On the orbits and masses of the satellites of the Pluto-Charon system

Two small satellites of Pluto, S/2005 P1 (hereafter P1) and S/2005 P2 (hereafter P2), have recently been discovered outside the orbit of Charon, and their orbits are nearly circular and nearly coplanar with that of Charon. Because the mass ratio of Charon-Pluto is ∼0.1, the orbits of P2 and P1 are significantly non-Keplerian even if P2 and P1 have negligible masses. We present an analytic theory, with P2 and P1 treated as test particles, which shows that the motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the potential rotating at the mean motion of Pluto-Charon, the epicyclic motion, and the vertical motion. The analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods, and this deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. In this analytic theory, the periapse and ascending node of each of the small satellites precess at nearly equal rates in opposite directions. From direct numerical orbit integrations, we show the increasing influence of the proximity of P2 and P1 to the 3:2 mean-motion commensurability on their orbital motion as their masses increase within the ranges allowed by the albedo uncertainties. If the geometric albedos of P2 and P1 are high and of order of that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. The variation in the orbital radius of P2 due to the forced oscillations is comparable in magnitude to that due to the best-fit Keplerian eccentricity, and there is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and the prograde precession of its longitude of periapse with a period of 5300 days should be easily detectable. If the albedos of P2 and P1 are as low as that of comets, the large inferred masses induce significant short-term variations in the epicyclic eccentricities and/or periapse longitudes on the 400-500-day timescales due to the proximity to the 3:2 commensurability. In fact, for the maximum inferred masses, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. Observations that sample the orbits of P2 and P1 well on the 400-500-day timescales should provide strong constraints on the masses of P2 and P1 in the near future.     

Mass distribution of Antarctic ordinary chondrites and the estimation of the fall-to-specimen ratios

Abstract— The cumulative mass distributions (mass range > 100 g) of each type of Japanese and U.S. Antarctic ordinary chondrites are compared with those of non-Antarctic falls and those obtained from the present-day flux of meteorites. The steeper slope of the mass distribution of Antarctic chondrites is indicative of the presence of several chondrite showers. The fall-to-specimen ratio of Antarctic ordinary chondrites larger than 100 g is about 1:2, indicating that half of them are shower components. The fall-to-specimen ratios of each group range from 1:1 to 1:6; those of the Japanese and U.S. Antarctic meteorite collections are 1:1 to 1:2 and 1:4 for H chondrites, 1:1 to 1:2 and 1:2 for L chondrites, and 1:2 and 1:6 for LL chondrites, indicating that the Japanese collection includes less abundant shower components than the U.S. collection. The fall-to-specimen ratios of each H4-6 and L4-6 type range from 1:1 to 1:4, and U.S. H6 and Japanese H4 have the low ratios of 1:4.     

Cepheid kinematics and the Galactic warp

The space velocities of 200 long-period (P>5 days) classical Cepheids with known proper motions and line-of-sight velocities whose distances were estimated from the period-luminosity relation have been analyzed. The linear Ogorodnikov-Milne model has been applied, with the Galactic rotation having been excluded from the observed velocities in advance. Two significant gradients have been found in the Cepheid velocities, ?W/?Y = ?2.1 ± 0.7 km s^?1 kpc^?1 and ?V/?Z = 27 ± 10 km s^?1 kpc^?1. In such a case, the angular velocity of solid-body rotation around the Galactic X axis directed to the Galactic center is ?15 ± 5 km s^?1 kpc^?1.     

Maximum likelihood estimation of the mean parallax and kinematic parameters of the Pleiades

A simultaneous, maximum-likelihood determination of the distance and kinematic parameters of the Pleiades is made. The results are: distance of the cluster d = 135.56 ± 0.72 pc, dispersion σ_d = 7.66 ± 0.80 pc; space velocity V = 25.94 ± 0.13 km/s, dispersion σ_v = 0.58 ± 0.09 km/s coordinates of the convergent point A = 101.95° ± 0.47°, D = −41.36° ± 0.29°.     

Narrow-line Seyfert 1 galaxies and the evolution of galaxies and active galaxies

Narrow Line Seyfert 1 galaxies (NLS1s) are intriguing owing to their continuum as well as emission-line properties. The observed peculiar properties of the NLS1s are believed to be as a result of an accretion rate close to the Eddington limit. As a consequence of this, for a given luminosity, NLS1s have smaller black hole (BH) masses compared with normal Seyfert galaxies. Here we argue that NLS1s might be Seyfert galaxies in their early stage of evolution and as such may be low-redshift, low-luminosity analogues of high-redshift quasars. We propose that NLS1s may reside in rejuvenated, gas-rich galaxies. We also argue in favour of collisional ionization for production of Fe  ii in active galactic nuclei.     

Allan Sandage and the cosmic expansion

This is an account of Allan Sandage’s work on (1) The character of the expansion field. For many years he has been the strongest defender of an expanding Universe. He later explained the CMB dipole by a local velocity of 220±50 km s⁻¹ toward the Virgo cluster and by a bulk motion of the Local supercluster (extending out to ∼3500 km s⁻¹) of 450–500 km s⁻¹ toward an apex at l=275, b=12. Allowing for these streaming velocities he found linear expansion to hold down to local scales (∼300 km s⁻¹). (2) The calibration of the Hubble constant. Probing different methods he finally adopted—from Cepheid-calibrated SNe Ia and from independent RR Lyr-calibrated TRGBs—H ₀=62.3±1.3±5.0 km s⁻¹ Mpc⁻¹.     

On gravitational orbits and the virial theorem

We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)–E _kin/E _pot.R is calculated as a function of the eccentricity (e) and of the energy (E). Whent, independently ofe andE, R1/2 for closed orbits (this clearly illustrates the fulfillment of the virial theorem in classical mechanics); whereasR1, at any time, for open orbits.     

Astrophysical bounds on the photon charge and magnetic moment

If the photon possessed an electric charge or a magnetic moment, light waves propagating through magnetic fields would acquire new quantum mechanical phases. For a charged photon, this is an Aharonov–Bohm phase, and the fact that we can resolve distant galaxies using radio interferometry indicates that this phase must be small. This in turn constrains the photon charge to be smaller that if all photons have the same charge and smaller than if there are both positively and negatively charged photons. The best bound on the magnetic moment comes from the observed absence of wavelength-independent photon birefringence. Birefringence measurements, which compare the relative phases of right- and left-circularly polarized waves, restrict the magnetic moment to be less than . This is just a few orders of magnitude weaker than the experimental bounds on the electron and neutron electric dipole moments.     

Comparison of the classical and the global solutions of the Ideal Resonance Problem

The Ideal Resonance Problem is defined by the Hamiltonian $$F = B(y) + 2\varepsilon A(y) \sin ^2 x,\varepsilon \ll 1.$$ The classical solution of the Problem, expanded in powers of ε, carries the derivativeB′ as a divisor and is, therefore, singular at the zero ofB′, associated with resonance. With α denoting theresonance parameter, defined by $$\alpha \equiv - B'/|4AB''|^{1/2} \mu ,\mu = \varepsilon ^{1/2} ,$$ it is shown here that the classical solution is valid only for $$\alpha ^2 \geqslant 0(1/\mu ).$$ In contrast, the global solution (Garfinkelet al., 1971), expanded in powers ofμ=ε^1/2, removes the classical singularity atB′=0, and is valid for all α. It is also shown here that the classical solution is an asymptotic approximation, for largeα ², of the global solution expanded in powers ofα ^?2. This result leads to simplified expressions for resonancewidth and resonantamplification. The two solutions are compared with regard to their general behavior and their accuracy. It is noted that the global solution represents a perturbed simple pendulum, while the classical solution is the limiting case of a pendulum in a state offast circulation.     

The Coma-Leo I distance ratio and the Hubble constant

The diameter-velocity dispersion relation in B, V, and K for three early-type galaxies in the Leo I (M96) group is derived from published photometry and kinematic data. The relations in all three colors have slopes which agree well with those for the Coma cluster. The RMS scatter of the Leo I galaxies in each color is extremely small, consistent with the group's compactness. These relations yield estimates of the Coma-Leo I distance ratio of 9.01 ± 0.51, 8.77 ± 0.43, and 8.82 ± 0.31, respectively, with a weighted mean of 8.84 ± 0.23. The general agreement among the three colors indicates that the early-type galaxies in Leo I and Coma have similar stellar populations.

The Coma-Leo I distance ratio coupled with estimates of the absolute distance to the Leo I group allows the Hubble constant to be determined, free of the uncertainties which arise when working with the Virgo cluster. Several high quality distance estimates are available from a variety of techniques: Cepheids in M96 (Tanvir, N.R., et al., 1995, Natur, 377, 27) and M95 (Graham, J.A., et al., 1997, ApJ, 477, 535), surface brightness fluctuations (Tonry, J.L., et al., 1997, ApJ, 475, 399), planetary nebulae luminosity functions (Ciardullo, R., et al., 1993, ApJ, 419, 479), and the luminosity of the red giant branch tip (Sakai, S., Freedman, W.L., & Madore, B.F., 1996, in: Formation of the Galactic Halo, Inside and Out, eds. H. Morrison & A. Sarajedini, PASP Conf. Series Vol. 92). Adopting a cosmic recession velocity of the Coma cluster in the microwave background frame of 7200 ± 300 km s⁻¹, these distance estimates lead to values of the Hubble constant ranging from 70 to 81 km s⁻¹ Mpc⁻¹, with an unweighted mean of 75 ± 6 km s⁻¹ Mpc⁻¹.     

Zero-Metallicity Stars and the Effects of the First Stars on Reionization

We present a model that relates the width of the broad emission lines of active galactic nuclei (AGNs) to the Keplerian velocity of an accretion disk at a critical distance from the central black hole. This critical distance falls in a region bounded on the inward side by the transition radius between the radiation pressure- and the gas pressure-dominated region of the accretion disk and on the outward side by the maximum radius below which a stabilizing, radially accreting and vertically outflowing corona exists. We show that in the framework of this picture, the observed range of Hbeta FWHMs from broad-line to narrow-line type 1 AGNs is well reproduced as a function of the accretion rate. This interval of velocities is the only permitted range and goes from approximately 20,000 km s-1 for sub-Eddington accretion rates to approximately 1000 km s-1 for Eddington accretion rates.     

Method of locating the Pc 1 source and hot plasma parameters in the generation region

A method of estimating hot and cold plasma parameters using ground Pc 1 observations is proposed. The values of both hot and cold plasma concentrations, proton energy and temperature anisotropy in the Pc 1 generation region are calculated. It is shown that the most appropriate (effective) indicator of the L-shell, where Pc 1 are generated, is the group delay of wave packets.     

A note concerning the 2:1 and the 3:2 resonances in the asteroid belt

The dynamical behavior of asteroids inside the 2:1 and 3:2 commensurabilities with Jupiter presents a challenge. Indeed most of the studies, either analytical or numerical, point out that the two resonances have a very similar dynamical behavior. In spite of that, the 3:2 resonance, a little outside the main belt, hosts a family of asteroids, called the Hildas, while the 2:1, inside the main belt, is associated to a gap (the Hecuba gap) in the distribution of asteroids.In his search for a dynamical explanation for the Hecuba gap, Wisdom (1987) pointed out the existence of orbits starting with low eccentricity and inclination inside the 2:1 commensurability and going to high eccentricity, and thus to possible encounters with Mars. It has been shown later (Henrard et al.), that these orbits were following a path from the low eccentric belt of secondary resonances to the high eccentric domain of secular resonances. This path crosses a bridge, at moderate inclination and large amplitude of libration, between the two chaotic domains associated with these resonances.The 3:2 resonance being similar in many respects to the 2:1 resonance, one may wonder whether it contains also such a path. Indeed we have found that it exists and is very similar to the 2:1 one. This is the object of the present paper.     

Emission of helium in prominences and the chromosphere

The excitation of the levels (2¹ P, 3¹ D, 5¹ D, 6¹ D and 7¹ D) of helium in quiescent prominences and the chromosphere is considered using the observations made during the 1952, 1961 and 1970 solar eclipses (Thomas and Athay, 1961; Athay and Orrall, 1957; Rigutti and Russo, 1964; Kubota et al., 1972) as well as by means of high altitude coronographs (Jefferies and Orrall, 1962). It is shown that the lower levels of the singlet series of helium, like the lower levels of hydrogen, are excited by resonance (λ = 584 Å) and photospheric radiation. The higher levels are populated by transitions from the triplet system, so that a relative state LTE is established between the systems for n ? 6.     

Possibility of investigation of the microstreams and associations by the radiotomographic method

This article contains the tomographic problem's solution of the radiants distribution study by the meteor radar data. It was received the distribution of meteors velocities for the parts of celestial sphere with angular dimensions 10° × 10° and 1° × 1°. Was shown that the angular dimensions of most of radiants are equal 1° – 3° and larger part of the sporadic background looks like a totality of microstreams.     

On the distribution of haloes, galaxies and mass

The stochasticity in the distribution of dark haloes in the cosmic density field is reflected in the distribution function   P _V ( N _h| δ _m)  , which gives the probability of finding N _h haloes in a volume V with mass density contrast δ _m. We study the properties of this function using high-resolution N -body simulations, and find that   P _V ( N _h| δ _m)  is significantly non-Poisson. The ratio between the variance and the mean goes from ∼1 (Poisson) at  1+ δ _m≪1  to <1 (sub-Poisson) at  1+ δ _m∼1  to >1 (super-Poisson) at  1+ δ _m≫1  . The mean bias relation is found to be well described by halo bias models based on the Press–Schechter formalism. The sub-Poisson variance can be explained as a result of halo exclusion, while the super-Poisson variance at high δ _m may be explained as a result of halo clustering. A simple phenomenological model is proposed to describe the behaviour of the variance as a function of δ _m. Galaxy distribution in the cosmic density field predicted by semi-analytic models of galaxy formation shows similar stochastic behaviour. We discuss the implications of the stochasticity in halo bias to the modelling of higher order moments of dark haloes and of galaxies.     

On the inclination and the axial velocity of spicules

This paper studies two properties of chromospheric spicules: their angular distribution and the plasma velocity along their axes. To investigate the first property, we measured the apparent tilt of spicules at the limb, and then computed their actual distribution in space. This was achieved by solving first kind Fredholm or Volterra integral equations by various methods. The distribution of the axial velocity of the spicule plasma was studied on the basis of two types of observations: (1) the height variation of the spicules as a function of time and (2) the Doppler shift of the spectral lines. The resulting velocity distributions, using the experimental data of these two sets of observations, are quite different. The average velocity based on the Doppler shift measurements ( 40 km s^–1) is greater than that based on height variation of spicules ( 20 km s^–1). This is due to the ionization of the material as it penetrates the corona.     

Periodic orbits in the general three-body problem and the relationship between them

We study the regions of finite motions in the vicinity of three simple stable periodic orbits in the general problem of three equal-mass bodies with a zero angular momentum. Their distinctive feature is that one of the moving bodies periodically passes through the center of mass of the triple system. We consider the dynamical evolution of plane nonrotating triple systems for which the initial conditions are specified in such a way that one of the bodies is located at the center of mass of the triple system. The initial conditions can then be specified by three parameters: the virial coefficient k and the two angles, φ₁ and φ₂, that characterize the orientation of the velocity vectors for the bodies. We scanned the region of variation in these parameters k∈(0, 1); φ₁, φ₂∈(0, π) at steps of δk=0.01; δφ₁=δφ₂=1° and identified the regions of finite motions surrounding the periodic orbits. These regions are isolated from one another in the space of parameters (k, φ₁, φ₂). There are bridges that correspond to unstable orbits with long lifetimes between the regions. During the evolution of these metastable systems, the phase trajectory can “stick” to the vicinity of one of the periodic orbits or move from one vicinity to another. The evolution of metastable systems ends with their breakup.     

On the accretion of the earth and moon

The bodies which produced the premare impact craters on the moon contained a much higher proportion of smaller bodies in the earliest observable times than subsequently. This suggests that the earth and moon accreted from small objects with only an occasional large planetoid.If the earliest observable lunar craters are 4.3 × 10⁹ yr old, the half-life of the primitive planetesimals which produced the giant lunar craters larger than 161 km in diameter, was 143 × 10⁶ yr, while the half-life of the primitive planetesimals which produced lunar craters larger than 1 km in diameter was only 88 × 10⁶ yr. The half-life of the bodies which produced 1 km craters was still shorter, about 75 × 10⁶ yr.     

Unreddened stars and the two-phase model of the interstellar medium

We have computed two phase models of the interstellar medium, with cosmic rays and X-rays assumed to be the main ionizing agents, heating due to photoelectron ejection from the interstellar grains. We show that it is possible to have a hot and tenuous intercloud medium in pressure equilibrium with the interstellar clouds for a wide range of physical conditions, possibly existing in the interstellar space. The atomic and ionic line observations towards Sco are shown to be consistent with the origin of these lines in the intercloud medium for a range of values of the ionizing flux. It is suggested that the intercloud medium may be predominantly neutral, with ionization rates consistent with the limits imposed by molecular observations. The mean fractional ionization of the intercloud medium is 1%.On leave from Tata Institute of Fundamental Research, Bombay, India.