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

Gaia Focused Product Release:Asteroid orbital solution. Properties and assessment

Context. We report the exploitation of a sample of Solar System observations based on data from the third Gaia Data Release (Gaia DR3) of nearly 157 000 asteroids. It extends the epoch astrometric solution over the time coverage planned for the Gaia DR4, which is not expected before the end of 2025. This data set covers more than one full orbital period for the vast majority of these asteroids. The orbital solutions are derived from the Gaia data alone over a relatively short arc compared to the observation history of many of these asteroids.Aims. The work aims to produce orbital elements for a large set of asteroids based on 66 months of accurate astrometry provided by Gaia and to assess the accuracy of these orbital solutions with a comparison to the best available orbits derived from independent observations. A second validation is performed with accurate occultation timings.Methods. We processed the raw astrometric measurements of Gaia to obtain astrometric positions of moving objects with 1D sub-mas accuracy at the bright end. For each asteroid that we matched to the data, an orbit fitting was attempted in the form of the best fit of the initial conditions at the median epoch. The force model included Newtonian and relativistic accelerations to derive the observation equations, which were solved with a linear least-squares fit.Results. Orbits are provided in the form of state vectors in the International Celestial Reference Frame for 156 764 asteroids, including near-Earth objects, main-belt asteroids, and Trojans. For the asteroids with the best observations, the (formal) relative uncertainty σa/a is better than 10−10. Results are compared to orbits available from the Jet Propulsion Laboratory and MPC. Their orbits are based on much longer data arcs, but from positions of lower quality. The relative differences in semi-major axes have a mean of 5 × 10−10 and a scatter of 5 × 10−9

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

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

WIMP Annual Modulation with Opposite Phase in Late-Infall Halo Models

We show that in the late-infall model of our galactic halo by P. Sikivie the expected phase of the annual modulation of a WIMP halo signal in direct detection experiments is opposite to the one usually expected. If a non-virialized halo component due to the infall of (collisionless) dark matter particles cannot be rejected, an annual modulation in a dark matter signal should be looked for by experimenters without fixing the phase a-priori. Moreover, WIMP streams coming to Earth from directions above and below the galactic plane should be expected, with a characteristic pattern of arrival directions.Comment: 15 pages, 5 figure

Prognostic factors for tumour response, progression-free survival and toxicity in metastatic colorectal cancer patients given irinotecan (CPT-11) as second-line chemotherapy after 5FU failure

Our purpose was to determine, in patients with metastatic colorectal carcinoma treated with irinotecan single-agent after 5-FU failure, the most significant predictive parameters for tumour response, progression-free survival and toxicity. Between October 1992 and April 1995, 455 patients with 5-FU resistant metastatic colorectal carcinoma entered four consecutive phase II trials. The first two studies assessed tumour response, the other two were randomized studies which assessed the efficacy of racecadotril to prevent irinotecan-induced diarrhoea. Due to homogeneous main eligibility criterias, data from those studies could be pooled for statistical analysis. Potential clinical and biological predictive factors (PF) for toxicity, tumour growth control, e.g. response or stabilization and progression-free survival (PFS), were studied in multivariate analysis. 363 patients were evaluable for response, 432 were evaluable for PFS, 368 for neutropenia and 416 for delayed diarrhoea, respectively. Normal baseline haemoglobin level (Hb), time since diagnosis of colorectal carcinoma, grade 3 or 4 neutropenia or diarrhoea at first cycle and a low number of organs involved were the most PF for tumour growth control (P< 0.05). Significant prognostic variables for PFS were WHO Performance Status, liver and lymph-node involvement, time since diagnosis, age and CEA value (P≤ 0.02). Six groups of patients based on the number of unfavourable prognostic factors are presented. Baseline bilirubin, haemoglobin level, number of organs involved and time from diagnosis were PF for neutropenia; PS, serum creatinine, leukocyte count, time from 5-FU progression and prior abdominopelvic irradiation were PF for delayed diarrhoea (P≤ 0.05). These PF should help clinicians to anticipate for a given patient the probability to observe a response/stabilization or a toxicity. These results should also be prospectively confirmed in ongoing or future trials using irinotecan, both as a single agent and in combination with other drugs. © 2000 Cancer Research Campaig

The first accurate parallax distance to a black hole

Using astrometric VLBI observations, we have determined the parallax of the black hole X-ray binary V404 Cyg to be 0.418 +/- 0.024 milliarcseconds, corresponding to a distance of 2.39 +/- 0.14 kpc, significantly lower than the previously accepted value. This model-independent estimate is the most accurate distance to a Galactic stellar-mass black hole measured to date. With this new distance, we confirm that the source was not super-Eddington during its 1989 outburst. The fitted distance and proper motion imply that the black hole in this system likely formed in a supernova, with the peculiar velocity being consistent with a recoil (Blaauw) kick. The size of the quiescent jets inferred to exist in this system is less than 1.4 AU at 22 GHz. Astrometric observations of a larger sample of such systems would provide useful insights into the formation and properties of accreting stellar-mass black holes.Comment: Accepted for publication in ApJ Letters. 6 pages, 2 figure

Tidal evolution of exo-planetary systems: WASP-50, GJ 1214 and CoRoT-7

We perform numerical simulations to investigate tidal evolution of two single-planet systems, that is, WASP-50 and GJ 1214 and a two-planet system CoRoT-7. The results of orbital evolution show that tidal decay and circularization may play a significant role in shaping their final orbits, which is related to the initial orbital data in the simulations. For GJ 1214 system, different cases of initial eccentricity are also considered as only an upper limit of its eccentricity (0.27) is shown, and the outcome suggests a possible maximum initial eccentricity (0.4) in the adopted dynamical model. Moreover, additional runs with alternative values of dissipation factor $Q^\prime_1$ are carried out to explore tidal evolution for GJ 1214b, and these results further indicate that the real $Q^\prime_1$ of GJ 1214b may be much larger than its typical value, which may reasonably suggest that GJ 1214b bears a present-day larger eccentricity, undergoing tidal circularization at a slow rate. For the CoRoT-7 system, tidal forces make two planets migrating towards their host star as well as producing tidal circularization, and in this process tidal effects and mutual gravitational interactions are coupled with each other. Various scenarios of the initial eccentricity of the outer planet have also been done to investigate final planetary configuration. Tidal decay arising from stellar tides may still work for each system as the eccentricity decreases to zero, and this is in association with the remaining lifetime of each planet used to predict its future.Comment: 9 pages, 12 figures, accepted for publication in "SCIENCE CHINA Physics,Mechanics & Astronomy

Global and Local Three-dimensional Studies of The Residual Vector Field from 2MASS and Hipparcos-2 Catalog

[EN] The Gaia mission will provide a six-parameter solution for millions of stars, including a tridimensional map of our Galaxy. The estimation of distances has been made for the Tycho-Gaia Astrometric Solution (TGAS), while to contrast the proper motions it is interesting to consider positions from the different Gaia Data Release with older ones given in ground-based massive catalogs. This process has been followed to build, for example, the PMA catalog using the 2MASS. Our aim is to improve the positions of this catalog (although the process is applicable to any other). The first stage, presented here, consists of carrying out a three-dimensional study using vector spherical harmonics (VSH) development of the systematisms in position for the stars common with Hipparcos-2; we take into account the distances, magnitudes, and spectral types. To this aim, we use linear polynomial regression of first order that fits vector fields and the derivatives of their components. We verify that the coefficients of the developments of first order have different behavior according to the characteristics of stars and distances. To deepen the study, we focus on the conservative component of the field, applying the Helmholtz theorem. Each potential function is obtained solving a Poisson equation on the sphere, after finding the divergence of the corresponding vector field. Both vector and potential fields present patterns, at certain points, that depend on the three considered parameters (distance, magnitude, and spectral type); their sources and shrinks correspond to maxima and minima. In this sense, we observe that these critical points are also critical points of the surface that represents the VT magnitude of Tycho-2, which makes sense because this catalog was used in the reduction of 2MASS positions. Finally, we selected some stars near the critical points of the vector fields and apply the adjustments obtained in the previous sections. 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PEXO : a global modeling framework for nanosecond timing, microsecond astrometry, and μm/s radial velocities

54 pages, 2 tables, 19 figures, accepted for publication in ApJS, PEXO is available at https://github.com/phillippro/pexoThe ability to make independent detections of the signatures of exoplanets with complementary telescopes and instruments brings a new potential for robust identification of exoplanets and precision characterization. We introduce PEXO, a package for Precise EXOplanetology to facilitate the efficient modeling of timing, astrometry, and radial velocity data, which will benefit not only exoplanet science but also various astrophysical studies in general. PEXO is general enough to account for binary motion and stellar reflex motions induced by planetary companions and is precise enough to treat various relativistic effects both in the solar system and in the target system. We also model the post-Newtonian barycentric motion for future tests of general relativity in extrasolar systems. We benchmark PEXO with the pulsar timing package TEMPO2 and find that PEXO produces numerically similar results with timing precision of about 1 ns, space-based astrometry to a precision of 1{\mu}as, and radial velocity of 1 {\mu}m/s and improves on TEMPO2 for decade-long timing data of nearby targets, due to its consideration of third-order terms of Roemer delay. PEXO is able to avoid the bias introduced by decoupling the target system and the solar system and to account for the atmospheric effects which set a practical limit for ground-based radial velocities close to 1 cm/s. Considering the various caveats in barycentric correction and ancillary data required to realize cm/s modeling, we recommend the preservation of original observational data. The PEXO modeling package is available at GitHub (https://github.com/phillippro/pexo).Peer reviewe