Dimension of the Earth's General Ellipsoid

The problem of specifying the Earth's mean (general)ellipsoid is discussed. This problem has been greatly simplified in the era of satellite altimetry, especially thanks to the adopted geoidal geopotential value, W₀ = (62 636 856.0 ± 0.5) m² s^-2.Consequently, the semimajor axis a of the Earth's mean ellipsoid can be easily derived. However, an a priori condition must be posed first. Two such a priori conditions have been examined, namely an ellipsoid with the corresponding geopotential that fits best W₀ in the least squares sense and an ellipsoid that has the global geopotential average equal to W₀. It has been demonstrated that both a priori conditions yield ellipsoids of the same dimension, with a–values that are practically identical to the value corresponding to the Pizzetti theory of the level ellipsoid: a = (6 378 136.68 ± 0.06) m.     

GEOS-II and 13th order terms of the geopotential

The resonance of GEOS-II (1968-002A) with 13th-order terms of the geopotential is analyzed. The odd-degree geopotential coefficients (13, 13), (15, 13), and (17, 13) given by Yionoulis most accurately model the resonance effects on GEOS-II of any of the published sets of 13th-order coefficients. However, this set is not adequate for precision orbit determination; additional even-degree coefficients are required.Values ofC _14,13(=0.57×10^–21) andS _14,13(=6.5×10^–21) to be used with the odd-degree set of Yionoulis were obtained from an analysis of the observed along-track position variation of GEOS-II. These coefficients, when used with those of Yionoulis, yield greatly improved fits to the data and orbital prediction capability. However, further refinement is possible because the small effects of the remaining even-degree resonant terms were not modeled.The composite coefficientsC _13,13(=1.7×10^–20) andS _13,13(=+2.7×10^–20) were obtained under the assumption that the (13, 13) spherical harmonic of the geopotential is responsible for all of the observed along-track variation of GEOS-II due to resonance. The good agreement of these deliberately composite values with some published values ofC _13,13 andS _13,13 suggests that some of the published values may also be composite to some extent.These coefficients are hereinafter referred to as the APL coefficients.     

Long-Term Stability Of Geoidal Geopotential FromTopex/Poseidon Satellite Altimetry 1993–1999

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993to October 24, 1999 (cycles 11–261) was used for investigating thelong-term variations in the geoidal geopotential W₀ and/orin the geopotential scale factor R₀ = GM/W₀ (GM is theadopted geocentric gravitational constant). The mean valuesdetermined for the whole period covered are: W₀ =(62 636 856.161 ± 0.002) m² s^-2, R₀ =(6 363 672.5448 ± 0.0002) m. The actual accuracy is limited bythe altimeter calibration error (2–3 cm) and it isestimated to be about ± 0.5 m² s^-2 (± 5 cm).The yearly variations of the above mean values are at the formalerror level. No long-term trend in W₀, representing the oceanvolume change, was found for the seven years period 1993–9 on thebasis of T/P altimeter (AVISO) data. No sea surface topography modelwas used in the solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Refinement of the geopotential scale factorR 0 on

Altimetric measurements of the GEOSAT satellite were used for the determination of geopotential scale factorR ₀. The geopotential valueW ₀ on the geoid surface was then computed (W ₀ =GM/R ₀).The GEOSAT Geophysical Data Records (GDR's) covering an initial period of the Exact Repeat Mission (ERM) were filtered and processed. The necessary corrections were made in order to allow a precise detection of the sea surface. Gravitational geopotential, rotation and permanent tides were taken into account and the equipotential surface which is the best approximation of the sea surface was found.The determination of the potential valueW ₀ on the mean geoid surface in this way is very promising. An associated value withW ₀ - the geopotential scale factorR ₀ - seems to be a very good Earth dimension defining quantity. Moreover, there are many possible applications ofW ₀ (R ₀) in modern geophysics.The incorporation of one of these parameters - we now recommendR ₀ - into the set of the Primary Geodetic Parameters (PGP) is discussed and suggested.     

Estimation of low degree geopotential coefficients using SLR data

Geodetic satellites have been providing the low frequency part of the geopotential models used for precise orbit determination purposes (e.g. JGM3, EGM96, …). Nevertheless they can be used to estimate the temporal variation of selected coefficients, helping to clarify the complex interrelations in the earth-ocean-atmosphere system. In this paper we present the two years long analysis of SLR data from the seven available geodetic satellites (Lageos I–II, Stella, Starlette, Ajisai, Etalon I–II) to recover monthly estimates of low degree geopotential coefficients; the results are obtained analysing the satellites separately and in proper combination. An accurate modelling of the satellite orbits is required in order to separate the geopotential coefficients: we assume as a priori geopotential the JGM3 model together with its associated tides and we take care of non-gravitational effects on the satellites by means of proper empirical estimated accelerations. The time series of the estimated coefficients (J₂, J₃, J₄, J₅) are inspected to detect the sub-annual perturbations related to seasonal variation of mass distribution. Huge residual seasonal signals in the orbit of Stella indicate a strong model deficiency related to the Sun's influence on the environment. The remaining six satellites are homogeneously modelled and build up a three cycles per year oscillation on J₂ and a seasonal oscillation (1 year and six month periods) revealed on the J₄. The origin and possible causes of these signals are further discussed in the text. We also present a preliminary estimate, using twelve years of Lageos-I and Lageos-II observations, that is compared with previous obtained values.     

Artificial halo orbits for low-thrust propulsion spacecraft

We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L ₁ and L ₂ in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points inside L ₁ and beyond L ₂ where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum amplitude of halo orbits about artificial equilibrium points inside L ₁ decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L ₂ in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first increases and then decreases after the thrust acceleration exceeds 0.415 mm/s². Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times and require a reasonably small low-thrust acceleration 0.0593 mm/s².     

On the impact of the Yarkovsky effect on Apophis’ orbit

In October 2009, a new set of optical observations of Apophis, a potentially hazardous asteroid, was published. These data have significantly expanded the interval of observations and their total number. In the article we compare the results of refinement of Apophis’ orbit made at the Jet Propulsion Laboratory (JPL, United States), the University of Pisa (Italy), and the Institute of Applied Astronomy (IAA) of the Russian Academy of Sciences with consideration for new observations. New orbits lead to a significant decrease in the probability of Apophis’ collision with the Earth in 2036. As a result of processing a large number of observations of asteroids approaching the Earth and main belt asteroids less than 40 km in size, with a large number of optical and, in many cases, radar observations in different oppositions, one of the authors revealed that additional acceleration affects their motion. This acceleration can be represented by the transversal component A ₂ in the orbital coordinate system. The presence of this acceleration can be interpreted as the Yarkovsky effect. The statistical properties of distribution of A ₂ for asteroids, for which it is determined quite reliably, evidence in favor of this interpretation. The value of additional acceleration for bodies the size of Apophis falls in the range ±10⁻¹³ AU/day². In this paper we have calculated the probability of Apophis colliding with the Earth in 2036 at different values of the transversal component of additional acceleration A ₂. For the resulting points, a plot of the probability of the collision against the A ₂ value has been constructed. At A ₂ = −8.748 × 10⁻¹⁴ AU/day² (and zero values of the radial A ₁ and normal A ₃ components) the nominal solution for Apophis’ orbit on April 13, 2029, is only 90 m from the middle of a “keyhole” 600 m in width, which leads to a collision of Apophis with the Earth in 2036. Since the scattering ellipse in the target plane in 2029 significantly overlaps the keyhole, the probability of collision at the given additional acceleration value is 0.0022. This result has been verified by the Monte Carlo method. Tests of 10000 random sets of orbital elements, which were found taking into account their correlation, have shown that 22 cases have resulted in virtual asteroids colliding with Earth in 2036. A plot of the probability of the collision against the value of A ₂ has been constructed.     

A new estimate of the quadrupole moment of the sun

Recent solar observations at Pic du Midi are reported that yield a value of J ₂=(2.57 ± 2.36) x 10^–6 for the quadrupole moment of the Sun. These observations were conducted from July 1993 to July 1994 after several improvements of the scanning heliometer. This instrument operates by fast photoelectric scans of opposite limbs of the Sun quasi-simultaneously, which provides the distance between both inflection points of the limb profiles. Any number of solar diameters in any position angle can be measured within a time interval short enough to minimize the scattering of the observational parameters. Errors due to atmospheric deterioration are discussed. From our results, compared to previous values obtained by other authors, it can be concluded than an upper limit for J ₂ is probably 1.0 × 10^-5.     

Estimation of the dissociation energy of CO+ from spectroscopic data

The potential energy curves for theX ² Σ⁺ andB ² Σ⁺ states of CO⁺ have been constructed by the Rydberg-Klein-Rees (RKR) method as modified by van der Sliceet al. The dissociation energy is estimated to be 7.70±0.19 eV by the method of curve fitting using the five parameter Hulburt-Hirschfelder’s function. The estimated value is in good agreement with the value (7.839 eV) given by Misraet al. Carefull observation of the results reveals that accurateD ₀ value for CO⁺ is 8.33 eV     

Numerical Exploration of Chermnykh’s Problem

We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L₁. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L₁ in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies.     

The two components in the distribution of sunspot groups with respect to their maximum areas

From an analysis of the distribution of sunspot groups with respect to their maximum areas we find that this distribution consists of two distinct components. One component contributes to spot groups of all possible values of A_* with a distribution density varying as ∼ exp (b₁ á _* ^1/2 ) with b₁ nearly constant from cycleto cycle and having a mean value ∼10^-4 km^-1. The other component is predominantly responsible for spot groups withA* ≲, 30 *10^-6 hemisphere but may provide a few spot groups even above 50 * l0^-6 hemisphere. This component may follow a distribution density ∼ exp (-b₂ A_*). We also determine the widths of the latitude zones over which spot groups in various intervals of A_* appear and study their variation with time. These widths and their variations indicate that the two statistical samples of spot groups may be produced by two families of flux-tube clusters as suggested earlier in a phenomenological model. Very thin flux-tube clusters in the statistical samples seem to be related to the ephemeral active regions and X-ray bright points.     

Two new LBV candidates in the M 33 galaxy

We present two new luminous blue variable (LBV) candidate stars discovered in the M33 galaxy. We identified these stars as massive star candidates at the final stages of evolution, presumably with a notable interstellar extinction. The candidates were selected from the Massey et al. catalog based on the following criteria: emission in H _α , V<18^./m 5 and 0_.^m 35 < (B - V) < 1_.^m 2. The spectra of both stars reveal a broad and strong H _α emission with extended wings (770 and 1000 kms⁻¹). Based on the spectra we estimated the main parameters of the stars. Object N45901 has a bolometric luminosity log(L/L_⊙) = 6.0–6.2 with the value of interstellar extinction A _V = 2.3 ± 0.1. The temperature of the star’s photosphere is estimated as T⋆ ∼ 13000–15000 K, its probable mass on the Zero Age Main Sequence is M∼ 60–80 M_⊙. The infrared excess in N 45901 corresponds to the emission of warm dust with the temperature Twarm ∼ 1000 K, and amounts to 0.1%of the bolometric luminosity. A comparison of stellar magnitude estimates from different catalogs points to the probable variability of the object N45901. Bolometric luminosity of the second object, N125093, is log(L/L_⊙) = 6.3 − 6.6, the value of interstellar extinction is A _V = 2.75 ± 0.15. We estimate its photosphere’s temperature as T⋆∼ 13000–16000K, the initial mass as M ∼ 90–120 M_⊙. The infrared excess in N125093 amounts to 5–6% of the bolometric luminosity. Its spectral energy distribution reveals two thermal components with the temperatures T_warm ∼ 1000K and T_cold ∼ 480 K. The [Ca II] λλ7291, 7323 lines, observed in LBV-like stars Var A and N93351 in M33 are also present in the spectrum of N 125093. These lines indicate relatively recent gas eruptions and dust activity linked with them. High bolometric luminosity of these stars and broad H α emissions allow classifying the studied objects as LBV candidates.     

The expansion field: the value of <Emphasis Type="Italic">H</Emphasis><Subscript>0</Subscript>

Any calibration of the present value of the Hubble constant (H ₀) requires recession velocities and distances of galaxies. While the conversion of observed velocities into true recession velocities has only a small effect on the result, the derivation of unbiased distances which rest on a solid zero point and cover a useful range of about 4–30 Mpc is crucial. A list of 279 such galaxy distances within v < 2,000 km s⁻¹ is given which are derived from the tip of the red-giant branch (TRGB), from Cepheids, and/or from supernovae of type Ia (SNe Ia). Their random errors are not more than 0.15 mag as shown by intercomparison. They trace a linear expansion field within narrow margins, supported also by external evidence, from v = 250 to at least 2,000 km s⁻¹. Additional 62 distant SNe Ia confirm the linearity to at least 20,000 km s⁻¹. The dispersion about the Hubble line is dominated by random peculiar velocities, amounting locally to <100 km s⁻¹ but increasing outwards. Due to the linearity of the expansion field the Hubble constant H ₀ can be found at any distance >4.5 Mpc. RR Lyr star-calibrated TRGB distances of 78 galaxies above this limit give H ₀ = 63.0 ± 1.6 at an effective distance of 6 Mpc. They compensate the effect of peculiar motions by their large number. Support for this result comes from 28 independently calibrated Cepheids that give H ₀ = 63.4 ± 1.7 at 15 Mpc. This agrees also with the large-scale value of H ₀ = 61.2 ± 0.5 from the distant, Cepheid-calibrated SNe Ia. A mean value of H ₀ = 62.3 ± 1.3 is adopted. Because the value depends on two independent zero points of the distance scale its systematic error is estimated to be 6%. Other determinations of H ₀ are discussed. They either conform with the quoted value (e.g. line width data of spirals or the D _n −σ method of E galaxies) or are judged to be inconclusive. Typical errors of H ₀ come from the use of a universal, yet unjustified P–L relation of Cepheids, the neglect of selection bias in magnitude-limited samples, or they are inherent to the adopted models.     

The relationship betweenG andh in a closed Universe

In a closed expanding-contracting Universe, matter will be subject to an inward acceleration large enough to prevent perpetual expansion. A closed Universe must also perform a simple harmonic motion, which might consist either of one single cycle or of an infinite series of oscillations about a central point. It is the purpose of this study to find the rate ofa ₀, the cosmic acceleration, from which the gravitational constantG can be determined. It will be shown from Ampère's equation and Planck's radiation law that it is possible to derivea ₀=7.623×10^–12 ms^–2, a value which also conforms with the uncertainty principle. The relationship betweena ₀ and electromagnetic radiation is based on the concept that charges (such as electrons) must emit radiation while accelerating. The rate ofa ₀ yields a universal gravitational constant ofG=6.645×10^–11 N m² kg^–2.     

HD/H<Subscript>2</Subscript> molecular clouds in the early Universe: The problem of primordial deuterium

We have detected new HD absorption systems at high redshifts, z _abs = 2.626 and z _abs = 1.777, identified in the spectra of the quasars J0812+3208 and Q1331+170, respectively. Each of these systems consists of two subsystems. The HD column densities have been determined: log N _HD^A = 15.70 ± 0.07 for z _A = 2.626443(2) and log N _HD^B = 12.98 ± 0.22 for z _B = 2.626276(2) in the spectrum of J0812+3208 and log N _HD^C = 14.83 ± 0.15 for z _C = 1.77637(2) and log N _HD^D = 14.61 ± 0.20 for z _D = 1.77670(3) in the spectrum of Q1331+170. The measured HD/H₂ ratio for three of these subsystems has been found to be considerably higher than its values typical of clouds in our Galaxy.We discuss the problem of determining the primordial deuterium abundance, which is most sensitive to the baryon density of the Universe Ω_b. Using a well-known model for the chemistry of a molecular cloud, we have estimated the isotopic ratio D/H=HD/2H₂ = (2.97 ± 0.55) × 10⁻⁵ and the corresponding baryon density Ω_b h ² = 0.0205_−0.0020^+0.0025. This value is in good agreement with Ω_b h ² = 0.0226_−0.0006^0.0006 obtained by analyzing the cosmic microwave background radiation anisotropy. However, in high-redshift clouds, under conditions of low metallicity and low dust content, hydrogen may be incompletely molecularized even in the case of self-shielding. In this situation, the HD/2H₂ ratio may not correspond to the actual D/H isotopic ratio. We have estimated the cloud molecularization dynamics and the influence of cosmological evolutionary effects on it.     

Study of the dependence of the star formation rate in the nuclear regions of 39 Kazarian galaxies on their integral parameters

A statistical study of the dependence of the star formation rate in the nuclear regions of 39 Kazarian galaxies on the integral parameters of these galaxies is carried out on the basis of spectra from SDSS DR6. The value of SFR/kpc² for our sample lies in the range 0.013÷2.04M _⨀ year⁻¹kpc⁻² (with the maximum value of 2.04 corresponding to the Kaz 98 (merger)). It is found that the surface density of the rate of star formation correlates positively with the bar structure parameter and EW(Hα), and that, for spiral galaxies of early morphological types, SFR/kpc² is greater than for the later types. It is shown that the color B-R for the galaxies and the color (u − g) _nucl for the nuclear region correlate positively with the total absorption A(Hα) in the Ha line for the nuclear region. The average value of A(Hα) for our samples is found to be A(Hα)=1.3±0.09 magnitudes. Translated from Astrofizika, Vol. 52, No. 2, pp. 211–224 (May 2009).     

The significance of coral reefs as global carbon sinks— response to Greenhouse

Coral reefs are net sinks for C, principally as CaCO₃ accretion. It is possible to predict quite accurately the rate of production, given adequate information about any particular reef environment. The best data set for an extensive region is that for the Great Barrier Reef (GBR). Careful analysis of this region and the incorporation of previously documented present day system calcification rates suggest net production (G) from G = 1 (kg CaCO₃ m⁻² yr⁻¹) for fringing reefs, to G = 1.9 for planar (infiled platform) reefs, G = 3 for ribbon reefs and lagoonal reefs. The 20,055 km² of reefs in the GBR are thus estimated to average G = 2.4, resulting in a total production of 50 million tonnes yr⁻¹. In a 50–100 year Greenhouse scenario of rising sealevel, we predict that recolonisation of present day reef flats will be extensive and prolific. Production will increase substantially, and this could be by as much as 40% (ranging from 0% for deep shoals to 180% for fringing reefs) to give 70 million tonnes yr⁻¹ if the rate of sealevel rise reaches or exceeds 6–8 mm yr⁻¹We estimate 115,000 km² of oceanic atolls worldwide. Drawing on points equivalence from the detailed analysis of the GBR, we estimate the atolls presently produce 160 million tonnes yr⁻¹. We predict that a similar 40% increase could be possible in the next 100 years or so resulting in a production of 220 million tonnes.Accepting an existing estimate of 617,000 km² for reefs worldwide, drawing from our projections from the GBR and the atolls, and making some assumptions about the remaining reef types (we suggest fringing reefs to dominate) we estimate global reef production at the present time to be 900 million tonnes yr⁻¹. Within the next 100 years or so, we suggest this rate could almost double to 1800 million tonnes. In the long term (several centuries) we predict that the continuing trend of recolonisation, particularly of fringing and planar reefs could result in the production of > 3000 million tonnes yr⁻¹ if rates of sealevel rise approaching or exceeding 6–8 mm yr⁻¹ are achieved. Eventually (> 500 yr), reefs could actually “drown” due to inability to match the rate of sealevel increase if that rate significantly exceeds 6–8 mm yr⁻¹.Thus, coral reefs at present act as a sink for 111 million tonnes C yr⁻¹, the equivalent of 2% of present output of anthropogenic CO₂. In the short term Greenhouse scenario (100 yr) we predict this could increase to the equivalent of 4% of the present CO₂ output. In the much longer term (several centuries), if all trends continue, this could increase to the equivalent of as much as 9% of the present CO₂ output.Unfortunately, we also predict that this considerable sink for C will be most likely of negative value in alleviating Greenhouse because of the immediate effect of CaCO₃ precipitation is to raise the P_CO2 of the surface oceans — ie, ot encourage CO₂ efflux to the atmosphere. We do not attempt to quantify this effect.Other Greenhouse changes such as seawater temperature increase, changes in cloud cover, increased rainfall and runoff, increased storm activity, and changes in dissolved CO₂ concentration and surface ocean circulation may complicate the reef response. However, we suggest that sealevel rise will be the dominant influence, at least during the next 100 years or so.     

A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars

Using the shape model of Mars GTM090AA in terms of spherical harmonics complete to degree and order 90 and gravitational field model of Mars GGM2BC80 in terms of spherical harmonics complete to degree and order 80, both from Mars Global Surveyor (MGS) mission, the geometry (shape) and gravity potential value of reference equipotential surface of Mars (Areoid) are computed based on a constrained optimization problem. In this paper, the Areoid is defined as a reference equipotential surface, which best fits to the shape of Mars in least squares sense. The estimated gravity potential value of the Areoid from this study, i.e. W ₀ = (12,654,875 ± 69) (m²/s²), is used as one of the four fundamental gravity parameters of Mars namely, {W ₀, GM, ω, J ₂₀}, i.e. {Areoid’s gravity potential, gravitational constant of Mars, angular velocity of Mars, second zonal spherical harmonic of gravitational field expansion of Mars}, to compute a bi-axial reference ellipsoid of Somigliana-Pizzetti type as the hydrostatic approximate figure of Mars. The estimated values of semi-major and semi-minor axis of the computed reference ellipsoid of Mars are (3,395,428 ± 19) (m), and (3,377,678 ± 19) (m), respectively. Finally the computed Areoid is presented with respect to the computed reference ellipsoid.     

Neutron star sequences and the starquake glitch model for the Crab and the Vela pulsars

We construct for the first time, the sequences of stable neutron star (NS) models capable of explaining simultaneously, the glitch healing parameters, Q, of both the pulsars, the Crab (Q≥0.7) and the Vela (Q≤0.2), on the basis of starquake mechanism of glitch generation, whereas the conventional NS models cannot give such consistent explanation. Furthermore, our models also yield an upper bound on NS masses similar to those obtained in the literature for a variety of modern equations of state (EOSs) compatible with causality and dynamical stability. If the lower limit of the observational constraint of (i) Q≥0.7 for the Crab pulsar and (ii) the recent value of the moment of inertia for the Crab pulsar (evaluated on the basis of time-dependent acceleration model of the Crab Nebula), I _Crab,45≥1.93 (where I ₄₅=I/10⁴⁵ g cm²), both are imposed together on our models, the models yield the value of matching density, E _b =9.584×10¹⁴ g cm⁻³ at the core-envelope boundary. This value of matching density yields a model-independent upper bound on neutron star masses, M _max≤2.22M _⊙, and the strong lower bounds on surface redshift z _R ≃0.6232 and mass M≃2.11M _⊙ for the Crab (Q≃0.7) and the strong upper bound on surface redshift z _R ≃0.2016, mass M≃0.982M _⊙ and the moment of inertia I _Vela,45≃0.587 for the Vela (Q≃0.2) pulsar. However, for the observational constraint of the ‘central’ weighted mean value Q≈0.72, and I _Crab,45>1.93, for the Crab pulsar, the minimum surface redshift and mass of the Crab pulsar are slightly increased to the values z _R ≃0.655 and M≃2.149M _⊙ respectively, whereas corresponding to the ‘central’ weighted mean value Q≈0.12 for the Vela pulsar, the maximum surface redshift, mass and the moment of inertia for the Vela pulsar are slightly decreased to the values z _R ≃0.1645, M≃0.828M _⊙ and I _Vela,45≃0.459 respectively. These results set an upper and lower bound on the energy of a gravitationally redshifted electron-positron annihilation line in the range of about 0.309–0.315 MeV from the Crab and in the range of about 0.425–0.439 MeV from the Vela pulsar.     

Heat flow of the Earth and resonant capture of solar <Superscript>57</Superscript>Fe axions

In a very conservative approach, supposing that all heat flow of the Earth is exclusively due to resonant capture inside the Earth of axions emitted by ⁵⁷Fe nuclei on Sun, we obtain limit on the mass of hadronic axion: m _a < 1.8 keV. Taking into account release of heat from decays of ⁴⁰K, ²³²Th, ²³⁸U inside the Earth, this estimation could be improved to the value: m _a < 1.6 keV. Both the values are less restrictive than limits set in devoted experiments to search for ⁵⁷Fe axions (m _a < 216–745 eV), but are much better than limits obtained in experiments with ⁸³Kr (m _a < 5.5 keV) and ⁷Li (m _a < 13.9–32 keV). Published in Ukrainian in Kinematika i Fizika Nebesnykh Tel, 2009, Vol. 25, No. 2, pp. 143–149. The article was translated by the authors.