A Study of the Rotation of the Solar Corona

Synoptic photoelectric observations of the coronal Fexiv and Fex emission lines at 530.3 nm and 637.4 nm, respectively, are analyzed to study the rotational behavior of the solar corona as a function of latitude, height, time and temperature between 1976 (1983 for Fex) and 2001. An earlier similar analysis of the Fexiv data at 1.15 R over only one 11-year solar activity cycle (Sime, Fisher, and Altrock, 1989, Astrophys. J. 336, 454) found suggestions of solar-cycle variations in the differential (latitude-dependent) rotation. These results are tested over the longer epoch now available. In addition, the new Fexiv 1.15 R results are compared with those at 1.25 R and with results from the Fex line. I find that for long-term averages, both ions show a weakly-differential rotation period that may peak near 80° latitude and then decrease to the poles. However, this high-latitude peak may be due to sensing low-latitude streamers at higher latitudes. There is an indication that the Fexiv rotation period may increase with height between 40° and 70° latitude. There is also some indication that Fex may be rotating slower than Fexiv in the mid-latitude range. This could indicate that structures with lower temperatures rotate at a slower rate. As found in the earlier study, there is very good evidence for solar-cycle-related variation in the rotation of Fexiv. At latitudes up to about 60°, the rotation varies from essentially rigid (latitude-independent) near solar minimum to differential in the rising phase of the cycle at both 1.15 R and 1.25 R . At latitudes above 60°, the rotation at 1.15 R appears to be nearly rigid in the rising phase and strongly differential near solar minimum, almost exactly out of phase with the low-latitude variation.     

Earth Tides and Lense–Thirring Effect

The general relativistic Lense—Thirring effect can be measured by inspecting a suitable combination of the orbital residuals of the nodes of LAGEOS and LAGEOS II and the perigee of LAGEOS II. The solid and ocean Earth tides affect the recovery of the parameter by means of which the gravitomagnetic signal is accounted for in the combined residuals. Thus an extensive analysis of the perturbations induced on these orbital elements by the solid and ocean Earth tides is carried out. It involves the l=2 terms for the solid tides and the l=2,3,4 terms for the ocean tides. The perigee of LAGEOS II turns out to be very sensitive to the l=3 part of the ocean tidal spectrum, contrary to the nodes of LAGEOS and LAGEOS II. The uncertainty in the solid tidal perturbations, mainly due to the Love number k ₂, ranges from 0.4% to 1.5%, while the ocean tides are uncertain at 5–15% level. The obtained results are used in order to check in a preliminary way which tidal constituents the Lense-Thirring shift is sensitive to. In particular it is tested if the semisecular 18.6-year zonal tide really does not affect the combined residuals. It turns out that, if modeled at the level of accuracy worked out in the paper, the l=2,4 m=0 and also, to a lesser extent, the l=3, m=0 tidal perturbations cancel out.This revised version was published online in October 2005 with corrections to the Cover Date.     

On the Abundance of Holmium in the sun

The abundance of holmium (Z=67) in the Sun remains uncertain. The photospheric abundance, based on lines of Hoii, has been reported as + 0.26±0.16 (on the usual scale where log(H) = 12.00), while the meteoritic value is + 0.51±0.02. Cowan-code calculations have been undertaken to improve the partition function for this ion by including important contributions from unobserved levels arising from the (4f ¹¹6p+4f ¹⁰(5d+6s)²) group. Based on 6994 computed energy levels, the partition function for Hoii is 67.41 for a temperature of 6000 K. This is 1.5 times larger than the value derived from the 49 published levels. The new partition function alone leads to an increase in the solar abundance of Ho to log (Ho) =+ 0.43. This is within 0.08 dex of the meteoritic abundance. Support for this result has been obtained through LTE spectrum synthesis calculations of a previously unidentified weak line at 3416.38. Attributing the feature to Hoii, the observations may be fitted with log (Ho) =+ 0.53. This calculation assumes log (gf)=0.25 and is uncertain by at least 0.1 dex.     

On the coupling of lunisolar resonances for Earth satellite orbits

The resonance C1 occurs when the longitude of the perigee measured from the equinox becomes a slow angle in the doubly averaged equations of motion. This resonance is one of the critical inclination family with I 46°. For prograde Earth satellite orbits, up to five critical points can be identified. Only simple pitchfork bifurcations occur for the single resonance C1. A two degrees of freedom system is studied to check how a coupling of two lunisolar resonances affects the results furnished by the analysis of an isolated resonance case. In the system with two critical angles (g+h and h,+2 , seven types of critical points have been identified. The critical points arise and change their stability through 11 bifurcations. If the initial conditions are selected close to the critical points, the system becomes chaotic as shown in Poincaré maps.     

On the Rectilinear Non-Collision Motion

We systematically investigate the rectilinear non-collision motion, i.e., the rectilinear one with C>0, where C is the angular momentum integral. This kind of motion appears in stellar dynamics when considering encounters of stars. For a short enough segment of a star's path, it is a very good approximation to the real motion of the star. Moreover, we derive also an analogue to Kepler's equation for this motion, and, considering the barycentric orbits of the stars, we find their minimal mutual distance.     

Similarities between chromospheric and photospheric quiet-Sun magnetograms

Simultaneous observations of chromospheric (H) and photospheric (Fei 5324.19 Å) magnetograms in quiet solar regions enable us to study the spatial configuration of the magnetic field in the solar atmosphere. With the typical spatial resolution of the Huairou magnetograph, the photospheric and chromospheric magnetic structures of the quiet Sun maintain a very similar pattern. Moreover, the vertical magnetic flux is almost the same from the photosphere to the chromosphere. As an intermediate step, we analyze the formation of the working lines used by the Huairou video magnetograph of the Beijing Astronomical Observatory. The Stokes V contribution function of H and Fei 5324.19 Å are calculated. It is found that our H magnetograms provide the distribution of the chromospheric magnetic field at a height some 1000–1500 km above the photosphere.     

Infrared Spectroscopy from San Fernando Observatory: He I 1083 nm, O I 1316 nm, and Fe I 1565 nm

Imaging spectroscopy of the Sun was carried out at the California State University Northridge San Fernando Observatory using an InGaAs near-IR video camera. Using the Sii 1082.71 nm and Hei 1083.03 nm lines the Evershed effect is measured simultaneously in the photosphere and the chromosphere for three sunspots; the speed of the Evershed flow is measured to be between 3 to 8 times greater in the Hei line than in the Sii line, and the direction is radially inward in the chromosphere and outward in the photosphere. Telluric absorption lines prevented a meaningful measurement of Oi 1128.7 nm limb emission, but an upper limit of 20×10^–3 B is measured for chromospheric limb emission at Oi 1316.3 nm. Zeeman splitting in Fei 1564.9 nm was observed in six sunspot umbrae, and a linear relationship between magnetic field and umbral continuum intensity is confirmed.     

Radial Flows in Supergranules

We determine the radial component of the supergranular flow velocity by examining the center-to-limb variation of the Doppler velocity signal. We acquire individual Doppler images obtained with the MDI instrument on the SOHO spacecraft and process them to remove the p-mode oscillation signal, the axisymmetric flows, the convective blueshift signal, and instrumental artifacts. The remaining Doppler signal contains only non-axisymmetric flow structures. The Doppler signal from the horizontal flows in these structures varies like sin, where is the heliocentric angle from disk center. The Doppler signal from radial flows varies like cos. We fit the center-to-limb variation of the mean squared velocity signal to a straight line in sin² over the central portion of the disk. The intercept of this line at disk center gives the amplitude of the radial component of the flow. The slope of the line gives the amplitude of the horizontal component. We find that the radial flows for typical supergranules have speeds about 10% that of their associated horizontal flows or about 30 m s^–1. The ratio of the radial to horizontal flow speed increases from 9% to about 18% as the size of the structure decreases from >60 Mm to 5 Mm. We use data simulations to check these results and find a ratio that increases from 5% to only about 12% over the same range of sizes. These smaller ratios are attributed to an underestimation of the horizontal flow speeds due to the fact that the transverse component of the horizontal flow is not detected by Doppler measurements.     

Crossing of Various Cantori

We find the form of cantori surrounding an island of stable motion in the standard map for various values of the nonlinearity parameter K near the value K=5 (much larger than the critical value K _cr=0.971635...). The asymptotic curves of unstable periodic orbits inside the cantorus cross it after a certain time and then escape to the large chaotic sea. For K=5 the crossing time (in appropriate units) is t=1 and the escape time is t=2. For K=4.998 the crossing time is t=7 and the escape time t=23000. This delay of escape is due to the existence of higher order cantori, with very small gaps. We found that, as K increases the noble torus [2,4,1,1,..] is destroyed before the destruction of the higher order tori [2,4,1,1,1,1,2,1,...] and [2,4,1,1,1,1,3,1,...]. Thus the torus with the simplest noble number is not the last KAM curve to be destroyed. Then we find that nearby orbits deviate considerably, but the average times spent near various resonance before escape are very similar.     

Synthetic Proper Elements for Outer Main Belt Asteroids

For the orbits with low to moderate inclination and eccentricity, in the asteroid main belt, the analytically computed proper elements are accurate to a level very close to the best result achievable by any analytical theory. This fundamental limitation results from the infinite web of resonances and because of the occurrence of chaotic motions. Still, there are some regions of the belt in which these proper elements are of degraded accuracy, thus preventing a reliable definition of asteroid families and detailed studies of the dynamical structure. We have used a different method to compute asteroid proper elements, following the approach introduced in the LONGSTOP project to describe the secular dynamics of the major outer planets. By applying purely numerical techniques, we produced so-called synthetic proper elements for a catalog of 10,256 asteroids with osculating semimajor axes between 2.5 and 4.0AU.The procedure consisted of simultaneous integration of asteroid and planetary orbits for 2Myr, with online filtering of the short-periodic perturbations. The output of the integration was spectrally resolved, and the principal harmonics (proper values) extracted from the time series. For each asteroid we have also tested the accuracy and stability in time of the proper elements, and estimated the maximum Lyapunov Characteristic Exponent to monitor the chaotic behaviors. This provided information on the reliability of the data for each orbit, in particular allowing to select 1,852 cases for an extended integration (10Myr) of the orbits showing instability. The results indicate that for more than half of the cases the proper elements have a time stability improved by more than a factor 3 with respect to the elements computed by the previous analytical theory. But of course there are also unstable cases for which the proper elements are less accurate and reliable, the extreme examples being 23 orbits exhibiting hyperbolic escape from the solar system. This form of escape from the asteroid belt could be responsible for a significant mass loss over the age of the solar system.     

Wavelength Shifts in the Solar Photospheric Spectrum

Wavelength shifts converted to velocities between solar lines observed at disc center and laboratory wavelengths of Fei, Feii, Tii, Nii, and Fei lines in the near infrared are plotted as a function of the logarithm of their solar equivalent width in milliångstroms. The need for wavelengths based on the wavelength standards is stressed. A comparison of photographic Fei solar wavelength is shown to agree, on the average, with Fourier Transform Spectrometer solar wavelengths within less than 0.5 milliångstroms. Using Balthasar's limb effect tables we convert the disc center velocities to limb velocities and find, though the scatter is large, that there is little evidence for a super-gravitational red shift.     

The geometry of the Roche coordinates

The exact geometry of the Roche curvilinear coordinates (, , ) in which corresponds to the zero-velocity surfaces is investigated numerically in the plane, as well as in the spatial, case for various values of the mass-ratio between the two point-masses (m ₁,m ₂) constituting a binary system.The geometry of zero-velocity surfaces specified by -values at the Lagrangian points are first discussed by taking their intersections with various planes parallel to thexy-, xz- andyz-planes. The intersection of the zero-velocity surface specified by the -value at the Lagrangian equilateral-triangle pointsL _4,5 with the planex=1/2 discloses two invariable curves passing through the pointsL _4,5 and situated symmetrically with respect to thexy-plane whose form is independent of the mass-ratio.The geometry of the remaining two coordinates (, ) orthogonal to the zero-velocity surfaces is investigated in thexy- andxz-planes from extensive numerical integrations of differential equations generated from the orthogonality relations among the coordinates. The curves (x, y)=constant in thexy-plane are found to be separated into three families by definite envelopes acting as boundaries whose forms depend upon the mass-ratio only: the inner -constant curves associated with the masspointm ₁, the inner -constant curves associated with the mass-pointm ₂ and the outer -constant curves. All the -constant curves in thexy-plane coalesce at either of the Lagrangian equilateraltriangle pointsL _4,5, except for a limiting case coincident with thex-axis. The curves (x, z)=constant in thexz-plane are also separated by definite envelopes depending upon the mass-ratio into different families: the inner -constant curves associated with the mass-pointm ₁, the inner -constant curves associated with the mass-pointm ₂ and the outer -constant curves on both sides out of the envelopes. For larger values ofz, the curves =constant tend asymptotically to the line perpendicular to thex-axis and passing through the centre of mass of the system, except for a limiting case coincident with thex-axis. The geometrical aspects of the envelopes for the curves (x, y)=constant in thexy-plane and the curves (x, z)=constant in thexz-plane are also discussed independently.In the three-dimensional space, the Roche coordinates can be conveniently defined in such a way as to correspond to the polar coordinates in the immediate neighbourhood of the origin, and to the cylindrical coordinates at great distances. From numerical integrations of simultaneous differential equations generating spatial curves orthogonal to the zero-velocity surfaces, the surfaces (x, y, z)=constant and the surfaces (x, y, z)=constant are constructed as groups of such spatial curves with common values of some parameters specifying the respective surfaces.On leave of absence from the University of Tokyo as an Honorary Fellow of the Victoria University of Manchester.     

Electron densities above a polar coronal hole based on improved Si IX density diagnostics

Using new close-coupling excitation rates for the C-like ion Siix, density-diagnostic ratios based on Siix lines have been re-evaluated and applied to a sequence of CDS observations taken above a polar coronal hole. The derived electron densities are in excellent agreement with previous values of N_eestimated from the N-like ion Siviii for another coronal hole. The confirmed trend is for a fall-off of one order of magnitude within the first 0.3 Rabove the limb. These densities are well fitted with an analytic formula for the density profile out to at least 8 R, by which stage the electron density has fallen to 4×10³ cm^–3, from 1.5×10⁸ cm^–3at 1.0 R.     

Why do Trojan ASCs (not) Escape?

The orbits of 12 Trojan asteroids, which have Lyapunov times T _L10⁵ years and were previously classified as ASCs(=asteroids in stable chaos), are integrated for 50 Myrs, along with a group of neighbouring initial conditions for each nominal orbit. About 40% of the orbits present strong instabilities in the inclination, which may be attributed primarily to the action of the ₁₆ secular resonance; two escapes are also recorded. Higher-order secular resonances, involving the nodes of the outer planets, are also found to be responsible for chaotic motion. Orbital stability depends critically on the choice of initial conditions and, thus, these objects can be regarded as being on the edge of strong chaos.     

Short-Term Periodicities in the Time Series of Solar Radio Emissions at Different Solar Altitudes

A spectral analysis of the time series of daily values of 12 parameters, namely, ten solar radio emissions in the range 275–1755 MHz, 2800 MHz solar radio flux, and sunspot numbers for six continuous intervals of 132 values each during June 1997–July 1999 showed considerable differences from one interval to the next, indicating a nonstationary nature. A 27-day periodicity was noticed in Interval 2 (26.8 days), 3 (27.0 days), 5 (25.5 days), 6 (27.0 days). Other periodicities were near 11.4, 12.3, 13.3, 14.5, 15.5, 16.5, 35, 40, 50–70 days. Periodicities were very similar in a large vertical span of the coronal region corresponding to 670–1755 MHz. Above this region, the homogeneity disappeared. Below this region, there were complications and distortions due to localized solar surface phenomena.     

Soft X-ray emission lines of Ni XVIII in the solar spectrum

R-matrix calculations of electron impact excitation rates in Nixviii are used to derive theoretical electron-temperature-sensitive emission line ratios involving 3s–4p,3p–4d,3p –4s, and 3d–4f transitions in the 41–53 Å wavelength range. A comparison of these with solar flare observations from a rocket-borne X-ray spectrograph (XSST) reveals generally excellent agreement between theory and experiment (within the experimental and theoretical uncertainties), which provides support for the atomic data adopted in the analysis. However the 3s 2S–4p 2P1/2 line of Nixviii at 41.22 Å appears to be blended with the Fexix 13.74 Å feature observed by XSST in third order. In addition, the measured Nixviii intensity ratio I(3p 2P3/2– 4s 2S)/I(3p 2P1/2–4s 2S)=I(51.02 Å)/I(50.26 Å)=0.56, a factor of 3.8 smaller than the theoretical (temperature and density-insensitive) value of 2.1. The reason for this discrepancy is currently unexplained, but is unlikely to be due to blending of the 50.26 Å line, as the intensity of this feature is consistent with that expected from the other Nixviii lines in the XSST spectrum. Future observations of the Nixviii lines by the Advanced X-ray Astrophysics Facility (AXAF) should allow this problem to be resolved, and may also permit the use of the lines as electron-temperature diagnostics.     

Dynamics of Blinkers

The relative Doppler and non-thermal velocities of quiet-Sun and active-region blinkers identified in Ov with CDS are calculated. Relative velocities for the corresponding chromospheric plasma below are also determined using the Hei line. Ov blinkers and the chromosphere directly below, have a preference to be more red-shifted than the normal transition region and chromospheric plasma. The ranges of these enhanced velocities, however, are no larger than the typical spread of Doppler velocities in these regions. The anticipated ranges of Doppler velocities of blinkers are 10–15 km s^–1 in the quiet Sun (10–20 km s^–1 in active regions) for Hei and 25–30 km s^–1 in the quiet Sun (20–40 km s^–1 in active regions) for Ov. Blinkers and the chromosphere below also have preferentially larger non-thermal velocities than the typical background chromosphere and transition region. Again the increase in magnitude of these non-thermal velocities is no greater than the typical ranges of non-thermal velocities. The ranges of non-thermal velocities of blinkers in both the quiet Sun and active regions are estimated to be 15–25 km s^–1 in Hei and 30–45 km s^–1 in Ov. There are more blinkers with larger Doppler and non-thermal velocities than would be expected in the whole of the chromosphere and transition region. The recently suggested mechanisms for blinkers are revisited and discussed further in light of the new results.     

Characteristics of Flares with Hα Emission Protruding over Major Sunspot Umbrae

A sample of 47 importance 1 flares whose H emission occurred or protruded over umbrae of major sunspots (so called Z-flares) was studied to investigate characteristics of the associated dm–m radio, microwave and soft X-ray emission as the energy release site permeats into regions of strong magnetic fields. A close time association was found between the microwave burst peak and the `contact' of the H emission with the sunspot umbra. The H emission attained maximum close to or a few minutes after the contact. The soft X-ray bursts were delayed more, attaining maximum 0–10 min after the contact. The onset of bursts in the dm–m wavelength range was associated with the period of growth or the peak of the microwave burst. Two categories of type III and IV bursts could be recognized: the ones starting some ten minutes before the microwave peak, and those that begin close to the microwave burst peak. Type III bursts occur preferably when the microwave burst peaks simultaneously with or after the contact. The results are explained presuming that the contact reveals a permeation of the energy release process into a region of strong magnetic fields, where the process intensifies, and where the accelerated particles have access to magnetic field lines extending to large coronal heights. Different manifestations of the energy release process in various magnetic field topologies are considered to account for the various time sequences observed.     

Comparative morphology of EIT/SOHO images and He ii excitation

Morphological differences between coronal images on the one hand, and a Hei image on the other, are used to demonstrate the independence of Heii excitation from coronal radiation. The distribution of magnetic flux is found to be more important for Heii excitation. Collisional excitation by non-thermal electrons produced in nano-flare events is proposed as the mechanism for Heii excitation.