The diversity of planetary interiors should be expected. Neither our conservative estimates in Table 4.4 nor the estimates for habitable zone terrestrial exoplanets in Table 4.3 should be taken as an explicit interpretation of the interiors of any existing planet orbiting these studied host stars, but only the plausible ranges constrained by different scenarios as demonstrated in the paper. The previous studies [e.g. Santos et al., 2015; Weiss et al., 2016; Brugger et al., 2017] usually state that their analyses are for an explicit planet around a parent star but this statement should be taken with caution. For example, the core mass fraction (wt%) of Kepler-10b has been pre- viously estimated to be 27.5 ± 1.7 [Santos et al., 2015], 17 ± 11 [Weiss et al., 2016], and 10-33 [Brugger et al., 2017], which seem to approximate our conservative esti- mate B (31.2) for a ‘warm’ rocky planet orbiting Kepler 10. Whereas, those previous estimates are achieved by fixing all Fe into the core [Santos et al., 2015] or relying on Mg# (= Mg/(Mg + Fe)) [Weiss et al., 2016; Brugger et al., 2017], without considering oxygen fugacity/budget that controls the oxidation state of a planet. If one general- izes those fixed assumptions to potential rocky planets in different distances to the same star, the same chemistry and interiors for these planets would result. Although taking into account planetary mass and radius, the modeling results could be more specific to such planets but those results would still be degenerate to a degree, to which that oxygen fugacity/budget would vary in the disk. When targeting a poten- tially habitable planet for further characterization with future missions, we should particularly be cautious with this kind of ‘explicit’ claim, which may only assemble one scenario of possible interior properties of rocky exoplanets orbiting in different distances to their host stars. The depletion of oxygen in Kepler-10 planets relative to the host star is not considered in Dorn et al. [2017b], but they assume Fe/Si mantle =
An icy satellite whose interior is composed of a homogeneous ice/rock mixture must avoid melting during its entire history, including during itsformation when it was heated by deposition of accretional energy and short-lived radioisotopes. Estimates of the temperature rise associated with radiogenic and accretional heating, coupled with limits on satellite melting can be used to constrain the timing of formation of a partially differentiated satellite relative to the origin of the calcium–aluminum-rich inclusions (CAI’s) as a function of its accretion timescale and the protosatellite disk temperature (T d ). Geological characterization and spacecraft radio tracking data suggest that Callisto, the outermost regular satellite of Jupiter, and Saturn’s mid-sized satellite Rhea, are partially differentiated if their interiors are in hydrostatic equilibrium. Because the speciﬁc conditions during the satellites’ formation are uncertain, we determine accretional temperature proﬁles for a range of values for T d and accretion time scales with the limiting assumption that impactors deposit all their energy close to the surface, leading to maximally effective radiative cooling. We ﬁnd that Callisto can remain unmelted during formation if it accreted on a time scale longer than 0.6 Myr. Considering both radiogenic and accretional heating, Callisto must have ﬁnished accreting no earlier than ∼ 4 Myr after formation of CAI’s for T d = 100 K. Warmer disks or larger impactors that deposit their energy at depth in the satellite would require longer and/or later formation times. If Rhea accreted slowly (in 10 5 to 10 6 years), its growth must have ﬁnished no earlier than ∼ 2 Myr after CAI’s for 70 K T d 250 K to avoid early melting. If Rhea formed quickly ( 10 3 yr), itsformation must have been delayed until at least 2 to 7 Myr after CAI’s and in a disk with T d < 190 K in the small impactor limit. If the satellites form in slow-inﬂow-supplied disks as proposed by Canup and Ward [Canup, R.M., Ward, W.R., 2002. Astron. J. 124, 3404–3423], the implied satellite ages suggest that gas inﬂow to the giant planets ceased no earlier than ∼ 4 Myr after CAI’s, comparable to average nebular lifetimes inferred from observations of circumstellar disks.
After noticing that Kepler-432b sits all alone in the M p versus a parameter space, it is natural to wonder
why, and we suggest two potential explanations, each of which may contribute to this apparent planetary desert. In the first, we consider that Kepler-432b may simply be a member of the tail of the period distribution of planets around massive and intermediate-mass main-sequence stars. That is, perhaps massive main-sequence stars sim- ply harbor very few planets with separations less than 1 AU. If this occurrence rate is a smooth function of stel- lar mass, then because Kepler-432 would most accurately be called intermediate mass, it might not be so surpris- ing that it harbors a planet with a separation of 0.3 AU while its more massive counterparts do not. If this is the case, then as we detect more giant planets orbiting giant stars (and main-sequence stars above the Kraft break), we can expect to find a sparsely populated tail of planetsinterior to 1 AU. This may ultimately prove to be re- sponsible for the observed distribution, and would have important implications for giant planet formation and migration around intermediate mass stars in comparison to Sun-like stars, but it cannot be confirmed now. It will require additional planet searches around evolved stars and improvements in detecting long period planets or- biting rapidly rotating main-sequence stars.
Disc fragmentation happens fast, so that large, unstable discs or discs that are currently undergoing fragmentation should be rarely observed . Moreover, observations of early-stage discs are challenging as these discs are deeply embedded in their parental clouds and their presence has to be inferred from radiative transfer modelling. There have been a few candidates of relatively massive discs in Class 0 and Class I objects [29–36], in a few of which the disc status has been confirmed by (i) HCO + 3 − 2 line observations revealing signs of Keplerian rotation [e.g. L1489-IRS; 37], or (ii) scattered light images [L1527; 38]. An interesting example of a massive disc is the one around HL Tau (a 0.3-M Class II object), which has a mass of around 0.1 M and extends to at least 100 AU . The frequency of occurrence of extended massive discs is uncertain as a recent survey  using the PdBI (1.3 mm) found no discs larger than its resolution limits (∼ 100 AU).
Figure 50 shows planet mass versus planet radius for all 30 transiting planets. (We exclude the 12 planets with uncertainties in density greater than 6.5 g cm −3 .) Planet mass increases monotonically with radius, as seen in Figure 49. Here, masses less secure than 2σ , and even negative masses, are included in the plot. We specifically allowed our MCMC analysis to include negative planet masses in the solution. Among the 42 transiting planets, 4 of them had a peak in the posterior mass distribution that was negative (see Table 2). Such unphysical masses are a normal outcome of fluctuations in the RV measurements from both RV errors and unknown planets, which will be mostly uncorrelated in orbital phase with the known planets, aside from mean motion resonances. Negative masses arise naturally from RV uncertainties of m s −1 for planets that induce RV semi- amplitudes, K, that are smaller (due to small planet mass and/or long period). RV errors may cause measured RVs to be high when the actual RV is low, and vice versa, due to those errors. For the low mass planets, such RV non-detections are expected, yielding equal numbers of apparently positive and “negative” masses.
In practice, every inward-proceeded part of the numerical integration of Equations (11)-(13), when it is started in a distance larger than zero, ends with the implication of the inner physical surface. (In principle, the numerical integration from a finite distance can end in the center with finite energy density and pressure. This is, however, only a single of infinite variety of possibilities. If there is no special attention to the choice of initial conditions, the probability of its occurrence approaches zero.) Such the property can be also expected for some other equa- tions of state, not only the Chandrasekhar’s Equation (7) and Equation (8). (Actually, the same qualitative beha- vior occurs using, e.g., the polytrope. And, the energy-density and pressure maximum in a finite distance also occurs for the equation state of radiation, E = 3 P .) On the other-hand side, there is possible to construct a model of NS in the form of full sphere, if the integration starts in the center. (Then, we force the single of the in- finite variety of possibilities to be the case.) In this section, let us reveal the conditions implying the full-sphere model of NS.
The importance of ‘sight’ and of receiving light is an important philosophic and hermetic principle. All life needs a certain level of light and the lack of it is detrimental and dangerous. Think about a pot plant that is kept in a dark cupboard. No matter how much you water it, the lack of light will eventually lead to its death. So, too in astrology, the notion that a planet can see the ‘light’, in this case either the Sun or the Moon, which are also known as “the Lights” suggests that the ancients wanted to enshrine this principle in each of the planets’ relationships to the luminaries in charge of their sect, either the diurnal or nocturnal.
In spring 2013, after the failure of two reaction wheels, the spacecraft could not maintain for long terms its pointing stability anymore, which was fundamental for obtaining the ultra-high-precise pho- tometry that yielded thousands of planetary candidates. However, considering the great successes in terms of planet discoveries achieved in the previous years, a new program (named K2), with a new observing strategy, was undertaken. Even though the main goal of the K2 program is still pointed towards finding new planetary systems with the transit technique, several other side projects, from microlensing to extragalactic science (Gould & Horne 2013; Edelson et al. 2015), have been included and will be performed in the coming months. The pointing stability of the Kepler space telescope can be reestablished thanks to the solar wind, but this limits the observations towards the ecliptic- plane directions only. With this new strategy, Kepler is currently observing selected fields along the ecliptic plane for roughly 80 days, providing almost the same performances reached in the previous mission (Howell et al. 2014). After only six months from the release of the data of the first field, nu- merous interesting planetary discoveries have been already announced, e.g. Crossfield et al. (2015b); Sanchis-Ojeda et al. (2015); Armstrong et al. (2015).
We develop a GPU-accelerated hybrid code to tackle these challenges. We realize that star clusters and plane- tary systems are very different, and that they have to be modeled with their own dedicated algorithms. We first inte- grate the host YMCs (without planets) using NBODY6++GPU (Spurzem 1999; Aarseth 2003; Wang et al. 2015b). The sim- ulation is stored at a very high time resolution using an incremental adaptive storage scheme (Farr et al. 2012; Cai et al. 2015). The storage scheme, namely “Block time step (BTS) storage scheme”, stores only the most recently up- dated particles, and thereby allows very high temporal res- olution with reasonable file sizes. With the BTS data, we are then able to reconstruct the details of close encounters; the close encounters details are then inserted into the IAS15 integrator (Rein & Spiegel 2015) of the planetary system dynamics code rebound (Rein & Liu 2012). The planetary system integrator queries the position vector of the closest neighbor at a timestep of years. Such a query is implemented by interpolating the BTS data on the GPUs (graphic pro- cessing units). The communication of perturbation data is implemented with the AMUSE 1 (Pelupessy et al. 2013; Porte- gies Zwart et al. 2013; Portegies Zwart & McMillan 2018) framework. Given that the density of YMCs is very high, especially in the cluster center, we include 5 nearest per- turbers 2 .
The vastness of railways – cars, cargo, track, countries and conditions presents a massive challenge for management of rolling stock and rail operations. IPICO’s low cost, passive RF technolog y enables consistently accurate identification and control of assets in virtually any operating environment. As a freight giant, the railway industry is looking forward to improve the utilization of the wagons and has been on a look out for an online system for tracking wagons on its 62000 km worth of rail network. It is expected to identify the possible problem areas and come out with strategies to eliminate them. Under the Information Technology Vision 2012, announced in the Railway Budget for 2008-09 and 2009-10, the railway ministry plans to give the Railways a modern look and feel by implementing Modern Communication systems such as RFID, GPS and GIS. Modernisation of Indian Railways has always been a question in focus for the development of the basic infrastructure of India. Since the railways represent one of the best modes of transport available to the common people, it would be impossible to just keeping increasing the fares to meet the costs incurred due to maintenance, the large workforce and the expansion activities. The Railways should therefore, consider upgrading itself to cutting-edge technologies for better efficiency and cost reduction.
3. Thus, for the best formation of conscience we see the importance of trying to create good, loving environments when growing up; for good, accepting and loving environments when dealing with one's life as an adult (sometimes counseling, support groups, 12-step groups, etc.); espe- cially consistently praying with a strong community of faith. We should not underestimate the influence of things like praying together before meals or at other times as a family; taking time to discuss events of the day or week and reflect on the moral quality of responses; modeling good listening, forgiving, and caring skills; building into our lives routines of Sunday worship, Christian service outreach, and contact with people we admire. A well-formed conscience is to be trusted and followed, but it takes intentional focus and ongoing formation to be well-formed.
It remains unclear how USPs settle so close to their host stars, but the multiplicity of these systems (P < 50 days) hints that they form via inward migration mechanisms involving multiple planets. For example, Hansen & Zink (2015) demonstrated that tidal decay of 55 Cnc e from beyond its current orbit would have sent the planet through multiple secular resonances, exciting its orbital eccentricity and inclination. A shrinking periastron distance would subsequently boost tidal evolution and increase the rate of orbital decay. However, unless the perturber has a mass comparable to Jupiter, secular interactions are usually too weak to overcome relativistic precession at short orbital periods (Lee & Chiang, 2017). Thus, secular interactions can only explain USP systems that also host close-in giant planets like 55 Cnc and WASP-47. Alternatively, USPs might have migrated through a gas disk to their current orbits via mean motion resonances (MMRs) with other planets. However, companions of USPs detected to date are not in MMR. It is possible that resonant companions were engulfed by the star or collided to form a single object. Formation of USPs via MMR would require the disk to extend very close to the star. USPs could also have been gravitationally scattered inwards by another companion, but this is difficult to reconcile with the observed presence of multiple companions on close-in orbits, which would be unstable at modest eccentricities. Lee & Chiang (2017) show that the observed USP population is consistent with in-situ formation or disk migration followed by tidal migration. Any complete theory of planet formation must account for the presence of these rocky ∼ 5-10 M ⊕ USPs with close neighbors.
realizations as burn-in and thinning the chain by saving every 10th entry, for a ﬁ nal chain length of 10 6 . The marginalized posterior distributions are shown in Figure 9. It is apparent that while the parameters of the inner planet are very well constrained, there is a high-eccentricity tail of solutions for the outer planet that cannot be ruled out by RVs alone ( we investigate this further using N-body simulations in Section 8 ) . Because several of the posteriors are non-Gaussian, we cannot simply adopt the median and central 68.3% con ﬁ dence interval as our best- ﬁ t parameters and 1 σ errors as we normally might. Instead, we adopt best- ﬁ t parameters from the mode of each distribution, which we identify from the peak of the probability density function ( PDF ) . We generate the PDFs using a Gaussian kernel density estimator with bandwidths for each parameter chosen according to Silverman ’ s rule. We assign errors from the region that encloses 68.3% of the PDF, and for which the bounding values have identical probability densities. That is, we require the ± 1 σ values to have equal likelihoods. The resulting orbital solution using these parameters has velocity residuals larger than expected from the nominal RV uncertainties. We attribute this to some combination of astrophysical jitter ( e.g., stellar activity or additional undetected planets ) and imperfect treatment of the various noise sources described in Section 4. An analysis of the residuals does not reveal any signi ﬁ cant periodicity, but given our measurement precision, we would not expect to detect any additional planets unless they were also massive gas giants, or orbiting at very small separations. To account for the observed velocity residuals, we re-run our MCMC with the inclusion of an additional RV jitter term. Tuning this until c 2 is equal to the
the impact parameter b, the limb-darkening coefficients, the photometric contamination by third light, and information about the epoch of the transit (useful for the study of transit timing variations). Next steps involve spectroscopic characterization of the host star to reject false alarms (see [23, 24]) and to calculate absolute values for the relative planetary parameters obtained from the light curve analysis. Stellar parameters obtained from spectroscopic analysis are model dependent, however transiting planets provide an useful constrain for those models: the stellar log g from the transit fit (see the discussion in  and, in this volume, the contribution from J. Valenti). However, current models include a certain uncertainty in the stellar parameters, which are typically larger than 10% for the mass and the radius . Asteroseismology can overcome these limitations, but it is only feasible from space for bright targets (see [26–28] and, in this volume, the contribution from A. Moya). The uncertainty in the stellar parameters is directly translated into the uncertainty of the planetary parameters, where precisions of a few percent are required to distinguish between different compositions and internal structures [29–35].
Until now, the project’s experiences have led to a decision to base developments of migration strategies on enhancement of existing tools. The applicability of this approach at present and in the future will be argued for in this paper. First the current situation concerning migration tools is outlined as it serves as the context for the approach. Then two claims that form the arguments for the pragmatic approach to migration tools in the Planets project will be discussed. As quality is an important part of the Planets approach, challenges and further work concerning migration tool quality for available tools will also be discussed as part of the approach description. These sections will be followed by a discussion on the arguments that form the basis for the approach and a conclusion.
If these indirect arguments are valid, how might the mass have been lost? The an- swer to this question is not known, but there are several conjectures in the literature. For example, some part of the initial mass might have been lost by dynamical erosion. Neptune cannot do the job, depleting the mass of the belt by only a factor of a few over the age of the solar system except for orbits in its immediate vicinity. A passing star might substantially erode the belt, but it is not obvious that the remnant left behind would be like the Kuiper belt in detail. Perhaps the mass was lost through collisional grinding. In this, the KBOs collide and shatter, producing a cascade of particles of sizes all the way down to dust. At the smallest sizes, these particles become responsive to radiation drag forces, and would spiral into the Sun. However, bodies larger than ∼50 km to 100 km are not easily shattered and the collisional grinding model only works if the initial size distribution in the Kuiper belt were so steep that most of the mass was held by the smallest (most destructable) bodies. It is unclear whether this size distribution ever prevailed.
The detection of Hg on Jupiter furnished astronomers with a potentiaUy useful probe of the physical conditions of the jovian ionosphere (D rossart et al 1989). Since 1989 a num ber of questions have been answered about Hg and its existence on Jupiter. The emission was found to originate around the 0.1 to 10"^ /zbar level (D rossart e t al 1989). The tem perature ranges from around 600 K (Oka and GebaUe 1991) to over 1000 K (MiUer et al 1990, MaiUard e t al 1990. Hg column density can be as high as 10^^ cm“ ^. Spectra (MiUer et al 1991) and images of Jupiter at wavelength sensitive to Hg emission showed th a t auroral Hg emission is more closely associated with open magnetic field Unes connecting to the m agnetotail th an the lo Plasm a Torus (IP T )(B aron e t al 1991, 1992, S at oh e t al 1993). This would mean th a t the mechanism responsible for Hg emission was different th an the then accepted processes responsible for the U.V. and hydrocarbon emissions. W ith the new Hubble images, however, the U.V. aurorae have now come back into Une with the I.R. d ata (G érard et al 1994).
To summarize, the radial velocity method gives access to diﬀerent orbital parameters, but is limited to stars showing very many spectral lines in order to increase the measurement precision. Fortunately, this is the case of solar type and cooler stars, the most abundant ones in the Galaxy. Most of the known extrasolar planets were discovered with this method. Naturally, at the beginning the method was biased towards short periods planets, but with time one begins to detect planets more comparable to Jupiter in terms of period. It is also biased towards more massive planets which induce larger velocity shifts. In order to detect an Earth around a Sun, an accuracy of the order of few cm · s −1 would be required, still far beyond the present instrumental capabilities. Furthermore, since lots of photons are necessary to reach the needed accuracy, up to now only stars in the solar neighborhood are monitored. Last, the method has some limitations inherent to the star itself. For instance, photospheric activity related to spots at the stellar surface, chromospheric activity and seismic activity due to some stellar oscillations (e.g. [10, 11]), can very well mimic radial velocity variations. With the increasing instrumental precision, these very common stellar activities are becoming an important issue. Also, confusion cases can arise from stellar blends such as grazing binaries, small stellar companions or eclipsing binaries in a triple stellar system.
Three other factors need to also be taken into account. First, the position of the mass of the Moon with respect to the location where calibration measurements are taken, which represents a possible relative distance swing of up to 13000 km of the lunar mass due to the daily rotation of the Earth, in subtraction from the mass of the Earth when the Moon reaches the zenith relative to the measurement location and in addition as it reaches the relative nadir; second, the cyclic variation in the local gravity field intensity from the Sun as the Earth-Sun distance varies on a yearly basis (a cyclic swing of about 5 million km), and third, the distance in the process of decreasing between the Solar system and the centre of the galaxy due to the much longer cycle of the motion of the whole Solar system on its elliptical orbit about the centre of the galaxy.
Pipeline for economic development. Thus, African governments are resenting De Beers’ operations that prohibit African interests. However, the goals of African countries are still far-fetched. For example, with political and economical instability, the power of African governments single-handedly to manage and supply their diamond trade, without the support, knowledge or intelligence of a powerful player like De Beers is questionable. In addition, it is seen that while Angola produces many higher-grade stones, outside sales have been negligible due to lack of management experience and increased corruption in the country. Overall, even after loss of control over certain areas in Angola, which produces approximate of 9% of world production, De Beers remains a solid, dependable supplier of diamonds with regular client base and inexhaustible market knowledge and intelligence. 15 Nevertheless, by leaving much of the upside of the value to only the art of manufacturing and cutting the diamonds reduces the possibility of manufactures to complain, but has increased the possibility of mining countries to complain. De Beers should strongly consider in addressing this issue as, De Beers will be able to sustain its position only as long as the mining countries have confidence and stand at a gain in working with De Beers.