Summary lecture

This summary lecture makes no attempt to summarize what was actually said at the meeting, since this is well covered by the other contributors. Instead I have structured my presentation in three parts: First I try to demonstrate why the Sun is unique by comparing it with laboratory plasmas. This is followed by some personal reminiscences that go back a significant fraction of the century. I conclude in the form of a poem about this memorable conference in honor of the centennial anniversary of the Kodaikanal Observatory.     

Migration of giant planets in planetesimal discs

Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of 10⁻⁴– 0.01 M_⊙ , can migrate inward a large distance and can survive only if the inner disc is truncated or as a result of tidal interaction with the star. In this case the semimajor axis, a , of the planetary orbit is less than 0.1 au. Orbits with larger a are obtained for smaller values of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain not only several of the orbital features of the giant planets that have been discovered in recent years orbiting nearby stars, but also the metallicity enhancement found in several stars associated with short-period planets.     

Chemical Evolution of the System of Galactic Planetary Nebulae

The problem of the chemical evolution of the system of Galactic planetary nebulae, starting with the early stage of development of the Galaxy, is investigated. The radial and vertical gradients of C, N, O, Ne, Ar, Cl, and S abundances are determined for different ages of the precursor stars of the nebulae. A statistically significant age dependence of the gradients is derived.     

Maximum-likelihood method for estimating the mass and period distributions of extrasolar planets

We investigate the distribution of mass M and orbital period P of extrasolar planets, taking account of selection effects caused by the limited velocity precision and duration of existing surveys. We fit the data on 72 planets to a power-law distribution of the form  d n = CM ^−α P ^−β(d M / M )(d P / P )  , and find  α= 0.11 ± 0.10  ,  β=−0.27 ± 0.06  for   M ≲ 10 M _J  , where   M _J  is the mass of Jupiter. The correlation coefficient between these two exponents is −0.31, indicating that uncertainties in the two distributions are coupled. We estimate that 4 per cent of solar-type stars have companions in the range  1 M _J < M < 10 M _J  ,  2_d < P < 10 yr  .     

行星状星云NGC2346核星的食光变现象的消失

本文给出了对行星状星云NGC2346核星AGK3—0°695从1981年到1987年这段期间内所做的照相观测结果。从中我们看到该天体自1981年底开始出现的大变幅食光变现象持续数年之后,从1986年开始其光变幅度迅速减小,由85年的Δm～4~m减小到86年的Δm～1~m.1。而且到1987年其光变曲线仅存Δm～0~m.4的不规则亮度起伏,已无明显的周期性光变现象,文中对此现象做了初步分析讨论。     

On the unmodeled perturbations in the motion of uranus

In this paper we apply a numerical method to determine unmodeled perturbations in an attempt to explain the observed discrepancies in the motion of Uranus. We find that the estimated perturbation shows some significant periods that could be attributed to insufficient knowledge of the perturbations from some of the known planets. On the assumption that the gravitational attraction of an unknown planet is the origin of the deviations, the best planar solution of the inverse problem is a planet of 0.6 Earth masses, with true longitude of 133° (1990.5), semi major axis a = 44 AU and eccentricity e = 0.007.     

On the damping of the bending waves in Saturn’s ring

We study numerically the motion of a single particle in the bending wave of finite thickness in Saturn’s ring. We include the forcing due to the planet, a moon, the coriolis force and the self gravity of the ring. In particular, we compute the variation of the velocity arising due to the variation of the amplitude and the phase of the epicyclic motion across the local vertical height of the ring. We suggest that the dissipation of energy due to the collision of ring particles in this shear layer damps out the bending wave of Saturn’s ring at the 5:3 vertical resonance of Mimas within a distance of 150 km from the site of its launching as is observed in Voyager data.     

Moonlet Collisions and the Effects of Tidally Modified Accretion in Saturn's F Ring

We both test and offer an alternative to a meteoroid bombardment model (M. R. Showalter 1998, Science282, 1099-1102) and suggest that anomalous localized brightenings in the F ring observed by Voyager result from disruptive collisions involving poorly consolidated moonlets, or “rubble piles.” This model can also explain the transient events observed during ring plane crossing. We have developed an evolutionary model that considers both the competing effects of accretion and disruption at the location of the F ring. Our numerical model is a Markov process where probabilities of mass transfer between the states of the system form a “transition matrix.” Successive multiplications of this matrix by the state vector generate expectation values of the distribution after each time step as the system approaches quasi-equilibrium. Competing effects of accretion and disruption in the F ring are found to lead to a bimodal distribution of ring particle sizes. In fact, our simulation predicts the presence of a belt of kilometer-sized moonlets in the F ring. These moonlets may continually disrupt one another and re-accrete on short time scales. We also agree with J. N. Cuzzi and J. A. Burns (1988, Icarus74, 284-324), who suggest that the classical F ring itself may be the consequence of a relatively recent collision between two of the largest of these yet unseen objects. Cassini observations can confirm the existence of the moonlet belt by directly observing these objects or the waves they create in the rings.     

On the multiple jet flows in Jupiter''s atmosphere

Measurements by the Galileo probe in Jupiter's deep atmosphere support the possibility that the mean zonal multiple-jet flows in Jupiter's atmosphere are deep rooted. As a consequence of Jupiter's high rotation rate, the primary dynamics of the zonal flows must be geostrophic, i.e., the dynamic balance is largely between the Coriolis and pressure forces. This paper describes a new analytical theory for the generation of zonal multiple-jet flows on the basis of the nonlinear interaction of slowly traveling, nearly two-dimensional and non-axisymmetric geostrophic waves. An explicit analytical expression for the geostrophic waves is obtained as the leading-order solution of the weakly nonlinear problem. In the high-order problem taking into account of nonlinear effects, an analytical expression for an alternating multiple-jet flow is derived. Implications of the theory for Jupiter and other planets are discussed.     

Dynamical and ionization structure of planetary nebulae in three dimensions. A simulation for NGC3132

Using a numerically accurate radiation-gas dynamical method we investigate the winds scenario for aspherical planetary nebulae (PNe). Our model includes the interaction of two winds: as low high mass-loss rate wind (a `super wind'); and a fast wind; low mass-loss rate wind. Our model also includes the evolution of the UV spectrum of the PNe centeral star. As stated in the section3 of Paper I (Ganbari and Khesali, 2001), we consider a three dimensional density distribution ρ(r,θφ for the super wind, in this way we enter the effects of cooling and heating mechanisms in our model. Taking into account the above assumptions, we introduce the code (DIS3D) and numerically we study the dynamical and ionization properties of the planetary nebula NGC3132. We show that it is possible by simulations to reproduce the shape of PNe in three dimensions, and calculating the physical quantities throughout the entire nebula. This revised version was published online in July 2006 with corrections to the Cover Date.     

Study by MOA of extrasolar planets in gravitational microlensing events of high magnification

A search for extrasolar planets was carried out in three gravitational microlensing events of high magnification, MACHO  98–BLG–35  , MACHO  99–LMC–2  and OGLE  00–BUL–12  . Photometry was derived from observational images by the MOA and OGLE groups using an image subtraction technique. For MACHO  98–BLG–35  , additional photometry derived from the MPS and PLANET groups was included. Planetary modelling of the three events was carried out in a supercluster computing environment. The estimated probability for explaining the data on MACHO  98–BLG–35  without a planet is <1 per cent. The best planetary model has a planet of mass ∼(0.4–1.5)× M _Earth at a projected radius of either ∼1.5 or ∼2.3 au. We show how multiplanet models can be applied to the data. We calculate exclusion regions for the three events and find that Jupiter-mass planets can be excluded with projected radii from as wide as about 30 au to as close as around 0.5 au for MACHO  98–BLG–35  and OGLE  00–BUL–12  . For MACHO  99–LMC–2  , the exclusion region extends out to around 10 au and constitutes the first limit placed on a planetary companion to an extragalactic star. We derive a particularly high peak magnification of ∼160 for OGLE  00–BUL–12  . We discuss the detectability of planets with masses as low as Mercury in this and similar events.     

The formation of an eccentric gap in a gas disc by a planet in an eccentric orbit

We investigate the effect of a planet on an eccentric orbit on a two-dimensional low-mass gaseous disc. At a planet eccentricity above the planet's Hill radius divided by its semimajor axis, we find that the disc morphology differs from that exhibited by a disc containing a planet in a circular orbit. An eccentric gap is created with eccentricity that can exceed the planet's eccentricity and precesses with respect to the planet's orbit. We find that a more massive planet is required to open a gap when the planet is on an eccentric orbit. We attribute this behaviour to spiral density waves excited at corotation resonances by the eccentric planet. These act to increase the disc's eccentricity and exert a torque opposite in sign to that exerted by the Lindblad resonances. The reduced torque makes it more difficult for waves driven by the planet to overcome viscous inflow in the disc.     

The vertical structure of planet-induced gaps in protoplanetary discs

Giant planets embedded in circumstellar discs are expected to open gaps in these discs. We examine the vertical structure of the gap edges. We find that the planet excites spiral arms with significant (Mach number of a half) vertical motion of the gas, and discuss the implications of these motions. In particular, the spiral arms will make the edge appear 'puffed up' relative to the bulk of the disc. Infrared observations (sensitive to dust) would be dominated by the light from the thick inner edge of the disc. Submillimetre observations (sensitive to gas velocities) would appear to be hot in 'turbulent' motions (actually the ordered motion caused by the passage of the spiral arms), but cold in chemistry. Resolved submillimetre maps of circumstellar discs might even be able to detect the spiral arms directly.