Hubble Law Research Articles

A larger and more turbulent Universe

THE modern version of the Hubble diagram in which the log of the redshift is plotted against apparent magnitude corrected for redshift and absorption effects of clusters of galaxies, is in principle capable of yielding several cosmologically useful pieces of information. In this letter I report evidence for a significant and substantial departure from the expected redshift for the Virgo cluster of galaxies. A peculiar velocity of 658 ± 96 km s−1 is derived but because of Virgo's membership in the Local Supercluster, such a value is not unexpected. Thus the turbulence recently observed by Smoot et al.1 for the Galaxy's motion within the Hubble expansion is present elsewhere in the Universe as well. Because the Virgo cluster does not exactly follow the Hubble law, a new value for the Hubble constant equal to 43.4 ± 2.6 km s−1 Mpc−1 is found leading to an observable Universe 1/4 to 1/3 again as large as was previously recognised.

Interpretation of the metric tensor components based on possible astrophysical implications

In this paper we shall consider the following question: ‘If the whole galactical system expands and if galaxies are separating away from one another just as much as they are separating from our galaxy, can we assume that such a reality will have repercussions on the formulation of basic physical laws in our surroundings?’ Considering a confirmative answer, we performed an attempt to find a physical interpretation of the perturbations of the metric tensor components. It was shown that they can be expressed in terms of the dilatation function which also appears to be one reason which prohibits the precise measurement of real time and distance. Considering that an observer in our wold knows nothing of the aperiodicity of atomic oscillations which ‘determine’ the unit of time, we discerned the meaning of time in two ways: (i) the time as it is accepted in special relativity and (ii) the ‘time’ based on the reading of clocks which suffer dilatation. The usual procedure for establishing equations of the gravitational field was then carried out. These equations reduce to those of the classical theory, if the dilatation function is proportional to Newtonian gravitational potential. On this basis, considering the Earth's expansion as a process which exists as a cosmological manifestation, we discussed the observed fact of the agreement between the rate of the Earth's radius and that of the universe, according to Hubble's law.

Theory of Gravitational‐Inertial Field of Universe. II. On Critical Systems in Universe

AbstractApplication of the equations of the gravitational‐inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which 1. all Galaxies in the Universe “disperse” from each other according to Hubble's law, 2. the “dispersion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, 3. for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian.All critical systems (with Schwarzschild radius) are specific because they exist in maximalinertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius.In high‐potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational “annihilation”. At the maximal value of inertial and gravitational potentials (= c2) the material mass is being completely “evaporated” transforming into radiation mass. The latter is being concentrated in the “horizon” of the critical system.All critical systems‐black holes‐represent geon systems, i.e. local formations of gravitational‐electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown.

Theory of Gravitational‐Inertial Field of Universe

AbstractIn this paper the basic proposition is a generalization of the metric tensor by introduction of an inertial field tensor satisfying ∇iglm  glm;i ≠ 0. On the basis of variational equations a system of more general covariant equations of gravitational‐inertial field is obtained. In Einstein's approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems of generl taheory of relativity by means of the new equations give the same results as Einstein's equations. However application of these equations to the cosmologic problem leads to following results: 1. All Galaxies in the Universe (actually all bodies if gravitational attraction is not considered) “disperse” from each other according to Hubble's law. Thus contrary to Friedmann's theory (according to which the “expansion of Universe” began from the singular state with an infinite velocity) the velocity of “dispersion” of bodies begins from the zero value and in the limit tends to the velocity of light. 2. The “dispertion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free bodies in the inertial field ‐ the law of inertia.All critical systems (with Schwarzschild radius) are specific because they exist in maximal inertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In the high‐potential inertial and gravitational fields the material mass in a static state or in the process of motion with decelleration is subject to an inertial and gravitational “annihilation”. Under the maximal value of inertial and gravitational potentials (= c2) the material mass is completely “evaporated” transforming into a radiation mass. The latter is concentrated in the “horizon” of the critical system.All critical systems –“black holes”‐ represent geon systems, i.e., the local formations of gravitational‐electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown.The Universe is in a state of dynamical equilibrium. Near the external part of its boundary surface a transformation of matter into electromagnetic‐gravitational‐neutrineal energy (geon mass) takes place. Inside the Universe, in the galaxies takes place the synthesis of matter from geon mass, penetrating from the external part of the world (from geon crown) by means of a tunneling mechanism.The geon system may be considered as a natural entire cybernetic system.

Theory of Gravitational‐Inertial Field of Universe. I. Gravitational‐Inertial Field Equations

AbstractIn the series of present articles the original proposition is a generalization of the real world tensor by the introduction of a inertial field tensor. From this generalization it follows, particularly, that ∇iglm  glm;i ≠ 0. This allows to use as a Lagrangian density of the field the expression Ag = k1 glm;iglm ;kgik. On the basis of variational equations a system of more general covariant equations of the gravitational‐inertial field is obtained. In the Einstein approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems in the general theory of relativity by means of the new equations gives the same results as the solution by means of Einstein's equations. However, application of these equations to the cosmologic problem gives a result different from that obtained by Friedmann's theory. In particular, the solution gives the Hubble law as the law of motion of a free body in the inertial field ‐ in contrast to Galileo‐Newton's law.

Continuous increase of Hubble modulus behind clusters of galaxies

VARIOUS authors have suggested the existence of real fluctuations to Hubble's law (proportionality of redshift to distance) as a function of the position of sources on the sky map. Karoji and Nottale1 have examined the possibility of a variation of the Hubble constant H associated with the passage of incoming light through rich clusters of galaxies. We confirm here their positive answer by a more detailed and precise statistical analysis. We show that there is an effective continuous effect depending on the relative distance of the line of sight of any given source to the centre of the intervening clusters. We thus conclude that we are dealing with a real physical effect, tied to the presence of these clusters.

Cosmological lore?and some heresies

Cosmology is based on a number of well-founded assumptions, which include Hubble's law and the cosmological principle. Most cosmologists and astronomers also tacitly accept a number of other assumptions and beliefs which constitute a sort of traditional cosmological lore. Among these are the notions that the universe is finite, that if it is not, then there must be an observational horizon which renders it finite for all practical purposes, that it is valid to employ the special relativistic Doppler formula to interpret large cosmological redshifts, and that the expansion of the universe is slowing down toward its ultimate reversal. It is argued that none of these notions is incontrovertible and that some of them involve serious inconsistencies. An alternative approach is proposed which assumes that the universe is expanding uniformly and that it constitutes a fundamental reference frame for light propagation as implied by the Robertson-Walker metric. This approach leads to a model of the universe which is possibly infinite but without a specific observational horizon, and which satisfies the requirements of relativity. It is shown that the proposed model is theoretically consistent and that recent astronomical evidence supports its assumptions and predictions; it therefore presents a serious challenge to commonly held views about the universe.

The structure of elliptical and cD galaxies.

view Abstract Citations (333) References (50) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The structure of elliptical and cD galaxies. Oemler, A., Jr. Abstract A method of photographic photometry is described which permits surface photometry of galaxies to be extended to very low (5v > 28 mag arcsec -2) surface brightnesses. It has been used to study ellfptical galaxies in three clusters and a number of cD galaxies, with the following results. Ignoring flattening, elliptical galaxies form a one-parameter family with light distributions which are well described by an exponentially truncated Hubble law. Their limiting radii R1 L0213, where L0 is an envelope-independent luminosity. There is no evidence that R1 is determined by tidal interactions with other galaxies. The core radii of ellipticals decrease with decreasing luminosity, but make a sudden jump at Mv -15. The cD galaxies and other elliptical brightest cluster members appear to be very bright-but otherwise normal-giant elliptical galaxies with very diffuse, extended envelopes superposed. The extent and luminosity of these outer envelopes is a strong function of cluster richness; in the most extreme case the envelope extends to a radius of 2 Mpc. There appears to be some hope of explaining the occurrences and properties of cD galaxies by the effects of dynamical friction within clusters. Subject headings: galaxies: formation - galaxies: photometry - galaxies: structure Publication: The Astrophysical Journal Pub Date: November 1976 DOI: 10.1086/154769 Bibcode: 1976ApJ...209..693O full text sources ADS | data products NED (68) SIMBAD (13)

The big bang is not needed

Recent computer simulations indicate that a system ofn gravitating masses breaks up, even when the total energy is negative. As a result, almost any initial phase-space distribution results in a universe that eventually expands under the Hubble law. Hence Hubble expansion implies little regarding an initial cosmic state. Especially it does not imply the singularly dense superpositioned state used in the big bang model.

On the Formation of Elliptical Galaxies

Simple collapse and violent relaxation models produce sharply cut off envelopes with rho (r) proportionalr$sup -4$, whereas actual elliptical galaxies have more extended envelopes approximately given by rho (r) Ir$sup -3$ as implied by Hubble's law. Numerical models are presented, showing that when cosmological infall effects are included, galaxies are produced with envelopes having a rho (r) Ir$sup -2$.$sup 8$ dependence in excellent agreement with Hubble's law. A realistic rotating model is computed of an E5 galaxy which includes infall effects and where the angular momentum of the galaxy is gained through tidal interactions with neighboring protogalaxies. The envelope displays a Hubble dependence but at great distances shows a cutoff due to the tidal effects. The model gives an outstandingly good fit to the envelope of the E5 galaxy NGC 4697. Except for simple scaling, this fit is produced without the use of any free- fitting parameters. A mass-to-light ratio for NGC 4697 is also computed. (AIP)

The Hubble law and the spiral structures of galaxies from equations of motion in general relativity

Fully exploiting the Lie group that characterizes the underlying symmetry of general relativity theory, Einstein's tensor formalism factorizes, yielding a generalized (16-component) quaternion field formalism. The associated generalized geodesic equation, taken as the equation of motion of a star, predicts the Hubble law from one approximation for the generally covariant equations of motion, and the spiral structure of galaxies from another approximation. These results depend on the imposition of appropriate boundary conditions. The Hubble law follows when the boundary conditions derive from the oscillating model cosmology, and not from the other cosmological models. The spiral structures of the galaxies follow from the same boundary conditions, but with a different time scale than for the whole universe. The solutions that imply the spiral motion areFresnel integrals. These predict the star's motion to be along the “Cornu Spiral.” The part of this spiral in the first quadrant is the imploding phase of the galaxy, corresponding to a motion with continually decreasing radii, approaching the galactic center as time increases. The part of the “Cornu Spiral” in the third quadrant is the exploding phase, corresponding to continually increasing radii, as the star moves out from the hub. The spatial origin in the coordinate system of this curve is the inflection point, where the explosion changes to implosion. The two- (or many-) armed spiral galaxies are explained here in terms of two (or many) distinct explosions occurring at displaced times, in the domain of the rotating, planar galaxy.

Synchrotron and Inverse Compton Processes in X-Ray Clusters of Galaxies

The third UHURU catalogue of X-ray sources lists 64 sources at galactic latitudes higher than 20°, many of which have been identified with galaxies and clusters of galaxies. One of the best criteria for identifying a cluster of galaxies with an X-ray source is the extended nature of the X-ray source. Table I is a compilation of all clusters of galaxies known to be within the boundaries of X-ray error boxes. Not all have measured X-ray angular sizes (see column 3). Since the southern sky has been inspected too (Vidal 1975a), we believe that this list may represent a complete sample (down to the sensitivity of the UHURU satellite and the completeness of the Abell catalogue and the southern survey). Column 1 gives the optical identification, column 2 the 3U designation, column 3 the X-ray angular radius, column 4 the radio spectral index (see below), column 5 the redshift (corrected for galactic rotation) and column 6 the X-ray luminosities assuming the Hubble law. Numbers in parentheses give the references for the entries. When no such references are given, the data have been taken from Kellogg et al. (1973) and Bancall (1974).

Relativistic invariance and the expansion of the Universe

Assuming the propagation of electromagnetic quanta to be governed by a rigorous continuity equation, we show that the requirement that this equation have the form of the usual Lorentz-covariant electromagnetic wave equation in vacuum implies properties of space-time which an observer is likely to describe as a uniform expansion in agreement with Hubble's law. By this approach the interference properties of quanta are also derived. The possible small-scale variations of the Hubble constant, suggested by observations of some extra-galactic objects, would with this interpretation of the galactic redshift appear less mysterious.

Relativistic hierarchical cosmology

An account of hierarchical cosmology is given that is based on general relativity, being split up into three pieces for ease of assimilation. Part II will treat of specific solutions relevant to the observed Universe, while Part III compares these models with available empirical data in an effort to pick a model that agrees with observation. Part I derives a metric for a system based on the assumptions of (i) spherical symmetry about any local observer, (ii) a density distribution falling off as ϕ = ϕ0(t)r−2 from any local origin with the hierarchy delineated by step functions, (iii) the Universe was denser and more compact at some epoch in the past. These assumptions (Sections 1, 2) serve to derive a metric (Section 2) that allows of the definition of an effective scale factorS′(t) for Hubble's law, but which involves (Section 3) a curvature (k) and a parameter for measuring the radial coordinate (r/R0) that both vary with epoch:k=k(t), R0=R0(t). The metric reduces in a special case (k=constant,R0=constant,S′(t)=S(t) defined by the Friedmann equations) to that of a Robertson/Walker Universe. Spacetime in the hierarchy (Section 4) can be open or closed depending on the behaviour of the dust. The equations of motion (or the field equations, equivalently) yield two equations analogous to the Friedmann equations, but including terms in the time-derivative of the curvature and a space-variable density of matter. Relativistic hierarchical cosmology provides a wider field of possible investigation with a view to describing the Universe (Section 6) than do the conventional uniform Robertson/Walker models.

On the Formation of Elliptical Galaxies

Simple collapse and violent relaxation models produce sharply cut off envelopes with ϱ(r) ∝ r–4, whereas actual elliptical galaxies have more extended envelopes approximately given by ϱ(r) ∝ r–3 as implied by Hubble's Law. Numerical models are presented, showing that when cosmological infall effects are included, galaxies are produced with more extended envelopes having a ϱ(r) ∝ r–2.8 dependence in excellent agreement with Hubble's Law. We have also computed a realistic rotating model of an E5 galaxy which includes infall effects and where the angular momentum of the galaxy is gained through tidal interactions with neighboring protogalaxies. The envelope displays a Hubble dependence but at great distances shows a cutoff due to the tidal effects. The model is compared to the E5 galaxy NGC 4697 and provides an outstandingly good fit to the observations. Except for simple scaling, this excellent fit is produced without the use of any free fitting parameters.

Quasar absorption lines and sites of absorbing media

A method for the determination of distances of quasars and sites of absorbing media is presented. It is illustrated by application to 3C 191 and PKS 0237-23. The results are compared with those obtained from the traditional Hubble Law.

Early Stages of the Universe

When I was young theoretical cosmology was more a series of exercises in geometry than a branch of astrophysics. Moreover these exercises were based on little more than the Hubble law of red shifts and a general impression that on a large scale the Universe was roughly homogeneous and isotropic. Now all that has changed. While geometrical considerations retain their importance through the dominant role played by general relativity, cosmology has also become highly astrophysical. As a result we can now say a great deal about the early stages of the Universe. My aim is to give a brief account of our present understanding of this fascinating subject, at the same time highlighting the most important problems that remain.

Discrepant Redshifts of QSOs in Clusters of Galaxies and a Close QSO Pair

ALTHOUGH it is the majority view that QSO redshifts are cosmological in origin and related to distance by Hubble's law, several workers1–3 have proposed that QSOs may be more local objects. The strongest direct evidence for the conventional view is provided by observations of a number of QSOs which have been shown to have redshifts (z) which agree to within about 1% with the redshifts of apparently associated clusters of galaxies4–8. These QSO-cluster associations have all been found in searches restricted to QSOs with z<0.36 since on the cosmological hypothesis it is only for such low values of z that the associated galaxies would be readily visible. But, as Burbidge and O'Dell9 have pointed out, by assuming at the outset that the redshifts are cosmological these investigations fail to test the non-cosmological hypothesis. For the past several years we have been attempting to carry out a study of QSOs in clusters or groups which would be free from this objection. Although our results are by no means complete, we present here some of our preliminary findings as they seem to be of relevance to the present controversy.

A Newtonian Big-Bang Hierarchical Cosmological Model

view Abstract Citations (36) References (5) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Newtonian Big-Bang Hierarchical Cosmological Model Wertz, James R. Abstract Hierarchical cosmology deals with models having multiple clustering in the matter distribution of the Universe. A continuous representation of a hierarchical universe is introduced and applied, within the framework of Newtonian cosmology, to a more or less realistic model. In general, the mean mass-density is a function of both position and size of the volume considered, and generally decreases with increasing radius. (Observationally, de Vaucouleurs has determined p 7 in the range 10 <r < 1027 cm.) Similarly, the Hubble parameter depends on the order of the cluster involved and is, therefore, a function of the density. If a common origin of clusters is assumed, the relative expansion of the niverse may be determined directly from the density-radius relation. For realistic models (big-bang hierarchy with p at the present epoch), a Hubble law characteristic of the' hierarchy and, at least in principle, subject to observational verification is obtained. (For a reasonable choice of parameters, the graph is nearly linear but does' not intersect the origin.) The history of such a big-bang hierarchy is briefly discussed. Publication: The Astrophysical Journal Pub Date: March 1971 DOI: 10.1086/150834 Bibcode: 1971ApJ...164..227W full text sources ADS |

Cosmological Theory of Gravitation

I HAVE already described1,2 a model of a uniformly expanding universe in terms of a family of mutually receding galaxies and associated fundamental observers. It was assumed that the distance, r(t), between any pair of fundamental observers is related to their mutual recession velocity, w, and their measure of cosmic time, t, by the Hubble law where r and w are the estimates of these quantities by each fundamental observer from his light-intensity and Doppler redshift measurements, and where the present value of t is given by the reciprocal of the Hubble constant. I further assumed following McCrea3 that this system of mutually receding galaxies (the fundamental particles of our model) defines a basic reference frame or substratum for the propagation of light and indeed of all forms of energy.