4,369 research outputs found
Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions
In recent years several pairs of extrasolar planets have been discovered in
the vicinity of mean-motion commensurabilities. In some cases, such as the
Gliese 876 system, the planets seem to be trapped in a stationary solution, the
system exhibiting a simultaneous libration of the resonant angle theta_1 = 2
lambda_2 - lambda_1 - varpi_1 and of the relative position of the pericenters.
In this paper we analyze the existence and location of these stable
solutions, for the 2/1 and 3/1 resonances, as function of the masses and
orbital elements of both planets. This is undertaken via an analytical model
for the resonant Hamiltonian function. The results are compared with those of
numerical simulations of the exact equations.
In the 2/1 commensurability, we show the existence of three principal
families of stationary solutions: (i) aligned orbits, in which theta_1 and
varpi_1 - varpi_2 both librate around zero, (ii) anti-aligned orbits, in which
theta_1=0 and the difference in pericenter is 180 degrees, and (iii) asymmetric
stationary solutions, where both the resonant angle and varpi_1 - varpi_2 are
constants with values different of 0 or 180 degrees. Each family exists in a
different domain of values of the mass ratio and eccentricities of both
planets. Similar results are also found in the 3/1 resonance.
We discuss the application of these results to the extrasolar planetary
systems and develop a chart of possible planetary orbits with apsidal
corotation. We estimate, also, the maximum planetary masses in order that the
stationary solutions are dynamically stable.Comment: 25 pages, 10 figures. Submitted to Ap
On planetary mass determination in the case of super-Earths orbiting active stars. The case of the CoRoT-7 system
This investigation uses the excellent HARPS radial velocity measurements of
CoRoT-7 to re-determine the planet masses and to explore techniques able to
determine mass and elements of planets discovered around active stars when the
relative variation of the radial velocity due to the star activity cannot be
considered as just noise and can exceed the variation due to the planets. The
main technique used here is a self-consistent version of the high-pass filter
used by Queloz et al. (2009) in the first mass determination of CoRoT-7b and
CoRoT-7c. The results are compared to those given by two alternative
techniques: (1) The approach proposed by Hatzes et al. (2010) using only those
nights in which 2 or 3 observations were done; (2) A pure Fourier analysis. In
all cases, the eccentricities are taken equal to zero as indicated by the study
of the tidal evolution of the system; the periods are also kept fixed at the
values given by Queloz et al. Only the observations done in the time interval
BJD 2,454,847 - 873 are used because they include many nights with multiple
observations; otherwise it is not possible to separate the effects of the
rotation fourth harmonic (5.91d = Prot/4) from the alias of the orbital period
of CoRoT-7b (0.853585 d). The results of the various approaches are combined to
give for the planet masses the values 8.0 \pm 1.2 MEarth for CoRoT-7b and 13.6
\pm 1.4 MEarth for CoRoT 7c. An estimation of the variation of the radial
velocity of the star due to its activity is also given.The results obtained
with 3 different approaches agree to give masses larger than those in previous
determinations. From the existing internal structure models they indicate that
CoRoT-7b is a much denser super-Earth. The bulk density is 11 \pm 3.5 g.cm-3 .
CoRoT-7b may be rocky with a large iron core.Comment: 12 pages, 11 figure
Dynamics of two planets in co-orbital motion
We study the stability regions and families of periodic orbits of two planets
locked in a co-orbital configuration. We consider different ratios of planetary
masses and orbital eccentricities, also we assume that both planets share the
same orbital plane. Initially we perform numerical simulations over a grid of
osculating initial conditions to map the regions of stable/chaotic motion and
identify equilibrium solutions. These results are later analyzed in more detail
using a semi-analytical model. Apart from the well known quasi-satellite (QS)
orbits and the classical equilibrium Lagrangian points L4 and L5, we also find
a new regime of asymmetric periodic solutions. For low eccentricities these are
located at , where \sigma is
the difference in mean longitudes and \Delta\omega is the difference in
longitudes of pericenter. The position of these Anti-Lagrangian solutions
changes with the mass ratio and the orbital eccentricities, and are found for
eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation
to one of the planets, and analyzed its effect on an initially asymmetric
periodic orbit. We found that the resonant solution is preserved as long as the
mass variation is adiabatic, with practically no change in the equilibrium
values of the angles.Comment: 9 pages, 11 figure
Evolution of Migrating Planet Pairs in Resonance
In this paper we present numerical simulations of the evolution of planets or massive satellites captured in the 2/1 and 3/1 resonances, under the action of an anti-dissipative tidal force. The evolution of resonant trapped bodies show a richness of solutions: librations around stationary symmetric solutions with aligned periapses (w1-w2=0) or anti-aligned periapses (w1-w2=180 deg), and librations around stationary solutions in which the periapses configuration is fixed, but with w1-w2 taking values in a wide range of angles. Many of these solutions exist for large values of the eccentricities and, during the semimajor axis drift, the solutions show turnabouts from one configuration to another. These results are valid for other non-conservative forces leading to adiabatic covergent migration and capture into one of these resonances
Management of Montados and Dehesas for High Nature Value: an interdisciplinary pathway
Mediterranean oak woodlands, Montados in Portugal and Dehesas in Spain have long been acknowledged as potential land use systems of high nature and social value providing relevant ecosystem services and biodiversity conservation. Nevertheless, these systems are now under severe threat, both due to abandonment in certain areas and overuse in others, extremes that may be limited by appropriate management practices and strategies. The High Nature Value concept can be a pathway for the understanding and assessment of management practices best adapted to the balance of the Montado and Dehesa, and also to the assessment of the thresholds of change, so that the long term sustainability of the Montado systems is preserved. This special issue aims to contribute for the understanding of how the Montado and Dehesa classification as High Nature Value may be a path for sustainable management. This classification can be achieved by different ways and implies different components of the Montado, and thus the first four papers of this special issue address different approaches and methodologies for the identification of HNV Dehesas and Montados, the following seven papers deal mostly with the effect of management practices on biodiversity and other Dehesas and Montados values and finally the last two papers address the causes for Montado decline and suggest mitigation measures for that decline
Doped carrier formulation of the t-J model: the projection constraint and the effective Kondo-Heisenberg lattice representation
We show that the recently proposed doped carrier Hamiltonian formulation of
the t-J model should be complemented with the constraint that projects out the
unphysical states. With this new important ingredient, the previously used and
seemingly different spin-fermion representations of the t-J model are shown to
be gauge related to each other. This new constraint can be treated in a
controlled way close to half-filling suggesting that the doped carrier
representation provides an appropriate theoretical framework to address the t-J
model in this region. This constraint also suggests that the t-J model can be
mapped onto a Kondo-Heisenberg lattice model. Such a mapping highlights
important physical similarities between the quasi two-dimensional heavy
fermions and the high-T superconductors. Finally we discuss the physical
implications of our model representation relating in particular the small
versus large Fermi surface crossover to the closure of the lattice spin gap.Comment: corrected and enlarged versio
Planetary Migration and Extrasolar Planets in the 2/1 Mean-Motion Resonance
We analyze the possible relationship between the current orbital elements
fits of known exoplanets in the 2/1 mean-motion resonance and the expected
orbital configuration due to migration. It is found that, as long as the
orbital decay was sufficiently slow to be approximated by an adiabatic process,
all captured planets should be in apsidal corotations. In other words, they
should show a simultaneous libration of both the resonant angle and the
difference in longitudes of pericenter.
We present a complete set of corotational solutions for the 2/1
commensurability, including previously known solutions and new results.
Comparisons with observed exoplanets show that current orbital fits of three
known planetary systems in this resonance are either consistent with apsidal
corotations (GJ876 and HD82943) or correspond to bodies with uncertain orbits
(HD160691).
Finally, we discuss the applicability of these results as a test for the
planetary migration hypothesis itself. If all future systems in this
commensurability are found to be consistent with corotational solutions, then
resonance capture of these bodies through planetary migration is a working
hypothesis. Conversely, If any planetary pair is found in a different
configuration, then either migration did not occur for those bodies, or it took
a different form than currently believed.Comment: Submitted to MNRA
A new analysis of the GJ581 extrasolar planetary system
We have done a new analysis of the available observations for the GJ581
exoplanetary system. Today this system is controversial due to choices that can
be done in the orbital determination. The main ones are the ocurrence of
aliases and the additional bodies - the planets f and g - announced in Vogt et
al. 2010. Any dynamical study of exoplanets requires the good knowledge of the
orbital elements and the investigations involving the planet g are particularly
interesting, since this body would lie in the Habitable Zone (HZ) of the star
GJ581. This region,for this system, is very attractive of the dynamical point
of view due to several resonances of two and three bodies present there. In
this work, we investigate the conditions under which the planet g may exist. We
stress the fact that the planet g is intimately related with the orbital
elements of the planet d; more precisely, we conclude that it is not possible
to disconnect its existence from the determination of the eccentricity of the
planet d. Concerning the planet f, we have found one solution with period
days, but we are judicious about any affirmation concernig this
body because its signal is in the threshold of detection and the high period is
in a spectral region where the ocorruence of aliases is very common. Besides,
we outline some dynamical features of the habitable zone with the dynamical map
and point out the role played by some resonances laying there.Comment: 12 pages, 9 figure
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