Before turning to the derivation of the virial theorem, it is appropriate to review the origin of the fundamental structural equations of stellar astrophysics. This not only provides insight into the basic conservation laws implicitly assumed in the description of physical systems, but by their generality and completeness graphically illustrates the complexity of the complete description that we seek to circumvent. Since lengthy and excellent texts already exist on this subject, our review will of necessity be a sketch. Any description of a physical system begins either implicitly or explicitly from certain general conservation principles. Such a system is considered to be a collection of articles, each endowed with a spatial location and momentum which move under the influence of known forces. If one regards the characteristics of spatial position and momentum as being highly independent, then one can construct a multi-dimensional space through which the particles will trace out unique paths describing their history.

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The virial theorem in stellar astrophysics

Lyapunov functions and isolating blocks

Computer simulation of the formation of planetary systems

Motivated by recent observation of Lanzetta et al. that most luminous galaxies at low redshifts produce $\lya$ absorption at impact parameter $l\lsim 160 \kpch$, we propose that these absorbers are clouds confined by the pressure of ambient hot gas in galactic haloes. We determine the properties of this hot gas and of the absorption systems on the basis of observational and theoretical constraints. The absorbing clouds need to be replenished on about one orbital time ($\sim 10^9$ yrs) in the galactic halo. The pressure and temperature of the gas at radius $r\sim 100\kpc$ are $P=(10-100){\rm cm^{-3} K}$, $T=10^{(5.5-6.5)}{\rm K}$. The model requires that about 10 per cent of the gas in low-redshift galactic haloes is in the hot phase. Such gas in galactic haloes emits x-ray with bolometric luminosity of the order $10^{37-40}{\rm erg\,s^{-1}}$. The plausibility for such gas to exist in current models of galaxy formation is discussed.

F. D. Kahn

Papers

Introduction to the Mechanics of Stellar Systems