Nonlinear density waves in planetary rings

We discuss the steady-state structure of the nonlinear density waves generated in a planetary ring at the Lindblad resonances of a satellite. We show that strong density waves lead to an enhancement of the background surface density in the wave zone.     

The [Sii] electron density distribution over the planetary nebula NGC 7009

Electron densities have been measured from [Sii] 6716/6731 Å line ratios for a grid of points over the surface of the planetary nebula NGC 7009 using a photon counting detector. The radial dependence of the electron density has been modelled, and the relationship provides possible evidence that the planetary nebula shell is driven by a strong stellar wind.     

Tracing spiral density waves in M81

We use Spitzer IRAC 3.6 and 4.5 μm near-infrared data from the Spitzer Infrared Nearby Galaxies Survey (SINGS), optical B, V and I and Two-Micron All-Sky Survey K _s-band data to produce mass surface density maps of M81. The IRAC 3.6- and 4.5-μm data, whilst dominated by emission from old stellar populations, are corrected for small-scale contamination by young stars and polycyclic aromatic hydrocarbon emission. The I -band data are used to produce a mass surface density map by a   B − V   colour correction, following the method of Bell and de Jong. We fit a bulge and exponential disc to each mass map, and subtract these components to reveal the non-axisymmetric mass surface density. From the residual mass maps, we are able to extract the amplitude and phase of the density wave, using azimuthal profiles. The response of the gas is observed via dust emission in the 8-μm IRAC band, allowing a comparison between the phase of the stellar density wave and gas shock. The relationship between this angular offset and radius suggests that the spiral structure is reasonably long-lived and allows the position of corotation to be determined.     

Spectrophotometry of the planetary nebula KjPn 8

Flux-calibrated low-resolution spectra covering the optical wavelength range from 3400 to 7500 Å have been obtained over the central region and the surroundings of the extraordinary planetary nebula (PN) KjPn 8 (PNG 112.5-00.1). The spectrum from the core is of low excitation with T _e(N  II ) = 8000 K and n _e(S  II ) = 550 cm⁻³. KjPn 8 is found to be a Type I PN according to the original classification scheme of Peimbert & Torres-Peimbert, with enriched He/H and N/O ratios with respect to mean values for PN. Increased O/H, Ne/H and Ar/H ratios over those of average PN reflect the possible metal-rich environment from which the progenitor star formed, and also are similar to those found in the extreme Type I PN He 2-111. The N/H ratio is found to be only moderately high compared to the average PN and consequently, the large O abundance pulls the N/O ratio towards the lower limit of the criterion for Type I planetary nebulae (PNe) in this case. In addition, the spectra of some knots and faint regions in the KjPn 8 surroundings are presented, which show only a few spectral lines. Low electron densities ranging from 100 to 300 cm⁻³ have been derived in these outer regions.     

Propagation of spiral density waves in a magneto-active disk

The propagation of spiral density waves in a differentially rotating, self-gravitating, magnetoactive and highly flattened disk is investigated by using the asymptotic theory for tightly wound spirals developed by Lin and his collaborators. We adopt the continuum fluid model as the primary basis, and our treatment will be largely analytical. The disk plasma is studied in the frozen field approximation and inhomogenceous magnetic fields in the plane of the disk are considered in detail.In a differentially rotating disk with strong magnetic fields, the field lines will be considerably distorted and the mutual influence of magnetic fields and differential rotation is by no means obvious.In this paper we present a new asymptotic dispersion relation for tightly wound spiral density waves with magnetic fields along the spiral armsB (r). The effects of the magnetic fields lead to such terms likek ²(a ² +V _A ² ), wherek is the wave number,a represents the speed of sound,V _A = (B ²/4)^1/2 is the Alfvén speed,B denotes the field strength, and is the plasma density. These terms depict the well-known magnetoacoustic waves and could have been anticipated without a detailed computation. However the interaction of magnetic fields and differential rotation may give rise to other significant terms which are not so easy to foresee.We also present a more exact local dispersion relation by using the WKB approximation and study the effects of magnetic fields on the growth rate through the parametersQ andJ defined in the literature.Although the effects of the magnetic fields are rather insignificant for applications to Galactic dynamics, the effects of the magnetic fields are important for applications to star formation and problems related to the solar nebula.     

High-speed knots in the hourglass-shaped planetary nebula Hubble 12

We present a detailed kinematical analysis of the young compact hourglass-shaped planetary nebula Hb 12. We performed optical imaging and long-slit spectroscopy of Hb 12 using the Manchester echelle spectrometer with the 2.1-m San Pedro Mártir telescope. We reveal, for the first time, the presence of end caps (or knots) aligned with the bipolar lobes of the planetary nebula shell in a deep [N  ii ]λ6584 image of Hb 12. We measured from our spectroscopy radial velocities of  ∼120 km s⁻¹  for these knots.
We have derived the inclination angle of the hourglass-shaped nebular shell to be ∼65° to the line of sight. It has been suggested that Hb 12's central star system is an eclipsing binary which would imply a binary inclination of at least 80°. However, if the central binary has been the major shaping influence on the nebula, then both nebula and binary would be expected to share a common inclination angle.
Finally, we report the discovery of high-velocity knots with Hubble-type velocities, close to the core of Hb 12, observed in Hα and oriented in the same direction as the end caps. Very different velocities and kinematical ages were calculated for the outer and inner knots showing that they may originate from different outburst events.     

Precessing collimated outflows in the planetary nebula IC 4846

We present [N  ii ] and H α images and high-resolution long-slit spectra of the planetary nebula IC 4846, which reveal, for the first time, its complex structure and the existence of collimated outflows. The object consists of a moderately elongated shell, two (and probably three) pairs of collimated bipolar outflows at different orientations, and an attached circular shell. One of the collimated pairs is constituted by two curved, extended filaments the properties of which indicate a high-velocity, bipolar precessing jet. A difference of ≃10 km s⁻¹ is found between the systemic velocity of the precessing jets and the centroid velocity of the nebula, as recently reported for Hu 2-1. We propose that this difference is as a result of orbital motion of the ejection source in a binary central star. The orbital separation of 30 au and period 100 yr estimated for the binary are similar to those in Hu 2-1, linking the central stars of both planetary nebulae to interacting binaries. Extraordinary similarities also exist between IC 4846 and the bewildering planetary nebula NGC 6543, suggesting a similar formation history for both objects.     

Evolutionary status of WR-type planetary nebula nuclei

In this paper we review the evolutionary paths that lead to the different types of planetary nebulae nuclei, including hydrogen and helium-burning central stars. Starting from the empirical definition of WR central stars, based on stellar spectra, we examine the theoretical work produced to account for the observed configurations. Then we discuss the constraints provided by recent galactic and extragalactic observations, and finally state the possible developments in this field to achieve a better understanding of the subject.     

The distribution of mass in the planetary system and solar nebula

A model solar nebula is constructed by adding the solar complement of light elements to each planet, using recent models of planetary compositions. Uncertainties in this approach are estimated. The computed surface density varies approximately asr ^–3/2. Mercury, Mars and the asteroid belt are anomalously low in mass, but processes exist which would preferentially remove matter from these regions. Planetary masses and compositions are generally consistent with a monotonic density distribution in the primordial solar nebula.     

Formation of solar nebula and mass distribution in the planetary system

The formation of the solar nebula and the distribution of mass in its planetary system is studied. The underlying idea is that the protosun, fragmented out from an interstellar cloud as a result of cluster formation, gathered the planetary material and, hence, spin angular momentum by gravitational accretion during its orbital motion around the centre of the Galaxy. The study gives the initial angular momentum of the solar nebula nearly equal to the present value of the solar system.     

Protostellar angular momentum transport by spiral density waves

The gravitational collapse of molecular clouds or cloud cores is expected to lead to the formation of stars that begin their lives in a state of rapid rotation. It is known that, in at least some specific cases, rapidly rotating, slf-gravitating bodies are subject to instabilities that cause them to assume ellipsoidal shapes. In this paper we investigate the consequences of such instabilities on the angular momentum evolution of a star in the process of formation from a collapsing cloud, and surrounded by a protostellar disk, with a view toward applications to the formation of the Solar System. We use a specific model of star formation to demonstrate the possibility that such a star would become unstable, that the resulting distortion of the star would generate spiral density waves in the circumstellar disk, and that the torque associated with these waves would regulate the angular momentum of the star as it feeds angular momentum to the disk. We conclude that the angular momentum so transported to the disk would not spread the disk to, say, Solar System dimensions, by the action of the spiral density waves alone. However, a viscous disk could effectively extract stellar angular momentum and attain Solar System size. Our results also indicate that viscous disks could feed mass and angular momentum to a growing protostar in such a manner that distortions of the star would occur before gravitational torques could balance the influx of angular momentum. In other situations (in which the viscosity was small), a gap could be cleared between the disk and star.     

The optical spectrum of the planetary nebula NGC 6543

With the Hamilton echelle spectrograph at the Lick Observatory, emission-rich spectral lines of the planetary nebula NGC 6543 were secured in the wavelength range from 3550 to 10 100 Å. We chose two bright regions, ∼8 arcsec east and ∼13 arcsec north of the central star, the physical conditions and chemical abundances of which may differ as a result of the different physical characteristics involving the mass ejection of different epochs. By combining Hamilton echelle observations with archive UV data secured with the International Ultraviolet Explorer ( IUE ), we obtain improved diagnostics and chemical compositions for the two observed regions. The diagnostic diagram gives the average value of T _e=8000∼8300 K, and the electron number density near N _e∼5000 cm⁻³ for most ions, while some low-excitation lines indicate much higher temperatures, i.e. T _e∼10 000 K. With the construction of a photoionization model, we try to fit the observed spectra in a self-consistent way: thus, for most elements, we employ the same chemical abundances in the nebular shell; and we adopt an improved Sobolev approximation model atmosphere for the hydrogen-deficient Wolf–Rayet type central star. Within the observational errors, the chemical abundances do not seem to show any positional variation except for helium. The chemical abundances of NGC 6543 appear to be the same as in average planetary nebulae. The progenitor star may have been an object of one solar mass, most of the heavier elements of which were less plentiful than in the Sun.     

Spectroscopic study of the variable planetary nebula IC 4997

Based on our spectroscopic observations of the variable planetary nebula IC 4997 in 2003–2009, we have obtained the relative fluxes in optical emission lines. The interstellar extinction c = 0.35 has been found from the Balmer decrement by taking into account the effect of self-absorption in hydrogen lines in dense nebular regions. The variations in the Balmer decrement point to variability of the self-absorption and circumstellar extinction. We have investigated the variations in the relative intensities of some spectral lines and their ratios with time. The drop in the ratios F(λ4363)/F(Hγ) and F(λ363)/F(λ4959) that began back in 1990–1995 has continued, suggesting a decrease in the electron density and temperature in the central nebular region. The ratio F(λ6731)/F(λ6717) has remained constant. It gives an estimate for the electron density in the outer regions of IC 4997, N _e ∼ 10⁴ cm⁻³.