On properties of the fourier harmonics in the limit-cycle models of classical cepheids

The Fourier coefficients of the hydrodynamic variables are calculated for the limit-cycle models of classical Cepheids having periods from 7.2 to 10.9 days. In adiabatically pulsating layers of the stellar envelope, each Fourier harmonic of orderk 8 is shown to be identified with a corresponding standing wave, so that the pulsation motions of the adiabatic layers may be represented as a superposition of standing waves. Each Fourier harmonic of orderk may also be identified with the eigenfunction of orderl of the linear adiabatic wave equation when the resonance condition _l /₀ =k is fulfilled. The spectra of the oscillatory moment of inertia and the spectra of kinetic energy obey the power law for the Fourier harmonics of orderk 15, the spectrum slope being steeper for shorter pulsation periods. In the helium and hydrogen ionizing regions all of the Fourier harmonics drive the pulsation instability, whereas in the radiative damping region the mechanical work done by each Fourier harmonic is negative. In classical Cepheids having periods shorter than 10 days the period dependence of the secondary bump is due to phase changes of the second order Fourier harmonic in the outer nonadiabatic layers of the stellar envelope. At a pulsation period of II 9.7 days the second order Fourier harmonic is identified with the second overtone. At periods II > 10 days the second order Fourier harmonic tends to be attracted by the fundamental mode in such a way that their phases coincide in the outer layers of the stellar envelope.     

Variation of the solar constant during the solar cycle

Measurements of the Nimbus-7 and Solar Maximum Mission satellites reported temporary large decreases of the solar constant of the order of a few tenths of a percent on a time-scale from days to weeks. Our investigations show that these decreases were caused by active sunspot groups with fast development and complex structure. This connection between the solar constant variation and the appearance of the active groups seems to be more clear in the maximum of the solar activity. At the time of the solar minimum, mainly in the second part of 1984, there were not any active sunspot groups practically on the solar disk, the value of the solar constant only fluctuated around its mean without large variation. The results of time series analyses show that the periodicity of the solar constant values, of young and active spot areas was nearly 23.5 days in 1980, which increases to 28 days towards the minimum of the solar cycle till 1983. During this time interval the main periodicity of the old, passive spot areas was around 28 days. In 1984, at the time of the solar minimum, there were not any obvious periodicities practically in the projected areas of the different types of the sunspot groups.     

Photometry of Comet 9P/Tempel 1 during the 2004/2005 approach and the Deep Impact module impact

The results of the 9P/Tempel 1 CARA (Cometary Archive for Amateur Astronomers) observing campaign is presented. The main goal was to perform an extended survey of the comet as a support to the Deep Impact (DI) Mission. CCD R, I and narrowband aperture photometries were used to monitor the Afρ quantity. The observed behavior showed a peak of 310 cm 83 days before perihelion, but we argue that it can be distorted by the phase effect, too. The phase effect is roughly estimated around 0.0275 mag/degree, but we had no chance for direct determination because of the very similar geometry of the observed apparitions. The log-slope of Afρ was around −0.5 between about 180-100 days before the impact but evolved near the steady-state like 0 value by the impact time. The DI module impact caused about a 60% increase in the value of Afρ and a cloud feature in the coma profile which was observed just after the event. The expansion of the ejecta cloud was consistent with a fountain model with initial projected velocity of 0.2 km/s and β=0.73. Referring to a 25,000 km radius area centered on the nucleus, the total cross section of the ejected dust was 0.06 days after the impact, and 1.93 days after the impact (A is the dust albedo). Five days after the event no signs of the impact were detected, nor deviations from the expected activity referring both to the average pre-impact behavior and to the previous apparitions.     

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.     

Observations of the inner coma of C/1995O1 (Hale-Bopp)—gas and dust production

Hale-Bopp (C/1995 O1) was the most productive recent comet observed in terms of gas and dust output. Since its discovery in 1995 at a distance of 7.14 AU from the Sun, the comet has been well observed, revealing the dynamics of a rare and large comet. Hale-Bopp showed strong emissions of the principle cometary gases CN, C₃, and C₂, as well as an abundance of dust. The production rates of these gases were found to be 1.45×10²⁸, 1.71×10²⁸, and , respectively, with dust production, in terms of Afρ, , as measured in the green continuum (5260 Å). The observations for this paper are presented in two groups spanning 10 days each, one group centered near 32 days prior to and the other 21 days after perihelion. The averages of dust and gas production rates show a slightly higher value for each prior to perihelion than after perihelion, consistent with a possible peak in production a few weeks prior to perihelion passage.     

Dependence of the meridional motions of sunspot groups on life spans and age of the groups,and on the phase of the solar cycle

We have analyzed data on sunspot groups compiled during 1874–1981 and investigated the following: (i) dependence of the `initial' meridional motion (v <sub>ini</sub>()) of sunspot groups on the life span () of the groups in the range 2–12 days, (ii) dependence of the meridional motion (v(t)) of sunspot groups of life spans 10–12 days on the age (t) of the spot groups, and (iii) variations in the mean meridional motion of spot groups of life span 2–12 days during the solar cycle. In each of the latitude intervals 0°–10°, 10°–20° and 20°–30°, the values of both v <sub>ini</sub>() and v(t) often differ significantly from zero. In the latitude interval 20°–30°, the forms of v <sub>ini</sub>() and v(t) are largely systematic and mutually similar in both the north and south hemispheres. The form of v(t) suggests existence of periodic variation in the solar meridional motion with period of 4 days and amplitude 10–20 m s<sup>–1</sup>. Using the anchoring depths of magnetic structures for spot groups of different and testimated earlier, (Javaraiah and Gokhale, 1997), we suggest that the forms of v <sub>ini</sub>() and v(t) may represent radial variation of meridional flow in the Sun's convection zone, rather than temporal variation of the flow. The meridional flows (v <sub>e</sub>(t)) determined from the data during the last few days (i.e., age t: 10–12 days) of spot groups of life spans of 10–12 days are found to have magnitudes (10–20 m s<sup>–1</sup>) and directions (poleward) similar to the those of the surface meridional plasma flows determined from the Dopplergrams and magnetograms. The mean meridional velocity of sunspot groups living 2–12 days seems to vary during the solar cycle. The velocity is not significantly different from zero during the rising phase of the cycle and there is a suggestion of equatorward motion (a few m s<sup>–1</sup>at lower latitudes and 10 m s<sup>–1</sup>at higher latitudes) during the declining phase (last few years) of the cycle. The variation during the odd numbered cycles seems to anticorrelate with the variation during the even numbered cycles, suggesting existence of 22-year periodicity in the solar meridional flow. The amplitude of the anticorrelation seems to be depending on latitude and the cycle phase. In the latitude interval 20°–30° the `surface plasma meridional motion', v _e(t), is found to be poleward during maximum years (v _e(t) 20 m s^–1at 4th year) and equatorward during ending years of the cycle (v _e(t) –17 m s^–1at 10th year).     

Observational Study about the Influence of the Solar Wind on the Earth's Rotation

The data on the variation of the Earth's rotation from IERS and the parameters of the solar wind measured by IPM 8 from July 1992 to September 1995 were used for a regression analysis. The results show that there seems to be a weak linear correlation between the velocity of the solar wind near the Earth, V, and the variation of the length of the day, lod₁ calculated from UT1 and averaged over five days. The correlation coefficient is R=0.186. The preliminary conclusion is that the Earth's rotation could be influenced by the variation of the velocity of the solar wind with a short time scale of several days.     

The Relationship Between Kinematics and Spatial Structure of the Large-Scale Solar Magnetic Field

The rotation of large-scale solar magnetic fields has been investigated by analysing a 20-yr series of synoptic maps of the radial magnetic field. For this purpose, a specially adapted method of spectral analysis was used. We calculated rotation spectra of the magnetic field as functions of the rotation period, heliographic latitude, and longitudinal wave number, k. These spectra reveal the existence of a number of discrete, rigidly rotating components (modes) of the magnetic field, whose rotation periods lie in the wide range from 26.5 to 30.5 days. The significant spectral maxima lie in the (rotation period–latitude) plane close to the curve that represents the differential rotation of small-scale magnetic features. For the first harmonic of the magnetic field (k=1) the properties of the rotation spectra are consistent with those reported by Antonucci, Hoeksema, and Scherrer (1990). However, the distribution of the rigidly rotating modes over rotation period and their latitudinal structure change systematically with the harmonic number k. As k increases, the mean distance P in rotation period between the modes decreases, from 1.2 days for k=1 to 0.3–0.5 days for k=4. This decreasing period separation is accompanied by a decrease of the characteristic latitude separation between the mode maxima. The latitudinal and longitudinal discrete spatial scales of the non-axisymmetric magnetic field appear to be connected with each other, as well as with the temporal scale P.     

LASCO observations of the coronal rotation

The near-rigid rotation of the corona above the differential rotation of the photosphere has important implications for the form of the global coronal magnetic field. The magnetic reconfiguring associated with the shear region where the rigidly-rotating coronal field lines interface with the differentially-rotating photospheric field lines could provide an important energy source for coronal heating. We present data on coronal rotation as a function of altitude provided by the Large Angle Spectrometric Coronagraph (LASCO) instrument aboard the Solar and Heliospheric Observatory (SOHO) spacecraft. LASCO comprises of three coronagraphs (C1, C2, and C3) with nested fields-of-view spanning 1.1 R to 30 R. An asymmetry in brightness, both of the Fexiv emission line corona and of the broad-band electron scattered corona, has been observed to be stable over at least a one-year period spanning May 1996 to May 1997. This feature has presented a tracer for the coronal rotation and allowed period estimates to be made to beyond 15R, up to 5 times further than previously recorded for the white-light corona. The difficulty in determining the extent of differential motion in the outer corona is demonstrated and latitudinally averaged rates formed and determined as a function of distance from the Sun. The altitude extent of the low latitude closed coronal field region is inferred from the determined rotation periods which is important to the ability of the solar atmosphere to retain energetic particles. For the inner green line corona (<2 R) we determine a synodic rotation period of (27.4±0.1) days, whereas, for the outer white- light corona, (>2.5 R) we determine a rotation period of (27.7±0.1) days.     

Rotational modulation of Ca K flux ratio and sunspot number

The results of daily monitoring of the Ca K flux variations of integrated sunlight during the period 1 July 1979–18 February 1980 are presented, and the data analyzed by both power spectrum and autocorrelation methods. The latter method is found to be superior; in it the autocorrelation function is fit to a model having three parameters, viz. the maximum long-term autocorrelation c ₁, the rotational period ₀ and an effective lifetime ₁. Values of c ₁ = 0.26, ₀ = 25.9 days, and ₁ = 500 days are obtained for the Ca K flux ratio; somewhat different values of c ₁ = 0.77, ₀ = 28.0 days, and ₁ = 89 days are obtained for the sunspot number for the same period. Rotational modulation is clearly evident for the relatively weak chromosphere of the Sun and should be even more easily observed for more active stars.     

On the eruption of prominences and disappearance of quiescent filaments

We suggest the following heuristic model for the evolution of a quiescent filament. The middle part of the filament rises due to heating, while its ends remain anchored in the chromosphere; and a kink appears in the H filament due to projection and line-of-sight effects. Further, the top segment of the filament rises rapidly above the solar surface 1–2 days before the disappearance of a filament or eruption of a prominence. The top of the filament attains a high temperature due to further heating, thereby becoming invisible in H, giving the impression that the filament has split into two parts. It is expected that this gap between the H filament can be seen in the observations in high-temperature lines and soft X-rays.     

Short period Miras and Galactic Structure

Red Giants on the Asymptotic Giant Branch typically are more luminous than M _K = -7 mag. Therefore, a new Two Micron Sky Survey which will go as faint as m _K = 10 mag will be able to observe most of these stars in the Milky Way. Such a complete census will enable us to develop a much better understanding of Galactic Structure. It will be important to separate the luminous red giants into their different subclasses because these subclasses trace different Galactic Populations. For example, Miras with periods less than 300 days can be used to study the thick disk while Miras with periods greater than 300 days belong to the thin disk.     

Post-sunset cooling behavior of the lunar surface

Differential infrared flux scans at 22m have been made across the nighttime lunar surface over a range of phases before and after new Moon. The differential chopping technique effectively cancels atmospheric emission in the beam path but records the flux difference between adjacent resolution elements on the lunar disk. The scans show that the brightness temperature gradient across the highlands after sunset is much greater than that across the western maria. The large gradients consistently disappear approximately 3.5 days after sunset. The post-sunset enhancement could be due to surface roughness in the highlands or to a significant surface rock population with a mean size of approximately 0.5 m. The effect can be seen in the 10m measurements of other investigators, but its global nature was not detected in their limited data sets.     

A remarkable configuration of sector boundaries

A study of all the observed and well-defined sector boundaries from January 1957 to February 1975, published by Svalgaard (1974, 1975a, b), indicated that sector boundary key-dates, transformed into Bartels' days, have a significant preference to occur on certain days of the solar rotation. The eclectic distribution of these sector boundaries give some Bartels' days that are empty of cases, while on other days there is a significant excess over the average. Using this effect, we can predict, in high levels of significance, the possible occurrence of a (+,–) or (–,+) boundary within particular days of the solar rotation.     

Hydrodynamic models for population-II cepheids

The nonlinear self-excited pulsations of population-II stars with mass 0.6M and luminosities from 128 to 1280L are studied. The pulsation periods are found to be in the range of 1.3 to 19 days. An increase of the stellar luminosity is shown to be accompanied by an increasing nonadiabaticity and decreasing efficiency of the radiative damping region. This leads to both an increase of the growth rate while pulsations are exciting and an increase of the oscillation amplitude of the limit cycle. In the models withL800L the efficiency of the radiative damping region becomes so small that amplitude growth ceases due to a dissipation of the mechanical energy by shocks in the stellar atmosphere. The models with periods of from 1.3 to 3 days show the bump on their light curves. The bump is connected with a travelling pulse generated at the antinode of the second overtone at maximum compression. The time delays estimated for the pulses reflected of the stellar core are in a good agreement with the pulse resonance condition proposed by Aikawa and Whitney (1983). The model with the period of 2.1 days revealed double resonance ₀ = 2₂, 2₀ = 3₁ causing alternating oscillations with slightly different periods and amplitudes. The models with period of 10 days and longer reveal the resonance ₀ = 2₁. This resonance causes the flat top on the light curve at a period of about 10 days and appearance of a shallow alternating minimum at longer periods, as is observed in RV Tau variables. The theoretical period-luminosity relation proposed for population-II cepheids is in good agreement with that obtained from observations.     

Spectral studies of the time-series of the geomagnetic activities

The geomagnetic effect of active centers of the Sun has been investigated statistically dividing into three groups according to the values of — Bo of the active centers and using the method of superposed epochs. Some interesting results between active centers and recurrent and sporadic storm days have been found; that is, recurrent storm days do not increase significantly while the frequency of sporadic storm days increases when the active centers approach to the Sun-Earth line. We have also investigated new periodicities of aa, Ap and Ci indices using Discrete Fourier Transforms, and have found some new periodicities and confirmed the known ones.     

How well was the Sun observed during the Maunder Minimum?

In this paper we examine how well the Sun and sunspots were observed during the Maunder Minimum from 1645 to 1715. Recent research has given us the dates of observations by Hevelius, Picard, La Hire, Flamsteed, and about 70 other observers. These specific observations allow a lower estimate of the fraction of the time the Sun was observed to be deduced. It is found that 52.7% of the days have recorded observations. There are additional 12 observers who provide general statements that no sunspots were observed during specific years or intervals despite diligent efforts. Taking these statements to mean, unrealistically, that every day during these intervals was observed, gives an upper estimate of 98% of the days. If the general statements are relaxed by assuming that 100 ± 50 days per year were actually observed by these diligent observers, than our best estimate is that 68%±7% of the days during the Maunder Minimum were observed. In short, this supports the view that the Maunder Minimum existed and was not an artifact of few observations. Some sunspots are probably still missed in modern compilations, but the existence of a prolonged sunspot minimum would not be threatened by their discovery in future research. Additional support for intense scrutiny of the Sun comes from a report of a white-light flare in 1705 and from the numerous reports of new sunspots entering the disk of the Sun.     

Hemispherical asymmetries in sunspot areas and auroral frequencies

One thousand and fifty-two aurorae boreales and 554 aurorae australes recorded during the nineteenth century at medium latitudes 55° N or 55° S are compared statistically with the known hemispherical asymmetry of the sums of the areas of sunspots. According to the present study, the solar hemispherical asymmetry may be accompanied by an analogous pattern of the hemispherical frequency of auroral days. For the number of auroral days in each hemisphere beyond the two auroral ovals, a remarkable degree of phase equality with the sunspot areas during the second Gleissberg cycle can be demonstrated.     

The eclipsing binary system W Cru

PhotoelectricUBV photometry of the long period southern eclipsing binary system W Cru gathered over an 18-mo period in 1984–1985 is presented and examined.The light curve is characterized by continuous Beta Lyrae-like variation: unexpected in such a long period (198.5 days) system; together with peculiar irregularities, of the order of 0.1 mag (or more inU) and time-scales of a few days.A high mass model (total mass 70M ) could be made to be roughly consistent with the data, though alternative models of much lower mass are also possible, and may turn out to be preferable, in terms of goodness-of-fit, as well as for theoretical reasons. The low mass models would require, though, the more massive component to be unseen (as now generally supposed for Lyrae itself).The photometry alone, or even combined with a known spectroscopic mass-function, seems unlikely to be able to furnish a single definitive solution, and more guidelines from reliable theoretical expectation may prove helpful in interpreting the data.