Tidal Distortion Research Articles

Galaxy Merger Candidates in High-redshift Cluster Environments

Abstract We compile a sample of spectroscopically and photometrically selected cluster galaxies from four high-redshift galaxy clusters ( ) from the Spitzer Adaptation of the Red-Sequence Cluster Survey (SpARCS), and a comparison field sample selected from the UKIDSS Deep Survey. Using near-infrared imaging from the Hubble Space Telescope, we classify potential mergers involving massive ( ) cluster members by eye, based on morphological properties such as tidal distortions, double nuclei, and projected near neighbors within 20 kpc. With a catalog of 23 spectroscopic and 32 photometric massive cluster members across the four clusters and 65 spectroscopic and 26 photometric comparable field galaxies, we find that after taking into account contamination from interlopers, of the cluster members are involved in potential mergers, compared to of the field galaxies. We see no evidence of merger enhancement in the central cluster environment with respect to the field, suggesting that galaxy–galaxy merging is not a stronger source of galaxy evolution in cluster environments compared to the field at these redshifts.

Applicability of transfer functions for relative sea-level reconstructions in the southern North Sea coastal region based on salt-marsh foraminifera

Abstract We studied the foraminiferal distribution in two naturally grown salt marshes from the southern North Sea with respect to the tidal frame, salinity, grain size and pH. The salt marshes are situated on the landward sides of the islands of Sylt (Rantum, Germany) and Fano (Sonderho, Denmark). In both study areas, foraminifera have a vertical distribution with respect to water level, but also show inter-site variability, which can be related to environmental differences (e.g., in salinity and pH) and different flooding dynamics of the coastal salt marsh (Rantum) and the tidal-creek salt marsh (Sonderho). We developed different transfer functions, based on the widely applied standardized water level index (SWLI) approach and on three flooding parameters (duration of submergence (DoS), mean submergence time (MST), and flooding frequency (FF)), in order to assess their predictive ability for relative sea-level estimates for the southern North Sea coastal region. The water-level data used for these approaches are determined based on local water-level conditions, corrected for tidal distortions using water-level measurements for the Sonderho salt marsh and the Rantum tide gauge. The SWLI approach shows a precision (root mean squared error of prediction (RMSEP) of 0.23 m), which is around 15% of the tidal range. All three flooding approaches show comparable results at around mean tide level to mean high water, while at higher elevations, foraminiferal distribution becomes non-linearly correlated to flooding parameters resulting in lower precision of > 1.0 m. Our results suggest that the SWLI approach performs well and that the flooding approaches offer a suitable addition for assessing relative sea-level estimates in the North Sea region. We enhanced the knowledge on changing precision for tide level reconstructions along the elevational gradient in a storm dominated tidal area where elevation and flooding parameters are non-linear correlated.

Star formation histories in NGC 147 and NGC 185

NGC 147 and NGC 185 are two of the most massive satellites of the Andromeda galaxy (M 31). With similar mass and morphological type dE, they possess different amounts of interstellar gas and tidal distortion. The question therefore is, how do their histories compare? We present the first reconstruction of the star formation histories of NGC 147 and NGC 185 using long-period variable stars (LPVs). LPVs are low- to intermediate-mass stars at the asymptotic giant branch, which their luminosity is related to their birth mass. Combining near-infrared photometry with stellar evolution models, we construct the mass function and hence the star formation history. For NGC 185 we found that the main epoch of star formation occurred 8.3 Gyr ago, followed by a much lower, but relatively constant star formation rate. In the case of NGC 147, the star formation rate peaked only 7 Gyr ago, staying intense until ∼ 3 Gyr ago, but no star formation has occurred for at least 300 Myr. Despite their similar masses, NGC 147 has evolved more slowly than NGC 185 initially, but more dramatically in more recent times.

THE M2 AND M4 TIDES IN THE PARÁ RIVER ESTUARY

The Pará River estuary is a complex and special system in amazon continental shelf, with micro and mesoscale physical processes generated by forces of different sources (e.g., astronomical tides and river discharge). In this study, the main semidiurnal (M2) and the overtide (M4) components were analyzed by quantifying distortions degrees and identifying tidal asymmetries in the Pará River estuary. Two submersible tidal gauges were moored to measure the water level. One on the right margin (point #RG) and another on the left margin (#LF) recorded measurements 6 months (from September 2014 to March 2015). Furthermore, we used harmonic charts from Marine Studies Foundation (FEMAR, Fundação de Estudos do Mar). Lateral variations were also identified between #RG and #LF points from the amplitude and phase cotidal charts, with about 10 minutes delay and variation of 2 cm in tidal amplitude. We verified that the tidal wave enters in system by the right margin (#RF). The results show distortion degrees higher than 10% and positive asymmetry of the tidal wave in the Pará River, and the tidal attenuation in the estuary may be greater than 400 km upstream along the drainage basin.Keywords: Tidal distortion, Tidal asymmetry, Tidal components, Lateral variations.

Limb and gravity-darkening coefficients for the TESS satellite at several metallicities, surface gravities, and microturbulent velocities

We present new gravity and limb-darkening coefficients for a wide range of effective temperatures, gravities, metallicities, and microturbulent velocities. These coefficients can be used in many different fields of stellar physics as synthetic light curves of eclipsing binaries and planetary transits, stellar diameters, line profiles in rotating stars, and others. The limb-darkening coefficients were computed specifically for the photometric system of the space mission TESS and were performed by adopting the least-square method. In addition, the linear and bi-parametric coefficients, by adopting the flux conservation method, are also available. On the other hand, to take into account the effects of tidal and rotational distortions, we computed the passband gravity-darkening coefficients $y(\lambda)$ using a general differential equation in which we consider the effects of convection and of the partial derivative $\left(\partial{\ln I(\lambda)}/{\partial{\ln g}}\right)_{T_{\rm eff}}$. To generate the limb-darkening coefficients we adopt two stellar atmosphere models: ATLAS (plane-parallel) and PHOENIX (spherical, quasi-spherical, and $r$-method). The specific intensity distribution was fitted using five approaches: linear, quadratic, square root, logarithmic, and a more general one with four terms. These grids cover together 19 metallicities ranging from 10$^{-5}$ up to 10$^{+1}$ solar abundances, 0 $\leq$ log g $\leq$ 6.0 and 1500 K $\leq$ T$_{\rm eff}$ $\leq$ 50000 K. The calculations of the gravity-darkening coefficients were performed for all plane-parallel ATLAS models.

Tidal Distortion of the Envelope of an AGB Star IRS 3 near Sgr A*

Abstract We present radio and millimeter continuum observations of the Galactic center taken with the Very Large Array (VLA) and ALMA at 44 and 226 GHz, respectively. We detect radio and millimeter emission from IRS 3, lying ∼4.″5 NW of Sgr A*, with a spectrum that is consistent with the photospheric emission from an AGB star at the Galactic center. Millimeter images reveal that the envelope of IRS 3, the brightest and most extended 3.8 μm Galactic center stellar source, consists of two semicircular dust shells facing the direction of Sgr A*. The outer circumstellar shell, at a distance of 1.6 × 104 au, appears to break up into “fingers” of dust directed toward Sgr A*. These features coincide with molecular CS (5–4) emission and a near-IR extinction cloud distributed between IRS 3 and Sgr A*. The NE–SW asymmetric shapes of the IRS 3 shells seen at 3.8 μm and radio are interpreted as structures that are tidally distorted by Sgr A*. Using the kinematics of CS emission and the proper motion of IRS 3, the tidally distorted outflowing material from the envelope after 5000 yr constrains the distance of IRS 3 to ∼0.7 pc in front of or ∼0.5 pc behind Sgr A*. This suggests that the mass loss by stars near Sgr A* can supply a reservoir of molecular material near Sgr A*. We also present dark features in radio continuum images coincident with the envelope of IRS 3. These dusty stars provide examples in which high-resolution radio continuum images can identify dust-enshrouded stellar sources embedded in an ionized medium.

The most massive heartbeat: an in-depth analysis of ι Orionis

{\iota} Ori is a well studied massive binary consisting of an O9 III + B1 III/IV star. Due to its high eccentricity (e = 0.764) and short orbital period (P orb = 29.13376 d), it has been considered to be a good candidate to show evidence of tidal effects; however, none have previously been identified. Using photometry from the BRITE-Constellation space photometry mission we have confirmed the existence of tidal distortions through the presence of a heartbeat signal at periastron. We combine spectroscopic and light curve analyses to measure the masses and radii of the components, revealing {\iota} Ori to be the most massive heartbeat system known to date. In addition, using a thorough frequency analysis, we also report the unprecedented discovery of multiple tidally induced oscillations in an O star. The amplitudes of the pulsations allow us to empirically estimate the tidal circularization rate, yielding an effective tidal quality factor Q $\approx 4 \times 10^{4}$ .

Measuring neutron star tidal deformability with Advanced LIGO: A Bayesian analysis of neutron star-black hole binary observations

The pioneering discovery of gravitational waves (GWs) by Advanced LIGO has ushered us into an era of observational GW astrophysics. Compact binaries remain the primary target sources for GW observation, of which neutron star-black hole (NSBH) binaries form an important subset. GWs from NSBH sources carry signatures of (a) the tidal distortion of the neutron star by its companion black hole during inspiral, and (b) its potential tidal disruption near merger. In this paper, we present a Bayesian study of the measurability of neutron star tidal deformability ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}\ensuremath{\propto}(R/M{)}_{\mathrm{NS}}^{5}$ using observation(s) of inspiral-merger GW signals from disruptive NSBH coalescences, taking into account the crucial effect of black hole spins. First, we find that if nontidal templates are used to estimate source parameters for an NSBH signal, the bias introduced in the estimation of nontidal physical parameters will only be significant for loud signals with signal-to-noise ratios greater than $\ensuremath{\simeq}30$. For similarly loud signals, we also find that we can begin to put interesting constraints on ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ (factor of 1--2) with individual observations. Next, we study how a population of realistic NSBH detections will improve our measurement of neutron star tidal deformability. For an astrophysically likely population of disruptive NSBH coalescences, we find that 20--35 events are sufficient to constrain ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ within $\ifmmode\pm\else\textpm\fi{}25%--50%$, depending on the neutron star equation of state. For these calculations we assume that LIGO will detect black holes with masses within the astrophysical mass gap. In case the mass gap remains preserved in NSBHs detected by LIGO, we estimate that approximately 25% additional detections will furnish comparable ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ measurement accuracy. In both cases, we find that it is the loudest 5--10 events that provide most of the tidal information, and not the combination of tens of low-SNR events, thereby facilitating targeted numerical-GR follow-ups of NSBHs. We find these results encouraging, and recommend that an effort to measure ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NS}}$ be planned for upcoming NSBH observations with the LIGO-Virgo instruments.

Planet-induced Stellar Pulsations in HAT-P-2's Eccentric System

Abstract Extrasolar planets on eccentric short-period orbits provide a laboratory in which to study radiative and tidal interactions between a planet and its host star under extreme forcing conditions. Studying such systems probes how the planet’s atmosphere redistributes the time-varying heat flux from its host and how the host star responds to transient tidal distortion. Here, we report the insights into the planet–star interactions in HAT-P-2's eccentric planetary system gained from the analysis of ∼350 hr of 4.5 μm observations with the Spitzer Space Telescope. The observations show no sign of orbit-to-orbit variability nor of orbital evolution of the eccentric planetary companion, HAT-P-2 b. The extensive coverage allows us to better differentiate instrumental systematics from the transient heating of HAT-P-2 b’s 4.5 μm photosphere and yields the detection of stellar pulsations with an amplitude of approximately 40 ppm. These pulsation modes correspond to exact harmonics of the planet’s orbital frequency, indicative of a tidal origin. Transient tidal effects can excite pulsation modes in the envelope of a star, but, to date, such pulsations had only been detected in highly eccentric stellar binaries. Current stellar models are unable to reproduce HAT-P-2's pulsations, suggesting that our understanding of the interactions at play in this system is incomplete.

Long-period variable stars in NGC 147 and NGC 185 – I. Their star formation histories

NGC 147 and NGC 185 are two of the most massive satellites of the Andromeda galaxy (M 31). Close together in the sky, of similar mass and morphological type dE, they possess different amounts of interstellar gas and tidal distortion. The question therefore is, how do their histories compare? Here we present the first reconstruction of the star formation histories of NGC 147 and NGC 185 using long-period variable stars. These represent the final phase of evolution of low- and intermediate-mass stars at the asymptotic giant branch, when their luminosity is related to their birth mass. Combining near-infrared photometry with stellar evolution models, we construct the mass function and hence the star formation history. For NGC 185 we found that the main epoch of star formation occurred 8.3 Gyr ago, followed by a much lower, but relatively constant star formation rate. In the case of NGC 147, the star formation rate peaked only 7 Gyr ago, staying intense until ~ 3 Gyr ago, but no star formation has occurred for at least 300 Myr. Despite their similar masses, NGC 147 has evolved more slowly than NGC 185 initially, but more dramatically in more recent times. This is corroborated by the strong tidal distortions of NGC 147 and the presence of gas in the centre of NGC 185.

Ocean forecasting for the German Bight: from regional to coastal scales

Abstract. This paper describes recent developments based on advances in coastal ocean forecasting in the fields of numerical modeling, data assimilation, and observational array design, exemplified by the Coastal Observing System for the North and Arctic Seas (COSYNA). The region of interest is the North and Baltic seas, and most of the coastal examples are for the German Bight. Several pre-operational applications are presented to demonstrate the outcome of using the best available science in coastal ocean predictions. The applications address the nonlinear behavior of the coastal ocean, which for the studied region is manifested by the tidal distortion and generation of shallow-water tides. Led by the motivation to maximize the benefits of the observations, this study focuses on the integration of observations and modeling using advanced statistical methods. Coastal and regional ocean forecasting systems do not operate in isolation but are linked, either weakly by using forcing data or interactively using two-way nesting or unstructured-grid models. Therefore, the problems of downscaling and upscaling are addressed, along with a discussion of the potential influence of the information from coastal observatories or coastal forecasting systems on the regional models. One example of coupling coarse-resolution regional models with a fine-resolution model interface in the area of straits connecting the North and Baltic seas using a two-way nesting method is presented. Illustrations from the assimilation of remote sensing, in situ and high-frequency (HF) radar data, the prediction of wind waves and storm surges, and possible applications to search and rescue operations are also presented. Concepts for seamless approaches to link coastal and regional forecasting systems are exemplified by the application of an unstructured-grid model for the Ems Estuary.

Tidal distortion caused by the resonance of sexta‐diurnal tides in a micromesotidal embayment

AbstractDouble high water and double‐peak flood current were observed in Daya Bay (DYB), China, which is a shallow, mixed, mainly semidiurnal‐tide dominated bay with a micro to mesotidal range. Harmonic analysis reveals that the quarter and especially the sexta‐diurnal constituents are getting much stronger as tides propagating into the bay. The astronomical tides‐induced tidal asymmetry is yet dominant at the bay entrance but overtaken by the sexta‐diurnal tides at the end of the bay. Both the M4 and M6 tide meet the requirement proposed in previous studies but still unable to produce a double high water alone. Therefore, the conditions to produce a double high water between a fundamental tide and its higher harmonics need to be revisited. Analytical solutions were obtained in this paper, which fit the numerical solutions very well. Modeling result indicates M6 alone with M2 can produce the double high water in DYB but limited in some regions, while the combination of M2, M4, and M6 tides would enhance the capability. The amplification of sexta‐diurnal tides in DYB is dominated by resonance and followed by shoaling effect. Bottom friction damped M6 a lot and largely confined its amplification. However, the quadratic friction and other nonlinear processes are just responsible for about 10% of the total M6 increase.

Magnetic activity of interacting binaries

AbstractInteracting binaries provide unique parameter regimes, both rapid rotation and tidal distortion, in which to test stellar dynamo theories and study the resulting magnetic activity. Close binaries such as cataclysmic variables (CVs) have been found to differentially rotate, and so can provide testbeds for tidal dissipation efficiency in stellar convective envelopes, with implications for both CV and planet-star evolution. Furthermore, CVs show evidence of preferential emergence of magnetic flux tubes towards the companion star, as well as large, long-lived prominences that form preferentially within the binary geometry. Moreover, RS CVn binaries also show clear magnetic interactions between the two components in the form of coronal X-ray emission. Here, we review several examples of magnetic interactions in different types of close binaries.

RADIAL VELOCITY MONITORING OF KEPLER HEARTBEAT STARS*

ABSTRACT Heartbeat stars (HB stars) are a class of eccentric binary stars with close periastron passages. The characteristic photometric HB signal evident in their light curves is produced by a combination of tidal distortion, heating, and Doppler boosting near orbital periastron. Many HB stars continue to oscillate after periastron and along the entire orbit, indicative of the tidal excitation of oscillation modes within one or both stars. These systems are among the most eccentric binaries known, and they constitute astrophysical laboratories for the study of tidal effects. We have undertaken a radial velocity (RV) monitoring campaign of Kepler HB stars in order to measure their orbits. We present our first results here, including a sample of 22 Kepler HB systems, where for 19 of them we obtained the Keplerian orbit and for 3 other systems we did not detect a statistically significant RV variability. Results presented here are based on 218 spectra obtained with the Keck/HIRES spectrograph during the 2015 Kepler observing season, and they have allowed us to obtain the largest sample of HB stars with orbits measured using a single instrument, which roughly doubles the number of HB stars with an RV measured orbit. The 19 systems measured here have orbital periods from 7 to 90 days and eccentricities from 0.2 to 0.9. We show that HB stars draw the upper envelope of the eccentricity–period distribution. Therefore, HB stars likely represent a population of stars currently undergoing high eccentricity migration via tidal orbital circularization, and they will allow for new tests of high eccentricity migration theories.

Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.

Internal structure of charged AdS black holes

When an electrically charged black hole is perturbed its inner horizon becomes a singularity, often referred to as the Poisson-Israel mass inflation singularity. Ori constructed a model of this phenomenon for asymptotically flat black holes, in which the metric can be determined explicitly in the mass inflation region. In this paper we implement the Ori model for charged AdS black holes. We find that the mass function inflates faster than the flat space case as the inner horizon is approached. Nevertheless, the mass inflation singularity is still a weak singularity: although spacetime curvature becomes infinite, tidal distortions remain finite on physical objects attempting to cross it.

Cosmic tidal reconstruction

The gravitational coupling of a long-wavelength tidal field with small-scale density fluctuations leads to anisotropic distortions of the locally measured small-scale matter correlation function. Since the local correlation function is known to be statistically isotropic in the absence of such tidal interactions, the tidal distortions can be used to reconstruct the long-wavelength tidal field and large-scale density field in analogy with the cosmic microwave background lensing reconstruction. In this paper we present the theoretical framework of cosmic tidal reconstruction and test the reconstruction in numerical simulations. We find that the density field on large scales can be reconstructed with good accuracy and the cross-correlation coefficient between the reconstructed density field and the original density field is greater than 0.9 on large scales $(k\lesssim0.1\ h/\mathrm{Mpc})$, with the filter scale $\sim1.25\ \mathrm{Mpc}/h$. This is useful in the 21cm intensity mapping survey, where the long-wavelength radial modes are lost due to a foreground subtraction process.

A HUBBLE SPACE TELESCOPE STUDY OF THE ENIGMATIC MILKY WAY HALO GLOBULAR CLUSTER CRATER*

ABSTRACT We analyze the resolved stellar populations of the faint stellar system, Crater, based on deep optical imaging taken with the Advanced Camera for Surveys on the Hubble Space Telescope. Crater’s color–magnitude diagram (CMD) extends ∼4 mag below the oldest main-sequence (MS) turnoff. Structurally, we find that Crater has a half-light radius of ∼20 pc and no evidence for tidal distortions. We model Crater’s CMD as a simple stellar population (SSP) and alternatively by solving for its full star formation history. In both cases, Crater is well described by an SSP with an age of ∼7.5 Gyr, a metallicity of [M/H] ∼ −1.65, a total stellar mass of , and a luminosity of , located at a distance of d ∼ 145 kpc, with modest uncertainties due to differences in the underlying stellar evolution models. We argue that the sparse sampling of stars above the turnoff and subgiant branch are likely to be 1.0–1.4 blue stragglers and their evolved descendants, as opposed to intermediate-age MS stars. We find that Crater is an unusually young cluster given its location in the Galaxy’s outer halo. We discuss scenarios for Crater’s origin, including the possibility of being stripped from the SMC or the accretion from lower-mass dwarfs such as Leo I or Carina. Despite uncertainty over its progenitor system, Crater appears to have been incorporated into the Galaxy more recently than z ∼ 1 (8 Gyr ago), providing an important new constraint on the accretion history of the Galaxy.

Local and remote response of the North Sea dynamics to morphodynamic changes in the Wadden Sea

The response of the tidal system in the southern North Sea to morphodynamic changes was investigated in a modelling study using fine resolution bathymetric observations available for 1982–2011. The Semi-implicit Cross-scale Hydroscience Integrated System Model (SCHISM) was set up for the different sets of bathymetries. One set of bathymetry was compiled from a large number of bathymetric measurements over many years, while the other two reflected bathymetry state in the area of Wadden Sea during 2000 and 2011, respectively. The temporal and spatial evolution of bathymetry was dominated by migration of tidal channels. The M4 tide showed larger sensitivity to bathymetric change in the Wadden Sea than the M2 tide, whereas the structure of the latter remained rather robust. The largest change of the tidal wave due to the differences in bathymetries was located off the North Frisian Wadden Sea. Traces of changes were also found far away from the regions of their origin because the tidal waves in the North Sea propagate the local disturbances basin-wide. This illustrated an efficient physical mechanism of teleconnectivity, i.e. effecting the local responses to the larger-scale or remote change of ocean bottom caused by erosion and deposition. The tidal distortion resulting from the relatively small bathymetric changes was substantial, particularly in the coastal zone. This is a manifestation of the nonlinear tidal transformation in shallow oceans and is crucial for the sediment transport and the morphodynamic feedback, because of the altered tidal asymmetry.

The deep Earth may not be cooling down

Abstract The Earth is a thermal engine generating the fundamental processes of geomagnetic field, plate tectonics and volcanism. Large amounts of heat are permanently lost at the surface yielding the classic view of the deep Earth continuously cooling down. Contrary to this conventional depiction, we propose that the temperature profile in the deep Earth has remained almost constant for the last ∼4.3 billion years. The core–mantle boundary (CMB) has reached a temperature of ∼4400 K in probably less than 1 million years after the Moon-forming impact, regardless the initial core temperature. This temperature corresponds to an abrupt increase in mantle viscosity atop the CMB, when ∼60% of partial crystallization was achieved, accompanied with a major decrease in heat flow at the CMB. Then, the deep Earth underwent a very slow cooling until it reached ∼4100 K today. This temperature at, or just below, the mantle solidus is suggested by seismological evidence of ultra-low velocity zones in the D”-layer. Such a steady thermal state of the CMB temperature excludes thermal buoyancy from being the predominant mechanism to power the geodynamo over geological time. An alternative mechanism to sustain the geodynamo is mechanical forcing by tidal distortion and planetary precession. Motions in the outer core are generated by the conversion of gravitational and rotational energies of the Earth–Moon–Sun system. Mechanical forcing remains efficient to drive the geodynamo even for a sub-adiabatic temperature gradient in the outer core. Our thermal model of the deep Earth is compatible with an average CMB heat flow of 3.0 to 4.7 TW. Furthermore, the regime of core instabilities and/or secular changes in the astronomical forces could have supplied the lowermost mantle with a heat source of variable intensity through geological time. Episodic release of large amounts of heat could have remelted the lowermost mantle, thereby inducing the dramatic volcanic events that occurred during the Earth's history. In this scenario, because the Moon is a necessary ingredient to sustain the magnetic field, the habitability on Earth appears to require the existence of a large satellite.