571 research outputs found
Secular evolution of a satellite by tidal effect. Application to Triton
Some of the satellites in the Solar System, including the Moon, appear to
have been captured from heliocentric orbits at some point in their past, and
then have evolved to the present configurations. The exact process of how this
trapping occurred is unknown, but the dissociation of a planetesimal binary in
the gravitational field of the planet, gas drag, or a massive collision seem to
be the best candidates. However, all these mechanisms leave the satellites in
elliptical orbits that need to be damped to the present almost circular ones.
Here we give a complete description of the secular tidal evolution of a
satellite just after entering a bounding state with the planet. In particular,
we take into account the spin evolution of the satellite, which has often been
assumed synchronous in previous studies. We apply our model to Triton and
successfully explain some geophysical properties of this satellite, as well as
the main dynamical features observed for the Neptunian system.Comment: 4 pages, 1 figur
Kinematics of Black Hole X-ray Binary GRS 1915+105
The space velocity of a stellar black hole encodes the history of its
formation and evolution. Here we measure the 3-dimensional motion of the
microquasar GRS 1915+105, using a decade of astrometry with the NRAO Very Long
Baseline Array, together with the published radial velocity. The velocity in
the Galactic Plane deviates from circular rotation by 53-80 +_ 8 km/s, where
the range covers any specific distance from 6-12 kpc. Perpendicular to the
plane, the velocity is only 10 +_ 4 km/s. The peculiar velocity is minimized at
a distance 9-10 kpc, and is then nearly in the radial direction towards the
Galactic Center. We discuss mechanisms for the origin of the peculiar velocity,
and conclude that it is most likely a consequence of Galactic velocity
diffusion on this old binary, rather than the result of a supernova kick during
the formation of the 14 Mo black hole. Finally, a brief comparison is made with
4 other BH binaries whose kinematics are well determined.Comment: 16 pages, 4 figures. ApJ accepte
Australian participation in the Gaia follow-up network for solar system objects
The Gaia satellite, planned for launch by the European Space Agency (ESA) in 2013, is the next-generation astrometry mission following Hipparcos. Gaia’s primary science goal is to determine the kinematics, chemical structure, and evolution of the Milky Way Galaxy. In addition to this core science goal, the Gaia space mission is expected to discover thousands of Solar System objects. Because of orbital constraints, Gaia will only have a limited opportunity for astrometric follow-up of these discoveries. In 2010, the Gaia Data Processing and Analysis Consortium (DPAC) initiated a program to identify ground-based optical telescopes for a Gaia follow-up network for Solar System Objects to perform the following critical tasks: confirmation of discovery, identification of body, object tracking to constrain orbits. To date, this network comprises 37 observing sites (representing 53 instruments). The Zadko Telescope, located in Western Australia, was highlighted as an important network node because of its southern location, longitude, and automated scheduling system. We describe the first follow-up tests using the fast moving Potentially Hazardous Asteroid 2005 YU55 as the target
Astrometric Effects of a Stochastic Gravitational Wave Background
A stochastic gravitational wave background causes the apparent positions of
distant sources to fluctuate, with angular deflections of order the
characteristic strain amplitude of the gravitational waves. These fluctuations
may be detectable with high precision astrometry, as first suggested by
Braginsky et al. in 1990. Several researchers have made order of magnitude
estimates of the upper limits obtainable on the gravitational wave spectrum
\Omega_gw(f), at frequencies of order f ~ 1 yr^-1, both for the future
space-based optical interferometry missions GAIA and SIM, and for VLBI
interferometry in radio wavelengths with the SKA. For GAIA, tracking N ~ 10^6
quasars over a time of T ~ 1 yr with an angular accuracy of \Delta \theta ~ 10
\mu as would yield a sensitivity level of \Omega_gw ~ (\Delta \theta)^2/(N T^2
H_0^2) ~ 10^-6, which would be comparable with pulsar timing. In this paper we
take a first step toward firming up these estimates by computing in detail the
statistical properties of the angular deflections caused by a stochastic
background. We compute analytically the two point correlation function of the
deflections on the sphere, and the spectrum as a function of frequency and
angular scale. The fluctuations are concentrated at low frequencies (for a
scale invariant stochastic background), and at large angular scales, starting
with the quadrupole. The magnetic-type and electric-type pieces of the
fluctuations have equal amounts of power.Comment: 23 pages, 2 figures, references added and minor text correction
Detectability of Weakly Interacting Massive Particles in the Sagittarius Dwarf Tidal Stream
Tidal streams of the Sagittarius dwarf spheroidal galaxy (Sgr) may be
showering dark matter onto the solar system and contributing approx (0.3--23)%
of the local density of our Galactic Halo. If the Sagittarius galaxy contains
WIMP dark matter, the extra contribution from the stream gives rise to a
step-like feature in the energy recoil spectrum in direct dark matter
detection. For our best estimate of stream velocity (300 km/sec) and direction
(the plane containing the Sgr dwarf and its debris), the count rate is maximum
on June 28 and minimum on December 27 (for most recoil energies), and the
location of the step oscillates yearly with a phase opposite to that of the
count rate. In the CDMS experiment, for 60 GeV WIMPs, the location of the step
oscillates between 35 and 42 keV, and for the most favorable stream density,
the stream should be detectable at the 11 sigma level in four years of data
with 10 keV energy bins. Planned large detectors like XENON, CryoArray and the
directional detector DRIFT may also be able to identify the Sgr stream.Comment: 26 pages, 4 figure
On the equilibrium rotation of Earth-like extra-solar planets
The equilibrium rotation of tidally evolved "Earth-like" extra-solar planets
is often assumed to be synchronous with their orbital mean motion. The same
assumption persisted for Mercury and Venus until radar observations revealed
their true spin rates. As many of these planets follow eccentric orbits and are
believed to host dense atmospheres, we expect the equilibrium rotation to
differ from the synchronous motion. Here we provide a general description of
the allowed final equilibrium rotation states of these planets, and apply this
to already discovered cases in which the mass is lower than twelve
Earth-masses. At low obliquity and moderate eccentricity, it is shown that
there are at most four distinct equilibrium possibilities, one of which can be
retrograde. Because most presently known "Earth-like" planets present eccentric
orbits, their equilibrium rotation is unlikely to be synchronous.Comment: 4 pages, 2 figures. accepted for publication in Astronomy and
Astrophysics. to be published in Astronomy and Astrophysic
Tidal friction in close-in satellites and exoplanets. The Darwin theory re-visited
This report is a review of Darwin's classical theory of bodily tides in which
we present the analytical expressions for the orbital and rotational evolution
of the bodies and for the energy dissipation rates due to their tidal
interaction. General formulas are given which do not depend on any assumption
linking the tidal lags to the frequencies of the corresponding tidal waves
(except that equal frequency harmonics are assumed to span equal lags).
Emphasis is given to the cases of companions having reached one of the two
possible final states: (1) the super-synchronous stationary rotation resulting
from the vanishing of the average tidal torque; (2) the capture into a 1:1
spin-orbit resonance (true synchronization). In these cases, the energy
dissipation is controlled by the tidal harmonic with period equal to the
orbital period (instead of the semi-diurnal tide) and the singularity due to
the vanishing of the geometric phase lag does not exist. It is also shown that
the true synchronization with non-zero eccentricity is only possible if an
extra torque exists opposite to the tidal torque. The theory is developed
assuming that this additional torque is produced by an equatorial permanent
asymmetry in the companion. The results are model-dependent and the theory is
developed only to the second degree in eccentricity and inclination
(obliquity). It can easily be extended to higher orders, but formal accuracy
will not be a real improvement as long as the physics of the processes leading
to tidal lags is not better known.Comment: 30 pages, 7 figures, corrected typo
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
Tidal torques. A critical review of some techniques
We point out that the MacDonald formula for body-tide torques is valid only
in the zeroth order of e/Q, while its time-average is valid in the first order.
So the formula cannot be used for analysis in higher orders of e/Q. This
necessitates corrections in the theory of tidal despinning and libration
damping.
We prove that when the inclination is low and phase lags are linear in
frequency, the Kaula series is equivalent to a corrected version of the
MacDonald method. The correction to MacDonald's approach would be to set the
phase lag of the integral bulge proportional to the instantaneous frequency.
The equivalence of descriptions gets violated by a nonlinear
frequency-dependence of the lag.
We explain that both the MacDonald- and Darwin-torque-based derivations of
the popular formula for the tidal despinning rate are limited to low
inclinations and to the phase lags being linear in frequency. The
Darwin-torque-based derivation, though, is general enough to accommodate both a
finite inclination and the actual rheology.
Although rheologies with Q scaling as the frequency to a positive power make
the torque diverge at a zero frequency, this reveals not the impossible nature
of the rheology, but a flaw in mathematics, i.e., a common misassumption that
damping merely provides lags to the terms of the Fourier series for the tidal
potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the
magnitudes of the terms, too, get changed. Reinstating of this detail tames the
infinities and rehabilitates the "impossible" scaling law (which happens to be
the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial
text overlap with arXiv:0712.105
The effect of the motion of the Sun on the light-time in interplanetary relativistic experiments
In 2002 a measurement of the effect of solar gravity upon the phase of
coherent microwave beams passing near the Sun has been carried out with the
Cassini mission, allowing a very accurate measurement of the PPN parameter
. The data have been analyzed with NASA's Orbit Determination Program
(ODP) in the Barycentric Celestial Reference System, in which the Sun moves
around the centre of mass of the solar system with a velocity of
about 10 m/sec; the question arises, what correction this implies for the
predicted phase shift. After a review of the way the ODP works, we set the
problem in the framework of Lorentz (and Galilean) transformations and evaluate
the correction; it is several orders of magnitude below our experimental
accuracy. We also discuss a recent paper \cite{kopeikin07}, which claims wrong
and much larger corrections, and clarify the reasons for the discrepancy.Comment: Final version accepted by Classical and Quantum Gravity (8 Jan. 2008
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