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1.
Contemporary piece of writing devotes to the investigation of plane symmetric cosmological model with quark and strange quark matter in the deformations of the Einstein’s theory of General Relativity (GR). At small or large scales (ultraviolet or infrared gravity), deformations of the Einstein’s theory could provide a better handling of cosmic acceleration without magnetism (along with singularities). In particular, a proper deformation of GR in the ultraviolet regime could play the role of describing the transition between GR and quantum gravity. As a matter of fact, although with a different purpose in mind, it was Einstein himself who proposed in the 30’s the reformulation of GR by taking the field of orthonormal frames or tetrads as the dynamical variable instead of the metric tensor (Einstein, Phys. Math. Kl 217, 401, 1928). As per the observation, pressure and energy density of the model approaches the bag constant in negative and positive ways at \(t\rightarrow \infty \), i.e. \(p\rightarrow -B_c \) and \(\rho \rightarrow B_c \), the negative pressure due to the Dark Energy (DE) in the context of accelerated expansion of the universe. So the strange quark matter gives an idea of existence of dark energy in the universe and supports the observations of the SNe-I (Riess et al., Astron. J. 116,1009, 1998; Perlmutter et al., Astrophys. J. 517, 565, 1999). Also these results agree with the study of Aktas and Aygun (Chinese J. Phys. 55, 71, 2017) and Sahoo et al. (New. Astron. 60, 80, 2018).  相似文献   

2.
Here we report an in-depth reanalysis of an article by Vats et al. (Astrophys. J. 548, L87, 2001) that was based on measurements of differential rotation with altitude as a function of observing frequencies (as lower and higher frequencies indicate higher and lower heights, respectively) in the solar corona. The radial differential rotation of the solar corona is estimated from daily measurements of the disc-integrated solar radio flux at 11 frequencies: 275, 405, 670, 810, 925, 1080, 1215, 1350, 1620, 1755, and 2800 MHz. We use the same data as were used in Vats et al. (2001), but instead of the twelfth maxima of autocorrelograms used there, we use the first secondary maximum to derive the synodic rotation period. We estimate synodic rotation by Gaussian fit of the first secondary maximum. Vats et al. (2001) reported that the sidereal rotation period increases with increasing frequency. The variation found by them was from 23.6 to 24.15 days in this frequency range, with a difference of only 0.55 days. The present study finds that the sidereal rotation period increases with decreasing frequency. The variation range is from 24.4 to 22.5 days, and the difference is about three times larger (1.9 days). However, both studies give a similar rotation period at 925 MHz. In Vats et al. (2001) the Pearson’s factor with trend line was 0.86, whereas present analysis obtained a \({\sim}\,0.97\) Pearson’s factor with the trend line. Our study shows that the solar corona rotates more slowly at higher altitudes, which contradicts the findings reported in Vats et al. (2001).  相似文献   

3.
Our analysis in Papers I and II (Grechnev et al., Solar Phys. 289, 289, 2014b and Solar Phys. 289, 1279, 2014c) of the 18 November 2003 solar event responsible for the 20 November geomagnetic superstorm has revealed a complex chain of eruptions. In particular, the eruptive filament encountered a topological discontinuity located near the solar disk center at a height of about 100 Mm, bifurcated, and transformed into a large cloud, which did not leave the Sun. Concurrently, an additional CME presumably erupted close to the bifurcation region. The conjectures about the responsibility of this compact CME for the superstorm and its disconnection from the Sun are confirmed in Paper IV (Grechnev et al., Solar Phys. submitted, 2014a), which concludes about its probable spheromak-like structure. The present article confirms the presence of a magnetic null point near the bifurcation region and addresses the origin of the magnetic helicity of the interplanetary magnetic clouds and their connection to the Sun. We find that the orientation of a magnetic dipole constituted by dimmed regions with the opposite magnetic polarities away from the parent active region corresponded to the direction of the axial field in the magnetic cloud, while the pre-eruptive filament mismatched it. To combine all of the listed findings, we propose an intrinsically three-dimensional scheme, in which a spheromak-like eruption originates via the interaction of the initially unconnected magnetic fluxes of the eruptive filament and pre-existing ones in the corona. Through a chain of magnetic reconnections their positive mutual helicity was transformed into the self-helicity of the spheromak-like magnetic cloud.  相似文献   

4.
Coronal mass ejections (CMEs) are large-scale eruptions of plasma from the Sun, which play an important role in space weather. Faraday rotation is the rotation of the plane of polarization that results when a linearly polarized signal passes through a magnetized plasma such as a CME. Faraday rotation is proportional to the path integral through the plasma of the electron density and the line-of-sight component of the magnetic field. Faraday-rotation observations of a source near the Sun can provide information on the plasma structure of a CME shortly after launch. We report on simultaneous white-light and radio observations made of three CMEs in August 2012. We made sensitive Very Large Array (VLA) full-polarization observations using 1?–?2 GHz frequencies of a constellation of radio sources through the solar corona at heliocentric distances that ranged from 6?–?\(15~\mathrm{R}_{\odot}\). Two sources (0842+1835 and 0900+1832) were occulted by a single CME, and one source (0843+1547) was occulted by two CMEs. In addition to our radioastronomical observations, which represent one of the first active hunts for CME Faraday rotation since Bird et al. (Solar Phys., 98, 341, 1985) and the first active hunt using the VLA, we obtained white-light coronagraph images from the Large Angle and Spectrometric Coronagraph (LASCO) C3 instrument to determine the Thomson-scattering brightness [\(\mathrm{B}_{\mathrm{T}}\)], providing a means to independently estimate the plasma density and determine its contribution to the observed Faraday rotation. A constant-density force-free flux rope embedded in the background corona was used to model the effects of the CMEs on \(\mathrm{B}_{\mathrm{T}}\) and Faraday rotation. The plasma densities (\(6\,\mbox{--}\,22\times10^{3}~\mbox{cm}^{-3}\)) and axial magnetic-field strengths (2?–?12 mG) inferred from our models are consistent with the modeling work of Liu et al. (Astrophys. J., 665, 1439, 2007) and Jensen and Russell (Geophys. Res. Lett., 35, L02103, 2008), as well as previous CME Faraday-rotation observations by Bird et al. (1985).  相似文献   

5.
It has been argued (Gough and McIntyre in Nature 394, 755, 1998) that the only way for the radiative interior of the Sun to be rotating uniformly in the face of the differentially rotating convection zone is for it to be pervaded by a large-scale magnetic field, a field which is responsible also for the thinness of the tachocline. It is most likely that this field is the predominantly dipolar residual component of a tangled primordial field that was present in the interstellar medium from which the Sun condensed (Braithwaite and Spruit in Nature 431, 819, 2004), and that advection by the meridional flow in the tachocline has caused the dipole axis to be inclined from the axis of rotation by about \(60^{\circ}\) (Gough in Geophys. Astrophys. Fluid Dyn., 106, 429, 2012). It is suggested here that, notwithstanding its turbulent passage through the convection zone, a vestige of that field is transmitted by the solar wind to Earth, where it modulates the geomagnetic field in a periodic way. The field variation reflects the inner rotation of the Sun, and, unlike turbulent-dynamo-generated fields, must maintain phase. I report here a new look at an earlier analysis of the geomagnetic field by Svalgaard and Wilcox (Solar Phys. 41, 461, 1975), which reveals evidence for appropriate phase coherence, thereby adding support to the tachocline theory.  相似文献   

6.
This work is a continuation of our previous articles (Yermolaev et al. in J. Geophys. Res.120, 7094, 2015 and Yermolaev et al. in Solar Phys.292, 193, 2017), which describe the average temporal profiles of interplanetary plasma and field parameters in large-scale solar-wind (SW) streams: corotating interaction regions (CIRs), interplanetary coronal mass ejections (ICMEs, including both magnetic clouds (MCs) and ejecta), and sheaths as well as interplanetary shocks (ISs). Changes in the longitude angle, \(\varphi\), in CIRs from ?2 to \(2^{\circ}\) agree with earlier results (e.g. Gosling and Pizzo, 1999). We have also analyzed the average temporal profiles of the bulk velocity angles in sheaths and ICMEs. We have found that the angle \(\varphi\) in ICMEs changes from 2 to \(-2^{\circ}\), while in sheaths it changes from ?2 to \(2^{\circ}\) (similar to the change in CIRs), i.e. the angle in CIRs and sheaths deflects in the opposite sense to ICMEs. When averaging the latitude angle \(\vartheta\) on all the intervals of the chosen SW types, the angle \(\vartheta\) is almost constant at \({\sim}\,1^{\circ}\). We made for the first time a selection of SW events with increasing and decreasing \(\vartheta\) and found that the average \(\vartheta\) temporal profiles in the selected events have the same “integral-like” shape as for \(\varphi\). The difference in \(\varphi\) and \(\vartheta\) average profiles is explained by the fact that most events have increasing profiles for the angle in the ecliptic plane as a result of solar rotation, while for the angle in the meridional plane, the numbers of events with increasing and decreasing profiles are equal.  相似文献   

7.
Rapidly moving transient features have been detected in magnetic and Doppler images of super-active region NOAA 10486 during the X17/4B flare of 28 October 2003 and the X10/2B flare of 29 October 2003. Both these flares were extremely energetic white-light events. The transient features appeared during impulsive phases of the flares and moved with speeds ranging from 30 to 50 km?s?1. These features were located near the previously reported compact acoustic (Donea and Lindsey, Astrophys. J. 630, 1168, 2005) and seismic sources (Zharkova and Zharkov, Astrophys. J. 664, 573, 2007). We examine the origin of these features and their relationship with various aspects of the flares, viz., hard X-ray emission sources and flare kernels observed at different layers: i) photosphere (white-light continuum), ii) chromosphere (Hα 6563 Å), iii) temperature minimum region (UV 1600 Å), and iv) transition region (UV 284 Å).  相似文献   

8.
IUE has made very successful long term and intense short time-scale monitoring spectroscopic study of NGC 4151, a Seyfert 1 galaxy for over nearly 18 years from its launch in 1978 to 1996. The long-term observations have been useful in understanding the complex relation between UV continuum and emission line variability Seyfert galaxies. In this paper, we present the results of our studies on the short-timescale intense monitoring campaign of NGC 4151 undertaken during December 1–15, 1993. A most intense monitoring observation of NGC 4151 was carried out by IUE in 1993, when the source was at its historical high flux state with a shortest interval of 70 min between two successive observations. We present our results on emission line and continuum variability amplitudes characterized by \(F_{\mathrm{var}}\) method. We found highest variability of nearly 8.3% at 1325 \(\AA \) continuum with a smallest amplitude of 4% at 2725 \(\AA \). The relative variability amplitudes (\(R_\mathrm{max}\)) have been found to be 1.372, 1.319, 1.302 and 1.182 at 1325, 1475, 1655 and 2725 \(\AA \) continuum respectively. The continuum and emission line variability characteristics obtained in the present analysis are in very good agreement with the results obtained by Edelson et al. (1996) and Crenshaw et al. (1996) from the analysis of the same observational spectral data. The large amplitude rapid variability characteristics obtained in our study have been attributed to the continuum reprocessing of X-rays absorbed by the material in the accretion disk as proposed by Shakura and Sunyaev (1973). The continuum and emission light curves have shown four distinct high amplitude events of flux maxima during the intense monitoring campaign of 15 days, providing a good limit on the amplitude of UV variability and the BLR size in low luminosity Seyfert galaxies and are useful for constraining the continuum emission models. The decreasing \(F_{\mathrm{var}}\) amplitude of UV continuum with respect to increasing wavelength obtained in the present study and consistent with similar observations by Edelson et al. (1996) and Crenshaw et al. (1996) is a significant result of the intense monitoring observations.  相似文献   

9.
Fast Radio Bursts (FRBs) are short duration highly energetic dispersed radio pulses. We developed a generic formalism (Bera et al. 2016, MNRAS, 457, 2530) to estimate the FRB detection rate for any radio telescope with given parameters. By using this model, we estimated the FRB detection rate for two Indian radio telescope; the Ooty Wide Field Array (OWFA) (Bhattacharyya et al. 2017, J. Astrophys. Astr., 38, 17) and the upgraded Giant Metrewave Radio Telescope (uGMRT) (Bhattacharyya et al. 2018, J. Astrophys. Astr.) with three beam-forming modes. Here, we summarize these two works. We considered the energy spectrum of FRBs as a power law and the energy distribution of FRBs as a Dirac delta function and a Schechter luminosity function. We also considered two scattering models proposed by Bhat et al. (2004, Astrophys. J. Suppl. Series, 206, 1) and Macquart & Koay (2013, ApJ, 776, 125) for these works and we consider FRB pulse without scattering as a special case. We found that the future prospects of detecting FRBs by using these two Indian radio telescopes is good. They are capable to detect a significant number of FRBs per day. According to our prediction, we can detect \(\sim 10^5{-}10^8\), \(\sim 10^3{-}10^6\) and \(\sim 10^5{-}10^7\) FRBs per day by using OWFA, commensal systems of GMRT and uGMRT respectively. Even a non detection of the predicted events will be very useful in constraining FRB properties.  相似文献   

10.
This work is a continuation of our previous article (Yermolaev et al. in J. Geophys. Res. 120, 7094, 2015), which describes the average temporal profiles of interplanetary plasma and field parameters in large-scale solar-wind (SW) streams: corotating interaction regions (CIRs), interplanetary coronal mass ejections (ICMEs including both magnetic clouds (MCs) and ejecta), and sheaths as well as interplanetary shocks (ISs). As in the previous article, we use the data of the OMNI database, our catalog of large-scale solar-wind phenomena during 1976?–?2000 (Yermolaev et al. in Cosmic Res., 47, 2, 81, 2009) and the method of double superposed epoch analysis (Yermolaev et al. in Ann. Geophys., 28, 2177, 2010a). We rescale the duration of all types of structures in such a way that the beginnings and endings for all of them coincide. We present new detailed results comparing pair phenomena: 1) both types of compression regions (i.e. CIRs vs. sheaths) and 2) both types of ICMEs (MCs vs. ejecta). The obtained data allow us to suggest that the formation of the two types of compression regions responds to the same physical mechanism, regardless of the type of piston (high-speed stream (HSS) or ICME); the differences are connected to the geometry (i.e. the angle between the speed gradient in front of the piston and the satellite trajectory) and the jumps in speed at the edges of the compression regions. In our opinion, one of the possible reasons behind the observed differences in the parameters in MCs and ejecta is that when ejecta are observed, the satellite passes farther from the nose of the area of ICME than when MCs are observed.  相似文献   

11.
Stark broadening parameters for nine neutral oxygen (O I) lines have been determined within the impact approximation and the semiclassical perturbation method. The atomic data have been taken from the TOPbase and NIST atomic databases. The electron and proton Stark widths and shifts and ion broadening parameter values for these O I lines have been calculated for electron density of 10 16 cm ?3 and for 4 different electron temperatures in the range of 5000 K to 40000 K. These Stark broadening parameters are compared with our previous results (Ben Nessib, N. et al. 1996, Physica Scripta, 54, 603–613), where we calculated Stark broadening parameters for only four O I spectral lines and where Stark widths and shifts were compared with experimental and theoretical data available in the literature. In the present paper, we have also compared our results with the Griem’s book (Griem, H. R. 1974, Spectral line broadening by plasmas) and VALD (Ryabchikova, T. et al. 2015, Physica Scripta, 90, 054005) values.  相似文献   

12.
The 1982 model for the formation of Hulse–Taylor binary radio pulsar PSR B1913+16 is described, which since has become the ‘standard model’ for the formation of the double neutron stars, confirmed by the 2003 discovery of the double pulsar system PSR J0737-3039AB. A brief overview is given of the present status of our knowledge of the double neutron stars, of which 15 systems are presently known. The binary-recycling model for the formation of millisecond pulsars is described, as put forward independently by Alpar et al. (1982), Radhakrishnan & Srinivasan (1982) and Fabian et al. (1983). This now is the ‘standard model’ for the formation of these objects, confirmed by the discovery in 1998 of the accreting millisecond X-ray pulsars. It is noticed that the formation process of close double black holes has analogies to that of close double neutron stars, extended to binaries with larger initial component masses, although there are also considerable differences in the physics of the binary evolution at these larger masses.  相似文献   

13.
Estimating for the frequency drift rates of type III solar bursts is crucial for characterizing their source development in the solar corona. According to Melnik et al. (Solar Phys.269, 335, 2011), the analysis of powerful decameter type III solar bursts, observed in July?–?August 2002, found a linear approximation for the drift rate versus frequency. The conclusion contradicts reliable results of many other well-known solar observations. In this paper we report on the reanalysis of the solar data with a more advanced method. Our study shows that the decameter type III solar bursts of July?–?August 2002, as standard type III bursts, follow a power law in frequency drift rates. We explain the possible reasons for this discrepancy.  相似文献   

14.
Some quiet-Sun days observed by the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SDO) during the time interval in 2010?–?2017 were used to continue our previous analyses reported by Didkovsky and Gurman (Solar Phys.289, 153, 2014a) and Didkovsky, Wieman, and Korogodina (Solar Phys.292, 32, 2017). The analysis consists of determining and comparing spatial spectral ratios (spectral densities over some time interval) from spatial (segmentation-cell length) power spectra. The ratios were compared using modeled compatible spatial frequencies for spectra from the Extreme ultraviolet Imaging Telescope (EIT) on-board the Solar and Heliospheric Observatory (SOHO) and from AIA images. With the new AIA data added to the EIT data we analyzed previously, the whole time interval from 1996 to 2017 reported here is approximately the length of two “standard” solar cycles (SC). The spectral ratios of segmentation-cell dimension structures show a significant and steady increase with no detected indication of SC-related returns to the values that characterize the SC minima. This increase in spatial power at high spatial frequencies is interpreted as a dissipation of medium-size EUV network structures to smaller-size structures in the transition region. Each of the latest ratio changes for 2010 through 2017 spectra calculated for a number of consecutive short-term intervals has been converted into monthly mean ratio (MMR) changes. The MMR values demonstrate variable sign and magnitudes, thus confirming the solar nature of the changes. These changes do not follow a “typical” trend of instrumental degradation or a long-term activity profile from the He?ii (30.4 nm) irradiance measured by the Extreme ultraviolet Spectrophotometer (ESP) either. The ESP is a channel of the Extreme ultraviolet Variability Experiment (EVE) on-board SDO.  相似文献   

15.
The Heliospheric Imagers (HI) on the Solar TErrestrial RElations Observatory (STEREO) observe the solar wind and disturbances therein as it propagates from close to the Sun to 1 AU and beyond. In this article we use stellar photometry over much of the mission to date to make a determination of the long-term evolution of the photometric response of the inner (HI-1) cameras. We find very slow degradation rates of the order of 0.1 % per year, similar to those found for HI-2 by Tappin, Eyles and Davies (Solar Phys. 290, 2143, 2015) and significantly slower than rates found for other comparable instruments. We also find that it is necessary to make a small (\({\approx}\,1~\%\)) revision to the photometric calibration parameters used to convert instrument units into physical units. Finally, we briefly discuss the effects of pointing instabilities on the measurement of stellar count rates.  相似文献   

16.
Exploring weakly perturbed Keplerian motion within the restricted three-body problem, Lidov (Planet Space Sci 9:719–759, 1962) and, independently, Kozai (Astron J 67:591–598, 1962) discovered coupled oscillations of eccentricity and inclination (the KL cycles). Their classical studies were based on an integrable model of the secular evolution, obtained by double averaging of the disturbing function approximated with its first non-trivial term. This was the quadrupole term in the series expansion with respect to the ratio of the semimajor axis of the disturbed body to that of the disturbing body. If the next (octupole) term is kept in the expression for the disturbing function, long-term modulation of the KL cycles can be established (Ford et al. in Astrophys J 535:385–401, 2000; Naoz et al. in Nature 473:187–189, 2011; Katz et al. in Phys Rev Lett 107:181101, 2011). Specifically, flips between the prograde and retrograde orbits become possible. Since such flips are observed only when the perturber has a nonzero eccentricity, the term “eccentric Kozai–Lidov effect” (or EKL effect) was proposed by Lithwick and Naoz (Astrophys J 742:94, 2011) to specify such behavior. We demonstrate that the EKL effect can be interpreted as a resonance phenomenon. To this end, we write down the equations of motion in terms of “action-angle” variables emerging in the integrable Kozai–Lidov model. It turns out that for some initial values the resonance is degenerate and the usual “pendulum” approximation is insufficient to describe the evolution of the resonance phase. Analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space.  相似文献   

17.
We perform a statistical analysis on 157 M-class soft X-ray flares observed during 1997?–?2014 with and without deca-hectometric (DH) type II radio bursts aiming at the reasons for the non-occurrence of DH type II bursts in certain events. All the selected events are associated with halo Coronal Mass Ejections (CMEs) detected by the Solar and Heliospheric Observatory (SOHO) / Large Angle Spectrometric and COronograph (LASCO). Out of 157 events, 96 (61%; “Group I”) events are associated with a DH type II burst observed by the Radio and Plasma Wave (WAVES) experiment onboard the Wind spacecraft and 61 (39%; “Group II”) events occur without a DH type II burst. The mean CME speed of Group I is \(1022~\mbox{km}/\mbox{s}\) and that of Group II is \(647~\mbox{km}/\mbox{s}\). It is also found that the properties of the selected M-class flares such as flare intensity, rise time, duration and decay time are greater for the DH associated flares than the non-DH flares. Group I has a slightly larger number (56%) of western events than eastern events (44%), whereas Group II has a larger number of eastern events (62%) than western events (38%). We also compare this analysis with the previous study by Lawrance, Shanmugaraju, and Vr?nak (Solar Phys. 290, 3365L, 2015) concerning X-class flares and confirm that high-intensity flares (X-class and M-class) have the same trend in the CME and flare properties. Additionally we consider aspects like acceleration and the possibility of CME-streamer interaction. The average deceleration of CMEs with DH type II bursts is weaker (\(a = - 4.39\mbox{ m}/\mbox{s}^{2}\)) than that of CMEs without a type II burst (\(a = -12.21\mbox{ m}/\mbox{s}^{2}\)). We analyze the CME-streamer interactions for Group I events using the model proposed by Mancuso and Raymond (Astron. Astrophys. 413, 363, 2004) and find that the interaction regions are the most probable source regions for DH type II radio bursts.  相似文献   

18.
We present a preliminary analysis of X-ray data of quasars in the context of the 4D eigenvector 1 parameter space (Sulentic et al. 2000a, b). 4DE1 serves as a surrogate H-R diagram for representing empirical diversity among quasars and identifying the physical drivers of the diversity. The soft X-ray spectral index (Γsoft) was adopted as one of the key 4DE1 that correlates contrasting extremes in Type 1 properties. 4DE1 motivated the hypothesis of two quasar populations (A and B) divided by L/L EDD≈0.2. Pop. A is a largely radio-quiet population with FWHM H β<4000 km/s and often showing a soft X-ray excess. Pop. B is a mix of radio-quiet and a majority of RL quasars shows only a hard X-ray power-law SED. The X-ray separation was based upon earlier ROSAT and ASCA data but we now confirm this dichotomy with large samples of X-ray spectra obtained with XMM-Newton and SWIFT. One popular idea connects the soft excess in Pop. A quasars as a signature of thermal emission from a hot accretion disk in sources radiating close to the Eddington limit.  相似文献   

19.
The term “jumping” Trojan was introduced by Tsiganis et al. (Astron Astrophys 354:1091–1100, 2000) in their studies of long-term dynamics exhibited by the asteroid (1868) Thersites, which had been observed to jump from librations around \(L_4\) to librations around \(L_5\). Another example of a “jumping” Trojan was found by Connors et al. (Nature 475:481–483, 2011): librations of the asteroid 2010 TK7 around the Earth’s libration point \(L_4\) preceded by its librations around \(L_5\). We explore the dynamics of “jumping” Trojans under the scope of the restricted planar elliptical three-body problem. Via double numerical averaging we construct evolutionary equations, which allow analyzing transitions between different regimes of orbital motion.  相似文献   

20.
Continuing a work initiated in an earlier publication (Yamada et al. in Phys Rev D 91:124016, 2015), we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein–Infeld–Hoffmann form of equations of motion for N-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e., we take account of perturbations orthogonal to the orbital plane, as well as perturbations lying on it. It is found that the orthogonal perturbations depend on each other by the first post-Newtonian (1PN) three-body interactions, though these are independent of the lying ones likewise the Newtonian case. We also show that the orthogonal perturbations do not affect the condition of stability. This is because these do not grow with time, but always precess with two frequency modes, namely, the same with the orbital frequency and the slightly different one due to the 1PN effect. The condition of stability, which is identical to that obtained by the previous work (Yamada et al. 2015) and is valid for the general perturbations, is obtained from the lying perturbations.  相似文献   

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