Deg Yr Research Articles

Preimpact Mutual Orbit of the DART Target Binary Asteroid (65803) Didymos Derived from Observations of Mutual Events in 2003–2021

We modeled photometric observations of mutual events (eclipses and occultations) between the components of the binary near-Earth asteroid (65803) Didymos, the target of the Double Asteroid Redirection Test (DART) space mission, which were taken from 2003 to 2021. We derived parameters of the modified Keplerian mutual orbit (allowing for a quadratic drift in the mean anomaly, which is presumably caused by an interplay between the BYORP effect and mutual tides, or by differential Yarkovsky force) of the secondary, called Dimorphos, around the Didymos primary and estimated its diameter. The J2000 ecliptic longitude and latitude of the orbital pole are 320.°6 ± 13.°7 and −78.°6 ± 1.°8, respectively, and the orbital period is 11.921624 ± 0.000018 hr at epoch JD 2,455,873.0 (asterocentric UTC; all quoted uncertainties correspond to 3σ, except the density estimate below). We obtained the quadratic drift of the mean anomaly of 0.15 ± 0.14 deg yr−2. The orbital eccentricity is ≤0.03. We determined the ecliptic longitude and latitude of the radius vector of Dimorphos with respect to Didymos at the nominal time of the DART impact to Dimorphos (JD 2,459,849.46875 geocentric UTC) to be 222.°8 ± 7.°0 and −1.°6 ± 4.°2, respectively. We also estimated the bulk density of the system to be 2.37 ± 0.30 g cm−3 (1σ uncertainty).

Nodal precession of WASP-33b for 11 yr by Doppler tomographic and transit photometric observations

ABSTRACTWASP-33b, a hot Jupiter around a hot star, is a rare system in which nodal precession has been discovered. We updated the model for the nodal precession of WASP-33b by adding new observational points. Consequently, we found a motion of the nodal precession spanning 11 yr. We present homogenous Doppler tomographic analyses of eight data sets, including two new data sets from TS23 and HIDES, obtained between 2008 and 2019, to illustrate the variations in the projected spin–orbit obliquity of WASP-33b and its impact parameter. We also present its impact parameters based on photometric transit observations captured by MuSCAT in 2017 and MuSCAT2 in 2018. We derived its real spin–orbit obliquity ψ, stellar spin inclination is, and stellar gravitational quadrupole moment J2 from the time variation models of the two orbital parameters. We obtained $\psi = 108.19^{+0.95}_{-0.97}$ deg, $i_\mathit{ s} = 58.3^{+4.6}_{-4.2}$ deg, and $J_2=(1.36^{+0.15}_{-0.12}) \times 10^{-4}$. Our J2 value was slightly smaller than the theoretically predicted value, which may indicate that its actual stellar internal structure is different from the theoretical one. We derived the nodal precession speed $\dot{\theta }=0.507^{+0.025}_{-0.022}$ deg yr−1, and its period $P_{\mathrm{pre}}=709^{+33}_{-34}$ yr, and found that WASP-33b transits in front of WASP-33 for only ∼ 20 per cent of the entire nodal precession period.

Secular changes in the orbits of the quadruple system VW LMi

ABSTRACT VW LMi is the tightest known quadruple system with 2 + 2 hierarchy. It consists of a W UMa-type eclipsing binary (P12 = 0.477 55 d) and another detached non-eclipsing binary (P34 = 7.93 d) orbiting around a common centre of mass in about P1234 = 355 d. We present new observations of the system extending the time baseline to study long-term perturbations in the system and to improve orbital elements. The multidataset modelling of the system (four radial-velocity curves for the components and the timing data) clearly showed an apsidal motion in the non-eclipsing binary at a rate of 4.6 deg yr−1, but no other perturbations. This is consistent with the nearly co-planarity of the outer, 355-d orbit, and the 7.93-d orbit of the non-eclipsing binary. Extensive N-body simulations enabled us to constrain the mutual inclination of the non-eclipsing binary and the outer orbits to j34–1234 < 10 deg.

Geomagnetic forecasts driven by thermal wind dynamics in the Earth's core

There exists a fundamental as well as practical interest in being able to accurately forecast the future evolution of Earth's magnetic field at decadal to secular ranges. This work enables such forecasts by combining geomagnetic data with an Earth-like numerical model of a convection-driven fluid dynamo. The underlying data assimilation framework builds on recent progress in inverse geodynamo modelling, a method which estimates an internal dynamic structure for Earth's core from a snapshot of the magnetic field and its instantaneous rate of change at the surface, and takes advantage of linear relationships and long-range correlations between observed and hidden state variables. Here the method is further evolved into a single-epoch ensemble Kalman filter, in order to initialise at a given epoch an ensemble of states compatible with the observations and representative of the uncertainties in the estimation of hidden quantities. The ensemble dynamics, obtained by subsequent numerical integration of the prognostic model equations, are found to be governed by a thermal wind balance or equilibrium between buoyancy forces, the Coriolis force and the pressure gradient. The resulting core fluid flow pattern is a quasi-steady eccentric gyre organised in a column parallel to Earth's rotation axis, in equilibrium with a longitudinal hemispheric convective density anomaly pattern. The flow provides induction for the magnetic field, which also undergoes a realistic amount of diffusion. Predictions of the present magnetic field from data taken within the past century show that the ensemble has an average retaining good consistency with the true geomagnetic evolution and an acceptable spread well representative of prediction errors, up to at least a secular range. The predictability of the geodynamo thus appears to significantly exceed previous theoretical expectations based on the chaotic divergence of ensemble members. The assimilation generally outperforms the linear mathematical extrapolations from a 30-yr prediction range onwards, with a 40 per cent improvement in Earth-surface error at a secular range. The geomagnetic axial dipole decay observed over the past two centuries is predicted to continue at a similar pace in the next century, with a further loss of 1.1 ± 0.3 µT by year 2115. The focal (or minimum intensity) point of the South Atlantic geomagnetic anomaly is predicted to enter the South Pacific region in the next century, with the anomaly itself further deepening and widening. By year 2065, the minimum intensity is predicted to decrease by 1.46 ± 0.4 µT at the Earth surface and the focal point to move 12.8 ± 1.4 deg westwards with a slight northward component. This corresponds to a drift rate of 0.26 deg yr −1 , similar to the typical geomagnetic westward drift observed over the past four centuries. The same drift rate is also predicted until 2115 with a further (but more uncertain) intensity decrease

Mapping and spectroscopy of the planetary nebula NGC 7009 in the visual and infrared

NGC 7009 is a fascinating example of a high-excitation, elliptical planetary nebula (PN) containing circumnebular rings, and FLIERs and jets along the major axis. We present visual spectroscopy along multiple position angles through the nucleus, taken with the Observatorio Astronomico Nacional (Mexico); mid-infrared (MIR) spectroscopy and imaging acquired using the Infrared Space Observatory (ISO) and Spitzer Space Telescope (SST), and narrow-band imaging obtained using the Hubble Space Telescope (HST). The data show that the mid-infrared (MIR) continuum is dominated by a broad ≈100 K continuum, and a strong excess attributable to crystalline silicate emission. The primary peaks in this excess are similar to those observed in Forsterite and clino- and ortho-enstatite. The MIR images, by contrast, appear to be dominated by ionic transitions, with the 8.991 μm transition of [Ar iii] being important in the 8.0-μm band. The morphology and size of the envelope are found to vary with wavelength, with the largest dimensions occurring at 8.0 μm – a trend which is also reflected in an increase in the 8.0 μm/4.5 μm and 5.8 μm/4.5 μm ratios with distance from the nucleus. The visual spectroscopy permits us to map density and temperature throughout the shell, and confirm that the lowest values of ne are located close to the ansae, where densities appear to be of the order of 900–2600 cm−3. We provide mean line intensities for 116 transitions in six regions of the shell, and use mapping to confirm a systematic increase in excitation in the outer portions of the envelope. We finally use the ground-based spectroscopy, and ratioing of HST images to investigate the presence of shocks in the ansae and interior envelope. It is concluded that line ratios in the ansae may be partially consistent with shock excitation, although these features are primarily dominated by photoionization. We also note evidence for shock excitation at the limits of the interior elliptical shell, and for multiple bow-shock structures centred upon the ansae. The orientations of the easterly bow-shocks may have varied over time, indicating precession of the collimating engine at a rate of deg yr−1, whilst the outward splaying of the westerly ‘jet’ appears consistent with shock refraction modelling. We finally note that HST observations of the halo rings show them to have widths of the order of ∼1–3 arcsec, and steep changes in surface brightness consistent with local shock activity.

Prospects for measuring the moment of inertia of pulsar J0737-3039A

Here we consider the possibility-envisaged by many authors as feasible in the near future-of measuring at 10% or better the moment of inertia I of the pulsar J0737-3039A via the gravitomagnetic spin–orbit periastron precession (analogous to the Lense–Thirring pericentre precession in the case of a test-particle orbiting a central spinning mass). Such a gravitomagnetic effect is expected to be of the order of 10 - 4 deg yr - 1 and the present-day precision in measuring the periastron precession of J0737-3039A via pulsar timing is 6.8 × 10 - 4 deg yr - 1 . However the systematic uncertainty in the much larger first-order post-Newtonian (1PN) gravitoelectric precession (analogous to the Einstein Mercury’s perihelion precession in the weak-field and slow-motion approximation), which should be subtracted from the measured one in order to pick up the gravitomagnetic rate, is of primary importance. Indeed, by determining the sum of the masses by means of the third Kepler law, such a bias amounts to 0.03165 deg yr −1, according to the current level of accuracy in knowing the parameters of the J0737-3039 system. The major sources of uncertainty are the Keplerian projected semimajor axis x B of the component B and the post-Keplerian parameter s, identified with sin i ; their knowledge should be improved by three orders of magnitude at least; the bias due to the Keplerian projected semimajor axis x A of the component A amounts to ≈ 10 % today. The present-day level of accuracy in the eccentricity e would affect the investigated measurement at a percent level, while the impact of the orbital period P b is completely negligible. If, instead, the sum of the masses is measured by means of the post-Keplerian parameters r and s, it turns out that r should be measured five orders of magnitude better than now: according to the present-day level of accuracy, the total uncertainty in the 1PN periastron rate is, in this case, 2.11819 deg yr −1. In conclusion, the prospect of measuring the moment of inertia of PSR J0737-3039A at 10% accuracy or better seems unlikely given the limitations to the precision with which the system’s basic binary and post-Keplerian parameters can be measured via radio timing.

The post-Newtonian mean anomaly advance as further post-Keplerian parameter in pulsar binary systems

The post-Newtonian gravitoelectric secular rate of the mean anomaly ℳ is worked out for a two-body system in the framework of the General Theory of Relativity. The possibility of using such an effect, which is different from the well known decrease of the orbital period due to gravitational wave emission, as a further post-Keplerian parameter in binary systems including at least one pulsar is examined. The resulting effect is almost three times larger than the periastron advance $\dot{\omega}$ . E.g., for the recently discovered double pulsar system PSR J0737-3039 A+B it would amount to −47.79 deg yr−1. This implies that it could be extracted from the linear part of a quadratic fit of the orbital phase because the uncertainties both in the linear drift due to the mean motion and in the quadratic shift due to the gravitational wave are smaller. The availability of such additional post-Keplerian parameter would be helpful in further constraining the General Theory of Relativity, especially for such systems in which some of the other post-Keplerian parameters can be measured with limited accuracy. Moreover, also certain pulsar-white dwarf binary systems, characterized by circular orbits like PSR B1855+09 and a limited number of measured post-Keplerian parameters, could be used for constraining competing theories of gravity.

The effect of non-gravitational forces on the median inclination of short-period comets

The numbered Jupiter family comets (orbital periods P < 20 yr) have a median orbital inclination of about 10°0 ± 1°1. In this paper, we integrate the orbits of these comets into the future, under the influence of both typical non-gravitational forces and planetary perturbation, using a Bulirsch-Stoer integrator. In the case where non-gravitational forces were not acting, the median inclination of those comets that remained on P < 20 yr orbits increased at the rate of (1.92 ± 0.12) x 10- 3 deg yr -1 for the first 3600 yr of the integration. During this time the population of the original family decreases, such that the half-life is about 13 200 ± 800 yr. The introduction of non-gravitational forces slows down the rate of increase in inclination to a value of around (1.23 ± 0.16) x 10 -3 deg yr -1 . This rate of increase in inclination was found to be only weakly dependent on the non-gravitational parameters used during the integration. After a few thousand years, the rate of change in inclination decreases, and after 20 000 yr the inclinations of those initial Jupiter family members that still have orbits with P < 20 yr become constant at about 20°.0, independent of whether non-gravitational forces are acting or not. The presently known Jupiter family of comets is losing members at the rate of one in every 67 yr. To maintain the family in equilibrium, Jupiter has to capture comets at a similar rate, and these captured comets have to be of low inclination to compensate for the pumping up of inclinations by gravitational perturbation.

Origin of chaos in the Prometheus–Pandora system

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting, resulting in resonance overlap which causes the chaos. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 deg yr −1, respectively. A model with 1.5 degrees of freedom captures the essential features of the chaotic dynamics. We use it to show that the Lyapunov exponent of 0.3 yr −1 arises because the critical argument of the dominant member of the resonant quartet makes approximately two separatrix crossings every 6.2 year precessional cycle.

Inner-core anisotropy beneath Australia and differential rotation

Summary The inner-core anisotropy of P-wave velocity has been suggested since 1986. The detail of the anisotropic structure is now under discussion. We have studied a regional structure in the inner core beneath Australia to reveal the detail of the anisotropy using the residuals of the differential traveltimes of PKP (BC) minus PKP (DF). We have collected the rays not only nearly parallel to the Earth's rotation axis but also nearly parallel to the equatorial plane to distinguish the anisotropy from the isotropic heterogeneity in the inner core. The collected rays cross each other with different angles in the inner core beneath Australia. We have studied inner-core anisotropy assuming locally uniform transverse isotropy. The velocity anomalies decrease with the angles between the ray directions in the inner core and the Earth's rotation axis, which supports inner-core anisotropy beneath this region. The top 190 km of the inner core is isotropic with a velocity anomaly of 0.11 per cent and the deeper part shows the anisotropy with an amplitude of 3.1 per cent. The symmetry axis of the anisotropy crosses the Earth's surface at 80°N and 103°E. This result suggests that previous studies underestimated the size of the anisotropy in the inner core beneath this region. Because the symmetry axis is inclined from the Earth's rotation axis, we can observe the temporal variation of the velocity anomalies caused by the anisotropy in the inner core if it rotates at a different rate from the crust and the mantle. The possibility of differential rotation is studied by considering the regional structure of the inner-core anisotropy beneath Australia. We use seismograms recorded at Syowa station in Antarctica over the past 27 yr. We have found no evidence for significant differential rotation though we cannot rule out a small rate of about 0.2 deg yr−1 or less. Even if the inner core rotates faster than the crust and mantle, the difference is fairly small and we need not consider the influence of the differential rotation on the study of anisotropy in the inner core.

Timing observations of the 8 hour binary pulsar 2127 + 11C in the globular cluster M15

We present new results are presented on the position and characteristics of the 8 hr binary pulsar 2127 + 11C in the post-core-collapse (PCC) globular cluster M15. Our results indicate that PSR 2127 + 11C has been ejected from the cluster core via a close encounter with another binary system or isolated star. In particular, the position derived from a phase-connected timing solution places the PSR 2127 + 11C system 2.7 pc (projected) from the core, well outside the compact region containing the other four detected pulsars and the X-ray binary system X2127 + 11/AC 211. While PSR 2127 + 11C is likely still bound to the cluster, it is nonetheless probable that other compact binary pulsars have been totally ejected, thereby contributing to the population of field binary pulsars. Timing results from PSR 2127 + 11C also show a relativistic advance of periastron of 4.46 deg yr^(-1), indicating that the total mass of the system is 2.71 M_⊙.

Apsidal motion in the eclipsing binary system OX cas

Multi-colourWBVR photoelectric observations of the eclipsing binary OX Cas were carried out. The photometric elements, absolute parameters and the angular rate of the apsidal motion (\(\dot \omega \)= 9.1 deg yr−1 were obtained. The apsidal parameterk2 derived for this system is by 15–25% smaller than the theoretical parameterk2.

Apsidal motion in the eclipsing binary system of BW AQR

The first photoelectric light curve of the eclipsing binary system BW Aqr (F71V+F81V;P=6d.7;V=10 m .31), discovered by Miss Leavitt at the beginning of the century, was obtained. The photometric elements were detemined. The components of this system are considerably evolved stars: the age of the system is about 2×109 yr. It follows from the photometric data that the secondary component should have greater mass than the primary one The zero-age spectral classes of components were F2V and F1V. The system has an elliptical orbit with the eccentricitye=0.18. The angular rate of the apsidal motion (ωobs = 0.070 deg yr−1) and the corresponding value of the apsidal parameterk 2=0.0090 (the relativistic term included) were found. The derived valuek 2 exceeds by more than a factor of 2 the theoretical coefficient obtained from the modern theory of internal structure of stars with moderate masses $$\left( {\mathfrak{M} = {\text{1}}{\text{.35 }}\mathfrak{M}_ \odot } \right)$$ .

Velocity-dependent inertial induction and secular retardation of the earth’s rotation

According to the model of inertial induction proposed earlier, the inertia force consists of an acceleration-dependent term which comes out as identically equal to -ma. Besides, there is a velocity-dependent term which is exceedingly small to be easily detected. However, it has been shown that this results in a cosmological red shift of light coming from distant stars and galaxies; the magnitude of the red shift agrees very well with the observed values. Though this model yields correct results when applied to photons it needs modification before applying to other bodies. A modified form of the inertial induction model is now proposed where the proposed velocity-dependent inertia forces, when applied to the solar system, yields correct order of magnitude for the secular retardation of the earth’s rotation. Moreover, a combined model using the velocity term and the tidal friction also does not suggest any close proximity of the moon to the earth in the past. When the model is applied to the case of Phobos, a secular acceleration of the order of magnitude of 10−3 deg yr−2 is obtained.

Apsidal motion in the eclipsing binary system V 451 Ophiuchi

MulticolourWBVR photoelectric observations of the eclipsing binary V 451 Oph were carried out, and a highly accurate light curve was obtained. The angular velocity of the orbital rotation, ω=2.1 deg yr−1, and the apsidal motion constantk2=0.0045 are given.

Long-period geomagnetic secular variations since 12,000 yr BP

A comparison of secular variation records of the geomagnetic field inclination obtained from palaeomagnetic studies of European and North American post-Glacial and late-Glacial sediments suggests that geomagnetic westward drift has persisted through the past 12,000 yr. Between 12,000 and 2,500 yr BP the overall average drift rate was between 0.14 and 0.16 deg yr−1. At ∼2,500 yr BP it is tentatively suggested that the drift rate increased and rose to a maximum of nearly 0.5 deg yr−1 before decreasing to historically observed values of ∼0.25 deg yr−1.

Archaeomagnetic secular variation record of Mount Vesuvius

The lavas produced by historically recorded eruptions of Mt Vesuvius, and the Herculaneum mudflow resulting from the AD 79 eruption have been investigated archaeomagnetically. The mudflow carries a magnetically hard remanence, the direction of which is significantly different from that of the present-day field, suggesting that the remanence is primary. The secular variation curve for Vesuvius agrees well with the Rome record and with other curves from Italy and London. A model for westward drift which accounts for certain features of secular variation in Europe over the past 200 yr requires a mean deceleration rate of 0.004 deg yr−2. This is less than the current rate, suggesting that the deceleration rate was smaller 200 yr ago than it is today.