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75h) from central surface brightness. 2h. 0 for pure disk. h From photometry, corrected for inclination, etc. References: (1) Bahcall, Schmidt, and Soneira 1982. (2) Bahcall 1983. (3) van Albada et al. 1985. (4) Casertano 1983b. (5) Casertano 1983a. (6) Carignan and Freeman 1985. e f J. N. Bahcall and S. 2h, which is approximately valid for the other galaxies. 0015 M /pc3 . (3) These numerical values constitute benchmarks relative to which theories of spiral galaxy formation can be tested. Relations (1) and (2) are satisfied with a total dispersion of only ±30% in the values of MH /MD and ±50% for ρH /ρD .

Bahcall and S. Casertano neutral gas. Similarly, a hot gaseous halo would produce — by bremsstrahlung — a much higher total X-ray emission (>1042 erg sec−1 ) than is observed for typical spiral galaxies (Fabbiano, Trinchieri, and Macdonald 1984). At an intermediate temperature like 104 K, the emission measures in the models discussed here are sufficiently large that they could be observed with existing techniques. The best cases for detecting intermediate temperature gas are edge-on spirals for which the emission measure would be expected to be ∼40 cm−6 pc outside the Holmberg radius on the major axis and could be a factor of several higher along the minor axis.

14) In summary, a King model may be parametrized by the dimensionless ratio Rc /Rt . We may relate the escape velocity from the cluster to the virial velocity as follows. The mean escape velocity is 1 1 2 Mcl Vesc = 2 2 2 (r) = − dr4πr2 ρ∗ (r)Vesc dr4πr2 ρ∗(r)φ(r) = −2Eφ , where Eφ is the gravitational binding energy of the cluster and Mcl is its mass. By the virial theorem, Eφ = −2 · 12 Mcl Vm2 so we have the following general relation, 2 = 4 Vm2 . s. velocity of stars in the cluster. This is our first clue that the equilibrium configurations under consideration may not persist over many relaxation times.

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Astro 2

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