Martin Schwarzschild

Some Instabilities of a Completely Ionized Plasma

Two cases of equilibrium for a highly conducting plasma are investigated for their stability. In the first case, a plasma is supported against gravity by the pressure of a horizontal magnetic field. This equilibrium is found unstable, in close correspondence to the classical case of a heavy fluid supported by a light one. The second case refers to the so-called pinch effect. Here a plasma is kept within a cylinder by the pressure of a toroidal magnetic field which in turn is caused by an electric current within the plasma. This equilibrium is found unstable against lateral distortions.

Self-consistent models for galactic halos

Richstone has pioneered the use of the scale-free logarithmic potential for the study of the dynamics of galactic halos. Now modern computers make it practical to exploit that potential in its exact form without central softening. The orbital structure of the potential, which differs significantly from that of the separable Stackel potentials, has been explored systematically with the help of 2-D start spaces. Six triaxial nonrotating density models representative of various axis ratios have been selected. For each model 600 orbits have been integrated over a time interval equivalent to about 55 orbital periods, or 1 Hubble time

The orbital structure of galactic halos

Earlier numerical experiments have shown that the orbital structure in the halo of a triaxial logarithmic potential differs significantly from that in the main body of the potential; the usual box orbits are replaced by boxlets originating in higher resonances. Now we have further investigated this phenomenon, with the following results. First, as was shown earlier (e.g., Gerhard and Binney), a modified triaxial Hubble potential (ρ ∞ r -3 ) shows much the same replacement of boxes by boxlets in its halo as does the logarithmic potential (ρ ∞ r -2 ). This suggest that the dominant occurence of boxlets may be a fairly general phenomenon in triaxial galactic halos. (...)

HYDRODYNAMIC OSCILLATIONS IN THE SOLAR CHROMOSPHERE

Compression waves in the chromosphere, with the motions assumed vertical and of standing-wave character, are studied with the aim of accounting for the 5- minute oscillations recentiy discovered. For such waves the photosphere is found to provide an effectively solid bottom, while the corona can provide a free, largely reflective surface. The temperatures and depths in the chromosphere required to fit the observed period are not in discord with other evidence for the chromospheric temperature profile. (auth)

Jeans and Boltzmann Solutions for Oblate Galaxies with Flat Rotation Curves

A general solution of the Jeans equations for oblate scale-free logarithmic potentials is given. This provides all possible second velocity moments that can hold up a stellar population of flattened scale-free density against the gravity field. A two-parameter subset of second moments for the self-consistent density of Binneys model is examined in detail. These solutions have the desirable property that the observable dispersions in the radial and proper motions can be given explicitly. In the spherical limit, the potential of these models reduces to that of the singular isothermal sphere. The Jeans solutions for scale-free densities of arbitrary flattening that can correspond to physical three-integral distribution functions are identified. The problem of finding distribution functions associated with the Jeans solutions in flattened scale-free logarithmic potentials is then investigated for Binneys model. An approximate solution of the collisionless Boltzmann equation is found which provides a third (partial) integral of good accuracy for thin and near-thin tube orbits. It is a modification of the total angular momentum. This enables the construction of many simple three-integral distribution functions. The kinematic properties of these approximate DFs are shown to agree with a subset of the Jeans solutions --- which are thereby confirmed as good approximations to physical solutions.

Automatic Integration of Linear Second‐Order Differential Equations by Means of Punched Card Machines

It is shown how punched‐card‐relay calculators can be used for solving ordinary linear differential equations of sixth and lower order. The differential equations are replaced by difference equations which can be solved by the relay calculators automatically step by step. The final solution is obtained by repeating the integration several times, each time computing the truncation error and applying it as a correction in the subsequent integration.

An upper limit to the angular diameter of the nucleus of NGC 4151.

Half intensity angular diameter upper limit of Seyfert galaxy NGC 4151 nucleus, considering nonthermal continuum

Orbital contributions to the stability of triaxial galaxies

Goodmans indicator is used here to investigate the stability of perfect ellipsoids, which are prototypical nonrotating triaxial galaxy models. The contributions of the individual stellar orbits to the indicator are presented for three specific adiabatic perturbations, which change the axis ratios of the ellipsoids but leave the density profile invariant. It is found that for barlike perturbations, in which one axis is elongated and another is compressed, box orbits are predominantly destabilizing, while outer long-axis tubes are invariably stabilizing. Short-axis tubes and inner long-axis tubes may be both stabilizing and destabilizing. These results are combined with Statlers (1987) results to obtain tentative estimates of Goodmans indicator for self-consistent perfect ellipsoid models. 42 refs.

A comparison of stellar populations in the Andromeda galaxy and its elliptical companion

図1:太陽近傍星(PopI)とM3(PopII) の光度関数。同じ総光度(ゼロ等星1個?)に揃えてあ る。 定義はdN=φdMvisでいいのか? 右端あたりで積分すると軽くL>L(0等星)になりそ う。そうでもないか?仮に log(φ/Ltot)=-1+0.5Mvisとすると、Mvis=-2.5log(Ls,vis/Lo)から、 φ/(Ltot/Lo)=0.1*(Ls/Lo)**(-1.25), Mvis=-4から 4までこのφで積分するとして、 Ltot =∫Ls*φdM=Ltot*0.1*∫(Ls/Lo)*(Ls/Lo)**(-1.25)*1.08*d Ls/ Ls =Ltot*0.108*[(Ls,min/Lo)**(-0.25)-(Ls,max/Lo)**(-0.25)]/0.25 =Ltot*0.43*(2.5-0.4)=0.90*Ltot で確かに Loに揃えてある。 上の例では、Mvis<-2の星の数は PopIIの系が PopIの2-3倍となる。 この方法は近すぎる銀河ではCMDより劣るし、遠すぎると適用できない。M31対 NGC205最適。

Galactic Models with Moderate Stochasticity

G. Contopoulos has just described to us the particular type of chaotic behavior that seems to be the dominant one in galactic potentials. In contrast, I would like to walk with you through a sequence of potentials relevant for galaxies-starting with cases totally free of chaos, proceeding in five cautious steps through cases only mildly aflicted by chaos, and ending with cases containing much chaos, like those discussed by G. Contopoulos, or even worse.