B. Cameron Reed

Linear least‐squares fits with errors in both coordinates

York’s solution to the problem of linear least‐squares fits with errors in both coordinates [D. York, Can. J. Phys. 44, 1079 (1966)] is shown to be exact and not subject to the erroneous results that attempts to modify standard least‐squares algorithms can produce. Detailed examples of the use of York’s method are given; a fortran implementation suitable for use on personal computers is available to interested parties.

Linear least‐squares fits with errors in both coordinates. II: Comments on parameter variances

Corrected expressions for parameter variances in linear (straight‐line) least‐squares fits given in an earlier paper [B. C. Reed, Am. J. Phys. 57, 642–646 (1989)] are presented and discussed. In addition, some simplifications to the solution given in that paper are presented, and some comments made as to the role of weighting.

CATALOG OF GALACTIC OB STARS

An all-sky catalog of Galactic OB stars has been created by extending the Case-Hamburg Galactic plane luminous-stars surveys to include 5500 additional objects drawn from the literature. This work brings the total number of known or reasonably suspected OB stars to over 16,000. Companion databases of UBVβ photometry and MK classifications for these objects include nearly 30,000 and 20,000 entries, respectively.

New Estimates of the Scale Height and Surface Density of OB Stars in the Solar Neighborhood

Galactic latitudes and photographic magnitudes for large samples (N ~ 2000–4000) of OB stars within 10° of the Galactic plane and 4 kpc of the Sun are used to estimate the exponential scale height and surface density of these objects assuming a barometric extinction model. Depending upon the scale height and differential extinction of the absorbing layer, estimates of the OB-star scale height hOB vary from ~ 25 to 65 pc and of the surface density from ~ 6 to 80 stars per 105 pc2. Reasons for the wide spread in this latter figure are discussed. For an absorbing layer of scale height σ = 100 pc and B-band extinction of 2 mag kpc-1, we find hOB ~ 45 pc and ~ 26 stars per 105 pc2. The total Galactic population of these stars is estimated at ~ 60,000, and their formation rate at one every 40 years. Estimates of the scale height are found to be essentially independent of the assumed mean absolute magnitude for OB stars.

UBVβ Database for Case-Hamburg Northern and Southern Luminous Stars*

A database of photoelectric UBVβ photometry for stars listed in the Case-Hamburg northern and southern Milky Way luminous stars surveys has been compiled from the original research literature. Consisting of over 16,000 observations of some 7300 stars from over 500 sources, this database constitutes the most complete compilation of such photometry available for intrinsically luminous stars around the Galactic plane. Over 5000 stars listed in the Case-Hamburg surveys still lack fundamental photometric data.

THE SUN'S DISPLACEMENT FROM THE GALACTIC PLANE: LIMITS FROM THE DISTRIBUTION OF OB-STAR LATITUDES

Galactic latitudes and photographic magnitudes for large sample (N ~ 3600 - 12000) of OB stars within 10 degress of the galactic plane and 4 kpc of the Sun have been used to estimate the Suns displacement Zo from the galactic plane. Reasonable choices of average absolute magnitudes and extinction parameters limit Zo to not less than about 6 nor more than about 13 pc, with Zo = 10 - 12 pc mostly likely.

Vela OB1: Probable New Members and Hertzsprung-Russell Diagram

Several dozen stars are identified as probable previously unrecognized members of the association Vel OB1, including the Vela X-1 binary pulsar system. Based on a variable extinction analysis of 70 stars, the distance and ratio of total to selective absorption of the association are determined to be 1750 pc and 3.70, respectively. Vel OB1 may be significantly larger than previously appreciated, perhaps up to 600 by 300 pc in the sense of longitude by latitude. This physical extent, and the fact that the H-R diagram includes both low-mass evolved yellow supergiants and massive, early-type supergiants, indicates that Vel OB1 is probably not coeval.

Arthur Compton’s 1941 Report on explosive fission of U-235: A look at the physics

In November 1941, the third of three reports on atomic fission commissioned by Vannevar Bush through the National Academy of Sciences examined the prospects for explosive fission in U-235. This report, prepared by Arthur Compton, developed a model for estimating the critical mass and efficiency of an atomic bomb. I examine Compton’s physics, attempt to discern the provenance of the numbers he adopted for various parameters, and compare his results with those yielded by a full diffusion-theory approach with contemporary values for the fission parameters. I conclude that Compton’s physics is sound. A combination of somewhat optimistic parameter values and a conservative model for critical mass lead him to a numerical value for the bare critical radius of U-235 that is in fairly good accord with that yielded by diffusion theory. His estimated efficiency proved to be quite accurate for the Little Boy bomb.

A brief primer on tamped fission-bomb cores

A previously published discussion of the physics of fission-bomb cores is extended to incorporate the effects of a surrounding tamper/reflector. I examine the effect of a tamper of finite thickness on the calculation of critical mass in contrast to the infinite-thickness approximation usually invoked. An infinite-thickness tamper reduces the critical mass by a factor of eight; a more realistic estimate for a tamper of nonzero mass is a factor of about two. An approximate model of the Hiroshima Little Boy bomb results in a predicted explosive yield of about 13kilotons, in good agreement with the actual value of approximately 12kilotons, although this agreement might be fortuitous. A spreadsheet for estimating the critical masses of tamped and untamped cores and expected bomb yields and efficiencies is available.

MEAN ABSOLUTE MAGNITUDES OF OB+, OB, AND OB- STARS

Photoelectric Beta values for over 1200 stars listed in Stephenson and Sanduleaks Catalog of Luminous Stars in the Southern Milky Way are used in conjunction with Reed and Beattys (1995) MVBeta calibration to determine mean absolute magnitudes for Nassau and Stephensons (1960: NS) objective-prism based OB+, OB, and OB- classes of stars. The NS sequence proves to be one of decreasing luminosity, but a systematic effect is present: the mean absolute magnitude of stars in each class is a function of apparent magnitude V. MK-quality spectral classifications for a subset of over 300 stars indicates that the source of this effect appears to be inclusion of increasing numbers of dwarf stars in each NS class with increasing V. The MVBeta calibration indicates taht, at a given V, the OB+ (OB-) stars are intrinsically ~0.8 magnitudes brighter (fainter) than the OB stars; while these differences are statistically significant, the range of absolute magnitudes present in each type, sigma (MV) ~1.1, is large enough to render NS classifications only marginally useful as luminosity discriminants. However, our results can be of use in estimating absolute magnitudes for stars for which only an NS classification is available, and in checking for inconsistencies between NS classifications and Beta-V photometry.