Population I pulsating stars

Luminosities of Population I pulsating stars (Delta Scuti variables and classical cepheids) are investigated. From data for 80 Delta Scuti stars, semi-empirical period-luminosity-colour (P-L-C) relations and period-luminosity (P-L) relations are obtained for the four lowest modes of radial pulsations. The improvement of the accuracy of the stellar luminosity is determined when a P-L-C relation is used instead of the corresponding P-L relation. From data for 155 classical cepheids, empirical P-L relations are derived for short-period stars (logP1.1), long-period stars (logP>1.1), and s-cepheids. The comparison of the P-L relations for the two types of variable stars shows good agreement, but between them there is a gap with a dim nature.     

Period-luminosity relations for Cepheid variables: from mid-infrared to multi-phase

This paper discusses two aspects of current research on the Cepheid period-luminosity (P-L) relation: the derivation of mid-infrared (MIR) P-L relations and the investigation of multi-phase P-L relations.     

Σ-D Relations and Main Galactic Radio Loops

This paper represents the updated empirical Galactic andextragalactic Σ-D relations (relations between the surface brightness Σ and the diameter D) for supernova remnants(SNRs), with checking the connection of the main Galactic radio loops (Loop I, II, III and IV) with these relations. We present results which suggest, once again, that the radio loops may have an SNR origin. The updated relations for old SNRs have been measured to have slopes, β ≈ 2 in log-log space. The best Σ-D relations for M31 and M33 galaxies were derived and these relations are shown to be flatter (β ≲2) than those for Galactic SNRs alone. A Σ-D relation with168 reliable calibrators (both Galactic and extragalactic) is derived. This revised version was published online in July 2006 with corrections to the Cover Date.     

Empirical P-L-C relations for delta Scuti stars

Separate P-L-C relations have been empirically derived by sampling the Scuti stars according to their pulsation modes. The results based on these relations have been compared with those estimated from the model based P-L-C relations and the other existing empirical P-L-C relations. It is found that a separate P-L-C relation for each pulsation mode provides a better correspondence with observations.     

The inclination function in terms of nonsingular elements

Different formulas for computation of the inclination function in terms of nonsingular elements have been presented and compared. Among the ways to compute the inclination function presented below, the best one is based on the recurrence relations (eqs. 16) derived in this paper.     

Order-of-scattering of partially polarized radiation in inhomogeneous,anisotropically scattering atmospheres

Reciprocity and symmetry relationships, representing local invariants for the scattering phase-matrix, are derived for twelve cases of particle assemblies studied by van de Hulst (1957) including situations of scattering in an arbitrary direction, in the near forward and near backward directions. These relations are used to generate corresponding relations representing global invariants for the scattering and transmission matrices of atmospheres consisting of such assemblies. The latter relations are obtained from the matrix integro-differential equations for scattering and transmission; they apply to single scattering, any finite order of scattering, and after an arbitrary cumulation of scattering orders (finite or infinite). Our results are summarized in Tables I and II for general inhomogeneous atmospheres and for particular inhomogeneous atmospheres that are symmetrical with respect to their central level. The latter case includes homogeneous atmospheres as a special case. The largest set of local relations obtained contains three independent relations (called universal, reversal, exchange) which can further be combined to yield four additional dependent relations. This circumstance happens in three out of the above twelve cases. In the remaining cases fewer relations (both independent and dependent) remain valid. Likewise, a maximal set of three independent global relations is obtained for general inhomogeneous atmospheres; they too can be linearly combined to yield seven other dependent relations. For the symmetrically inhomogeneous atmospheres, three independent and seven dependent additional relations are obtained. On the basis of these tables, it becomes a trivial matter to provide the local and global invariants (both the independent and the dependent relations) for any assembly of particles and atmospheric inhomogeneity. A mixture of Rayleigh-Cabannes scattering by anisotropic molecules or extremely small particles and Mie scattering by large isotropic particles is considered for illustration. Lastly, the group properties of these invariants are studied.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the U.S. National Aeronautics and Space Administration.     

A structure and energy dissipation efficiency of relativistic reconfinement shocks

We present a semi-analytical hydrodynamical model for the structure of reconfinement shocks formed in astrophysical relativistic jets interacting with external medium. We take into account exact conservation laws, both across the shock front and in the zone of the shocked matter, and exact angular relations. Our results confirm a good accuracy of the approximate formulae derived by Komissarov & Falle. However, including the transverse pressure gradient in the shocked jet, we predict an absolute size of the shock to be about twice larger. We calculate the efficiency of the kinetic energy dissipation in the shock and show a strong dependence on both the bulk Lorentz factor and opening angle of the jet.     

Radial pulsation modes as a possible cause for the heterogeneity of the Delta Scuti stars

On the basis of observational data (Breger, 1979), a radial pulsation mode of 83 Delta Scuti stars is estimated in two ways. These stars can pulsate in four lowest modes—F, 1H, 2H, 3H— and, perhaps, in 4H and 5H. Our earlier suggestion—that the apparent heterogeneity of these objects in both the period-luminosity plane and the period-frequency distribution may be explained by means of pulsations in various modes—is confirmed. Semi-empirical period-luminosity relations for the four lowest modes are derived and the semi-empirical period ratios are compared with the theoretical ones.     

Thermal emission at radio frequencies from supernova remnants and a modified theoretical Σ–D relation

In this paper, we discuss known discrepancies between theoretically derived and empirically measured relations between the radio surface brightness Σ and the diameter D of supernova remnants (SNRs): these relations are commonly known as the Σ–D relations. We argue that these discrepancies may be at least partially explained by taking into account thermal emission at radio frequencies from SNRs at particular evolutionary stages and located in particular environments. The major contributions of this paper may be summarized as follows: (i) we consider thermal emission at radio frequencies from SNRs in the following scenarios: a relatively young SNR evolving in a dense molecular cloud environment (n  100–1000 cm⁻³) and an extremely evolved SNR expanding in a dense warm medium (n  1–10 cm⁻³). Both of these SNRs are assumed to be in the adiabatic phase of evolution. We develop models of the radio emission from both of these types of SNRs and each of these models demonstrate that through the thermal bremsstrahlung process significant thermal emission at radio frequencies is expected from both types of SNR. Based on a literature search, we claim that thermal absorption or emission at radio frequencies has been detected for one evolved Galactic SNR and four young Galactic SNRs with similar properties to our modelled evolved and young SNRs. (ii) We construct artificial radio spectra for both of these two types of SNRs: in particular, we discuss our simulated spectrum for the evolved Galactic SNR OA 184. By including thermal emission in our simulated spectra, we obtain different slopes in Σ–D relations: these new slopes are in closer agreement to empirically obtained relations than the theoretically derived relations which do not take thermal emission into account. (iii) Lastly, we present an additional modification to the theoretical Σ–D relation for SNRs in the adiabatic expansion phase. This modification is based on the convolution of the synchrotron emissivity with the emissivity derived in this paper for thermal bremsstrahlung emission from an ionized gas cloud (that is, a theoretical construct of an SNR).     

An analytical theory of planetary rotation rates

An approximate analytical theory is derived for the rate of rotation acquired by a planet as it grows from the solar nebula. This theory was motivated by a numerical study by Giuli, and yields fair agreement with his results. The periods of planetary rotation obtained are proportional to planetesimal encounter velocity, and appear to suggest lower values of this velocity than are commonly assumed to have existed during planetary formation.     

Applying an Expansion of the Second Derivatives of the Earth’s Gravitational Potential in Modified Spherical Harmonics for Constructing and Estimating Its Models

Second-order derivatives of the Earth’s potential in a local north-oriented coordinate system are expanded in series of modified spherical harmonics. Linear relations are derived between the spectral coefficients of these series and the spectrum of the geopotential. Based on these relations, recurrent procedures are developed for estimating the geopotential coefficients from the spectrum of each derivative and, conversely, for simulating the spectrum from a known geopotential model. The very simple structure of the expressions for the derivatives is convenient for estimating the coefficients of the geopotential by the least squares method at a certain step of processing satellite gradiometry data. Since the new series are orthogonal, the method with a quadrature formula can be applied, which helps avoid aliasing errors caused by the truncation of the series. The spectral coefficients of the derivatives are estimated using the derived relations for different models on an average orbital sphere of the GOCE satellite and at other altitudes above the Earth’s surface.

     

The clouds of Venus: An anisotropic scattering model

The phase function $\text{ω}\text{?}\text{(1 + a}\text{cos}\text{θ)}$ for anisotropic scattering is applied to a homogeneous atmospheric model to ascertain the effects of anisotropy on the near-infrared spectrum of Venus. L. D. G. Young's equivalent widths for the 820 Å CO₂ band are analyzed to derive allowed combinations of CO₂ specific abundance, continuum albedo, pressure, and degree of anisotropy. From these combinations, values are derived for the photon mean-free path and total optical thickness of the clouds. The Venera 10 measurement of the transmitted flux at 7200 Å is then used in conjunction with spherical albedo requirements to reduce the range of possible solutions to the equivalent-width analysis. Through the application of approximate similarity relations, the “true” (i.e., anisotropic) atmospheric parameters are derived from the isotropic values. For an assumed Mie scatterer with an average anisotropy factor of 〈cos θ〉 = 0.7, the results indicate a total optical thickness of about 55 with a single-scattering albedo of 0.9992 to 0.9995.     

Photometric study of an eclipsing binary in the field of M37

CCD photometric observations with B and V passbands were performed on the contact binary V3 in the field of open cluster M37. The solutions were obtained for data from both B and V passbands along with R passband given by Hartman et al.using the Wilson-Devinney code. The positive O'Connell effect was observed in all the three passbands and its associated cool spot parameters were derived. The results indicate that the spot parameters have not shown any significant variability during the last four years. The spot radius was found to be 40and located close to the equator of the secondary component. The absolute parameters of the system were derived using the empirical relations given by Gazeas et al.     

Theoretical studies of the infrared emission from circumstellar dust shells: the infrared characteristics of circumstellar silicates and the mass-loss rate of oxygen-rich late-type giants

We have modeled the infrared emission of spherically symmetric, circumstellar dust shells with the aim of deriving the infrared absorption properties of circumstellar silicate grains and the mass-loss rates of the central stars. As a basis for our numerical studies, a simple semianalytical formula has been derived that illustrates the essential characteristics of the infrared emission of such dust shells. A numerical radiative transfer program has been developed and applied to dust shells around oxygen-rich late-type giants. Free parameters in such models include the absorption properties and density distribution of the dust. An approximate, analytical expression is derived for the density distribution of circumstellar dust driven outward by radiation pressure from a central source. A large grid of models has been calculated to study the influence of the free parameters on the emergent spectrum. These results form the basis for a comparison with near-infrared observations. Observational studies have revealed a correlation between the near-infrared color temperature, Tc, and the strength of the 10 micrometers emission or absorption feature, A10. This relationship, which essentially measures the near-infrared optical depth in terms of the 10 micrometers optical depth, is discussed. Theoretical A10-Tc relations have been calculated and compared to the observations. The results show that this relation is a sensitive way to determine the ratio of the near-infrared to 10 micrometers absorption efficiency of circumstellar silicates. These results as well as previous studies show that the near-infrared absorption efficiency of circumstellar silicate grains is much higher than expected from terrestrial minerals. We suggest that this enhanced absorption is due to the presence of ferrous iron (Fe2+) color centers dissolved in the circumstellar silicates. By using the derived value for the ratio of the near-infrared to 10 micrometers absorption efficiency, the observed A10-Tc relation can be calibrated in terms of the total dust column density of the circumstellar shell and thus the mass-loss rate of late-type giants can easily be derived. Detailed models have been made of the infrared emission of three well-studied Miras: R Cas, IRC 10011, and OH 26.5+0.6, with the emphasis on the shape of the 10 micrometers emission or absorption feature. The results show that the intrinsic shape of the 10 micrometers resonance varies from a very broad feature in R Cas to a relatively narrower feature in OH 26.5+0.6, with IRC 10011 somewhere in between. Possible origins of this variation are discussed. The mass-loss rates from these objects are calculated to be 3 x 10(-7), 2 x 10(-5), and 2 x 10(-4) M Sun yr-1 for R Cas, IRC 10011, and OH 26.5+0.6, respectively. These results are compared to other determinations in the literature.     

Is there evolution in the infrared Tully–Fisher relation? Comparing two linear regressions

In a recent paper, Puech and co-workers compared K -band Tully–Fisher relations derived for nearby and distant galaxies, respectively. They concluded that the two relations differ, and deduced that there is evolution in the Tully–Fisher relations. The statistical comparison between the two regression lines is re-examined, and it is shown that the statistical test used gives non-significant results. It is argued that better results can be obtained by comparing the 'inverse' Tully–Fisher relations, and it is demonstrated by two different methods that the nearby- and distant-sample relations do indeed differ at a very high significance level. One of the statistical methods described is non-parametric, and can be applied very generally to compare linear regressions from two different samples.     

Solar activity in the sixteenth and seventeenth centuries (a revision)

Maximum relative sunspot numbers for the 16th and 17th century were computed by means of the dependence of the maximum relative sunspot numbers on the solar cycle rise time and on the cycle asymmetry. In these dependencies four separate modes of relations, two for odd and two for even cycles, were identified. These modes are coupled two and two in even-odd cycle pairs. The rise times and the asymmetries of solar cycles in the 16th and 17th centuries were taken from cycle extreme estimates by Schove (1979), from auroral and telescopic sunspot observations during this period, but with some necessary corrections. Annual relative sunspot numbers and decade averages were estimated from the cycle maxima and the epochs of extremes. In addition, the efficiency of auroral records in latitudes lower than 55 deg was computed for the time interval 1500–1868. For this purpose the dependence of occurrence numbers of aurorae on the cycle and decade means of the relative sunspot numbers was derived.     

Ground traces of artificial earth satellites

This paper considers the ground trace of an artificial earth satellite. It determines the effects of the trace caused by perturbations due to atmospheric drag, the oblateness of the earth, and the moon and the sun as a third body.The necessary mathematical relations giving these perturbations which are available in literature are utilized (Betz, 1967; Brouwer and Clemence, 1961; Brouwer and Hori, 1961; Danby, 1962; Escobal, 1965; Kentet al., 1963; Kozai, 1962). Those relations unavailable elsewhere are derived.The computation was done by programming in FORTRAN language and utilizing an IBM 360/65.Captain, USAF     

Ejecta size-velocity relation derived from the distribution of the secondary craters of kilometer-sized craters on Mars

The relation between the size and velocity of impact crater ejecta has been studied by both laboratory experiments and numerical modeling. An alternative method, used here, is to analyze the record of past impact events, such as the distribution of secondary craters on planetary surfaces, as described by Vickery (Icarus 67 (1986) 224; Geophys. Res. Lett. 14 (1987) 726). We first applied the method to lunar images taken by the CLEMENTINE mission, which revealed that the size-velocity relations of ejecta from craters 32 and 40 km in diameter were similar to those derived by Vickery for a crater 39 km in diameter. Next, we studied the distribution of small craters in the vicinity of kilometer-sized craters on three images from the Mars Orbiter Camera (MOC) on board the Mars Global Surveyor (MGS). If these small craters are assumed to be secondaries ejected from the kilometer-sized crater in each image, the ejection velocities are of hundreds of meters per second. These data fill a gap between the previous results of Vickery and those of laboratory studies.     

What Can the Redshift Observed in EXO 0748-676 Tell Us？

The mass-radius relations for bare and crusted strange stars are calculated with the bag model. Comparing these relations with the observed one derived from the redshift of EXO 0748-676, we come to the conclusion that it is incorrect to say that EXO 0748 676 cannot be a strange star. Various strange star models can show that EXO 0748-676 could have a mass of (1.3 - 1.7)M⊙ and a radius of(8.4 - 11.4) km. It is proposed that a proportion of nascent strange stars could be bare and have masses - 0.1 M⊙, and their masses increased over a long period of accretion.     

Empirical estimate of p-mode frequency shift for solar cycle 23

We have obtained empirical relations between the p-mode frequency shift and the change in solar activity indices. The empirical relations are determined on the basis of frequencies obtained from BBSO and GONG stations during solar cycle 22. These relations are applied to estimate the change in mean frequency for the cycle 21 and 23. A remarkable agreement between the calculated and observed frequency shifts for the ascending phase of cycle 23, indicates that the derived relations are independent of epoch and do not change significantly from cycle to cycle. We propose that these relations could be used to estimate the shift in p-mode frequencies for past, present and future solar activity cycles, if the solar activity index is known. The maximum frequency shift for cycle 23 is estimated to be 265±90 nHz, corresponding to a predicted maximum smoothed sunspot number 118.1±35.