Search

This is a reprinting of a paper by Jerome Kristian and Rainer K. Sachs, first published in 1966, in which they proposed a power-series scheme for reading out various parameters of the Universe directly from observations in a model-independent way. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis and by a brief biography of J. Kristian, compiled by A. Krasinski from internet sources.

We have monitored Supernova 1987A in optical/near-infrared bands using various high-speed photometers from a few weeks following its birth until early 1996 in order to search for a pulsar remnant. While we have found no clear evidence of any pulsar of constant intensity and stable timing, we have found emission with a complex period modulation near the frequency of 467.5 Hz – a 2.14 ms pulsar candidate. We first detected this signal in data taken on the remnant at the Las Campanas Observatory (LCO) 2.5-m Dupont telescope during 14–16 Feb. 1992 UT. We detected further signals near the 2.14 ms period on numerous occasions over the next four years in data taken with a variety of telescopes, data systems and detectors, at a number of ground- and space-based observatories. In particular, an effort during mid-1993 to monitor this signal with the U. of Tasmania 1-m telescope, when SN1987A was inaccessible to nearly all other observing sites due to high airmass, clearly detected the 2.14 ms signal in the first three nights' observations. The sequence of detections of this signal from Feb. `92 through August `93, prior to its apparent subsequent fading, is highly improbable (

Observations with the Wide-Field/Planetary Camera-2 of the Hubble Space Telescope (HST) are presented for three radio-loud quasars: 3C 48 (z=0.367), B2 1425+267 (z=0.366), and 3C 345 (z=0.594). All three quasars have luminous (~4 L^*) galaxies as hosts, which are either elliptical (B2 1425+267 and 3C 345) or interacting (3C 48), and all hosts are 0.5 - 1.0 mag bluer in (V-I) than other galaxies with the same overall morphology at similar redshifts to the quasars. The host of 3C 48 has many H II regions and a very extended tidal tail. All nine of the radio-loud quasars studied here and in Bahcall et al. (1997) either have bright elliptical hosts or occur in interacting systems. There is a robust correlation between the radio emission of the quasar and the luminosity of host galaxy; the radio-loud quasars reside in galaxies that are on average about 1 mag brighter than hosts of the radio-quiet quasars., Accepted for publication in ApJ. 3 postscript and 3 jpeg figures. Original figures may be found in ftp://eku.sns.ias.edu/pub/sofia/RadioLoud/

We present new, high signal-to-noise near-infrared observations of the Crab Nebula pulsar using the Solid State Photomultiplier instrument on the Multiple Mirror Telescope. Our observations cover the J (1.25 μm), H (1.65 μm), and K (2.2 μm) infrared wavebands and have 20 μs time resolution. Together with visible and UV observations made by the Hubble Space Telescope High-Speed Photometer, we have high time resolution observations covering over a decade in wavelength. We present the pulse profiles over this wavelength range, and we analyze the pulse shape as a function of wavelength, including the peak-to-peak phase separation, the peak full width half-maxima (FWHM), and the peak half-width half-maxima (HWHM). We also create both phase-averaged and phase-resolved color spectra of the pulsar emission. We find that the peak-to-peak phase separation shows a significant trend for an increase with wavelength, in rough agreement with models of the pulsar emission mechanism. The FWHM for peaks 1 and 2 also show a trend for increase with wavelength, again in qualitative agreement with the models. However, the HWHM for peaks 1 and 2 show significant differences in their wavelength dependences from the leading to trailing edges. This behavior is not predicted by current pulsar emission models, and the different wavelength dependences of the component HWHM values call into question the usefulness of FWHM measurements. Our spectral analyses show that the IR-UV dereddened phase-averaged color spectrum is essentially flat over more than a decade in frequency. This is in clear contrast to the X-ray and γ-ray regimes, where the spectrum is falling steeply. The color spectra of peaks 1 and 2 are also essentially flat, but the ratio of the two shows statistically significant variations from a constant value. Finally, the color spectra of peaks 1 and 2 show significant differences from the leading to trailing edges. As with the HWHM, this behavior is not predicted by current pulsar emission models.

We present evidence of wavelength-dependent variations within the infrared, optical, and ultraviolet pulse profile peaks of the Crab Nebula pulsar. The leading and trailing edge half-width half-maxima of the peaks display clear differences in their wavelength dependences. In addition, phase-resolved infrared-to-ultraviolet color spectra show significant variations from the leading to trailing edges of the peaks. The color variations between the leading and trailing edges remain significant over phase differences smaller than 0.0054, corresponding to timescales of $, 12 pages, 4 figures

We present Hubble Space Telescope WFPC2 images of elephant trunks in the H II region M16. There are three principle results of this study. First, the morphology and stratified ionization structure of the interface between the dense molecular material and the interior of the H II region is well understood in terms of photoionization of a photoevaporative flow. Photoionization models of an empirical density profile capture the essential features of the observations, including the extremely localized region of [S II] emission at the interface and the observed offset between emission peaks in lower and higher ionization lines. The details of this structure are found to be a sensitive function both of the density profile of the interface and of the shape of the ionizing continuum. Interpretation of the interaction of the photoevaporative flow with gas in the interior of the nebula supports the view that much of the emission from H II regions may arise in such flows. Photoionization of photoevaporative flows may provide a useful paradigm for interpreting a wide range of observations of H II regions. Second, we report the discovery of a population of small cometary globules that are being uncovered as the main bodies of the elephant trunks are dispersed. Several lines of evidence connect these globules to ongoing star formation, including the association of a number of globules with stellar objects seen in IR images of M16 or in the continuum HST images themselves. We refer to these structures as evaporating gaseous globules, or "EGGs." These appear to be the same type of object as the nebular condensations seen previously in M42. The primary difference between the two cases is that in M16 we are seeing the objects from the side, while in M42 the objects are seen more nearly face-on against the backdrop of the ionized face of the molecular cloud. We find that the "evaporating globule" interpretation naturally accounts for the properties of objects in both nebulae, while avoiding serious difficulties with the competing "evaporating disk" model previously applied to the objects in M42. More generally, we find that disk-like structures are relatively rare in either nebula. Third, the data indicate that photoevaporation may have uncovered many EGGs while the stellar objects in them were still accreting mass, thereby freezing the mass distribution of the protostars at an early stage in their evolution. We conclude that the masses of stars in the cluster environment in M16 are generally determined not by the onset of stellar winds, as in more isolated regions of star formation, but rather by disruption of the star forming environment by the nearby O stars.

Analysis of V and I band HST Planetary Camera images of the giant elliptical galaxy M87 show that its central starlight distribution is consistent with the black hole M_• = 2.6 X 10^9 M_☉ cusp model proposed for M87 by Young et al. [ApJ, 221, 721 (1978)]. A combined approach of image deconvolution and modeling is used to investigate the starlight distribution into limiting radii of ≈0".04 (3 pc at 16 Mpc). The central structure of M87 can be described by three components: a power-law starlight profile of the form µ(r)∝a:r^(-1/4) for r

A field of area 1.5 × 10 −5 sr was imaged with unprecendented sensitivity using the VLA at 5 GHz. The total integration time of 126 hr was spread over the D, C, and B configurations in order to obtain images of faint radio sources with angular scales between 1″ and 100″ with an rms noise of 2.5 μJy. Subsequent observations at 1.5 GHz provided spectral information about the sources. The inner part of this field, centered at α = 14 h 16 m and δ = 52.7° (1950.0) has also been imaged with the Palomar 200 in. 4-shooter CCD array. A complete (>95%) catalog of 62 sources with a peak flux density at 5 GHz greater than 16 μJy at 8″ resolution and a typical positional accuracy of 0.″2 is compiled

Submillisecond optical photometry of the black hole candidate GX 339 - 4 was obtained on August 1, 1989, (UT) using the 1.5 m telescope of the Cerro Tololo Inter-American Observatory. Eight second quasi-periodic oscillations of width 0.02-0.04 Hz and root mean square amplitude 4-6 percent are found. The visual magnitude of GX 339 - 4 at the beginning of the observation was m(v) = 17.7. Motch et al. (1985) have previously reported 7 s optical quasi-periodic oscillations when GX 339 - 4 was also m(v) = 17.7 and in an X-ray off-state. No X-ray observations were made during the present optical observations and so the X-ray state of GX 339 - 4 cannot be ascertained. In addition, Motch et al. have also reported 20 s optical quasi-periodic oscillations with 30-40 percent full amplitude but when GX 339 - 4 was much brighter, m(v) = 15.4, and in a hard X-ray state.

Images of Andromeda I in the visual and near-infrared show a giant branch characteristic of galactic globular clusters of intermediate metallicity. The distance of the galaxy is estimated from the tip of the giant branch to be 790 + or - 60 kpc. The physical dimensions and luminosity are similar to those of the dwarf spheroidal in Sculptor. There is no evidence for an intermediate age population in Andromeda I, and appropriate upper limits are specified. There is marginal evidence for a color gradient in the galaxy, a phenomenon not previously noted in a dwarf spheroidal. 21 refs.

This paper is a partial and preliminary report on a review of the optical and radio properties of 3CR sources (Kristian, 1977). It will treat the overall status of the identifications and a few of the optical properties of the identified sources, including evidence for a faint magnitude cutoff in the apparent brightness of 3CR quasars. A summary of the status of 3 CR identifications as of early 1976 has been prepared by Smith, Spinrad, and Smith (1976). The present work includes new data on several dozen sources, as well as a systematic reevaluation of previous identifications.

The optical properties of the Crab nebula pulsar are reviewed. The Crab nebula pulsar has a high degree of constancy at optical wavelengths. No time variations over short or long periods have been detected; the light curve is nearly the same in all colors. The intensity and color of the pulsar are V = 16.5, B − V = +0.5, U − B = −0.45 and V − R = −0.75. There is no precursor as found at radio wavelengths and the main pulse contains 65 per cent of the total energy. No lines have been detected.Searches for other pulsars have been unsuccessful.

An optical pulsar with frequency f = 1,968,629 Hz has been detected at the location of supernova 1987A in the LMC. The brightness of the pulsed light increased from magnitude 19 to 18 during a 7-hr observation period starting on 18.1 January 1987 UT. The frequency of the pulsar during this same period varied in a nearly sinusoidal manner, with an amplitude of 1.5 x 10 to the -3rd Hz and a period of 8 hr. If this is interpreted as the result of a binary orbit, it suggests that there may be a Jupiter-size object orbiting the pulsar at a distance of 10 to the 6th km.

A prism spectrograph with an associated SIT television camera, operating as a two-dimensional detector with digital readout, has been used at the 5-m Hale telescope. The system was tested for its ability to subtract the sky spectrum, and was found to produce difference spectra that are essentially photon noise limited. Redshifts of 14 galaxies in clusters with 0.01 ≤ z ≤ 0.4 were obtained, each with exposure times of 90 minutes or less. Nine of the redshifts are new. Redshifts for the remaining five agree with previous values to within the measuring errors. The speed and sky-subtraction capabilities of the instrument are sufficient to begin routine measurement of absorption-line redshifts for remote cluster galaxies in an effort to extend the Hubble diagram.

Spectrophotometry of the faint radio galaxy 3C 343.1 shows a strong emission line in the red. If identified with ⋋3727 of [O II], it yields z = 0.750. The identification is aided by noting that ⋋3869 of [Ne III] is marginally visible. The optical continuum is relatively blue in color; it is likely to be caused by a population of stars younger than often found in nearby E galaxies. By comparison with other distant galaxies of established z, the isophotal diameter of about 7" measured for 3C 343.1, is consistent with the proposed redshift and corresponds to a linear size of 70 kpc and to a surface brightness of µτ ≈ 26 mag arcsec^(-2).

This paper is a partial and preliminary report on a review of the optical and radio properties of 3CR sources (Kristian, 1977). It will treat the overall status of the identifications and a few of the optical properties of the identified sources, including evidence for a faint magnitude cutoff in the apparent brightness of 3CR quasars. A summary of the status of 3 CR identifications as of early 1976 has been prepared by Smith, Spinrad, and Smith (1976). The present work includes new data on several dozen sources, as well as a systematic reevaluation of previous identifications.

Two-dimensional SIT and CCD detectors have been used to measure the surface brightness of the peculiar elliptical radio galaxy M87. Measurements were made in three broad-band colors (B, V, and R) to a distance of 80" from the nucleus, with 1" spatial resolution and photometric accuracy of the order of 1%. The data are given in some detail and are compared with earlier photographic results. The most obvious feature of the data is a bright, barely resolved central luminosity spike, which is not seen in similar data on other nearby normal ellipticals. Also, attempts to fit isothermal or King models away from the nuclear spike show additional excess luminosity in the central regions of the galaxy (r < 10"), which cannot be fitted by such a model. A model-independent dynamical analysis, using the photometric data combined with spectrographic results by Sargent et al., shows that the nucleus of M87 contains a compact mass of low luminosity, with M = 5 x 10^9 M_⊙, r < 100 pc, and M/ℒ > 60. All of the existing data is well fitted by a King model containing a central black hole of mass M = 3 x 10^9 M_⊙ and a point luminosity source. While such a model is not uniquely required by the data, it is perhaps the most plausible of several possible models considered. At present, M87 is probably the best case for a hypothetical massive black hole in a galaxy nucleus.

The energy distribution and spectrum of the "blue" star near CP 1919 indicate that it is a normal early F, main-sequence star and therefore is not likely to be related to the radio source. No regular variations were found in the light from the star, to within an accuracy of a few tenths of 1 per cent.

The optical flux of Seo X-1 was continuously monitored on five separate nights between April and June 1967. Pulse counting was used with sampling intervals of 5 sec on the 100- and 200-inch telescopes and 15 sec on the 60-inch reflector. The error due to photon statistics per sample interval was smaller than 0.007 mag in all cases. The data were processed entirely by computer, using a variety of special digital techniques. Rapid optical flickering with amplitudes of ~0.02 mag on a time scale of minutes was found on all five nights. These high-frequency fluctuations are superposed on slower continuous variations with amplitudes ~0.15 mag, and on occasional bursts of 0.2 mag which last about 10 min with very short rise and decay times. Radial velocities have been measured by a digital method of cross-correlation of microphotometer records of the original photographic plates (Westphal 1966). Velocity changes of about 100 km sec^(-1) were found on two different singly trailed plates, each of 3 hours' duration. The hydrogen lines and He II (⋋4686) change in opposite directions, similar to the extar Cyg X-2, suggesting, but not proving, binary motion. Systematic changes of velocity from night to night are set out in Table 2. The distance to Seo X-1 is estimated to be D ≃ 500 pc by three methods, based on the strength of interstellar Ca II K, and on the old nova hypothesis. A firm lower limit of D ≥ 300 pc seems well established. The total X-ray power is ≃2 x 10^(37) h^2 ergs sec^1, where his the distance in units of 500 pc. If the Xray energy is due to bremsstrahlung, this level requires Seo X-1 to continuously pump energy into the hot plasma, replenishing the entire energy store of gas in the cooling time of t_c = 3 X 10^(-15) h^(-1) R^(3/2) sec where R is the radius (in centimeters) of the plasma system. Reasonable values of 10^(11) cm < R < 10^(12) cm give 100 h^(-1) < t_o < 3000 h^(-1) sec, which, remarkably, is the characteristic time of the light flicker. Mechanical energy due to some type of low-Q oscillation of the system, similar in many respects to that observed in the Sun, seems capable of providing 10^(37) ergs sec^(-1) to the plasma gas. The crucial experiment remains to simultaneously monitor the optical and the X-ray flux over periods of several hours. Detailed correlation of fluctuations is not expected, but the mean X-ray flux might plausibly be expected to vary in periods of fractions of an hour as the mean amplitude of the optical fluctuations changes.

Broad-band photoelectric measurements on nine nights between 1969 February and 1970 February show constant intensity and colors for the pulsar of V = 16.5, B - V = +0.5, U - B = -0.45, and V - R = -0.75, with an accuracy of 10-15 percent in each passband. The ratio of the intensity in the main pulse to that in the subpulse is about 1.8 in each color, with the same accuracy. In the passband λλ3800-6000, the pulsar intensity repeated within 3 percent on nights 2 months apart. Measurements of linear polarization on four nights in 1969 February, August, and October show repeatable behavior, with the amount of polarization changing smoothly through the pulse from at least 25 percent to near zero and the plane of polarization sweeping through 150° during 60° of the pulsar's rotation. The time behavior was similar in the main pulse and the subpulse. The discontinuous change of the pulsar's period in 1969 September had no discernible effect upon the intensity, colors, or polarization of the pulses. It is argued that the observed pulses are due to a fixed, polarized emission pattern which is azimuthally scanned as the object rotates, and the sweep of the plane of polarization is interpreted in terms of a very general geometrical model. If the model is valid, then the projection of the rotation axis of the pulsar on the plane of the sky is found directly from the data, with an ambiguity of 90°, and is either parallel or orthogonal to the integrated magnetic field of the nebula within 20" of the pulsar. This agreement between the angles of the rotation axis and the magnetic field of the nebula seems too close to be accidental, and implies that the external field, at least in the vicinity of the pulsar, was produced by the pulsar at some stage in its history.

The optical properties of the Crab nebula pulsar are reviewed. The Crab nebula pulsar has a high degree of constancy at optical wavelengths. No time variations over short or long periods have been detected; the light curve is nearly the same in all colors. The intensity and color of the pulsar are V = 16.5, B − V = + 0.5, U − B = − 0.45 and V − R = − 0.75. There is no precursor as found at radio wavelengths and the main pulse contains 65 per cent of the total energy. No lines have been detected.

Data obtained during five nights of continuous monitoring of the X-ray source Seo X-1 between April and June 1967 are shown in computer-generated point plots.

Spectra, photographs, and photometric measurements have been used to show that Maffei 2 has a distance of 5 ± 2 Mpc and that it has a morphological type near Sbc II-in agreement with similar conclusions made earlier by radio observers. We discuss the possible relationships between Maffei 2 and the elliptical galaxy Maffei 1; there are serious inconsistencies in the existing data which bear on this question.

We have analyzed charged coupled device (CCD) photometry in the g and r bands of three supergiant elliptical galaxies: NGC 4874 and NGC 4889 in the Coma cluster, and the radio galaxy NGC 6251. The profiles of NGC 4874 and NGC 4889 are closely fitted by King models. The profile of NGC 6251 cannot be fitted by a King model, nor by a King model plus a central point luminosity source (the presence of which is suggested by a blue trend in the colors at small radii). The previously studied profile of M87, when convolved with an appropriate Gaussian function to allow for the difference in distance, closely resembles the profile of NGC 6251 (but not those of NGC 4874 or NGC 4889). NGC 6251 was successfully fitted with a luminosity profile containing both a point luminosity source and a central point mass. The value of this point mass cannot be determined without additional dynamical data. However, if the core velocity dispersion is similar to that of other giant ellipticals of the same absolute magnitude, the point mass is likely to be about 2.4 x 10^9 M_⊙, similar to the value reported earlier for M87. The data are also used to derive upper limits for possible central point masses in NGC 4874 and NGC 4889.

Since March 1987 the optical flux from supernova 1987A for periodic pulsations has been sought. As of August 1988, after 38 separate observations, no pulsar has been detected. The typical upper limit placed on the pulsed fraction optical light from the supernova is 0.0002, for pulse frequencies in the range 0.03-5000 Hz. The best limit on the pulsed fraction of supernova light is 7 x 10 to the -6th, on January 22, 1988. On August 28, 1988 the faintest limit for the magnitude of the pulsar, dimmer than 20th mag is reached. These limits are based on Fourier transforms of up to 67 million points, covering a range of spindown rates.

Redshifts are given for 50 brightest cluster galaxies, extending as far as z = 0.75; BVR photometry is given for 33 clusters. These data are combined with earlier data of a similar kind in order to investigate several effects. The measured B - V and V - R colors as a function of redshift are well represented by Whitford's standard-galaxy K corrections, as far as these are defined (to z = 0.28 in B - V and z = 0.48 in V - R). This suggests both that the K corrections are valid over these ranges of z and that no major color change of the galaxies has occurred over the last 4-5 x 10^9 years. At larger redshifts, the colors, which start out being monotonically redder with z, turn over and become bluer with z. The data at large z seem to follow the prediction based upon ultraviolet photometry of NGC 4486 (M87), which is one extreme of a range of galaxies measured by Code and Welch. Other standard corrections to the measurements are discussed, and formal least-squares values of q_0 are computed. To explore the possibility that one might be stalemated by the fact that the value of q_0 must, in principle, be known a priori to compute the aperture correction, the data are corrected separately for assumed q_0 values of 0 and + 1. The subsequently computed values of q_0 differ by only 0.2 between the two cases, which indicates that a simple iterative procedure will converge to produce a self-consistent value of q_0. The new data do not significantly change earlier discussions of the corrections for cluster richness and Bautz-Morgan contrast type. If these two corrections are not made, the effect on the present data is to significantly increase the positive curvature of the Hubble diagram, as well as the dispersion in apparent magnitude. To within the limits of the present data, the absolute magnitude of the brightest cluster galaxy does not, in general, depend on whether it is also a bright radio source. The present sample, cut off at z = 0.4 to avoid selection effects and uncertainties in the data, shows the first significant evidence for curvature of the Hubble diagram, with V and R magnitudes giving similar results. The formal value of q_0 (with galaxy evolution ignored) is + 1.6 ± 0.4. The dispersion in absolute magnitude is less than 0.3 mag, with M_v = -23.28 ± 0.03 and M_R= -24.09 ± 0.03. The use of the Hubble diagram in cosmology now depends on a knowledge of brightness changes in galaxies, on the one hand, or of q_0 from other evidence, on the other. For example, if it were known with certainty that there has been no significant change in elliptical galaxy luminosities during the last 4 x 10^9 years, then the present data are nearly good enough for one to say definitively that the universe is closed and finite, with a finite lifetime. At the other extreme, if it were known with certainty from other evidence that the universe was nearly empty (q_0 ≈ 0), then the present data set the constraint that net galaxy luminosities have decreased by ~ 0.5 mag during the last 5 x 10^9 years, with a net color change Δ(B - V) ≤ 0.1 mag. It seems possible at present to construct a self-consistent model with q_0 ≈ 0 that satisfies the known data, but the case is not yet settled.

VLA maps in the 21 cm line of neutral hydrogen have been obtained for three S0 galaxies with polar rings, and an upper limit on H I has been obtained for a fourth system. Polar rings span a continuum, ranging from those in which the H I seems to be in a relatively stable configuration, producing stars throughout its extent, to those in which the H I is very asymmetric, with stars forming only at the inner edge of an H I disk. A deep CCD image of MGC -5-7-1 shows arcs and filaments, some of which coincide with the likewise chaotic H I. If the system formed as the result of the merger of a gas-rich system with an S0 galaxy, the gas-rich system must have included considerable numbers of stars. 25 references.

The age of the LMC red globular cluster NGC 1783 is estimated as 0.9 + or - 0.4 billion yr by photometry of the main-sequence turnoff. The accuracy of the estimate is limited chiefly by the uncertainty in the distance modulus of the cluster. At (m - M)0 = 18.2 the cluster is aged 1.1 + or - 0.2 Gyr; at (m - M)0 = 18.7 it is 0.7 + or - 0.2 Gyr. NGC 1783 is a sufficiently rich cluster that one can see the full development of red giants on the asymptotic giant branch from the M type, through S, to carbon-rich atmospheres.

Spectroscopy and direct imaging of Qll 15+080A,B,C with a CCD camera supports the hypothesis that they are gravitational images of a single object. Spectroscopy of the C III] λ1909 emission line shows all the images to have identical spectra and redshifts (to within 100 km s^(-1)), except that Bis slightly redder. The position and brightness of the three images has been accurately measured; the images A, B, and Care magnitudes 16.30,18.64, and 18.17, respectively, in the r band, B is 1". 77 from A in position angle 266°, and C is 2".28 away at position angle 322°. A and C have the same color, but B is redder by 0.23 mag in (g-r). There is no trace of a lens galaxy, which must have a surface brightness of less than 29 mag arcsec^(-2) at a distance of 5" -8" from Q1115+080. Three bright galaxies lie near Q1115+080, apparently forming a small group. Gravitational lens imaging by a massive spiral galaxy is explored, and we find a quintuple image model resembling Q1115+080 A,B,C. In this model, Q1115+080A is a highly magnified close pair of images oriented in position angle 23°. An elongation of Q1115+080A at this angle is seen in the CCD pictures.

Absorption-line redshifts for 37 galaxies in 31 remote clusters have been measured with the new sky-subtracting prism spectrograph, using an SIT television detector with digital readout. Twenty-five galaxies in the sample have redshifts larger than z = 0.20. New photoelectric BVR photometry has been obtained for 16 of the clusters. Magnitudes corrected for aperture effect, K-dimming, galactic absorption, cluster richness, and Bautz-Morgan contrast effect are listed. The data permit an improvement in the statistics of the Hubble diagram to z = 0.28 and a new determination of the dependence of the absolute magnitude of the brightest cluster galaxy on cluster richness. A small correlation with richness is found whose amplitude is 0.20 ± 0.18 mag over all Abell richness classes 0-4. As in previous studies, the shallowness of the correlation requires that if M(l) is governed by a general luminosity function, Φ(M), for fainter members, then the slope of Φ(M) at M(I) must be very steep. The 16 new clusters with photometry have a dispersion in M(l) of 0.26 mag. The dispersion of fully corrected magnitudes for the 65 clusters in the total sample is 0.276 mag. The new points in the Hubble diagram give no indication that the (m, z) relation deviates from the q_0(formal) = + 1 line (i.e. with no evolutionary correction applied), nor that 3C 295 is abnormally bright. The need for more data with z > 0.3 is stressed.

Further observations and theoretical work on Q0957+561 are presented. The galaxy responsible for causing multiple gravitational lens images of Q0957+561 has been reobserved spectroscopically, and we give a more accurate redshift z_d =0.36. In 1980 January, component B had brightened by 0.3 mag and was equal to A. We have further analyzed our CCD data on the surrounding cluster of galaxies, and we give a list of 180 objects (146 galaxies, 32 stars, and 2 QSO images) to a limiting magnitude r=24.5. The data indicate that the center of luminosity of the cluster is about 23" west of the QSO images. Detailed models of the gravitational lens effect have been computed. These models can explain all optical and radio data for the system. They predict time delays of up to 5 years between variations in the A and B images (with A preceding B). We believe the third image is rather faint and located close to the center of the lens galaxy. It is possible that the third image contributes to the observed galaxy core. We discuss the possibility that this system may be used to measure H_0. Given two time delays among the three images, such measurements may be successful if no further complications in the imaging arise.

The general problem of perturbations of the equipartition state is discussed, using the tensor virial approximation. The non-static equilibrium state leads to two additional terms in the characteristic value equation, one expressed by means of a vector field whose field lines move with the unperturbed fluid. The characteristic value problem is solved for the toroidal equilibrium state. It is found that the degeneracy of the Kelvin modes is lifted by the field; the Kelvin frequencies are corrected by terms linear in the field strengths, with equally spaced levels for small fields. (auth)

The spectroscopic binary BD+34 3815 (= HDE 226868) with a period of 5.6 days, which is the brightest object in the position box for the X-ray source Cyg X-1, is studied to determine whether it meets all the requirements for being a black hole. Evidence is presented that the mass of the secondary is larger than the upper limits for white dwarfs or neutron stars, but there is no conclusive evidence that the optical binary is an X-ray source, and that the secondary is a collapsed object.

IRC+10216 is an extended object located out of the galactic plane in an unreddened region. At 5 μ it is the brightest source observed outside the solar system; at 2.2 μ it varies by as much as 2 mag, with a time scale on the order of 600 days. Its energy distribution resembles that of a 650° K blackbody, and no spectral features have been observed in the wavelength range from 1.5 to 14 μ. The object is interpreted as being consistent with a galactic source surrounded by an optically thick dust shell.

Fluctuations of 0.04 mag on a time scale of minutes have been found in the optical flux of the candidate star for Cyg X-2. Comparison of radial velocities on a well-widened spectrogram with those of Lynds shows large changes, confirming an earlier suspicion of binary motion by E. M. Burbidge. The systemic velocity is y = -250 km/sec. A lower limit of 300 km/sec for the orbital velocity of one component relative to the other is indicated. The system parameters are m = m_1 + m_2 = 1, P < 0.4 M_☉ (days), and ɑ < 0.01 M_☉ a.u., indicative of a very close binary system (m = m_1 + m_2). Eclipses are probable and may have been observed. Spectroscopic evidence may be present for gas streams moving with speeds of greater than 700 km/sec. Three independent arguments are given why the optical flux cannot primarily be non-thermal radiation connected with the production of the X-rays.

Suggestion of the bright stars X Per and HD 77581 as possible candidates for the X-ray sources 2U 0352+30 and 2U 0900-40 respectively. The first is an active, rapidly rotating Be star which is losing mass. The second is similar to BD+34.3815 deg, a likely candidate for Cyg X-1, in spectral type and in the possibility that it may be a short-period binary.