VOI. 49, 1963 : F. D. KAHN 777

antennas at Stanford University, supported by the Office of Scientific Research of the U.S. Air Force under contract AF18(603)-53. I For actual records taken witlh a system that suppresses grating responses, see Bracewell, It. N., G. Swarup, and C. L. Seeger, Nature, 193, 412-416 (1962). D)ata processing procedures for correcting grating response numerically are given by Bracewell, R. N., Astrophys. J., 137, 175-183 (1963). 2 For a major contribution to the problem of designing a microwave line feed, see Cumming, WV. A., Microwave Journal, 6, 81 (1963). This describes test -results on a dual-polarized line source for use at S-band.

DYNAMICS OF H II REGIONS By F. D. KAHN'*

NATIONAL ASTRONOMY OBSERVATORY, GREEN BANK, WBST VIRGINIAt If one knows how the density varies in an H II region, then one can draw conclusions about the dynamics of such an object. We shall make the following assumptions: (i) The is almost complete out to the boundary of the region. (ii) Recombination within the H II region proceeds so rapidly that the bulk of the Lyman continuum radiation from the goes to keep up the ionization. This is justified, since the recombination rate in fully ionized at 104 degrees K is 3 X 10-13 no, where ne = electron density. If ne = 100 particles/ cm3, the lifetime of an before recombination is only 3 X 1010 seconds, or 1,000 years. (iii) The rate of cooling by O+ , in collision with , is so high that the is almost isothermal, at about 10,0000K. With the customary value of the abundance of 0 + ions, the cooling rate at 104 degrees K is about 10-12 n,. Let us also assume for the present that there is no signifleant ejection of matter from the in the H II region. Then we may use the results given by Golds- worthy (1961) in his section 8. To reproduce the variations of density described by Menon (1961b) for the and the Rosette Nebulae, we have to assume that we are dealing with H II regions whose outer boundaries are advancing at super- sonic speed into the neutral gas outside. This is the R-type case discussed by Goldsworthy. If so, we expect the H II region to be divided into two sections, separated by an isothermal shock. In the inner region, the gas density, and therefore the electron density, increase from a finite value at the center to a larger value at the isothermal shock. Beyond the shock, the gas has not yet had time enough to readjust itself to the change in pressure consequent on its being ionized and heated. Its density distribution therefore resembles that before ionization, and we expect it here to decrease with increasing distance from the center. Figure 1 shows a typical run of density. If the ionization front moves out relatively slowly, the shock comes relatively close behind the ionization front, and the density profile resembles that described by Menon for the case of the Rosette . But if the ionizing star is very bright and the ionization front moves ahead very fast, then the distance from the Downloaded by guest on September 28, 2021 778 ASTRONOMY: F. D. KAHN PROC. N. A. S.

star to the shock is only a small fraction of the radius of the H II region. The density profile then resembles that of the . It is an interesting feature of the density profile given by M\enon that it does not show the expected dip at the center. Since he would certainly have seen this dip if its radius had been as much as 5 minutes of arc, or 0.65 pc., this means that the shock must now be less than this distance from the exciting star. But in such an extreme case of rapid ionization, the shock moves at four times the (isothermal) , or at about 50 km/sec. Thus, the Orion Nebula certainly cannot be more than 13,000 years old. Alternatively, let us assume that our picture is wrong and that the Orion Nebula density

0 *S * distance shock ionizationI front FIG. 1. is in a steady state and is formed by the continuous ejection of matter from one or more stars at its center. Then Bernoulli's equation gives us that U2/2 + a2 log n = const. = A, say, (1) and the equation of continuity that nur2 = const. = F, say. (2) Here u = gas speed, r = radial distance, n = particle density, and a = speed of sound. The logarithm is to the base e. Now Figure 6 given by Menon (1961a) shows that in the Orion Nebula ne = 250 particles/cm3 at 5' of arc from the center, and 10 particles/cm3 at 20' of arc dis- tance. Since n is clearly proportional to n, this shows, by means of equation (2), that u(20):u(5) = 25:16. (3) But from equation (1), u2(20) - u2(5) = 2a2 log n(20)/n(5) = 1.1 X 103(km/sec.) (4) Thus, this model would require that u(20) equal 42 km/sec. This is in violent contradiction to the low velocity of expansion found for the Nebula by Wilson et al. (1959). We must conclude that the Nebula is thus a very young object. If this conclusion is correct, it clearly has some startling astrophysical implications. Downloaded by guest on September 28, 2021 VOL. 49, 1963 ASTRONOMY: R. MINKOWSKI 779

* On leave from the University of Manchester. t Operated by Associated Universities, Inc., under contract with the National Science Founda- tion. Goldsworthy, F. A., Phil. Trans. Roy. Soc. (A), 253, 277 (1961). Menon, T. K., 1961a, N.R.A.O. Publications 1, No. 1; 1961b, Talk to this symposium. See also Kahn, F. D., and T. K. Menon, these PROCEEDINGS, 47, 1712 (1961). Wilson, 0. C., G. Miinch, E. M. Flather, and M. F. Coffeen, Ap. J., Suppl. No. 40, 4, 199 (1959).

RADIO SOURCES, , AND CLUSTERS OF GALAXIES BY R. MINKOWSKI* MOUNT WILSON AND PALOMAR OBSERVATORIES, CARNEGIE INSTITUTION OF WASHINGTON, CALIFORNIA INSTITUTE OF TECHNOLOGY The identification of radio sources at high galactic latitudes has progressed to a stage at which it is possible to make the first tentative attempts at a statistical exploration of the results. The identification of the source 3C 48 shows that galactic sources may occur at high galactic latitudes, but the results of the' deter- mination of diameters of sources support the generally accepted assumption that most sources at high galactic latitudes are extragalactic. The great majority of the extragalactic objects with which sources have been identified seem to be completely normal; they show no features which mark them as peculiar in any manner, either in their appearance or in their spectra where these are available. This is in sharp contrast to the early identifications, most of which pointed to highly peculiar objects. Most of the identifications thus are not supported by peculiarities of the objects, but rest entirely on positional coincidence. In this case, an identification with a given object is accepted if the statistical chance is small that the object is accidentally within the error area. If E2 is the error area of a position and n(m,) the number per unit area of relevant objects that are brighter than the photographic magnitude mp, the statistically expected number of objects brighter than m, in the error area is E2n(m,). This number represents the chance that an identification is spurious. The policy of all investigators has been essen- tially to set the limit m, for the search for identifications'so that the chance of a spurious identification is less than 0.1. For bright objects, the chance is much smaller. The total fraction of spurious identifications should not be larger than a few per cent. If sound statistical conclusions are to be derived, it is desirable to use data that refer to a defined volume. The data are too limited for such a treatment if different types of objects are separated. But it is possible to compile lists of identifications which refer to a defined area in the sky in which the identifications may be assumed to be complete for all sources above a definite limiting radio magnitude. Two such lists have been prepared:' one from sources of the survey at 86.5 Mc/sec by Mills, Slee, and Hill2 ("MISH survey"), the other from the 3C survey at 159 Mc/sec by Ryle's group.3 A list of tentative identifications for the declination zone -20° to + 100 of the MSH survey has been given by Mills.4 This list has been revised after investiga- Downloaded by guest on September 28, 2021