arXiv subjects

Valeri V. Makarov

Publications and source records attributed to Valeri V. Makarov.

72 records · Page 4Linked to original sources

arXiv2015

Forced libration of tidally synchronized planets and moons

Tidal dissipation of kinetic energy, when it is strong enough, tends to synchronize the rotation of planets and moons with the mean orbital motion, or drive it into long-term stable spin-orbit resonances. As the orbital motion undergoes periodic acceleration due to a finite orbital eccentricity, the spin rate oscillates around the equilibrium mean value too, giving rise to the forced, or eccentricity-driven, librations. Both the shape and amplitude of forced librations of synchronous viscoelastic planets and moons are defined by a combination of two different types of perturbative torque, the tidal torque and the triaxial torque. Consequently, forced librations can be tidally dominated (e.g., Io and possibly Titan) or deformation-dominated (e.g., the Moon) depending on a set of orbital, rheological, and other physical parameters. With small eccentricities, for the former kind, the largest term in the libration angle can be minus cosine of the mean anomaly, whereas for the latter kind, it is minus sine of the mean anomaly. The shape and the amplitude of tidal forced librations determine the rate of orbital evolution of synchronous planets and moons, i.e., the rate of dissipative damping of semimajor axis and eccentricity. The known super-Earth exoplanets can exhibit both kinds of libration, or a mixture thereof, depending on, for example, the effective Maxwell time of their rigid mantles. Our approach can be extended to estimate the amplitudes of other libration harmonics, as well as the forced libration in non-synchronous spin-orbit resonances.

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arXiv2015

UrHip Proper Motion Catalog

Proper motions are computed and collected in a catalog using the Hipparcos positions (epoch 1991.25) and URAT1 positions (epoch 2012.3 to 2014.6). The goal is to obtain a significant improvement on the proper motion accuracy of single stars in the northern hemisphere, and to identify new astrometric binaries perturbed by orbital motion. For binaries and multiple systems, the longer baseline of Tycho2 (~ 100 yr) makes it more reliable despite its larger formal uncertainties. The resulting proper motions obtained for 67,340 stars have a consequent gain in accuracy by a factor of ~ 3 compared to Hipparcos. Comparison between UrHip and Hipparcos shows that they are reasonably close, but also reveals stars with large discrepant proper motions, a fraction of which are potential binary candidates.

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arXiv2015

Equilibrium rotation of semiliquid exoplanets and satellites

A wide range of exoplanet and exomoon models are characterized by a finite average rigidity and a viscosity much lower than the typical values for terrestrials. Such semiliquid bodies may or may not have rigid crusts with permanent figures. Unlike planets with solid mantles and Earth-like rheology, semiliquid bodies can be captured into stable pseudosynchronous spin resonance, where the average rate of rotation is higher than the synchronous 1:1 resonance. Two basic conditions are derived for capture of planets with a triaxial figure into pseudosynchronous rotation, one related to the characteristic tidal wave number (the product of the tidal frequency by the Maxwell time), and the other to the orbital eccentricity. If a semiliquid object does not satisfy either of the two conditions, it is captured into the synchronous resonance. For nearly axially symmetric bodies, only the first condition is in place, and the other is much relaxed, so they should predominantly be pseudosynchronous. It is also pointed out that the equilibrium pseudosychronous rotation rate can not reach the widely used asymptotic value from the constant time lag model but is in reality closer to the synchronous spin.

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arXiv2014

Radial velocities and binarity of southern SIM grid stars

We present analysis of precision radial velocities (RV) of 1134 mostly red giant stars in the southern sky, selected as candidate astrometric grid objects for the Space Interferometry Mission (SIM). Only a few (typically, 2 or 3) spectroscopic observations per star have been collected, with the main goal of screening binary systems. The estimated rate of spectroscopic binarity in this sample of red giants is 32% at the 0.95 confidence level, and 46% at the 0.75 confidence. The true binarity rate is likely to be higher, because our method is not quite sensitive to very wide binaries and low-mass companions. The estimated lower and upper bounds of stellar RV jitter for the entire sample are 24 and 51 m/s, respectively; the adopted mean value is 37 m/s. A few objects of interest are identified with large variations of radial velocities, implying abnormally high mass ratios.

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arXiv2014

Tidal dissipation in a homogeneous spherical body. II. Three examples: Mercury, Io, and Kepler-10 b

In Efroimsky & Makarov (2014), we derived from the first principles a formula for the tidal heating rate in a tidally perturbed homogeneous sphere. We compared it with the formulae used in the literature, and pointed out the differences. Using this result, we now present three case studies - Mercury, Kepler-10b, and a triaxial Io. A very sharp frequency-dependence of k2/Q near spin-orbit resonances yields a similarly sharp dependence of k2/Q on the spin rate. This indicates that physical libration may play a major role in tidal heating of synchronously rotating bodies. The magnitude of libration in the spin rate being defined by the planet's triaxiality, the latter should be a factor determining the dissipation rate. Other parameters equal, a synchronously rotating body with a stronger triaxiality should generate more heat than a similar body of a more symmetrical shape. Further in the paper, we discuss scenarios where initially triaxial objects melt and lose their triaxiality. Thereafter, dissipation in them becomes less intensive; so the bodies freeze. The tidal bulge becomes a new permanent figure, with a new triaxiality lower than the original. In the paper, we also derive simplified, approximate expressions for dissipation rate in a rocky planet of the Maxwell rheology, with a not too small Maxwell time. The three expressions derived pertain to the cases of a synchronous spin, a 3:2 resonance, and a nonresonant rotation; so they can be applied to most close-in super-Earth exoplanets detected thus far. In such bodies, the rate of tidal heating outside of synchronous rotation is weakly dependent on the eccentricity and obliquity, provided both these parameters are small or moderate. According to our calculation, Kepler-10b could hardly survive the great amount of tidal heating without being synchronised, circularised and also reshaped through a complete or partial melt-down.

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arXiv2013

Dynamical evolution and spin-orbit resonances of potentially habitable exoplanets. The case of GJ 667C

We investigate the dynamical evolution of the potentially habitable super-earth GJ 667Cc in the multiple system of at least two exoplanets orbiting a nearby M dwarf, paying special attention to its spin-orbital state. The published radial velocities for this star are re-analyzed and evidence is found for additional periodic signals, which could be taken for two additional planets on eccentric orbits. Such systems are not dynamically viable and break up quickly in numerical integrations. Limiting the scope to the two originally detected planets, we assess the dynamical stability of the system and find no evidence for bounded chaos in the orbital motion. The orbital eccentricity of the planets b and c is found to change cyclicly in the range 0.06 - 0.28 and 0.05 - 0.25, respectively, with a period of approximately 0.46 yr. Taking the eccentricity variation into account, numerical integrations are performed of the differential equations modeling the spin-orbit interaction of the planet GJ 667Cc with its host star assuming a terrestrial composition of its mantle. Depending on the interior temperature of the planet, it is likely to be entrapped in the 3:2 (probability 0.51) or even higher spin-orbit resonance. It is less likely to reach the 1:1 resonance (probability 0.24). The estimated characteristic spin-down times are quite short for the two planets, i.e., within 1 Myr for planet c and even shorter for planet b. Both planet arrived at their current and, most likely, ultimate spin-orbit states a long time ago. The rate of tidal dissipation of energy is formidably high in the planets of GJ 667, estimated at $10^{23.7}$ and $10^{26.7}$ J yr$^{-1}$ for c and b, respectively. This raises a question of how such relatively massive, close super-Earths could survive overheating and destruction.

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arXiv2013

Why is the Moon synchronously rotating?

If the Moon's spin evolved from faster prograde rates, it could have been captured into a higher spin-orbit resonance than the current 1:1 resonance. At the current value of orbital eccentricity, the probability of capture into the 3:2 resonance is as high as 0.6, but it strongly depends on the temperature and average viscosity of the Moon's interior. A warmer, less viscous Moon on a higher-eccentricity orbit is even more easily captured into supersynchronous resonances. We discuss two likely scenarios for the present spin-orbit state: a cold Moon on a low-eccentricity orbit and a retrograde initial rotation.

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arXiv2013

Dynamical evolution and spin-orbit resonances of potentially habitable exoplanets. The case of GJ 581d

GJ 581d is a potentially habitable super-Earth in the multiple system of exoplanets orbiting a nearby M dwarf. We investigate this planet's long-term dynamics, with an emphasis on its probable final rotation states acquired via tidal interaction with the host. The published radial velocities for the star are re-analysed with a benchmark planet detection algorithm, to confirm that there is no evidence for the recently proposed two additional planets (f and g). Limiting the scope to the four originally detected planets, we assess the dynamical stability of the system and find bounded chaos in the orbital motion. For the planet d, the characteristic Lyapunov time is 38 yr. Long-term numerical integration reveals that the system of four planets is stable, with the eccentricity of the planet d changing quasi-periodically in a tight range around 0.27, and with its semimajor axis varying only a little. The spin-orbit interaction of GJ 581d with its host star is dominated by the tides exerted by the star on the planet. We model this interaction, assuming a terrestrial composition of the mantle. Besides the customarily included secular parts of the triaxiality-caused and tidal torques, we also include these torques' oscillating components. It turns out that, dependent on the mantle temperature, the planet gets trapped into the 2:1 or an even higher spin-orbit resonance. It is very improbable that the planet could have reached the 1:1 resonance. This enhances the possibility of the planet being suitable for sustained life.

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arXiv2013

Tidal Friction and Tidal Lagging. Applicability Limitations of a Popular Formula for the Tidal Torque

Tidal torques play a key role in rotational dynamics of celestial bodies. They govern these bodies' tidal despinning, and also participate in the subtle process of entrapment of these bodies into spin-orbit resonances. This makes tidal torques directly relevant to the studies of habitability of planets and their moons. Our work begins with an explanation of how friction and lagging should be built into the theory of bodily tides. Although much of this material can be found in various publications, a short but self-consistent summary on the topic has been lacking in the hitherto literature, and we are filling the gap. After these preparations, we address a popular concise formula for the tidal torque, which is often used in the literature, for planets or stars.We explain why the derivation of this expression, offered in the paper by Goldreich (1966; AJ 71, 1 - 7) and in the books by Kaula (1968, eqn. 4.5.29), and Murray & Dermott (1999, eqn. 4.159), implicitly sets the time lag to be frequency independent. Accordingly, the ensuing expression for the torque can be applied only to bodies having a very special (and very hypothetical) rheology which makes the time lag frequency independent, i.e, the same for all Fourier modes in the spectrum of tide. This expression for the torque should not be used for bodies of other rheologies. Specifically, the expression cannot be combined with an extra assertion of the geometric lag (or the phase lag) being constant, because at finite eccentricities the said assumption is incompatible with the constant-time-lag condition.

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arXiv2013

No pseudosynchronous rotation for terrestrial planets and moons

We reexamine the popular belief that a telluric planet or satellite on an eccentric orbit can, outside a spin-orbit resonance, be captured in a quasi-static tidal equilibrium called pseudosynchronous rotation. The existence of such configurations was deduced from oversimplified tidal models assuming either a constant tidal torque or a torque linear in the tidal frequency. A more accurate treatment requires that the torque be decomposed into the Darwin-Kaula series over the tidal modes, and that this decomposition be combined with a realistic choice of rheological properties of the mantle. This development demonstrates that there exist no stable equilibrium states for solid planets and moons, other than spin-orbit resonances.

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arXiv2012

Revealing companions to nearby stars with astrometric acceleration

A subset of 51 Hipparcos astrometric binaries among FG dwarfs within 67pc has been surveyed with the NICI adaptive optics system at Gemini-S, directly resolving for the first time 17 sub-arcsecond companions and 7 wider ones. Using these data together with published speckle interferometry of 57 stars, we compare the statistics of resolved astrometric companions with those of a simulated binary population. The fraction of resolved companions is slightly lower than expected from binary statistics. About 10% of astrometric companions could be "dark" (white dwarfs and close pairs of late M-dwarfs). To our surprise, several binaries are found with companions too wide to explain the acceleration. Re-analysis of selected intermediate astrometric data shows that some acceleration solutions in the original Hipparcos catalog are spurious.

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arXiv2012

How terrestrial planets traverse spin-orbit resonances: A camel goes through a needle's eye

The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love numbers. The torque equations are integrated numerically with a small step in time, includng the oscillating triaxial torque components but neglecting the layered structure of the planet and assuming a zero obliquity. We find that a Mercury-like planet with its current value of orbital eccentricity (0.2056) is always captured in the 3:2 resonance. The probability of capture in the higher 2:1 resonance is approximately 0.23. These results are confirmed by a semi-analytical estimation of capture probabilities as functions of eccentricity for both prograde and retrograde evolution of spin rate. As follows from analysis of equilibrium torques, entrapment in the 3:2 resonance is inevitable at eccentricities between 0.2 and 0.41. Considering the phase space parameters at the times of periastron, the range of spin rates and phase angles, for which an immediate resonance passage is triggered, is very narrow, and yet, a planet like Mercury rarely fails to align itself into this state of unstable equilibrium before it traverses the 2:1 resonance.

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arXiv2011

Stability, chaos and entrapment of stars in very wide pairs

The relative motion of stars and other celestial objects in very wide pairs, separated by distances of the order of 1 pc, is strongly influenced by the tidal gravitational potential of the Galaxy. The Coriolis component of the horizontal tidal force in the rotating reference frame tends to disrupt such marginally bound pairs. However, even extremely wide pairs of bodies can be bound over intervals of time comparable to the Hubble time, under appropriate initial conditions. Here we show that for arbitrary chosen initial coordinates of a pair of stars, there exists a volume of the space of initial velocity components where the orbits remain bound in the planar tidal field for longer than 10 Gyr, even though the initial separation is well outside the Jacobi radius. The boundary of this phase space of stable orbits is fractal, and the motion at the boundary conditions is clearly chaotic. We found that the pairs may remain confined for several Gyr, and then suddenly disintegrate due to a particularly close rendezvous. By reversing such long-term stable orbits, we find that entrapment of unrelated stars into wide pairs is possible, but should be quite rare. Careful analysis of precision astrometry surveys revealed that extremely wide pairs of stars are present in significant numbers in the Galaxy. These results are expected to help discriminating the cases of genuine binarity and chance entrapment, and to make inroads in testing the limits of Newtonian gravitation.

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arXiv2011

The Worst Distortions of Astrometric Instruments and Orthonormal Models for Rectangular Fields of View

The non-orthogonality of algebraic polynomials of field coordinates traditionally used to model field-dependent corrections to astrometric measurements, gives rise to subtle adverse effects. In particular, certain field dependent perturbations in the observational data propagate into the adjusted coefficients with considerable magnification. We explain how the worst perturbation, resulting in the largest solution error, can be computed for a given non-orthogonal distortion model. An algebraic distortion model of full rank can be converted into a fully orthonormal model based on the Zernike polynomials for a circular field of view, or a basis of functions constructed from the original model by a variant of the Gram-Schmidt orthogonalization process for a rectangular field of view. The relative significance of orthonormal distortion terms is assessed simply by the numerical values of the corresponding coefficients. Orthonormal distortion models are easily extendable when the distribution of residuals indicate the presence of higher order terms.

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arXiv2010

Variability of surface flows on the Sun and the implications for exoplanet detection

The published Mount Wilson Doppler-shift measurements of the solar velocity field taken in 1967--1982 are revisited with a more accurate model, which includes two terms representing the meridional flow and three terms corresponding to the convective limb shift. Integration of the recomputed data over the visible hemisphere reveals significant variability of the net radial velocity at characteristic time scales of 0.1--10 years, with a standard deviation of 1.4 \ms. This result is supported by independent published observations. The implications for exoplanet detection include reduced sensitivity of the Doppler method to Earth-like planets in the habitable zone, and an elevated probability of false detections at periods of a few to several years.

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arXiv2009

"An Era of Precision Astrophysics: Connecting Stars, Galaxies and the Universe," an Astro2010 Science White Paper

Abridged: The golden age of astrophysics is upon us with both grand discoveries (extra-solar planets, dark matter, dark energy) and precision cosmology. Fundamental understanding of the working of stars and galaxies is within reach, thanks to newly available precision measurements. We highlight the importance of distances and model independent distances and masses. Distances are fundamental in astrophysics and their knowledge can change our perception of phenomena dramatically: e.g., in antiquity, the Heliocentric model was rejected because the predicted stellar parallaxes were not observed. Distance measurements are directly related to the history & fate of the uni- verse as they provide 2 of 3 methods available to date the universe. The 1st method is based on the ages of stars, which can be ascertained if their lumi- nosities (distances) are accurately known. The 2nd method relies on cosmolo- gical methods. To 1st order, the age of the universe is the inverse H_0. As stressed by the previous decadal report, "the fundamental goal of ... astrophysics is to understand how the universe ... galaxies [and] stars ... formed, how they evolved, and what their destiny will be." These questions can be answered partly by micro-arcsecond astrometry: 1) Galactic archeology: a detailed reconstruction of the formation history of the Milky Way and other Local Group galaxies, 2) the very oldest stars in the Milky Way and the age of the Universe, and 3) H_0 and concordance cosmology. These goals are achievable by combining muas-arcsecond astrometry from the proposed SIM-Lite mission supplemented with ground-based spectroscopy. The results of our proposed project will force the biggest reassessment of stellar astrophysics in 50 years, which will affect most branches of astrophysics.

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arXiv2007

Taking the Measure of the Universe: Precision Astrometry with SIM PlanetQuest

Precision astrometry at microarcsecond accuracy has application to a wide range of astrophysical problems. This paper is a study of the science questions that can be addressed using an instrument that delivers parallaxes at about 4 microarcsec on targets as faint as V = 20, differential accuracy of 0.6 microarcsec on bright targets, and with flexible scheduling. The science topics are drawn primarily from the Team Key Projects, selected in 2000, for the Space Interferometry Mission PlanetQuest (SIM PlanetQuest). We use the capabilities of this mission to illustrate the importance of the next level of astrometric precision in modern astrophysics. SIM PlanetQuest is currently in the detailed design phase, having completed all of the enabling technologies needed for the flight instrument in 2005. It will be the first space-based long baseline Michelson interferometer designed for precision astrometry. SIM will contribute strongly to many astronomical fields including stellar and galactic astrophysics, planetary systems around nearby stars, and the study of quasar and AGN nuclei. SIM will search for planets with masses as small as an Earth orbiting in the `habitable zone' around the nearest stars using differential astrometry, and could discover many dozen if Earth-like planets are common. It will be the most capable instrument for detecting planets around young stars, thereby providing insights into how planetary systems are born and how they evolve with time. SIM will observe significant numbers of very high- and low-mass stars, providing stellar masses to 1%, the accuracy needed to challenge physical models. Using precision proper motion measurements, SIM will probe the galactic mass distribution and the formation and evolution of the Galactic halo. (abridged)

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arXiv2005

Astrometric Effects of Secular Aberration

One of the main endeavors of fundamental astrometry is to establish a practical realization of an inertial reference frame anchored to celestial objects whose positions are defined in the barycentric coordinates of the solar system. The development of astrometric facilities operating from space at a microarcsecond level of precision makes the non-uniformity of the galactic motion of the barycenter an observable effect that violates the inertiality of the barycentric frame. Most of the observable effect is caused by secular acceleration of the barycenter with respect to the center of the Galaxy. The acceleration results in a pattern of secular aberration which is observable astrometrically as a systematic vector field of the proper motions of distant quasars. We employ the vector spherical harmonics to describe the predicted field of the proper motions and evaluate its amplitude at each point on the celestial sphere. It is shown that the pattern of secular aberration is fully represented by three low-order electric-type vector harmonics, and hence, it is easily distinguishable from the residual rotations of the reference frame and other possible effects, such as the hypothetical long-period gravitational waves. Comprehensive numerical simulations of the grid astrometry with SIM PlanetQuest are conducted. The full covariance matrix of the simulated grid solution is used to evaluate the covariances of the three electric harmonic coefficients, representing the secular aberration pattern of proper motions. We conclude that the grid astrometry with SIM PlanetQuest will be sensitive to the main galactocentric component of secular acceleration, while the peculiar acceleration of the Sun with respect to LSR is expected to be too small to be detected with this astrometric space interferometer.

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