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At least 1,063 records · Page 59

TOPEX/POSEIDON tides estimated using a global inverse model

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

Egbert, Gary D.↗

Phobos Ephemeris Improvement from Recent Spacecraft Observations

Despite 127 years of observations, there is still room for improvement in the ephemeris of the Martian satellite Phobos. Early in this history, Earth-based astrometric observations of Phobos and Deimos were used to estimate the mass and oblateness of Mars. As more data accumulated, it became clear that a secular acceleration in the longitude of Phobos was occurring, and this was attributed to tidal dissipation within Mars, yielding rough estimates of the tidal quality factor, or Q. At the epoch of the earliest spacecraft observations of Phobos, from Mariner 9 and the Viking Orbiters and Landers, the gravitational field of Mars, and resulting forces on Phobos, were still not particularly well known. Thus observations of natural and artificial satellite motions continued to contribute, each in their own way, to knowledge of the mass distribution within Mars. Improvements in tracking system accuracy, and the placement of satellites, like the 1996 Mars Global Surveyor and 2001 Mars Odyssey, in circular polar orbits has lead to dramatic improvements to knowledge of the Mars gravity field. The direct gravitational influence on Phobos is no longer expected to be a limiting factor in predicting its orbital motion. Despite that progress, a variety of observations of Phobos from recent orbiters and landers suggest that the best satellite ephemeris still has along-track orbit errors which are accumulating at a rate of 1.75 kilometers per year, with Phobos gaining on the predicted positions. These recent observations alone do not span sufficient time to separately resolve the positional error into changes in mean motion and changes in secular acceleration. However, combining them with earlier observations will allow improvements in both the mean motion and its first derivative. This latter parameter is particularly interesting, as it relates to tidal dissipation, and thus uniquely constrains the internal structure of Mars. The current best estimate of the secular acceleration rate of Mars implies a surprisingly low value for the tidal dissipation factor Q = (94 plus or minus 1). For the Earth, most tidal dissipation occurs within the oceans. The terrestrial mantle tidal Q is 280. An issue of interest is then: why, where, and how does Mars dissipate tidal energy so effectively.

Bills, B. G.↗

The Contribution of Io-Raised Tides to Europa's Diurnally-Varying Surface Stresses

Europa's icy surface records a rich history of geologic activity, Several features appear to be tectonic in origin and may have formed in response to Europa's daily-varying tidal stress [I]. Strike-slip faults and arcuate features called cycloids have both been linked to the patterns of stress change caused by eccentricity and obliquity [2J[3]. In fact, as Europa's obliquity has not been directly measured, observed tectonic patterns arc currently the best indicators of a theoretically supported [4] non-negligible obliquity. The diurnal tidal stress due to eccentricity is calculated by subtracting the average (or static) tidal shape of Europa generated by Jupiter's gravitational field from the instantaneous shape, which varies as Europa moves through its eccentric orbit [5]. In other words, it is the change of shape away from average that generates tidal stress. One might expect tidal contributions from the other large moons of Jupiter to be negligible given their size and the height of the tides they raise on Europa versus Jupiter's mass and the height of the tide it raises on Europa, However, what matters for tidally-induced stress is not how large the lo-raised bulge is compared to the Jupiter-raised bulge but rather the differences bet\Veen the instantaneous and static bulges in each case. For example, when Europa is at apocenter, Jupiter raises a tide 30m lower than its static tide. At the same time, 10 raises a tide about 0.5m higher than its static tide. Hence, the change in Io's tidal distortion is about 2% of the change in the Jovian distortion when Europa is at apocenter

Rhoden, Alyssa Rose↗

Deep Moonquake Focal Mechanisms: Recovery and Implications

A defining characteristic of deep moonquakes is their tendency to occur with tidal periodicity, prompting previous studies to infer that they are related to the buildup and release of tidal stress within the Moon. In studies of tidal forcing, a key constraint is the focal mechanism: the fault parameters describing the type of failure moonquakes represent. The quality of the lunar seismic data and the limited source/receiver geometries of the Apollo seismic network prohibit the determination of deep moonquake fault parameters using first-motion polarities, as is typically done in terrestrial seismology. Without being able to resolve tidal stress onto a known failure plane, we can examine only gross qualities of the tidal stress tensor with respect to moonquake occurrence, so we cannot fully address the role of tidal stress in moonquake generation. We will examine the extent to which shear (S) and compression (P) wave amplitude ratios can constrain moonquake fault geometry by determining whether, for a given cluster, there exists a focal mechanism that can produce a radiation pattern consistent with the amplitudes measured by the Apollo instruments. Amplitudes are read in the ray coordinate frame, directly from seismograms for which the P and S arrivals are clearly identifiable on all long-period channels of the four Apollo stations. We apply an empirical station correction to account for site effects and the differences between P- and S-wave attenuation. Instead of focusing on the best fitting solution only, we formulate the inverse problem using a falsification criterion: all source orientations that do not reproduce the observed SV/P ratios within an error margin derived from the uncertainty of amplitude readings are rejected. All others are accepted as possible solutions. The inversion is carried out using an exhaustive grid search on a regular grid with predefined step size, encompassing all possible combinations of strike, dip and slip. To assess the sensitivity of the inversion for the uncertainty of the lunar interior structure, we carry out repeated inversions with different velocity structures. Our data set consist of a total of 106 events from 25 deep moonquake clusters. The largest contribution of 37 events originates from the most active cluster, A001, while other clusters are represented by 1 to 9 events. Since the definition of a cluster implies that all events share the same source orientation, a comparison of the inversion results of all events from one cluster will reduce ambiguities of the inversion. Once we obtain a suite of fault parameters for a given source, we can attempt to further constrain the focal mechanism with refined analyses of tidal stresses and predictions based on synthetic seismograms.

Knapmeyer, Martin↗

The Interior and Orbital Evolution of Charon as Preserved in Its Geologic Record

Pluto and its largest satellite, Charon, currently orbit in a mutually synchronous state; both bodies continuously show the same face to one another. This orbital configuration is a natural end-state for bodies that have undergone tidal dissipation. In order to achieve this state, both bodies would have experienced tidal heating and stress, with the extent of tidal activity controlled by the orbital evolution of Pluto and Charon and by the interior structure and rheology of each body. As the secondary, Charon would have experienced a larger tidal response than Pluto, which may have manifested as observable tectonism. Unfortunately, there are few constraints on the interiors of Pluto and Charon. In addition, the pathway by which Charon came to occupy its present orbital state is uncertain. If Charon's orbit experienced a high-eccentricity phase, as suggested by some orbital evolution models, tidal effects would have likely been more significant. Therefore, we determine the conditions under which Charon could have experienced tidally-driven geologic activity and the extent to which upcoming New Horizons spacecraft observations could be used to constrain Charon's internal structure and orbital evolution. Using plausible interior structure models that include an ocean layer, we find that tidally-driven tensile fractures would likely have formed on Charon if its eccentricity were on the order of 0.01, especially if Charon were orbiting closer to Pluto than at present. Such fractures could display a variety of azimuths near the equator and near the poles, with the range of azimuths in a given region dependent on longitude; east-west-trending fractures should dominate at mid-latitudes. The fracture patterns we predict indicate that Charon's surface geology could provide constraints on the thickness and viscosity of Charon's ice shell at the time of fracture formation.

Tectonics↗

Important influence of respiration on human R-R interval power spectra is largely ignored

Frequency-domain analyses of R-R intervals are used widely to estimate levels of autonomic neural traffic to the human heart. Because respiration modulates autonomic activity, we determined for nine healthy subjects the influence of breathing frequency and tidal volume on R-R interval power spectra (fast-Fourier transform method). We also surveyed published literature to determine current practices in this burgeoning field of scientific inquiry. Supine subjects breathed at rates of 6, 7.5, 10, 15, 17.1, 20, and 24 breaths/min and with nominal tidal volumes of 1,000 and 1,500 ml. R-R interval power at respiratory and low (0.06-0.14 Hz) frequencies declined significantly as breathing frequency increased. R-R interval power at respiratory frequencies was significantly greater at a tidal volume of 1,500 than 1,000 ml. Neither breathing frequency nor tidal volume influenced average R-R intervals significantly. Our review of studies reporting human R-R interval power spectra showed that 51% of the studies controlled respiratory rate, 11% controlled tidal volume, and 11% controlled both respiratory rate and tidal volume. The major implications of our analyses are that breathing parameters strongly influence low-frequency as well as respiratory frequency R-R interval power spectra and that this influence is largely ignored in published research.

NASA Discipline Cardiopulmonary↗

(abstract) Effect of Long Period Ocean Tides on the Earth's Rotation

The second-degree zonal tide raising potential, which is responsible for tidal changes in the Earth's rotation rate and length-of-day, is symmetric about the polar axis and hence can excite the Earth's polar motion only through its action upon nonaxisymmetric features of the Earth such as the oceans. Ocean tidal excitation of polar motion in the diurnal and semidiurnal tidal bands has been previously detected and extensively examined. Here, the detection of ocean tidal excitation of polar motion in the long-period tidal band, specifically at the Mf' (13.63-day) and Mf (13.66-day) tidal frequencies, is reported.

tides oceans diurnal tidal bands Earth's rotation ↗

Global Barotropic Tide Modeling Using Inline Self‐Attraction and Loading in MPAS‐Ocean

Abstract We examine ocean tides in the barotropic version of the Model for Prediction Across Scales (MPAS‐Ocean), the ocean component of the Department of Energy Earth system model. We focus on four factors that affect tidal accuracy: self‐attraction and loading (SAL), model resolution, details of the underlying bathymetry, and parameterized topographic wave drag. The SAL term accounts for the tidal loading of Earth's crust and the self‐gravitation of the ocean and the load‐deformed Earth. A common method for calculating SAL is to decompose mass anomalies into their spherical harmonic constituents. Here, we compare a scalar SAL approximation versus an inline SAL using a fast spherical harmonic transform package. Wave drag accounts for energy lost by breaking internal tides that are produced by barotropic tidal flow over topographic features. We compare a series of successively finer quasi‐uniform resolution meshes (62.9, 31.5, 15.7, and 7.87 km) to a variable resolution (45 to 5 km) configuration. We ran MPAS‐Ocean in a single‐layer barotropic mode forced by five tidal constituents. The 45 to 5 km variable resolution mesh obtained the best total root‐mean‐square error (5.4 cm) for the deep ocean ( 1,000 m) tide compared to TPXO8 and ran twice as fast as the quasi‐uniform 8 km mesh, which had an error of 5.8 cm. This error is comparable to those found in other forward (non‐assimilative) ocean tide models. In future work, we plan to use MPAS‐Ocean to study tidal interactions with other Earth system components, and the tidal response to climate change.

54 ENVIRONMENTAL SCIENCES↗

THE FATE OF DWARF GALAXIES IN CLUSTERS AND THE ORIGIN OF INTRACLUSTER STARS. II. COSMOLOGICAL SIMULATIONS

We combine an N-body simulation algorithm with a subgrid treatment of galaxy formation, mergers, and tidal destruction, and an observed conditional luminosity function {Phi}(L|M), to study the origin and evolution of galactic and extragalactic light inside a cosmological volume of size (100 Mpc){sup 3}, in a concordance {Lambda}CDM model. This algorithm simulates the growth of large-scale structures and the formation of clusters, the evolution of the galaxy population in clusters, the destruction of galaxies by mergers and tides, and the evolution of the intracluster light (ICL). We find that destruction of galaxies by mergers dominates over destruction by tides by about an order of magnitude at all redshifts. However, tidal destruction is sufficient to produce ICL fractions f{sub ICL} that are sufficiently high to match observations. Our simulation produces 18 massive clusters (M{sub cl} > 10{sup 14} M{sub Sun }) with values of f{sub ICL} ranging from 1% to 58% at z = 0. There is a weak trend of f{sub ICL} to increase with cluster mass. The bulk of the ICL ({approx}60%) is provided by intermediate galaxies of total masses 10{sup 11}-10{sup 12} M{sub Sun} and stellar masses 6 Multiplication-Sign 10{sup 8} M{sub Sun} to 3 Multiplication-Sign 10{sup 10} M{sub Sun} that were tidally destroyed by even more massive galaxies. The contribution of low-mass galaxies to the ICL is small and the contribution of dwarf galaxies is negligible, even though, by numbers, most galaxies that are tidally destroyed are dwarfs. Tracking clusters back in time, we find that their values of f{sub ICL} tend to increase over time, but can experience sudden changes that are sometimes non-monotonic. These changes occur during major mergers involving clusters of comparable masses but very different intracluster luminosities. Most of the tidal destruction events take place in the central regions of clusters. As a result, the ICL is more centrally concentrated than the galactic light. Our results support tidal destruction of intermediate-mass galaxies as a plausible scenario for the origin of the ICL.

79 ASTRONOMY AND ASTROPHYSICS↗

REVEALING THE NATURE OF EXTREME CORONAL-LINE EMITTER SDSS J095209.56+214313.3

Extreme coronal-line emitter (ECLE) SDSS J095209.56+214313.3, known by its strong, fading, high-ionization lines, has been a long-standing candidate for a tidal disruption event; however, a supernova (SN) origin has not yet been ruled out. Here we add several new pieces of information to the puzzle of the nature of the transient that powered its variable coronal lines: (1) an optical light curve from the Lincoln Near Earth Asteroid Research (LINEAR) survey that serendipitously catches the optical flare, and (2) late-time observations of the host galaxy with the Swift Ultraviolet and Optical Telescope (UVOT) and X-ray telescope (XRT) and the ground-based Mercator telescope. The well-sampled, ∼10 yr long, unfiltered LINEAR light curve constrains the onset of the flare to a precision of ±5 days and enables us to place a lower limit on the peak optical magnitude. Difference imaging allows us to estimate the location of the flare in proximity of the host galaxy core. Comparison of the GALEX data (early 2006) with the recently acquired Swift UVOT (2015 June) and Mercator observations (2015 April) demonstrates a decrease in the UV flux over a ∼10 yr period, confirming that the flare was UV-bright. The long-lived UV-bright emission, detected 1.8 rest-frame years after the start of the flare, strongly disfavors an SN origin. These new data allow us to conclude that the flare was indeed powered by the tidal disruption of a star by a supermassive black hole and that tidal disruption events are in fact capable of powering the enigmatic class of ECLEs.

79 ASTRONOMY AND ASTROPHYSICS↗

Measuring Alignments between Galaxies and the Cosmic Web at z ∼ 2–3 Using IGM Tomography

Many galaxy formation models predict alignments between galaxy spin and the cosmic web (i.e., directions of filaments and sheets), leading to an intrinsic alignment between galaxies that creates a systematic error in weak-lensing measurements. These effects are often predicted to be stronger at high redshifts (z ≳ 1) that are inaccessible to massive galaxy surveys on foreseeable instrumentation, but IGM tomography of the Lyα forest from closely spaced quasars and galaxies is starting to measure the z ∼ 2–3 cosmic web with requisite fidelity. Using mock surveys from hydrodynamical simulations, we examine the utility of this technique, in conjunction with coeval galaxy samples, to measure alignment between galaxies and the cosmic web at z ∼ 2.5. We show that IGM tomography surveys with ≲5 h {sup −1} Mpc sightline spacing can accurately recover the eigenvectors of the tidal tensor, which we use to define the directions of the cosmic web. For galaxy spins and shapes, we use a model parameterized by the alignment strength, Δ〈cos θ〉, with respect to the tidal tensor eigenvectors from the underlying density field, and also consider observational effects such as errors in the galaxy position angle, inclination, and redshift. Measurements using the upcoming ∼1 deg{sup 2} CLAMATO tomographic survey and 600 coeval zCOSMOS-Deep galaxies should place 3σ limits on extreme alignment models with Δ〈cos θ〉∼0.1, but much larger surveys encompassing >10,000 galaxies, such as Subaru PFS, will be required to constrain models with Δ〈cos θ〉∼0.03. These measurements will constrain models of galaxy–cosmic web alignment and test tidal torque theory at z ∼ 2, improving our understanding of the physics of intrinsic alignments.

79 ASTRONOMY AND ASTROPHYSICS↗

SDSS-IV MaNGA: How Galaxy Interactions Influence Active Galactic Nuclei

We present a comparative study of active galactic nuclei (AGN) between galaxy pairs and isolated galaxies with the final data release of the MaNGA integral field spectroscopic survey. We build a sample of 391 kinematic galaxy pairs within the footprint of the survey and select AGN using the survey's spectra. We use the comoving volume densities of the AGN samples to quantify the effects that tidal interactions have on the triggering of nuclear accretion. Our hypothesis is that the pair sample contains AGN that are triggered by not only stochastic accretion but also tidally induced accretion and correlated accretion. With the level of stochastically triggered AGN fixed by the control sample, we model the strength of tidally induced accretion and correlated accretion as a function of projected separation (r p ) and compare the model expectations with the observed volume densities of dual AGN and offset AGN (single AGN in a pair). At r p ~ 10 kpc, we find that tidal interactions induce ~30% more AGN than stochastic fueling and cause ~12% of the offset AGN to become dual AGN because of correlations. The strength of both these effects decreases with increasing r p . We also find that the [O III ] luminosities of the AGN in galaxy pairs are consistent with those found in isolated galaxies, likely because stochastically fed AGN dominate even among close pairs. Our results illustrate that while we can detect tidally induced effects statistically, it is challenging to separate tidally induced AGN and stochastically triggered AGN in interacting galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Barotropic tides in MPAS-Ocean (E3SM V2): impact of ice shelf cavities

Abstract. Oceanic tides are seldom represented in Earth system models (ESMs) owing to the need for high horizontal resolution to accurately represent the associated barotropic waves close to coasts. This paper presents results of tides implemented in the Model for Prediction Across Scales–Ocean or MPAS-Ocean, which is the ocean component within the U.S. Department of Energy developed Energy Exascale Earth System Model (E3SM). MPAS-Ocean circumvents the limitation of low resolution using unstructured global meshing. We are at this stage simulating the largest semidiurnal (M2, S2, N2) and diurnal (K1, O1) tidal constituents in a single-layer version of MPAS-O. First, we show that the tidal constituents calculated using MPAS-Ocean closely agree with the results of the global tidal prediction model TPXO8 when suitably tuned topographic wave drag and bottom drag coefficients are employed. Thereafter, we present the sensitivity of global tidal evolution due to the presence of Antarctic ice shelf cavities. The effect of ice shelves on the amplitude and phase of tidal constituents are presented. Lower values of complex errors (with respect to TPXO8 results) for the M2 tidal constituents are observed when the ice shelf is added in the simulations, with particularly strong improvement in the Southern Ocean. Our work points towards future research with varying Antarctic ice shelf geometries and sea ice coupling that might lead to better comparison and prediction of tides and thus better prediction of sea-level rise and also the future climate variability.

58 GEOSCIENCES↗

Planetary tides during the Maunder Sunspot Minimum

In order to test the tidal theory of sunspots, sun-centered planetary conjunctions and tidal potentials are reconstructed for the period of the Maunder Minimum (1645 to 1715). These are found to be effectively indistinguishable from patterns of conjunctions and power spectra of tidal potential in the modern era of a well-established 11-yr sunspot cycle. The pattern of planetary tidal forces during the Maunder Minimum is then reconstructed to investigate the possibility that multiple-planet forces were somehow fortuituously cancelled at that time; i.e., the positions of the slower moving planets in the late 17th and early 18th centuries were such that conjunctions and tidal potentials were reduced in number and force. Calculations of daily positions for Mercury, Venus, earth, and Jupiter as well as daily values of the tidal potential for the period from 1450 to 2000 indicate no striking dissimilarities between the time of the Maunder Minimum and any other period considered.

Smythe, C. M.↗

The tides of Io

A theory is developed for the origin and evaluation of the orbital resonances between the Galilean satellites Io, Europa and Ganymede as a result of the effects of dissipative tides in Jupiter and its satellites. Following a preliminary consideration of the consequences of tidal interaction for satellite orbits and a comprehensive Hamiltonian theory of the resonance interactions which allows terms up to third order in eccentricity to be included, a dynamic model of the origin and evolution of the resonance locks is presented in which the relative expansion of the orbits by tidal torques from Jupiter together with tidal dissipation in Io lead to the rapid driving out of Io until it is captured into a 2:1 resonance with Europa and the resonance with Ganymede is achieved. Consideration of the effects of other commensurabilities on the orbital evolution of the system reveals that second-order Laplace-like resonances would act to excite free eccentricites, while the resonances associated with the two-body 3:1 commensurability could not have been encountered. Analysis of the hypothesis that the Laplace relation is primordial shows that the bounds on the tidal dissipation of Jupiter still can not be relaxed. Recent determinations of the tidal dissipation in Jupiter are discussed, and it is noted that none is sufficiently small to be consistent with the high heat flux estimates for Io. Finally, the possibility of the observational determination of the tidal dissipation in Jupiter by the measurement of the secular acceleration of Io's main motion is considered.

Yoder, C. F.↗

Global ocean tide mapping using TOPEX/Poseidon altimetry

The investigation's main goals are to produce accurate tidal maps of the main diurnal, semidiurnal, and long-period tidal components in the world's deep oceans. This will be done by the application of statistical estimation techniques to long time series of altimeter data provided by the TOPEX/POSEIDON mission, with additional information provided by satellite tracking data. In the prelaunch phase, we will use in our simulations and preliminary work data supplied by previous oceanographic missions, such as Seasat and Geosat. These results will be of scientific interest in themselves. The investigation will also be concerned with the estimation of new values, and their uncertainties, for tidal currents and for the physical parameters appearing in the Laplace tidal equations, such as bottom friction coefficients and eddy viscosity coefficients. This will be done by incorporating the altimetry-derived charts of vertical tides as boundary conditions in the integration of those equations. The methodology of the tidal representation will include the use of appropriate series expansions such as ocean-basin normal modes and spherical harmonics. The results of the investigation will be space-determined tidal models of coverage and accuracy superior to that of the present numerical models of the ocean tides, with the concomitant benefits to oceanography and associated disciplinary fields.

Sanchez, Braulio V.↗

A Long-Term Space Astrophysics Research Program. An X-Ray Perspective of the Components and Structure of Galaxies

We present optical and archival X-ray data on the disturbed morphology radio elliptical NGC 1316 (Fornax A) that displays numerous low surface brightness shells, loops and tails. An extended (81x27 min or 9x3 kpc) emission line region (EELR) at a projected distance of 35 kpc from the nucleus has been discovered in a approximately 9Ox35 kpc, approximately 3.Ox1O(solar luminosity(B)) tidal tail. The position and extreme size of the EELR suggest it is related to the merger process. We suggest that the ionization mechanism of the EELR is shock excitation, and the gas is remnant from the merger progenitor. X-ray emission is detected near two tidal tails. Hot, approximately 5 x 10(exp 6)K gas is probably the predominant gas component in the tidal tail ISM. However based on the current tidal tail (cold + warm + hot) gas mass, a large fraction of the tidal tail progenitor gas may already reside in the nucleus of NGC 1316. The numerous and varied tidal tail system suggests that a disk-disk or disk-E merger could have taken place greater than or equal to 1 Gyr ago, whilst a low mass, gas rich galaxy started to merge approximately 0.5 Gyr ago.

Fabbiano, G.↗

Lunar and Solar Torques on the Oceanic Tides

Brosche and Seiler recently suggested that direct lunar and solar tidal torques on the oceanic tides play a significant role in the earth's short-period angular momentum balance ("short-period" here meaning daily and sub-daily). We reexamine that suggestion here, concentrating on axial torques and hence on variations in rotation rate. Only those spherical harmonic components of the ocean tide having the same degree and order as the tidal potential induce nonzero torques. Prograde components (those moving in the same direction as the tide-generating body) produce the familiar secular braking of the earth's rotation. Retrograde components, however, produce rapid variations in UTI at twice the tidal frequency. There also exist interaction torques between tidal constituents, e.g. solar torques on lunar tides. They generate UTI variations at frequencies equal to the sums and differences of the original tidal frequencies. We give estimates of the torques and angular momentum variations for each of the important regimes, secular to quarter-diurnal. For the M(sub 2) potential acting on the M(sub 2) ocean tide, we find an associated angular momentum variation of amplitude 3 x 10(exp 19) N m. This is 5 to 6 orders of magnitude smaller than the angular momentum variations associated with tidal currents. We conclude that these torques do not play a significant role in the short-period angular momentum balance.

Ray, Richard D.↗