in outer planetary systems is controlled by a combination of planet-planet scattering and planetary interactions with an exterior disk of small bodies ("planetesimals"). Our results are based on 5000 long duration N-body simulations that follow the evolution of three planets from a few to 10 AU, together with a planetesimal disk containing 50 M ⊕from 10 to 20 AU. For large planet masses (M >~ M Sat), the model recovers the observed eccentricity distribution of extrasolar planets. For lower-mass planets, the range of outcomes in models with disks is far greater than that which is seen in isolated planet-planet scattering. Common outcomes include strong scattering among massive planets, sudden jumps in eccentricity due to resonance crossings driven by divergent migration, and re-circularization of scattered low-mass planets in the outer disk. We present the distributions of the eccentricity and inclination that result, and discuss how they vary with planet mass and initial system architecture. In agreement with other studies, we find that the currently observed eccentricity distribution (derived primarily from planets at a <~ 3 AU) is consistent with isolated planet-planet scattering. We explain the observed mass dependence―which is in the opposite sense from that predicted by the simplest scattering models―as a consequence of strong correlations between planet masses in the same system. At somewhat larger radii, initial planetary mass correlations and disk effects can yield similar modest changes to the eccentricity distribution. Nonetheless, strong damping of eccentricity for low-mass planets at large radii appears to be a secure signature of the dynamical influence of disks. Radial velocity measurements capable of detecting planets with K ≈ 5 m s-1and periods in excess of 10 years will provide constraints on this regime. Finally, we present an analysis of the predicted separation of planets in two-planet systems, and of the population of planets in mean-motion resonances (MMRs). We show that, if there are systems with ~ Jupiter-mass planets that avoid close encounters, the planetesimal disk acts as a damping mechanism and populates MMRs at a very high rate (50%-80%). In many cases, resonant chains (in particular the 4:2:1 Laplace resonance) are set up among all three planets. We expect such resonant chains to be common among massive planets in outer planetary systems.
Gravitational-wave signals from inspirals of binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave (GW) interferometers (LIGO, Virgo and GEO-600). We present parameter estimation results from our Markov-chain Monte Carlo code SPINspiral on signals from binaries with precessing spins. Two data sets are created by injecting simulated GW signals either into synthetic Gaussian noise or into LIGO detector data. We compute the 15-dimensional probability-density functions (PDFs) for both data sets, as well as for a data set containing LIGO data with a known, loud artefact ('glitch'). We show that the analysis of the signal in detector noise yields accuracies similar to those obtained using simulated Gaussian noise. We also find that while the Markov chains from the glitch do not converge, the PDFs would look consistent with a GW signal present in the data. While our parameter estimation results are encouraging, further investigations into how to differentiate an actual GW signal from noise are necessary.
The classical approach for determining stellar angular diameters is to use interferometry and to measure fringe visibilities. Indeed, in the case of a source having a diameter larger than typically λ/6B, B being the interferometer's baseline and λ the wavelength of observation, the fringe contrast decreases. Similarly, it is possible to perform angular diameter determinations by measuring the stellar leakage from a coronagraphic device or a nulling interferometer. However, all coronagraphic devices (including those using nulling interferometry) are very sensitive to pointing errors and to the size of the source, two factors with significant impact on the rejection efficiency. In this work, we present an innovative idea for measuring stellar diameter variations, combining coronagraphy together with interferometry. We demonstrate that, using coronagraphic nulling statistics, it is possible to measure such variations for angular diameters down to ≈λ/40B with 1σ error-bars as low as ≈λ/1500B. For that purpose, we use a coronagraphic implementation on a two-aperture interferometer, a configuration that significantly increases the precision of stellar diameter measurements. Such a design offers large possibilities regarding the stellar diameter measurement of Cepheids or Mira stars, at a 60-80 μas level. We report on a simulation of a measurement applied to a typical Cepheid case, using the VLTI-UT interferometer on Paranal.
The temporal change of the rotation vector of a rotating body is, in the first order, identical in a space-fixed system and in a body-fixed system. Therefore, if the motion of the rotation axis of the earth relative to a space-fixed system is given as a function of time, it should be possible to compute its motion relative to an earth-fixed system, and vice versa. This paper presents such a transformation. Two models of motion of the rotation axis in the space-fixed system are considered: one consisting only of a regular (i.e., strictly conical) precession and one extended by circular nutation components, which are superimposed upon the regular precession. The Euler angles describing the orientation of the earth-fixed system with respect to the space-fixed system are derived by an analytical solution of the kinematical Eulerian differential equations. In the first case (precession only), this is directly possible, and in the second case (precession and nutation), a solution is achieved by a perturbation approach, where the result of the first case serves as an approximation and nutation is regarded as a small perturbation, which is treated in a linearized form. The transformation by means of these Euler angles shows that the rotation axis performs in the earth-fixed system retrograde conical revolutions with small amplitudes, namely one revolution with a period of one sidereal day corresponding to precession and one revolution with a period which is slightly smaller or larger than one sidereal day corresponding to each (prograde or retrograde) circular nutation component. The peculiar feature of the derivation presented here is the analytical solution of the Eulerian differential equations.
Continued radial velocity (RV) monitoring of the nearby M4V red dwarf star GJ 876 with Keck/High Resolution Echelle Spectrograph has revealed the presence of a Uranus-mass fourth planetary companion in the system. The new planet has a mean period of Pe = 126.6 days (over the 12.6-year baseline of the RV observations), and a minimum mass of me sin ie = 12.9 ± 1.7 M ⊕. The detection of the new planet has been enabled by significant improvements to our RV data set for GJ 876. The data have been augmented by 36 new high-precision measurements taken over the past five years. In addition, the precision of all of the Doppler measurements have been significantly improved by the incorporation of a high signal-to-noise template spectrum for GJ 876 into the analysis pipeline. Implementation of the new template spectrum improves the internal rms errors for the velocity measurements taken during 1998-2005 from 4.1 m s-1 to 2.5 m s-1. Self-consistent, N-body fits to the RV data set show that the four-planet system has an invariable plane with an inclination relative to the plane of the sky of i = 59fdg5. The fit is not significantly improved by the introduction of a mutual inclination between the planets "b" and "c," but the new data do confirm a non-zero eccentricity, ed = 0.207 ± 0.055 for the innermost planet, "d." In our best-fit coplanar model, the mass of the new component is me = 14.6 ± 1.7 M ⊕. Our best-fitting model places the new planet in a three-body resonance with the previously known giant planets (which have mean periods of Pc = 30.4 and Pb = 61.1 days). The critical argument, phivLaplace = λ c - 3λ b + 2λ e , for the Laplace resonance librates with an amplitude of ΔphivLaplace = 40° ± 13° about phivLaplace = 0°. Numerical integration indicates that the four-planet system is stable for at least a billion years (at least for the coplanar cases). This resonant configuration of three giant planets orbiting an M dwarf primary differs from the well-known Laplace configuration of the three inner Galilean satellites of Jupiter, which are executing very small librations about phivLaplace = 180° and which never experience triple conjunctions. The GJ 876 system, by contrast, comes close to a triple conjunction between the outer three planets once per every orbit of the outer planet, "e."
In a previous paper, we have found that the resonance structure of the present Jupiter Trojan swarms could be split up into four different families of resonances. Here, in a first step, we generalize these families in order to describe the resonances occurring in Trojan swarms embedded in a generic planetary system. The location of these families changes under a modification of the fundamental frequencies of the planets and we show how the resonant structure would evolve during a planetary migration. We present a general method, based on the knowledge of the fundamental frequencies of the planets and on those that can be reached by the Trojans, which makes it possible to predict and localize the main events arising in the swarms during migration. In particular, we show how the size and stability of the Trojan swarms are affected by the modification of the frequencies of the planets. Finally, we use this method to study the global dynamics of the Jovian Trojan swarms when Saturn migrates outwards. Besides the two resonances found by Morbidelli et al. which could have led to the capture of the current population just after the crossing of the 2:1 orbital resonance, we also point out several sequences of chaotic events that can influence the Trojan population.
We have imaged the disk surrounding the nearby (D ~ 73 pc), ~12 Myr, classical T Tauri binary system V4046 Sgr with the Submillimeter Array (SMA) at an angular resolution of ~2''. We detect a rotating disk in 12CO(2-1) and 13CO(2-1) emission and resolve the continuum emission at 1.3 mm. We infer disk gas and dust masses of ~110 and ~40 Earth masses, respectively. Fits to a power-law disk model indicate that the molecular disk extends to ~370 AU and is viewed at an inclination of between ~33° and ~39° for dynamical stellar masses ranging from 1.8 M sun down to 1.5 M sun (the range of the total mass previously determined for the central, 2.4 day spectroscopic binary). This range of disk inclination is consistent with that assumed in deducing the central binary mass (i.e., 35°), suggesting that the V4046 Sgr binary system and its circumbinary, molecular disk are coplanar. In light of the system's age and binarity, the presence of an extensive molecular disk orbiting V4046 Sgr provides constraints on the timescales of processes related to Jovian planet formation and demonstrates that circumbinary Jovian planets potentially could form around close binary systems.
USNO-B1.0 and the Two Micron All Sky Survey (2MASS) are the most widely used all-sky surveys. However, 2MASS has no proper motions at all, and USNO-B1.0 published only relative, not absolute (i.e., on the International Celestial Reference Frame (ICRS), proper motions. We performed a new determination of mean positions and proper motions on the ICRS system by combining USNO-B1.0 and 2MASS astrometry. This catalog is called PPMXL (VO access to the catalog is possible via http://vo.uni-hd.de/ppmxl), and it aims to be completed from the brightest stars down to about V ≈ 20 all sky. PPMXL contains about 900 million objects, some 410 million with 2MASS photometry, and is the largest collection of ICRS proper motions at present. As representative for the ICRS, we chose PPMX. The recently released UCAC3 could not be used because we found plate-dependent distortions in its proper motion system north of -20° declination. UCAC3 served as an intermediate system for δ ≤ -20°. The resulting typical individual mean errors of the proper motions range from 4 mas yr-1 to more than 10 mas yr-1 depending on observational history. The mean errors of positions at epoch 2000.0 are 80-120 mas, if 2MASS astrometry could be used, 150-300 mas else. We also give correction tables to convert USNO-B1.0 observations of, e.g., minor planets to the ICRS system.
Context. Free core nutation (FCN) can be observed by its associated
resonance effects on the forced nutations of the Earth's figure axis, as
observed by very long baseline interferometry (VLBI), or on the
diurnal tidal waves, retrieved from the
time-varying surface gravity recorded by superconducting gravimeters (SG).
Aims. In this paper, we study the sensitivity of both techniques to
FCN parameters.
Methods. We analyze surface gravity data from 15 SG stations and VLBI delays accumulated
over the last 24 years.
Results. We obtain estimates of the FCN period and quality factor that are consistent
for both techniques. The inversion leads to a quality factor
centered on ~16 600 with an uncertainty of ~3500 from
SG and of ~900 from VLBI, and to a resonant period within
[ -423.3, -430.5] days for SG and [ -427.8, -431.4] days for VLBI
(3 σ interval).
We investigate the effect of internal masses redistributions on the position of the Earth rotational pole for the last 120 Myr. We use a geodynamic model based on plate reconstructions that estimates the location and rate of subducted slabs under the assumption that they sink vertically into the mantle (Ricard et al., 1993b). Our model also takes into account the effect of large-scale upwellings (domes) derived from an analysis of seismic tomography. Their location is assumed to remain stable with time. We then compute the geoid associated with the time-dependent mantle density heterogeneities. In order to reconcile the computed and observed geoids, we investigate the influence of the depth down to which the subducted Pacific plates beneath the Americas present a significant density contrast with respect to the surrounding mantle on the present-day geoid, and propose a plate model in which we obtain a variance reduction greater than 0.9 for the degree 2. We show that the vertical oscillation of domes within mantle only modulates the amplitude of the associated geoid. The temporal variation of the mantle density heterogeneities is consequently essentially due to changes in the subduction history. The temporal evolution of the Principal Inertia Axis (PIA) of the Earth derived from our model (the rotational axis is aligned to the maximum PIA) is then investigated, and finally compared to estimations of TPW. Both the maximum and intermediate PIAs have moved in a plane perpendicular to Africa, along a circle corresponding to the low of geoid induced by subduction around the Pacific. The minimum PIA seems to be relatively stable since 120 Myr, and close to the maximum degree 2 geoid high under Africa. This can account for observed TPW or African APW in the last 200 Myr.
The end-Triassic environmental crisis with major extinctions in the marine realm is followed by successive recovery in the lower Jurassic Hettangian Stage. Accurate timing of events is however still poorly constrained. In this study, combined field observations and physical and chemical proxy records, covering the uppermost Triassic and lower Jurassic marine successions of St Audrie's Bay and East Quantoxhead (UK), have been used to construct a floating astronomical time-scale of ~ 2.5 Myr in length. This time-scale is based on the recognition of meters thick cycles in limestone and (black) shale predominance and concurrent variability in physical and chemical proxy records. Three to five individual black-shale beds occur within these meter-scale sedimentary bundles and are interpreted to reflect precession-controlled changes in monsoon intensity, while the bundles are interpreted as forced by the ~ 100-kyr eccentricity cycle. On the basis of these findings, we propose an astronomically constrained duration of the Hettangian stage of 1.8 Myr in the UK and unequal duration of Hettangian ammonite zones (Psilocerasplanorbis zone: ~250 kyr; Alsatitesliasicus zone: ˜ 750 kyr; Schlotheimiaangulata zone: ˜ 800 kyr). Within this astronomical framework, the extinction interval and coinciding negative CIE represent 1 to 2 precession cycles (~ 20–40 kyr). The amount of time succeeding the end-Triassic negative carbon isotope excursion (CIE) and preceding the first Jurassic ammonite occurrence (in the UK) is constrained to 6 climatic precession cycles (~120 kyr). Cyclostratigraphic correlation to the astronomically-tuned sedimentary record of the continental Newark basin (USA) allows to locate the stratigraphic position of the marine defined Triassic–Jurassic and Hettangian–Sinemurian boundary in the continental realm. Continuous low δ13CTOC values throughout the Hettangian and early Sinemurian, succeeding volcanic activity in the Central Atlantic Magmatic Province (CAMP), may suggest a long-term change in Earth's global biogeochemical cycles, which do not fully recover for several million years.
The radio emitting X-ray binary GRS1915+105 shows a wide variety of X-ray and radio states. We present a decade of monitoring observations, with the Rossi X-ray Timing Explorer-All Sky Monitor and the Ryle Telescope, in conjunction with high-resolution radio observations using Multi-Element Radio-Linked Interferometer Network and the The Very Long Baseline Array. Linear polarization at 1.4 and 1.6GHz has been spatially resolved in the radio jets, on a scale of ~150 mas and at flux densities of a few mJy. Depolarization of the core occurs during radio flaring, associated with the ejection of relativistic knots of emission. We have identified the ejection at four epochs of X-ray flaring. Assuming no deceleration, proper motions of 16.5 to 27 mas per day have been observed, supporting the hypothesis of a varying angle to the line of sight per ejection, perhaps in a precessing jet.
We report recent ground-based photometry of the transiting super-Earth exoplanet GJ 1214b at several wavelengths, including the infrared near 1.25 μm (J band). We observed a J-band transit with the FLAMINGOS infrared imager and the 2.1 m telescope on Kitt Peak, and we observed several optical transits using a 0.5 m telescope on Kitt Peak and the 0.36 m Universidad de Monterrey Observatory telescope. Our high-precision J-band observations exploit the brightness of the M dwarf host star at this infrared wavelength as compared with the optical and are significantly less affected by stellar activity and limb darkening. We fit the J-band transit to obtain an independent determination of the planetary and stellar radii. Our radius for the planet (2.61+0.30 -0.11 R ⊕) is in excellent agreement with the discovery value reported by Charbonneau et al. based on optical data. We demonstrate that the planetary radius is insensitive to degeneracies in the fitting process. We use all of our observations to improve the transit ephemeris, finding P = 1.5804043 ± 0.0000005 days and T 0 = 2454964.94390 ± 0.00006 BJD.
What kinds of astronomical lab activities can high school and college astronomy students carry out easily in daytime? The most impressive is the determination of latitude and longitude from observations of the Sun. The ``shooting of a noon sight'' and its ``reduction to a position'' grew to become a daily practice at the start of the 19th century1 following the perfection of the marine chronometer by John Harrison and its mass production.2 This technique is still practiced by navigators in this age of GPS. Indeed, the U.S. Coast Guard exams for ocean-going licenses include celestial navigation.3 These techniques continue to be used by the military and by private sailors as a backup to all-too-fallible and jammable electronic navigation systems. A sextant, a nautical almanac,4 special sight reduction tables,5 and involved calculations are needed to determine position to the nearest mile using the Sun, Moon, stars, or planets. Yet, finding latitude and longitude to better than 30 miles from measurements of the Sun's altitude is easily within the capability of those taking astronomy or physics for the first time by applying certain basic principles. Moreover, it shows a practical application of astronomy in use the world over. The streamlined method described here takes advantage of the similar level of accuracy of its three components: 1.Observations using a homemade quadrant6 (instead of a sextant), 2. Student-made graphs of the altitude of the Sun over a day7 (replacing lengthy calculation using sight reduction tables), and 3. An averaged 20-year analemma used to find the Sun's navigational coordinates8,9 (rather than the 300+ page Nautical Almanac updated yearly).
The Kustaanheimo-Stiefel (KS) transform turns a gravitational two-body problem into a harmonic oscillator, by going to four dimensions. In addition to the mathematical-physics interest, the KS transform has proved very useful in N-body simulations, where it helps to handle close encounters. Yet the formalism remains somewhat arcane, with the role of the extra dimension being especially mysterious. This paper shows how the basic transformation can be interpreted as a rotation in three dimensions. For example, if we slew a telescope from zenith to a chosen star in one rotation, we can think of the rotation axis and angle as the KS transform of the star. The non-uniqueness of the rotation axis encodes the extra dimension. This geometrical interpretation becomes evident on writing KS transforms in quaternion form, which also helps to derive concise expressions for regularized equations of motion.
In recent years a large number of hot Jupiters orbiting in a very close orbit around the parent stars have been explored with the transit and Doppler effect methods. Here in this paper we study the gravitational microlensing effect of a binary lens on a parent star with a hot Jupiter revolving around it. Caustic crossing of the planet makes enhancements on the light curve of the parent star in which the signature of the planet can be detected by high-precision photometric observations. We use the inverse ray shooting method with tree code algorithm to generate the combined light curve of the parent star and the planet. In order to investigate the probability of observing the planet signal, we do a Monte Carlo simulation and obtain the observational optical depth of τ~ 10-8. We show that about 10 yr of observations of Galactic bulge with a network of telescopes will enable us detecting about 10 hot Jupiters with this method. Finally we show that the observation of the microlensing event in the infrared band will increase the probability for detection of the exoplanets.
Context: Among multi-planet planetary systems there are a large fraction of resonant systems. Studying the dynamics and formation of these systems can provide valuable informations on processes taking place in protoplanetary disks where the planets are thought have been formed. The recently discovered resonant system HD 60532 is the only confirmed case, in which the central star hosts a pair of giant planets in 3:1 mean motion resonance.
Aims: We intend to provide a physical scenario for the formation of HD 60532, which is consistent with the orbital solutions derived from the radial velocity measurements. Observations indicate that the system is in an antisymmetric configuration, while previous theroretical investigations indicate an asymmetric equilibrium state. The paper aims at answering this discrepancy as well.
Methods: We performed two-dimensional hydrodynamical simulations of thin disks with an embedded pair of massive planets. Additionally, migration and resonant capture are studied by gravitational N-body simulations that apply properly parametrized non-conservative forces.
Results: Our simulations suggest that the capture into the 3:1 mean motion resonance takes place only for higher planetary masses, thus favouring orbital solutions having relatively smaller inclination (i = 20°). The system formed by numerical simulations qualitatively show the same behaviour as HD 60532. We also find that the presence of an inner disk (between the inner planet and the star) plays a very important role in determining the final configurations of resonant planetary systems. Its damping effect on the inner planet's eccentricity is responsible for the observed antisymmetric state of HD 60532.
Of the 26 transiting exoplanet systems with measurements of the Rossiter-McLaughlin (RM) effect, eight have now been found to be significantly spin-orbit misaligned in the plane of the sky (i.e., RM misalignment angle |λ| >~ 30° and inconsistent with λ = 0°). Unfortunately, the RM effect does not constrain the complement misalignment angle between the orbit of the planet and the spin of its host star along the line of sight (LOS). I use a simple model of stellar rotation benchmarked with observational data to statistically identify 10 exoplanet systems from a sample of 75 for which there is likely a significant degree of spin-orbit misalignment along the LOS: HAT-P-7, HAT-P-14, HAT-P-16, HD 17156, Kepler-5, Kepler-7, TrES-4, WASP-1, WASP-12, and WASP-14. All 10 systems have host stellar masses M * in the range 1.2 M sun <~ M * <~ 1.5 M sun, and the probability of this occurrence by chance is less than one in ten thousand. In addition, the planets in the candidate-misaligned systems are preferentially massive and eccentric. The coupled distribution of misalignment from the RM effect and from this analysis suggests that transiting exoplanets are more likely to be spin-orbit aligned than expected given predictions for a transiting planet population produced entirely by planet-planet scattering or Kozai cycles and tidal friction. For that reason, there are likely two populations of close-in exoplanet systems: a population of aligned systems and a population of apparently misaligned systems in which the processes that lead to misalignment or to the survival of misaligned systems operate more efficiently in systems with massive stars and planets.
The Kuiper belt is a remnant of the primordial Solar System. Measurements of its size distribution constrain its accretion and collisional history, and the importance of material strength of Kuiper belt objects. Small, sub-kilometre-sized, Kuiper belt objects elude direct detection, but the signature of their occultations of background stars should be detectable. Observations at both optical and X-ray wavelengths claim to have detected such occultations, but their implied abundances are inconsistent with each other and far exceed theoretical expectations. Here we report an analysis of archival data that reveals an occultation by a body with an approximately 500-metre radius at a distance of 45 astronomical units. The probability of this event arising from random statistical fluctuations within our data set is about two per cent. Our survey yields a surface density of Kuiper belt objects with radii exceeding 250 metres of 2.1+4.8-1.7 × 107 deg-2, ruling out inferred surface densities from previous claimed detections by more than 5 σ. The detection of only one event reveals a deficit of sub-kilometre-sized Kuiper belt objects compared to a population extrapolated from objects with radii exceeding 50 kilometres. This implies that sub-kilometre-sized objects are undergoing collisional erosion, just like debris disks observed around other stars.
We present a comprehensive analysis of weak gravitational lensing by large-scale structure in the Hubble Space Telescope Cosmic Evolution Survey (COSMOS), in which we combine space-based galaxy shape measurements with ground-based photometric redshifts to study the redshift dependence of the lensing signal and constrain cosmological parameters. After applying our weak lensing-optimized data reduction, principal-component interpolation for the spatially, and temporally varying ACS point-spread function, and improved modelling of charge-transfer inefficiency, we measured a lensing signal that is consistent with pure gravitational modes and no significant shape systematics. We carefully estimated the statistical uncertainty from simulated COSMOS-like fields obtained from ray-tracing through the Millennium Simulation, including the full non-Gaussian sampling variance. We tested our lensing pipeline on simulated space-based data, recalibrated non-linear power spectrum corrections using the ray-tracing analysis, employed photometric redshift information to reduce potential contamination by intrinsic galaxy alignments, and marginalized over systematic uncertainties. We find that the weak lensing signal scales with redshift as expected from general relativity for a concordance CDM cosmology, including the full cross-correlations between different redshift bins. Assuming a flat CDM cosmology, we measure σ8(Ωm/0.3)0.51 = 0.75±0.08 from lensing, in perfect agreement with WMAP-5, yielding joint constraints Ωm = 0.266[+0.025 -0.023], σ8 = 0.802 [+0.028 -0.029] (all 68.3% conf.). Dropping the assumption of flatness and using priors from the HST Key Project and Big-Bang nucleosynthesis only, we find a negative deceleration parameter q0 at 94.3% confidence from the tomographic lensing analysis, providing independent evidence of the accelerated expansion of the Universe. For a flat wCDM cosmology and prior w Î[-2,0], we obtain w <-0.41 (90% conf.). Our dark energy constraints are still relatively weak solely due to the limited area of COSMOS. However, they provide an important demonstration of the usefulness of tomographic weak lensing measurements from space.
Ring Laser gyroscopes exploit the Sagnac effect and measure rotations absolute. They do not require an external reference frame and therefore provide an independent method to monitor Earth rotation. Large-scale versions of these gyroscopes promise to eventually provide a similar high resolution for the measurement of the variations in the Earth rotation rate as the established methods based on VLBI and GNSS. This would open the door to a continuous monitoring of LOD (Length of Day) and polar motion, which is not yet available today. Another advantage is the access to the sub-daily frequency regime of Earth rotation. The ring laser "G" (Grossring), located at the Geodetic Observatory Wettzell (Germany) is the most advanced realization of such a large gyroscope. This paper outlines the current sensor design and properties.
This paper is devoted to the dynamical stability of possible Trojan planets in binaries and in binary systems where one of the substellar companions is not larger than a brown dwarf. Using numerical integrations, we investigated how the size of the stable region around the Lagrangian point L4 depends on the mass parameter and the eccentricity of the secondary star. An additional goal of this work was to create a catalogue of all possible candidates, which could be useful for future observations to detect such objects.
Tesseral coefficients C21 and S21 derived from Gravity Recovery and Climate Experiment (GRACE) observations allow to compute the mass term of the polar-motion excitation function. This independent estimation can improve the geophysical models and, in addition, determine the unmodelled phenomena. In this paper, we intend to validate the polar motion excitation derived from GRACE's last release (GRACE Release 4) computed by different institutes: GeoForschungsZentrum (GFZ), Postdam, Germany; Center for Space Research (CSR), Austin, USA; Jet Propulsion Laboratory (JPL), Pasadena, USA, and the Groupe de Recherche en Géodésie Spatiale (GRGS), Toulouse, France. For this purpose, we compare these excitations functions first to the mass term obtained from observed Earth's rotation variations free of the motion term and, second, to the mass term estimated from geophysical fluids models. We confirm the large improvement of the CSR solution, and we show that the GRGS estimate is also well correlated with the geodetic observations. Significant discrepancies exist between the solutions of each centre. The source of these differences is probably related to the data processing strategy. We also consider residuals computed after removing the geophysical models or the gravimetric solutions from the geodetic mass term. We show that the residual excitation based on models is smoother than the gravimetric data, which are still noisy. Still, they are comparable for the χ2 component. It appears that χ2 residual signals using GFZ and JPL data have less variability. Finally, for assessing the impact of the geophysical fluids models choice on our results, we checked two different oceanic excitation series. We show the significant differences in the residuals correlations, especially for the χ1 more sensitive to the oceanic signals.
Massive black holes are key ingredients of the assembly and evolution of cosmic structures. Pulsar Timing Arrays (PTAs) currently provide the only means to observe gravitational radiation from massive black hole binary systems with masses >~ 107Modot. The whole cosmic population produces a signal consisting of two components: (i) a stochastic background resulting from the incoherent superposition of radiation from the all the sources, and (ii) a handful of individually resolvable signals that raise above the background level and are produced by sources sufficiently close and/or massive. Considering a wide range of massive black hole binary assembly scenarios, we investigate both the level and shape of the background and the statistics of resolvable sources. We predict a characteristic background amplitude in the interval hc(f = 10 8 Hz) ≈ 5 × 10 16-5 × 10 15, within the detection range of the complete Parkes PTA. On average, at least one resolvable source produces timing residuals that integrated over the typical time of observation lay in the range ~5-50 ns. We also quantify the capability of PTAs of measuring the parameters of individual sources, focusing on the astrophysically more likely monochromatic signals produced by binaries in circular orbit. We investigate how the results depend on the number and distribution of pulsars in the array, by computing the variance-covariance matrix of the parameter measurements. For plausible Square Kilometre Array (SKA) observations (100 pulsars uniformly distributed in the sky), and assuming a coherent signal-to-noise ratio of 10, the sky position of massive black hole binaries can be located within an ≈40 deg2 error box, opening promising prospects for detecting a putative electromagnetic counterpart to the gravitational wave emission. The planned SKA can plausibly observe these unique systems, although the number of detections is likely to be small. These observations would naturally complement on the high-mass end of the black hole distribution function future surveys carried out by the Laser Interferometer Space Antenna (LISA).
The observation of massive black hole binaries with pulsar timing arrays (PTAs) is one of the goals of gravitational-wave astronomy in the coming years. Massive (≳108Mȯ) and low-redshift (≲1.5) sources are expected to be individually resolved by upcoming PTAs, and our ability to use them as astrophysical probes will depend on the accuracy with which their parameters can be measured. In this paper we estimate the precision of such measurements using the Fisher-information-matrix formalism. For this initial study we restrict ourselves to “monochromatic” sources, i.e. binaries whose frequency evolution is negligible during the expected ≈10yr observation time, which represent the bulk of the observable population based on current astrophysical predictions. In this approximation, the system is described by seven parameters and we determine their expected statistical errors as a function of the number of pulsars in the array, the array sky coverage, and the signal-to-noise ratio (SNR) of the signal. At fixed SNR (regardless of the number of pulsars in the PTA), the gravitational-wave astronomy capability of a PTA is achieved with ≈20 pulsars; adding more pulsars (up to 1000) to the array reduces the source error box in the sky ΔΩ by a factor ≈5 and has negligible consequences on the statistical errors on the other parameters, because the correlations among parameters are already removed to a large extent. If one folds in the increase of coherent SNR proportional to the square root of the number of pulsars, ΔΩ improves as 1/SNR2 and the other parameters as 1/SNR. For a fiducial PTA of 100 pulsars uniformly distributed in the sky and a coherent SNR=10, we find ΔΩ≈40deg2, a fractional error on the signal amplitude of ≈30% (which constrains only very poorly the chirp mass―luminosity distance combination M5/3/DL), and the source inclination and polarization angles are recovered at the ≈0.3rad level. The ongoing Parkes PTA is particularly sensitive to systems located in the southern hemisphere, where at SNR=10 the source position can be determined with ΔΩ≈10deg2, but has poorer (by an order of magnitude) performance for sources in the northern hemisphere.
We construct evolutionary tracks for massive black hole binaries (MBHBs) embedded in a surrounding distribution of stars. The dynamics of the binary is evolved by taking into account the erosion of the central stellar cusp bound to the massive black holes, the scattering of unbound stars feeding the binary loss cone, and the emission of gravitational waves (GWs). Stellar dynamics is treated in a hybrid fashion by coupling the results of numerical three-body scattering experiments of bound and unbound stars to an analytical framework for the evolution of the stellar density distribution and for the efficiency of the binary loss-cone refilling. Our main focus is on the behavior of the binary eccentricity, in the attempt of addressing its importance in the merger process and its possible impact for GW detection with the planned Laser Interferometer Space Antenna (LISA), and ongoing and forthcoming pulsar timing array (PTA) campaigns. We produce a family of evolutionary tracks extensively sampling the relevant parameters of the system which are the binary mass, mass ratio and initial eccentricity, the slope of the stellar density distribution, its normalization and the efficiency of loss-cone refilling. We find that, in general, stellar dynamics causes a dramatic increase of the MBHB eccentricity, especially for initially already mildly eccentric and/or unequal mass binaries. This affects the overall system dynamics; high eccentricities enhance the efficiency of
The merger of a supermassive binary black hole (SBBH) is one of the most extreme events in the universe with a huge amount of energy released by gravitational radiation. Although the characteristic gravitational wave (GW) frequency around the merger event is far higher than the nHz regime optimal for pulsar timing arrays (PTAs), non-linear GW memory might be a critical smoking gun of the merger event detectable with PTAs. In this Letter, basic aspects of this interesting observation are discussed for SBBHs, and the detection numbers of their memory and inspiral GWs are estimated for ongoing and planned PTAs. We find that the expected detection number would be smaller than unity for the two types of signals even with the Square Kilometre Array. We also provide various scaling relations that would be useful to study detection probabilities of GWs from individual SBBHs with PTAs.
Our first-principles calculations show that both the compressional and shear waves of -Fe become elastically isotropic under the Earth's inner core conditions, with the variation in sound velocities along different angles from the c axis within 1%. We computed the thermoelasticity at high pressures and temperatures from quasiharmonic linear response linear-muffin-tin-orbital calculations in the generalized-gradient approximation. The calculated anisotropic shape and magnitude at ambient temperature agree well with previous first-principles predictions, and the anisotropic effects show strong temperature dependences. This implies that other mechanisms, rather than the preferential alignment of the -Fe crystal along the Earth's rotation axis, account for the seismic P-wave travel time anomalies. Either the inner core is not -Fe, and/or the seismologically observed anisotropy is caused by inhomogeneity, i.e., multiple phases.
We study Kelvin-Helmholtz (KH) instability at the interface of a disc and corona system by doing a linear perturbation analysis. The disc is assumed to be thin; however, the corona is considered to be nearly quasi-spherical because of its high temperature. Under these circumstances, the interface is subject to the KH instability for a given set of the input parameters. Growth rates of the KH unstable modes are calculated for a wide range of the input parameters. We show that for a certain range of the perturbations, the unstable KH perturbations are growing with time-scales comparable to the inverse of the angular velocity of the accretion disc (dynamical time-scale). Thus, KH instability at the interface of a disc-corona may have enough time to affect the dynamical structure of its underlying accretion disc by possible exchange of the mass, angular momentum or even energy. Our linear analysis shows that KH instability may provide a mechanism for such exchanges between a disc and its corona.
The holy grail of exoplanet searches is an exo-Earth, an Earth mass planet in the habitable zone (HZ) around a nearby star. Mass is one of the most important characteristics of a planet and can only be measured by observing the motion of the star around the planet-star center of gravity. The planet's orbit can be measured either by imaging the planet at multiple epochs or by measuring the position of the star at multiple epochs by space-based astrometry. The measurement of an exoplanet's orbit by direct imaging is complicated by a number of factors. One is the inner working angle (IWA). A space coronagraph or interferometer imaging an exo-Earth can separate the light from the planet from the light from the star only when the star-planet separation is larger than the IWA. Second, the apparent brightness of a planet depends on the orbital phase. A single image of a planet cannot tell us whether the planet is in the HZ or distinguish whether it is an exo-Earth or a Neptune-mass planet. Third is the confusion that may arise from the presence of multiple planets. With two images of a multiple planet system, it is not possible to assign a dot to a planet based only on the photometry and color of the planet. Finally, the planet-star contrast must exceed a certain minimum value in order for the planet to be detected. The planet may be unobservable even when it is outside the IWA, such as when the bright side of the planet is facing away from us in a "crescent" phase. In this paper we address the question: "Can a prior astrometric mission that can identify which stars have Earth-like planets significantly improve the science yield of a mission to image exo-Earths?" In the case of the Occulting Ozone Observatory, a small external occulter mission that cannot measure spectra, we find that the occulter mission could confirm the orbits of ~4 to ~5 times as many exo-Earths if an astrometric mission preceded it to identify which stars had such planets. In the case of an internal coronagraph we find that a survey of the nearest ~60 stars could be done with a telescope half the size if an astrometric mission had first identified the presence of Earth-like planets in the HZ and measured their orbital parameters.
We study in detail the motions of three planets interacting with each other under the influence of a central star. It is known that the system with more than two planets becomes unstable after remaining quasi-stable for long times, leading to highly eccentric orbital motions or ejections of some of the planets. In this paper, we are concerned with the underlying physics for this quasi-stability as well as the subsequent instability and advocate the so-called stagnant motion in the phase space, which has been explored in the field of a dynamical system. We employ the Lyapunov exponent, the power spectra of orbital elements, and the distribution of the durations of quasi-stable motions to analyze the phase-space structure of the three-planet system, the simplest and hopefully representative one that shows the instability. We find from the Lyapunov exponent that the system is almost non-chaotic in the initial quasi-stable state whereas it becomes intermittently chaotic thereafter. The non-chaotic motions produce the horizontal dense band in the action-angle plot whereas the voids correspond to the chaotic motions. We obtain power laws for the power spectra of orbital eccentricities. Power-law distributions are also found for the durations of quasi-stable states. With all these results combined together, we may reach the following picture: the phase space consists of the so-called KAM tori surrounded by satellite tori and imbedded in the chaotic sea. The satellite tori have a self-similar distribution and are responsible for the scale-free power-law distributions of the duration times. The system is trapped around one of the KAM torus and the satellites for a long time (the stagnant motion) and moves to another KAM torus with its own satellites from time to time, corresponding to the intermittent chaotic behaviors.
An analytical model of capped turbulent oscillatory bottom boundary layers (BBLs) is proposed using eddy viscosity of a quadratic form. The common definition of friction velocity based on maximum bottom shear stress is found unsatisfactory for BBLs under rotating flows, and a possible extension based on turbulent kinetic energy balance is proposed. The model solutions show that the flow may slip at the top of the boundary layer due to capping by the water surface or stratification, reducing the bottom shear stress, and that the Earth's rotation induces current and bottom shear stress components perpendicular to the interior flow with a phase lag (or lead). Comparisons with field and numerical experiments indicate that the model predicts the essential characteristics of the velocity profiles, although the agreement is rather qualitative due to assumptions of quadratic eddy viscosity with time-independent friction velocity and a well-mixed boundary layer. On the other hand, the predicted linear friction coefficients, phase lead, and veering angle at the bottom agreed with available data with an error of 3%-10%, 5°-10°, and 5°-10°, respectively. As an application of the model, the friction coefficients are used to calculate e-folding decay distances of progressive internal waves with a semidiurnal frequency.
Solar sail technology offer new capabilities for the analysis and design of space missions. This new concept promises to be useful in overcoming the challenges of moving throughout the solar system. In this paper, novel families of highly non-Keplerian orbits for solar sail spacecraft at linear order are investigated in the Earth-Moon circular restricted three-body problem, where the third body is a solar sail. In particular, periodic orbits near the collinear libration points in the Earth-Moon system will be explored along with their applications. The dynamics are completely different from the Earth-Sun system in that the sun line direction constantly changes in the rotating frame but rotates once per synodic lunar month. Using an approximate, first-order analytical solution to the nonlinear nonautonomous ordinary differential equations, periodic orbits can be constructed that are displaced above the plane of the restricted three-body system. This new family of orbits have the property of ensuring visibility of both the lunar far-side and the equatorial regions of the Earth, and can enable new ways of performing lunar telecommunications.
It has been suggested that moons around transiting exoplanets may cause an observable signal in transit photometry or in the Rossiter-McLaughlin (RM) effect. In this paper, a detailed analysis of parameter reconstruction from the RM effect is presented for various planet-moon configurations, described with 20 parameters. We also demonstrate the benefits of combining photometry with the RM effect. We simulated 2.7 × 109 configurations of a generic transiting system to map the confidence region of the parameters of the moon, find the correlated parameters and determine the validity of reconstructions. The main conclusion is that the strictest constraints from the RM effect are expected for the radius of the moon. In some cases, there is also meaningful information on its orbital period. When the transit time of the moon is exactly known, for example from transit photometry, the angle parameters of the moon's orbit will also be constrained from the RM effect. From transit light curves the mass can be determined, and combining this result with the radius from the RM effect, the experimental determination of the density of the moon is also possible.
We present an observation of the Rossiter-McLaughlin effect for the planetary system WASP-3. Radial velocity measurements were made during transit using the SOPHIE spectrograph at the 1.93-m telescope at Haute-Provence Observatory. The shape of the effect shows that the sky-projected angle between the stellar rotation axis and planetary orbital axis (λ) is small and consistent with zero within 2σ; λ = 15+10°-9°. WASP-3b joins the ~two-thirds of planets with measured spin-orbit angles that are well aligned and are thought to have undergone a dynamically gentle migration process such as planet-disc interactions. We find a systematic effect which leads to an anomalously high determination of the projected stellar rotational velocity (vsini = 19.6[+2.2 -2.1kms-1] compared to the value found from spectroscopic line broadening (vsini = 13.4 +/- 1.5kms-1). This is thought to be caused by a discrepancy in the assumptions made in the extraction and modelling of the data. Using a model developed by Hirano et al. designed to address this issue, we find vsini to be consistent with the value obtained from spectroscopic broadening measurements (vsini = 15.7[+1.4 -1.3kms-1].
This paper investigates the stability of equilibrium points in the restricted three-body problem, in which the masses of the luminous primaries vary isotropically in accordance with the unified Meshcherskii law, and their motion takes place within the framework of the Gylden-Meshcherskii problem. For the autonomized system, it is found that collinear and coplanar points are unstable, while the triangular points are conditionally stable. It is also observed that, in the triangular case, the presence of a constant κ, of a particular integral of the Gylden-Meshcherskii problem, makes the destabilizing tendency of the radiation pressures strong. The stability of equilibrium points varying with time is tested using the Lyapunov Characteristic Numbers (LCN). It is seen that the range of stability or instability depends on the parameter κ. The motion around the equilibrium points L i ( i=1,2,…,7)for the restricted three-body problem with variable masses is in general unstable.
This paper examines the effect of a constant κ of a particular integral of the Gylden-Meshcherskii problem on the stability of the triangular points in the restricted three-body problem under the influence of small perturbations in the Coriolis and centrifugal forces, together with the effects of radiation pressure of the bigger primary, when the masses of the primaries vary in accordance with the unified Meshcherskii law. The triangular points of the autonomized system are found to be conditionally stable due to κ. We observed further that the stabilizing or destabilizing tendency of the Coriolis and centrifugal forces is controlled by κ, while the destabilizing effects of the radiation pressure remain unchanged but can be made strong or weak due to κ. The condition that the region of stability is increasing, decreasing or does not exist depend on this constant. The motion around the triangular points L 4,5 varying with time is studied using the Lyapunov Characteristic Numbers, and are found to be generally unstable.
This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ c and unstable for μcleμ <1/2, where μ c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.
We numerically investigate the stability of systems of 1 ME planets orbiting a solar-mass star. The systems studied have either 2 or 42 planets per occupied semimajor axis, for a total of 6, 10, 126, or 210 planets, and the planets were started on coplanar, circular orbits with the semimajor axes of the innermost planets at 1 AU. For systems with two planets per occupied orbit, the longitudinal initial locations of planets on a given orbit were separated by either 60° (Trojan planets) or 180°. With 42 planets per semimajor axis, initial longitudes were uniformly spaced. The ratio of the semimajor axes of consecutive coorbital groups in each system was approximately uniform. The instability time for a system was taken to be the first time at which the orbits of two planets with different initial orbital distances crossed. Simulations spanned virtual times of up to 1 × 108, 5 × 105, and 2 × 105 years for the 6- and 10-planet, 126-planet, and 210-planet systems, respectively. Our results show that, for a given class of system (e.g., five pairs of Trojan planets orbiting in the same direction), the relationship between orbit crossing times and planetary spacing is well fit by the functional form log (tc / t0) = b β + c, where tc is the crossing time, t0 = 1 year, β is the separation in initial orbital semimajor axis (in terms of the mutual Hill radii of the planets), and b and c are fitting constants. The same functional form was observed in the previous studies of single planets on nested orbits (Smith and Lissauer 2009). Pairs of Trojan planets are more stable than pairs initially separated by 180°. Systems with retrograde planets (i.e., some planets orbiting in the opposite sense from others) can be packed substantially more closely than can systems with all planets orbiting in the same sense. To have the same characteristic lifetime, systems with 2 or 42 planets per orbit typically need to have about 1.5 or 2 times the orbital separation as orbits occupied by single planets, respectively.
I derive the physical properties of 30 transiting extrasolar planetary systems using a homogeneous analysis of published data. The light curves are modelled with the JKTEBOP code, with special attention paid to the treatment of limb darkening, orbital eccentricity and error analysis. The light from some systems is contaminated by faint nearby stars, which if ignored will systematically bias the results. I show that it is not realistically possible to account for this using only transit light curves: light-curve solutions must be constrained by measurements of the amount of contaminating light. A contamination of 5 per cent is enough to make the measurement of a planetary radius 2 per cent too low. The physical properties of the 30 transiting systems are obtained by interpolating in tabulated predictions from theoretical stellar models to find the best match to the light-curve parameters and the measured stellar velocity amplitude, temperature and metal abundance. Statistical errors are propagated by a perturbation analysis which constructs complete error budgets for each output parameter. These error budgets are used to compile a list of systems which would benefit from additional photometric or spectroscopic measurements. The systematic errors arising from the inclusion of stellar models are assessed by using five independent sets of theoretical predictions for low-mass stars. This model dependence sets a lower limit on the accuracy of measurements of the physical properties of the systems, ranging from 1 per cent for the stellar mass to 0.6 per cent for the mass of the planet and 0.3 per cent for other quantities. The stellar density and the planetary surface gravity and equilibrium temperature are not affected by this model dependence. An external test on these systematic errors is performed by comparing the two discovery papers of the WASP-11/HAT-P-10 system: these two studies differ in their assessment of the ratio of the radii of the components and the effective temperature of the star. I find that the correlations of planetary surface gravity and mass with orbital period have significance levels of only 3.1? and 2.3?, respectively. The significance of the latter has not increased with the addition of new data since Paper II. The division of planets into two classes based on Safronov number is increasingly blurred. Most of the objects studied here would benefit from improved photometric and spectroscopic observations, as well as improvements in our understanding of low-mass stars and their effective temperature scale.
We present the simplest model that permits a largely analytical exploration of the m = 1 counter-rotating instability in a `hot' nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using the Wentzel-Kramers-Brillouin approximation. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian disc must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.
Spin induced precessional modulations of gravitational wave signals from supermassive black hole binaries can improve the estimation of luminosity distance to the source by space based gravitational wave missions like the Laser Interferometer Space Antenna (LISA). We study how this impacts the ability of LISA to do cosmology, specifically, to measure the dark energy equation of state (EOS) parameter w. Using the ΛCDM model of cosmology, we show that observations of precessing binaries with mass ratio 10:1 by LISA, combined with a redshift measurement, can improve the determination of w up to an order of magnitude with respect to the nonprecessing case depending on the total mass and the redshift.
The black hole binary system LMC X-3 has been observed by virtually every X-ray mission since the inception of X-ray astronomy. Among the persistent sources, LMC X-3 is uniquely both habitually soft and highly variable. Using a fully relativistic accretion disk model, we analyze hundreds of spectra collected during eight X-ray missions that span 26 years. For a selected sample of 391 RXTE spectra, we find that to within »2% the inner radius of the accretion disk is constant over time and unaffected by source variability. Even considering an ensemble of eight X-ray missions, we find consistent values of the radius to within »4%-6%. Our results provide strong evidence for the existence of a fixed inner-disk radius. The only reasonable inference is that this radius is closely associated with the general relativistic innermost stable circular orbit. Our findings establish a firm foundation for the measurement of black hole spin.
This paper surveys some of the astrophysical environments in which the effects of Lense-Thirring precession and, more generally, frame dragging are expected to be important. We concentrate on phenomena that can probe in situ the very strong gravitational field and single out Lense-Thirring precession in the close vicinity of accreting neutron stars and black holes: these are the fast quasi periodic oscillations in the X-ray flux of accreting compact objects. We emphasize that the expected magnitude of Lense-Thirring/frame dragging effects in the regions where these signals originate are large and thus their detection does not pose a challenge; rather it is the interpretation of these phenomena that needs to be corroborated through deeper studies. Relativistic precession in the spin axis of radio pulsars hosted in binary systems hosting another neutron star has also been measured. The remarkable properties of the double pulsar PSR J0737-3039 has opened a new perspective for testing the predictions of general relativity also in relation to the precession of spinning bodies.
Aims: This paper tackles important aspects of comet dynamics from a statistical point of view. Existing methodology uses numerical integration to compute planetary perturbations to simulate such dynamics. This operation is highly computational. It is reasonable to investigate a way in which a statistical simulation of the perturbations can be handled more easily.
Methods: The first step to answer such a question is to provide a statistical study of these perturbations in order to determine their main features. The statistical tools used are order statistics and heavy-tailed distributions.
Results: The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the planets. These characteristics were validated through statistical testing and a theoretical study based on the Öpik theory.
Points on the surface of a sphere can be mapped by stereographic projection to points on the plane of complex numbers. If the points on the sphere are identified with the directions of incoming light rays, then the effect of a Lorentz transformation, a rotation plus a boost, is represented by a bilinear or Möbius transformation applied to points on the complex plane. This procedure allows the effects of the aberration of light, precession and nutation, required for computing the mean and apparent positions of celestial objects, to be accounted for in a common framework and yields expressions that are readily evaluated in practice. The general form of the bilinear transformation representing a pure Lorentz boost is derived. Explicit expressions are given for the bilinear transformations representing aberration, precession and nutation as well as frame bias and transformations to the Celestial Intermediate Reference System. The approach described simplifies, and is an alternative to, the standard matrix methods commonly used to perform coordinate system rotations.
The pulsar is a high-speed rotating neutron star with a stable rotational period, being not disturbed and destroyed artificially, and can be taken as the reference quantity of the absolute time. In this article a kind of pulsar time service method based on the Kalman filtering algorithm is proposed, and the simulation analysis of the clock error control based on the Kalman filtering and of the effect of the pulsar catalogue error and the measuring accuracy of the pulsar time of arrival (TOA) on the accuracy of time service is made by taking a certain solar synchronous orbit as an example. The result shows that by utilizing this method the clock error of the satellite-borne clock can be effectively eliminated and its time-dependent increase is restrained, thereby solving the problem that the accuracy of the spacecraft-borne low cost clock can not meet the needs.
SPIRE, the Spectral and Photometric Imaging REceiver, is the Herschel Space Observatory's submillimetre camera and spectrometer. It contains a three-band imaging photometer operating at 250, 350 and 500 μm, and an imaging Fourier-transform spectrometer (FTS) covering 194-671 μm (447-1550 GHz). In this paper we describe the initial approach taken to the absolute calibration of the SPIRE instrument using a combination of the emission from the Herschel telescope itself and the modelled continuum emission from solar system objects and other astronomical targets. We present the photometric, spectroscopic and spatial accuracy that is obtainable in data processed through the “standard” pipelines. The overall photometric accuracy at this stage of the mission is estimated as 15% for the photometer and between 15 and 50% for the spectrometer. However, there remain issues with the photometric accuracy of the spectra of low flux sources in the longest wavelength part of the SPIRE spectrometer band. The spectrometer wavelength accuracy is determined to be better than 1/10th of the line FWHM. The astrometric accuracy in SPIRE maps is found to be 2 arcsec when the latest calibration data are used. The photometric calibration of the SPIRE instrument is currently determined by a combination of uncertainties in the model spectra of the astronomical standards and the data processing methods employed for map and spectrum calibration. Improvements in processing techniques and a better understanding of the instrument performance will lead to the final calibration accuracy of SPIRE being determined only by uncertainties in the models of astronomical standards.