ABSTRACT It has been suggested that the comet-like activity of main belt comets (MBCs) is due to the sublimation of sub-surface water-ice that has been exposed as a result of their surfaces being ...impacted by meter-sized bodies. We have examined the viability of this scenario by simulating impacts between meter-sized and kilometer-sized objects using a smooth particle hydrodynamics approach. Simulations have been carried out for different values of the impact velocity and impact angle, as well as different target material and water-mass fractions. Results indicate that for the range of impact velocities corresponding to those in the asteroid belt, the depth of an impact crater is slightly larger than 10 m, suggesting that if the activation of MBCs is due to the sublimation of sub-surface water-ice, this ice has to exist no deeper than a few meters from the surface. Results also show that ice exposure occurs in the bottom and on the interior surface of impact craters, as well as on the surface of the target where some of the ejected icy inclusions are re-accreted. While our results demonstrate that the impact scenario is indeed a viable mechanism to expose ice and trigger the activity of MBCs, they also indicate that the activity of the current MBCs is likely due to ice sublimation from multiple impact sites and/or the water contents of these objects (and other asteroids in the outer asteroid belt) is larger than the 5% that is traditionally considered in models of terrestrial planet formation, providing more ice for sublimation. We present the details of our simulations and discuss their results and implications.
The purpose of this work was to study differences in apparent diffusion coefficient (ADC) values between benign and malignant head and neck lesions at 3T field strength imaging.
Our study population ...in this retrospective study was derived from the patient population who had undergone routine neck 3T MR imaging (for clinical indications) from December 2005 to December 2006. There were 33 patients identified: 17 with benign and 16 with malignant pathologies. In all of the subjects, conventional MR imaging sequences were performed apart from diffusion-weighted sequences. The mean ADC values in the benign and malignant groups were compared using an unpaired t test with unequal variance with a P < 0.05 considered statistically significant.
There was a statistically significant difference (P = .004) between the mean ADC values (in 10(-3) mm(2)/s) in the benign and malignant lesions (1.505 +/- 0.487; 95% confidence interval, 1.305-1.706, and 1.071 +/- 0.293; 95% confidence interval, 0.864-1.277, respectively). There were 2 malignant lesions with ADC values higher than 1.3 x 10(-3) mm(2)/s and 5 benign lesions with ADC values less than 1.3 x 10(-3) mm(2)/s. The lack of overlap of ADC values within 95% confidence limits suggests that a 3T ADC value of 1.3 x 10(-3) mm(2)/s may be the threshold value for differentiation between benign and malignant head and neck lesions.
ADC values of benign and malignant neck pathologies are significantly different at 3T imaging, though larger studies are required to establish threshold ADC values that can applied in daily clinical practice.
ABSTRACT
The presented work investigates the possible formation of terrestrial planets in the habitable zone (HZ) of the exoplanetary system HD 141399. In this system, the HZ is located approximately ...between the planets c (a = 0.7 au) and d (a = 2.1 au). Extensive numerical integrations of the equations of motion in the pure Newtonian framework of small bodies with different initial conditions in the HZ are performed. Our investigations included several steps starting with 500 massless bodies distributed between planets c and d in order to model the development of the disc of small bodies. It turns out that after some 106 yr, a belt-like structure analogue to the main belt inside Jupiter in our Solar system appears. We then proceed with giving the small bodies masses (∼ Moon mass) and take into account the gravitational interaction between these planetesimal-like objects. The growing of the objects – with certain percentage of water – due to collisions is computed in order to look for the formation of terrestrial planets. We observe that planets form in regions connected to mean motion resonances (MMR). So far there is no observational evidence of terrestrial planets in the system of HD 141399 but from our results we can conclude that the formation of terrestrial planets – even with an appropriate amount of water necessary for being habitable – in the HZ would have been possible.
The first Earth Trojan has been observed and found to be on an interesting orbit close to the Lagrange point L4. In the present study, we therefore perform a detailed investigation of the stability ...of its orbit and moreover extend the study to give an idea of the probability of finding additional Earth Trojans. Our results are derived using three different approaches. In the first, we derive an analytical mapping in the spatial elliptic restricted three-body problem to find the phase space structure of the dynamical problem. We then explore the stability of the asteroid in the context of the phase space geometry, including the indirect influence of the additional planets of our Solar system. In the second approach, we use precise numerical methods to integrate the orbit forward and backward in time in different dynamical models. On the basis of a set of 400 clone orbits, we derive the probability of capture and escape of the Earth Trojan asteroid 2010 TK7. To this end, in the third approach we perform an extensive numerical investigation of the stability region of the Earth’s Lagrangian points. We present a detailed parameter study of possible stable tadpole and horseshoe orbits of additional Earth Trojans, i.e. with respect to the semi-major axes and inclinations of thousands of fictitious Trojans. All three approaches lead to the conclusion that the Earth Trojan asteroid 2010 TK7 finds itself in an unstable region on the edge of a stable zone; additional Earth Trojan asteroids may be found in this regime of stability.
We report on an intensive observational campaign carried out with HARPS at the 3.6 m telescope at La Silla on the star CoRoT-7. Additional simultaneous photometric measurements carried out with the ...Euler Swiss telescope have demonstrated that the observed radial velocity variations are dominated by rotational modulation from cool spots on the stellar surface. Several approaches were used to extract the radial velocity signal of the planet(s) from the stellar activity signal. First, a simple pre-whitening procedure was employed to find and subsequently remove periodic signals from the complex frequency structure of the radial velocity data. The dominant frequency in the power spectrum was found at 23 days, which corresponds to the rotation period of CoRoT-7. The 0.8535 day period of CoRoT-7b planetary candidate was detected with an amplitude of 3.3 m s-1. Most other frequencies, some with amplitudes larger than the CoRoT-7b signal, are most likely associated with activity. A second approach used harmonic decomposition of the rotational period and up to the first three harmonics to filter out the activity signal from radial velocity variations caused by orbiting planets. After correcting the radial velocity data for activity, two periodic signals are detected: the CoRoT-7b transit period and a second one with a period of 3.69 days and an amplitude of 4 m s-1. This second signal was also found in the pre-whitening analysis. We attribute the second signal to a second, more remote planet CoRoT-7c . The orbital solution of both planets is compatible with circular orbits. The mass of CoRoT-7b is $4.8\pm0.8$ ($M_{\oplus}$) and that of CoRoT-7c is $8.4\pm 0.9$ ($M_{\oplus}$), assuming both planets are on coplanar orbits. We also investigated the false positive scenario of a blend by a faint stellar binary, and this may be rejected by the stability of the bisector on a nightly scale. According to their masses both planets belong to the super-Earth planet category. The average density of CoRoT-7b is $\rho=5.6\pm 1.3\mathrm{\,g\,cm^{-3}}$, similar to the Earth. The CoRoT-7 planetary system provides us with the first insight into the physical nature of short period super-Earth planets recently detected by radial velocity surveys. These planets may be denser than Neptune and therefore likely made of rocks like the Earth, or a mix of water ice and rocks.
We announce the discovery of a planetary system with seven transiting planets around a Kepler target, a current record for transiting systems. Planets b, c, e, and f are reported for the first time ...in this work. Planets d, g, and h were previously reported in the literature, although here we revise their orbital parameters and validate their planetary nature. Planets h and g are gas giants and show strong dynamical interactions. The orbit of planet g is perturbed in such a way that its orbital period changes by 25.7 hr between two consecutive transits during the length of the observations, which is the largest such perturbation found so far. The rest of the planets also show mutual interactions: planets d, e, and f are super-Earths close to a mean motion resonance chain (2:3:4), and planets b and c, with sizes below 2 Earth radii, are within 0.5% of the 4:5 mean motion resonance. This complex system presents some similarities to our solar system, with small planets in inner orbits and gas giants in outer orbits. It is, however, more compact. The outer planet has an orbital distance around 1 AU, and the relative position of the gas giants is opposite to that of Jupiter and Saturn, which is closer to the expected result of planet formation theories. The dynamical interactions between planets are also much richer.
The increasing number of free-floating planets discovered in recent years confirms earlier theoretical predictions and leads us to believe that the possibility of such an object intruding an existing ...planetary system is not negligible, especially in dense clusters. We present a theoretical dynamical study on the interaction of a free-floating planet (hereafter
FFP
) with an initially bound star–planet pair consisting of a Jupiter-sized planet (hereafter
BP
) orbiting a Sun-like star.
Our results could serve as a base for analytical, or semi-analytical, studies on the three-dimensional three-body scattering problem
. In our three-dimensional models, thousands of different trajectories for an incoming FFP with initially parabolic velocity are integrated, in order to investigate the interaction between the objects. The study is based on two independent approaches, in order to corroborate the significance of the results. In the first approach, the FFP interacts with a Solar-like system (hereafter
SlS
) consisting of the Sun and Jupiter at
5.2
AU
. In the second, we compute the trajectories of a FFP interacting with a closely bound exoplanetary system (hereafter
ES
) with the Jupiter-sized planet at an orbit of
1
AU
around its host, Sun-like star. For both approaches, the simulations have five free parameters, namely the initial phase of the BP,
ϕ
BP
, the mass,
m
FFP
, the initial inclination,
i
FFP
, the orientation of the velocity vector of the FFP and the impact parameter
d
FFP
=
d
. We focus on three possible final states, namely “flyby,” “capture” and “exchange.” One can observe that the overall picture does not change between the two models used. We present a statistical analysis of the data and the probabilities for the different outcomes for both. Capture and flyby are dominant, in almost equal parts, while the probability for an exchange is rather low. A close look of the orbital elements in case of a capture of the FFP provides more information on the dynamical behavior of the two models, allowing us to draw more precise conclusions, when it comes to the similarities and differences between them. Different mass, as well as different orientation of the velocity vector of the incoming planet, does affect the final outcome quantitatively and qualitatively, in both cases.
The problem of analytical determination of the stability domain around the points L4 or L5 of the Lagrangian equilateral configuration of the three-body problem has served in the literature as a ...basic celestial mechanical model probing the predictive power of the so-called Nekhoroshev theory of exponential stability in non-linear Hamiltonian dynamical systems. All analytical investigations in this framework have so far been based on the circular restricted three-body problem (CRTBP). In this work, we extend the analytical estimates of Nekhoroshev stability in the case of the planar elliptic-restricted three-body problem (ERTBP). To this end, we introduce an explicit symplectic mapping model for the planar ERTBP, obtained via Hadjidemetriou's method, which generalizes the family of mappings discussed in earlier papers. The mapping is based on an expansion of the disturbing function up to a sufficiently high order in the eccentricities and the variations of the semimajor axis, and it is given as a series around a period-one fixed point of the system. Within the domain of the mapping's convergence, we then compute a Birkhoff normal form for 4D symplectic mappings as well as the associated approximate integrals of motion which can be expressed in terms of proper elements. The variations of the integrals predicted by the remainder of the normal form series provide a lower bound for the domain of Nekhoroshev stability for a time at least equal to the age of the Solar System. In the case of Jupiter's Trojans, the domain of the mapping's convergence lies entirely within the region of librational motion, in which the longitude of the perihelion of the asteroid librates around a fixed point value of ϖ. For most asteroids outside this domain macroscopic chaotic diffusion cannot be ruled out. The present analysis provides a physically relevant estimate of the domain of Nekhoroshev stability for proper librations (Dp < 100), and marginal for proper eccentricities (ep < 0.01). The formalism is developed in a general way allowing for applications in both, our Solar System and extrasolar system dynamics.
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