Features of the 11-year variation of galactic cosmic rays in different periods of solar magnetic cycles

Variations of galactic cosmic ray intensity have been studied based on the neutron monitors and interplanetary magnetic field experimental data for different ascending and descending epochs of solar activity. The dependence of the diffusion coefficient on the cosmic ray particles rigidity R is stronger in the maxima epoch than in the minima epoch of solar activity. For the period of 1977–1981 (qA > 0) the diffusion coefficient for the minimum epoch is, χ_min ∝ R^{0.7 ± 0.04} and for the maximum χ_max ∝ R^{1.3 ± 0.05}; for the period of 1987–1990 (qA < 0), χ_min ∝ R^{0.8 ± 0.05} and χ_max ∝ R^{1.1 ± 0.04}. The exponents ν_y and ν_z of the power spectral density of the B_y and B_z components of the IMF in the region of the frequencies (10⁻⁶– 4 × 10⁻⁶) Hz are larger for the minimum epoch of 1987 (ν_y ≈ 2.0 and ν_z ≈ 1.93) than for the maximum epoch of 1990 (ν_y ≈ 1.43 and ν_z ≈ 1.27).     

XMM-Newton observations of the Mouse,SLX 1744–299 and SLX 1744–300

We observed the radio and X-ray source G359.23–0.82, also known as “the Mouse”, with XMM-Newton. The X-ray image of this object shows a point-like source at the Mouse’s “head”, accompanied by a “tail” that extends for about 40″ westward. The morphology is consistent with that observed recently with Chandra [Gaensler, B.M., van der Swaluw, E., Camilo, F., et al. The Mouse that soared: high resolution X-ray imaging of the pulsar-powered bow shock G359.23–0.82, ApJ 616, 383–402, 2004]. The spectrum of the head can be described by a power-law model with a photon index Γ ≃ 1.9. These results confirm that the Mouse is a bow-shock pulsar wind nebula (PWN) powered by PSR J1747–2958. We found that the hydrogen column density toward the Mouse, N_H = (2.60 ± 0.09) × 10²² cm⁻², is 20%–40% lower than those toward two serendipitously detected X-ray bursters, SLX 1744–299 and SLX 1744–300. At a plausible distance of 5 kpc, the X-ray luminosity of the Mouse, L(0.5–10 keV) = 3.7 × 10³⁴ erg s⁻¹, is 1.5% of the pulsar’s spin-down luminosity. We detected a Type I X-ray burst from SLX 1744–300 and found a possible decrease of N_H and persistent luminosity for this source, in comparison with those observed with ROSAT in 1992.     

The spatial distribution of galactic and anomalous cosmic rays in the heliosphere at solar minimum

The spatial distributions of galactic and anomalous cosmic rays in the heliosphere at the solar minima of Cycles 20/22 (qA > 0) and of Cycle 21 (qA < 0) are studied, using data from IMP 8, Voyagers 1/2 and Pioneer 10. It is found that the radial dependences of intensities J can be approximated by a power of radial distance r as J ∝ r^α with a different value of a constant in the inner and outer heliosphere with a transition at a radial distance of 10–15 AU. To study the physical meaning of these radial intensity profiles we examined the rigidity dependences of the intensity gradients by determining the particle mean free paths, using a simple one-dimensional modulation model. The particle mean free path λ was assumed to be a separable function of distance of the form r^γ and rigidity R of R^δ over the range of 0.5–3.0 GV in the inner and outer heliosphere. It was shown that λ of rigidity dependence of R^1.6 determined for Cycle 20/22 (qA > 0) with anomalous He is about 4–5 times larger than that of Cycle 21 (qA < 0) with R^0.9 at around 1 GV in the outer heliosphere, and that the radial dependences are r^1.4 and r^1.1, respectively, for Cycles 20/22 and for Cycle 21.     

Supernova remnant 1987A: The latest report from the Chandra X-ray Observatory

We continue monitoring supernova remnant (SNR) 1987A with the Chandra X-ray Observatory. As of 2004 January, bright X-ray spots in the northwest and the southwest are now evident in addition to the bright eastern ring. The overall X-ray spectrum, since 2002 December, can be described by a planar shock with an electron temperature of ∼2.1 keV. The soft X-ray flux is now 8 × 10⁻¹³ ergs cm⁻² s⁻¹, which is about five times higher than four years ago. This flux increase rate is consistent with our prediction based on an exponential density distribution along the radius of the SNR between the HII region and the inner ring. We still have no direct evidence of a central point source, and place an upper limit of L_X = 1.3 × 10³⁴ ergs s⁻¹ on the 3–10 keV band X-ray luminosity.     

Centre-to-limb variation of photospheric facular radiance and image resolution

We study the effect of the angular resolution on the determination of the angular properties of the facular radiance. We analyze photospheric intensity in the continuum, around the Ni 676.8 nm line, and longitudinal magnetic field along the line of sight, measured by the MDI instrument aboard SOHO with two spatial resolutions, 4″ and 1.2″ (2″ and 0.6″ pixels, respectively). The effect of the limited photometric sensitivity of the instrument and the limited information on the angular structure of the magnetic field tubes are considered. Our study of the high-resolution data shows that intensity contrast of magnetic features between 80 and 600 Gauss increases from centre to limb up to a maximum that occurs at higher heliocentric angles (θ) when obtained with higher resolution data than for lower resolution data. There is a suggestion that at heliocentric angles below about 75° there is only a monotonic increase in the contrast as one goes from cos (θ) = 1 to cos (θ) = 0.2.     

Modeling the effects of pitch-angle scattering processes on the transport of solar energetic particles along the interplanetary magnetic field

We present a Monte-Carlo technique to study the time-dependent transport of energetic particles in the interplanetary medium. We use the guiding center approximation between discrete finite pitch-angle scatterings to quantify the competing effects of focusing and pitch-angle scattering on energetic particles propagating along a Parker spiral magnetic field. We consider that the pitch-angle scattering process is produced by small-scale magnetic field irregularities frozen in the expanding solar wind. We also include the effects of both solar wind convection and adiabatic deceleration. We use a joint probability distribution P(h, μ′) = p(h; μ′)q(μ′; μ) to describe both the distance traveled by the particle between two scattering processes and the change in the particle pitch-angle after a scattering process. Here, p(h; μ′) is the conditional probability that the particle travels a distance h along the field line before the next scattering if it had a pitch-angle cosine μ′ after the previous scattering, and q(μ′; μ) is the conditional probability for the pitch-angle cosine μ′ if the pitch-angle cosine was μ before the scattering. We consider several functional forms to describe the processes of pitch-angle scattering, such as an isotropic scattering without any memory of the initial particle’s pitch-angle or processes in which the scattering result depends upon the initial particle’s pitch-angle. The results of our simulations are pitch-angle distributions and time-intensity profiles that can be directly compared to spacecraft observations. Comparison of our simulations with near-relativistic (45–290 keV) electron events observed by the Electron, Proton and Alpha Monitor on board the Advanced Composition Explorer allows us to estimate both the time dependence of the injection of near-relativistic electrons into the interplanetary medium and the conditions for electron propagation along the interplanetary magnetic field.     

Self-similar stochastic processes in solar wind turbulence

Solar wind data is used to estimate the autocorrelation function for the stochastic process x(τ) = y(t + τ) − y(t), considered as a function of τ, where y(t) is any one of the quantities B²(t), n_p(t)V²(t), or n_p(t). This process has stationary increments and a variance that increases like a power law τ^2γ where γ is the scaling exponent. For the kinetic energy density and the proton density the scaling exponent is close to the Kolmogorov value γ = 1/3, for the magnetic energy density it is slightly larger. In all three cases, it is shown that the autocorrelation function estimated from the data agrees with the theoretical autocorrelation function for a self-similar stochastic process with stationary increments and finite variance. This is far from proof, but it suggests that these stochastic processes may be self-similar for time scales in the small scale inertial range of the turbulence, that is, from approximately 10 to 10³ s.     

Gamma-ray observations of explosive nucleosynthesis products

In this review I discuss the various γ-ray emission lines that can be expected and, in some cases have been observed, from radioactive explosive nucleosynthesis products. The most important γ-ray lines result from the decay chains of ⁵⁶Ni, ⁵⁷Ni, and ⁴⁴Ti. ⁵⁶Ni is the prime explosive nucleosynthesis product of Type Ia supernovae, and its decay determines to a large extent the Type Ia light curves. ⁵⁶Ni is also a product of core-collapse supernovae, and in fact, γ-ray line emission from its daughter product, ⁵⁶Co, has been detected from SN1987A by several instruments. The early occurrence of this emission was surprising and indicates that some fraction of ⁵⁶Ni, which is synthesized in the innermost supernova layers, must have mixed with the outermost supernova ejecta.Special attention is given to the γ-ray line emission of the decay chain of ⁴⁴Ti (⁴⁴Ti → ⁴⁴Sc → ⁴⁴Ca), which is accompanied by line emission at 68, 78, and 1157 keV. As the decay time of ⁴⁴Ti is ∼86 yr, one expects this line emission from young supernova remnants. Although the ⁴⁴Ti yield (typically 10⁻⁵–10⁻⁴M_⊙) is not very high, its production is very sensitive to the energetics and asymmetries of the supernova explosion, and to the mass cut, which defines the mass of the stellar remnant. This makes ⁴⁴Ti an ideal tool to study the inner layers of the supernova explosion. This is of particular interest in light of observational evidence for asymmetric supernova explosions.The γ-ray line emission from ⁴⁴Ti has so far only been detected from the supernova remnant Cas A. I discuss these detections, which were made by COMPTEL (the 1157 keV line) and BeppoSAX (the 68 and 78 keV lines), which, combined, give a flux of (2.6 ± 0.4 ± 0.5) × 10⁻⁵ ph cm⁻² s⁻¹ per line, suggesting a ⁴⁴Ti yield of (1.5 ± 1.0) × 10⁻⁴M_⊙. Moreover, I present some preliminary results of Cas A observations by INTEGRAL, which so far has yielded a 3σ detection of the 68 keV line with the ISGRI instrument with a flux that is consistent with the BeppoSAX detections. Future observations by INTEGRAL-ISGRI will be able to constrain the continuum flux above 90 keV, as the uncertainty about the continuum shape, is the main source of systematic error for the 68 and 78 keV line flux measurements. Moreover, with the INTEGRAL-SPI instrument it will be possible to measure or constrain the line broadening of the 1157 keV line. A preliminary analysis of the available data indicates that narrow line emission (i.e., Δv < 1000 km s⁻¹) can be almost excluded at the 2σ level, for an assumed line flux of 1.9 × 10⁻⁵ ph cm⁻² s⁻¹.     

Excitations of nonmigrating diurnal tides in the mesosphere and lower thermosphere simulated by the Kyushu-GCM

Excitation mechanisms of nonmigrating diurnal tides in the MLT region simulated by the Kyushu-GCM are examined. It is shown that the westward propagating diurnal tide with zonal wavenumber s = 2 is mainly excited by nonlinear interactions between the migrating diurnal tide and the stationary planetary wave with zonal wavenumber s = 1, while the nonlinear excitation of the standing diurnal tide with zonal wavenumber s = 0 is less important than the excitation by tropospheric heating. Nonlinear interactions between the migrating diurnal tide and the stationary planetary wave with zonal wavenumber s = 2 are not dominant to excite the westward propagating diurnal tide with zonal wavenumber s = 3, and it is shown that the excitation by tropospheric heating is comparable to the nonlinear excitation. It is also shown that other nonmigrating diurnal tides are excited by tropospheric heating.     

Influence of dark matter on light propagation in solar system

We investigated the influence of dark matter on light propagation in the solar system. We assumed the spherical symmetry of spacetime and derived the approximate solution of the Einstein equation, which consists of the gravitational attractions caused by the central celestial body, i.e. the Sun, and the dark matter surrounding it. We expressed the dark matter density in the solar system in the following simple power-law form, ?(t,r)=ρ(t)(?/r)^k$?(t\text{,}r)=\rho (t)(?/r{)}^k$, where t is the coordinate time; r, the radius from the central body; ?, the normalizing factor; k, the exponent characterizing r  -dependence of dark matter density; and ρ(t)$\rho (t)$, the arbitrary function of time t. On the basis of the derived approximate solution, we focused on light propagation and obtained the additional corrections of the gravitational time delay and the relative frequency shift caused by the dark matter. As an application of our results, we considered the secular increase in the astronomical unit reported by Krasinsky and Brumberg (2004) and found that it was difficult to provide an explanation for the observed dAU/dt = 15 ± 4 m/century.     

Nusselt number for convection driven by tidal and radiogenic heating

The ‘traditional’ formulas giving the Nusselt number Nu as a function of Rayleigh number Ra cannot be used for low and moderate values of Ra. Moreover, the recent progress in 3D numerical modeling makes possible to determine the Nusselt number Nu as a function of Rayleigh number Ra for convection driven by radiogenic and tidal heating. We found that for low and moderate Ra: Nu(Ra) = ε(Ra+ξ)^λ where λ depends on rheology and boundary conditions, ε depends only on the mode of heating, and ξ = ε^−1/λ · Nu(Ra) makes possible to develop a parameterized theory of convection in medium size icy satellites. We also indicate some differences between convection driven by tidal and radiogenic heating and convection driven exclusively by radiogenic heating.     

Hard X-ray footpoint motions in solar flares: Comparing magnetic reconnection models with observations

Hard X-ray observations from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) of the October 29, 2003 GOES X10 two-ribbon flare are used together with magnetic field observations from the Michelson Doppler Imager (MDI) onboard SoHO to compare footpoint motions with predictions from magnetic reconnection models. The temporal variations of the velocity v of the hard X-ray footpoint motions and the photospheric magnetic field strength B in footpoints are investigated. The underlying photospheric magnetic field strength is generally higher (B ∼ 700–1200 G) in the slower moving (v ∼ 20–50 km s⁻¹) western footpoint than in the faster (v ∼ 20–100 km s⁻¹) moving eastern source (∼100–600 G). Furthermore, a rough temporal correlation between the HXR flux and the product vB² is observed.     

The role of drift and convection–diffusion mechanisms in small energy global cosmic ray modulation: Application to the hysteresis phenomenon of proton and alpha particle satellite data

The hysteresis effect for small energies of galactic cosmic rays is due to two effects. The first is the same as for neutron monitor energies – the delay of the interplanetary processes responsible for cosmic ray modulation with respect to the initiating solar processes, according to the effective velocity of solar wind and shock waves propagation. Then, the observed cosmic ray intensity is connected to the solar activity variations during many months before the time of cosmic ray measurement. The second is caused by the time delay of small energy cosmic ray diffusion from the boundary of modulation region to the Earth’s orbit. The model describing the connection between solar activity variation and cosmic ray convection–diffusion global modulation for neutron monitor energies is here developed by taking into account also the time-lag of the small energy particle diffusion in the Heliosphere. We use theoretical results on drifts and analytically approximate the dependences of drifts from tilt angle, and take into account the dependence from the sign of primary particles, and from the sign of polar magnetic field (A > 0 or A < 0). The obtained results are applied on proton and alpha-particle satellite data. We analyze satellite 5-min data of proton fluxes with energies >1 MeV, >2 MeV, >5 MeV, >10 MeV, >30 MeV, >50 MeV, >60 MeV, >100 MeV, and in intervals 10–30 MeV, 30–60 MeV, and 60–100 MeV during January 1986–December 1999. We exclude periods with great cosmic ray increases caused by particle acceleration in solar flare events. Then, we determine monthly averaged fluxes, as well as 5-month and 11-month smoothed data. We analyze also satellite 5-min data on alpha-particle fluxes in the energy intervals 60-160 MeV, 160–260 MeV and 330–500 MeV during January 1986–May 2000. We correct observation data for drifts and then compare with what is expected according to the convection–diffusion mechanism. We assume different dimensions of the modulation region (by the time propagation X₀ of solar wind from the Sun to the boundary of modulation region), for X₀ values from 1 to 60 average months, by one-month steps. For each value of X₀ we determine the correlation coefficient between variations of expected and observed cosmic ray intensities (the estimation of cosmic ray intensities values is given in Section 3 by Eq. (9), and the determination of correlation and regression coefficients in Section 3 by Eq. (8)). The dimension of modulation region is determined by the value of X_0 max, for which the correlation coefficient reaches the maximum value. Then the effective radial diffusion coefficient and residual modulation in small energy region can be estimated.     

A Gemini observation of the anomalous X-ray pulsar 1RXS J170849-400910

The anomalous X-ray pulsars (AXPs) represent a growing class of neutron stars discovered at X-ray energies. While the nature of their multi-wavelength emission mechanism is still under debate, evidence has been recently accumulating in favor of their magnetar nature. Their study in the optical and infrared (IR) wavelengths has recently opened a new window to constrain the proposed models. We here present a brief overview of AXPs and our Gemini-South observation of 1RXS J170849-400910, which is a relatively bright AXP discovered with ROSAT and later found to be an 11 s X-ray pulsar by ASCA. The observation was taken with the near-IR imager Flamingos in J (1.25 μm), H (1.65 μm), and K_s (2.15 μm). We confirm the recent detection by (ApJ, 589, L93–L96) of a source coincident with the CHANDRA source (candidate ‘A’). Our derived magnitudes of J = 20.6 (0.2), H = 18.6 (0.2), and K_s = 17.1 (0.2) are consistent with those derived by (ApJ, 589, L93–L96), and indicate that if this source is indeed the IR counterpart to 1RXS J170849-400910, then there is no evidence of variability from this AXP. However, given the lack of IR variability and the relatively high IR to X-ray flux of this source when compared to the other AXPs, we conclude that this source is unlikely the counterpart of the AXP, and that the other source (candidate ‘B’) within the CHANDRA error circle should not be ruled out as the counterpart. Further monitoring of these sources and a deep observation of this complex field are needed to confirm the nature of these sources and their association with the AXP.     

A spectroscopic measurement of high velocity spray plasma from an M-class flare and coronal mass ejection

The M1.5-class flare and associated coronal mass ejection (CME) of 16 February 2011 was observed with the Extreme ultraviolet Imaging Spectrometer on board the Hinode spacecraft. Spray plasma associated with the CME is found to exhibit a Doppler blue-shift of 850 km s^?1 – one of the largest values reported from spectroscopy of the solar disk and inner corona. The observation is unusual in that the emission line (Fe xii 193.51 Å) is not observed directly, but the Doppler shift is so large that the blue-shifted component appears in a wavelength window at 192.82 Å, intended to observe lines of O v, Fe xi and Ca xvii. The Fe xii 195.12 Å emission line is used as a proxy for the rest component of 193.51 Å. The observation highlights the risks of using narrow wavelength windows for spectrometer observations when observing highly-dynamic solar phenomena. The consequences of large Doppler shifts for ultraviolet solar spectrometers, including the upcoming Multi-slit Solar Explorer (MUSE) mission, are discussed.     

The plerionic supernova remnant G21.5-0.9: In and out

The absence of a supernova remnant (SNR) shell surrounding the Crab and other plerions (pulsar wind nebulae) has been a mystery for three decades. G21.5-0.9 is a particularly intriguing plerionic SNR in which the central powering engine is not yet detected. Early CHANDRA observations revealed a faint extended X-ray halo which was suggested to be associated with the SNR shell; however its spectrum was non-thermal, unlike what is expected from an SNR shell. On the other hand, a plerionic origin to the halo is problematic since the X-ray plerion would be larger than the radio plerion. We present here our analysis of an integrated 245 ks of archival CHANDRA data acquired with the High-Resolution Camera (HRC) and 520 ks acquired with the Advanced CCD Imaging Spectrometer (ACIS). This study provides the deepest and highest resolution images obtained to date. The resulting images reveal for the first time: (1) a limb-brightened morphology in the eastern section of the halo, and (2) a rich structure in the inner (40″-radius) bright plerion including wisps and a double-lobed morphology with an axis of symmetry running in the northwest–southeast direction. Our spatially resolved spectroscopic study of the ACIS-I data indicates that the photon index steepens with increasing distance from the central point source out to a radius of 40″ then becomes constant at ∼2.4 in the X-ray halo (for a column density N_H = 2.2 × 10²² cm⁻²). No line emission was found from the eastern limb; however marginal evidence for line emission in the halo’s northern knots was found. This study illustrates the need for deep CHANDRA observations to reveal the missing SNR material in Crab-like plerions.     

Optical properties of dust and the opacity of the Martian atmosphere

Particulate component of the Mars atmosphere composed by micron-sized products of soil weathering and water ice clouds strongly affects the current climate of the planet. In the absence of a dust storm so-called permanent dust haze with τ ≈ 0.2 in the atmosphere of Mars determines its thermal structure. Dust loading varies substantially with the season and geographic location, and only the data of mapping instruments are adequate to characterize it, such as TES/MGS and IRTM/Viking. In spite of vast domain of collected data, no model is now capable to explain all observed spectral features of dust aerosol. Several mineralogical and microphysical models of the atmospheric dust have been proposed but they cannot explain the pronounced systematic differences between the IR data (τ = 0.05–0.2) and measurements from the surface (Viking landers, Pathfinder) which give the typical “clear” optical depth of τ ≈ 0.5 from one side, and ground-based observations in the UV–visible range showing much more transparent atmosphere, on the other side. Also the relationship between τ₉ and the visible optical depth is not well constrained experimentally so far. Future focused measurements are therefore necessary to study Martian aerosol.     

Detection of thermal X-ray emission in the halo of the plerionic supernova remnant G21.5-0.9

The detection of a soft thermal X-ray component in the spectrum of a bright knot in the halo of the plerion G21.5-0.9 is reported. Using a collisional ionization equilibrium model for an hot optically thin plasma, a temperature of kT 0.12–0.24 keV, a mass of 0.3–1.0 M_⊙ and a density of 1.6–6 cm⁻³ is derived. The spectral analysis suggests a possible overabundance of Silicon with respect to the solar value in the knot; if this will be confirmed this object may be a clump of shocked ejecta.     

Real-time space debris monitoring with EISCAT

Following a feasibility study in 2000–2001 on using the EISCAT ionospheric research radars to detect centimetre-sized space debris in the frame of an ESA contract, we are now finishing a continuation study, aimed at achieving debris detection and parameter estimation in real-time. A requirement is to “piggy-back” space debris measurements on top of EISCAT’s normal ionospheric work, without interfering with that work, and to be able to handle about 500 h of measurements per year. We use a special digital receiver back-end in parallel with EISCAT’s standard receiver. We sample fast enough to correctly band-pass sample the EISCAT analog frequency band. To increase detection sensitivity, we use coherent pulse-to-pulse integration. The coherent integration is built-in in our method of parameter estimation, which we call the match function (MF) method. The method is derived from Bayesian statistical inversion, but reduces, with standard assumptions about noise and prior, to minimizing the least squares norm ∥z(t) − bχ(R,v,a;t)∥, where z is the measured signal and {bχ} is a set of model signals. Because the model signals depend linearly on the amplitude b, it is sufficient to maximize the magnitude of the inner product (cross correlation) between z and χ, the amplitude estimate is then determined by direct computation. The magnitude of the inner product, when properly normalized, is the MF. To construct the set of model signals, we sample the EISCAT transmission, in the same way as we sample the received signal, and apply linearly changing Doppler-shifts to it. Our initial implementation of the MF-method in 2001 was about four orders of magnitude too slow for real-time applications, but we have now gained the required speed factors. A factor of ten comes from using faster computers, another factor of ten comes from coding our key algorithms in C instead of Matlab. The largest factor, typically 100–300, comes from using a special, approximative, but in practice quite sufficient, method of finding the MF maximum. Test measurements show that we get real-time speed already when using a single dual-processor 2 GHz G5 Macintosh to do the detection computations.     

Spectral filter for signal identification in the kHz SLR measurements of the fast spinning satellite Ajisai

The high repetition rate satellite laser ranging (SLR) measurements to the fast spinning satellites contain a frequency signal caused by the rotational motion of the corner cube reflector (CCR) array. The spectral filter, developed here, is based on the Lomb algorithm, and is tested with the simulated and the observed high repetition rate SLR data of the geodetic satellite Ajisai (spin period ∼2 s). The filter allows for the noise elimination from the SLR data, and for identification of the returns from the single CCRs of the array – even for the low return rates. Applying the spectral filter to the simulated SLR data increases the S/N ratio by a factor 40–45% for all return rates. Filtering out the noise from the observed data strengthens the frequency signal by factor of ∼25 for the low return rates, which significantly helps to determine the spin phase of the satellite. The spectral filter is applied to the Graz SLR data and the spin rates of Ajisai are determined by two different methods: the frequency analysis and the phase determination of the spinning retroreflector array.The analysis of more than 8 years of the Graz SLR measurements indicates an exponential spin rate trend: f = 0.67034 exp(−0.0148542 Y) [Hz], RMS = 0.085 mHz, where Y is the year since launch. The highly accurate spin rate information demonstrates periodic changes related to the precession of the orbital plane of Ajisai, as it determines the amount of energy received by the satellite from the Sun. The rate of deceleration of Ajisai is not constant: the half life period of the satellite’s spin oscillates around 46.7 years with an amplitude of about 5 years.