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Six archival Chandra observations are matched with eight sets of radio data and studied in the context of the outflow method to measure and study the spin properties of $\rm{Sgr ~A^*}$. Three radio and X-ray data sets obtained simultaneously, or partially simultaneously, are identified as preferred for the purpose of measuring the spin properties of $\rm{Sgr ~A^*}$. Similar results are obtained with other data sets. Results obtained with the preferred data sets are combined and indicate a weighted mean value of the spin function of $\rm{F} = 0.62 \pm 0.10$ and dimensionless spin angular momentum of $\rm{a_*} = 0.90 \pm 0.06$. The spin function translates into measurements of the black hole rotational mass, $\rm{M_{rot}}$, irreducible mass, $\rm{M_{irr}}$, and spin mass-energy available for extraction, $\rm{M_{spin}}$, relative to the total black hole dynamical mass, $\rm{M_{dyn}}$. Weighted mean values of $\rm{(M_{rot}/M_{dyn}) = (0.53 \pm 0.06)}$, $\rm{({M_{irr}/M_{dyn})} = (0.85 \pm 0.04)}$, $\rm{({M_{spin}/M_{dyn})} = (0.15 \pm 0.04)}$, $\rm{{M_{rot}} = (2.2 \pm 0.3) \times 10^6 ~M_{\odot}}$, $\rm{{M_{irr}} = (3.5 \pm 0.2) \times 10^6 ~M_{\odot}}$, and $\rm{{M_{spin}} = (6.2 \pm 1.6) \times 10^5 ~M_{\odot}}$ are obtained; of course $\rm{{(M_{rot}/M_{irr})} = (0.62 \pm 0.10)}$ since $\rm{{(M_{rot}/M_{irr})} = F}$. Values obtained for $\rm{Sgr ~A^*}$ are compared with those obtained for M87 based on the published spin function which indicate that M87 carries substantially more rotational energy and spin mass-energy relative to the total (i.e., dynamical) black hole mass, the irreducible black hole mass, and in absolute terms., Comment: Accepted for publication in MNRAS on October 16, 2023

The rotational properties of astrophysical black holes are fundamental quantities that characterization the black holes. A new method to empirically determine the spin mass-energy characteristics of astrophysical black holes is presented and applied here. Results are obtained for a sample of 100 supermassive black holes with collimated dual outflows and redshifts between about zero and two. An analysis indicates that about two-thirds of the black holes are maximally spinning, while one-third have a broad distribution of spin values; it is shown that the same distributions describe the quantity $\rm{(M_{rot}/M_{irr})}$. The new method is applied to obtain the black hole spin mass-energy, $\rm{M_{spin}}$, available for extraction relative to: the maximum possible value, the irreducible black hole mass, and the total black hole mass, $\rm{M_{dyn}}$. The total energy removed from the black hole system and deposited into the circumgalactic medium via dual outflows over the entire outflow lifetime of the source, $\rm{E_T}$, is studied relative to $\rm{M_{dyn}}$ and relative to the spin energy available per black hole, $\rm{E_{spin}/(M_{\odot}c^2)}$. The mean value of $\rm{Log(E_T/M_{dyn})}$ is about $(-2.47\pm 0.27)$. Several explanations of this and related results are discussed. For example, the energy input to the ambient gas from the outflow could turn off the accretion, or the impact of the black hole mass loss on the system could destabilize and terminate the outflow. The small values and restricted range of values of $\rm{Log(E_T/M_{dyn})}$ and $\rm{Log(E_T/E_{spin})}$ could suggest that these are fundamental properties of the primary process responsible for producing the dual collimated outflows., Comment: 16 pages, 20 figures, 3 tables

Mass accretion rates in dimensionless and physical units, and efficiency factors describing the total radiant luminosity of the disk and the beam power of the outflow are studied here. Four samples of sources including 576 LINERs, 100 classical double (FRII) radio sources, 80 relatively local AGN, and 103 measurements of four stellar mass X-ray binary systems, referred to as Galactic Black Holes (GBH), are included in the study. All of the sources have highly collimated outflows leading to compact radio emission or powerful extended (FRII) radio emission. The properties of each of the full samples are explored, as are those of the four individual GBH, and sub-types of the FRII and local AGN samples. Source types and sub-types that have high, medium, and low values of accretion rates and efficiency factors are identified and studied. A new efficiency factor that describes the relative impact of black hole spin and mass accretion rate on the beam power is defined and studied, and is found to provide a new and interesting diagnostic. Mass accretion rates for 13 sources and efficiency factors for 6 sources are compared with values obtained independently, and indicate that similar values are obtained with independent methods. The mass accretion rates and efficiency factors obtained here substantially increase the number of values available, and improve our understanding of their relationship to source types. The redshift dependence of quantities is presented and the impact on the results is discussed., Comment: 30 pages, 13 figures, 6 tables

The mass of a black hole is the sum of the irreducible mass and the mass associated with the rotational or spin energy of the black hole. The contribution of spin energy (divided by $c^2$) to the total black hole mass is studied here for four samples of sources including 576 LINERs, 100 classical double radio sources, 80 relatively local AGN, and 102 measurements of four stellar mass X-ray binary systems. The spin mass-energy of a black hole may be extracted causing the mass of the black hole to decrease. The ratio of spin mass-energy to black hole mass ranges from about ten to thirty percent for the sources studied here, where the maximum possible value of this quantity is close to thirty percent. Typical fractions of the black hole mass available for extraction for the samples studied are about $0.2 \pm 0.1$. The spin energy of black holes represents a major reservoir that when tapped may impact the immediate and extended black hole environment, decrease the black hole mass, and perhaps modify relationships between black hole mass and galaxy properties. These results are consistent with expectations based on other observations and numerical simulations., Comment: 13 pages, 7 figures, 1 table

Black hole systems, comprised of a black hole, accretion disk, and collimated outflow are studied here. Three AGN samples including 753 AGN, and 102 measurements of 4 GBH are studied. Applying the theoretical considerations described by Daly (2016), general expressions for the black hole spin function and accretion disk magnetic field strength are presented and applied to obtain the black hole spin function, spin, and accretion disk magnetic field strength in dimensionless and physical units for each source. Relatively high spin values are obtained; spin functions indicate typical spin values of about (0.6 - 1) for the sources. The distribution of accretion disk magnetic field strengths for the three AGN samples are quite broad and have mean values of about $10^4$ G, while those for individual GBH have mean values of about $10^8$ G. Good agreement is found between spin values obtained here and published values obtained with well-established methods; comparisons for 1 GBH and 6 AGN indicate that similar spin values are obtained with independent methods. Black hole spin and disk magnetic field strength demographics are obtained and indicate that black hole spin functions and spins are similar for all of the source types studied including GBH and different categories of AGN. The method applied here does not depend upon any specific accretion disk emission model, and does not depend upon a specific model that relates jet beam power to compact radio luminosity, hence the results obtained here can be used to constrain and study these models., Comment: 40 pages, 14 figures, 5 tables; to appear in the Astrophysical Journal

Black hole systems with outflows are characterized by intrinsic physical quantities such as the outflow beam power, $L_j$, the bolometric accretion disk luminosity, $L_{bol}$, and black hole mass or Eddington luminosity, $L_{Edd}$. When these systems produce compact radio emission and X-ray emission, they can be placed on the fundamental plane (FP), an empirical relationship between compact radio luminosity, X-ray luminosity, and black hole mass. We consider a fundamental line (FL) of black hole activity written in terms of dimensionless intrinsic physical quantities: $\rm{log} (L_j/L_{Edd}) = A ~\rm{log}(L_{bol}/L_{Edd}) +B$ or equivalently $\rm{log} (L_j/L_{bol}) = (A-1) ~\rm{log}(L_{bol}/L_{Edd}) +B$, and show that the FP may be written in the form of the FL. The FL has a smaller dispersion than the FP suggesting the FP derives from the FL. Disk-dominated and jet-dominated systems have consistent best fit FL parameters suggesting they are governed by the same physics. There are sharp cutoffs at $L_{bol}/L_{Edd} \simeq 1$ and $L_j/L_{Edd} \simeq 0.2$, and no indication of a strong break as $L_{bol}/L_{Edd} \rightarrow 1$. Consistent values of $A$ are obtained for numerous samples including FRII sources, LINERS, AGNs with compact radio emission, and Galactic black holes, which indicate a weighted mean value of $A \simeq 0.45 \pm 0.01$. The results suggest that a common physical mechanism related to the dimensionless bolometric luminosity of the disk controls the jet power relative to the disk power. The beam power $L_j$ can be obtained by combining FP best-fit parameters and compact radio luminosity for sources that fall on the FP., Comment: Published in the Astrophysical Journal, 863, 117-122; 6 pages; 2 tables; 2 figures

Relationships between beam power and accretion disk luminosity are studied for a sample of 55 HERG, 13 LERG, and 29 RLQ with powerful outflows. The ratio of beam power to disk luminosity tends to be high for LERG, low for RLQ, and spans the full range of values for HERG. Writing general expressions for the disk luminosity and beam power and applying the empirically determined relationships allows a function that parameterizes the spins of the holes to be estimated. Interestingly, one of the solutions that is consistent with the data has a functional form that is remarkably similar to that expected in the generalized Blandford-Znajek model with a magnetic field that is similar in form to that expected in MAD and ADAF models. Values of the spin function, obtained independent of specific outflow models, suggest that spin and AGN type are not related for these types of sources. The spin function can be used to solve for black hole spin in the context of particular outflow models, and one example is provided., Comment: Accepted for publication in MNRAS Letters

Supermassive black holes may be described by their mass and spin. When supermassive black holes are active, the activity provides a probe of the state of the black hole system. The spin of a hole can be estimated when the black hole mass and beam power of the source are known for sources with powerful outflows. Seventy-five sources for which both the black hole mass and beam power could be obtained are identified and used to obtain estimates of black hole spins. The 75 supermassive black holes studied include 52 FRII radio galaxies and 23 FRII radio loud quasars with redshifts ranging from about zero to two. The new values are combined with those obtained previously for 19 FRII radio galaxies, 7 FRII radio loud quasars, and 29 radio sources associated with CD galaxies to form samples of 71 FRII radio galaxies, 30 FRII quasars, and a total sample of 130 spin values; all of the sources are associated with massive elliptical galaxies. The new values obtained are similar to those obtained earlier at similar redshift, and range from about 0.1 to 1 for FRII sources. The overall results are consistent with those obtained previously: the spins tend to decrease with decreasing redshift for the FRII sources studied. There is a hint that the range of values of black hole spin at a given redshift is larger for FRII quasars than for FRII radio galaxies. There is no indication of a strong correlation between supermassive black hole mass and spin for the supermassive black holes studied here. The relation between beam power and black hole mass is obtained and used as a diagnostic of the outflows and the dependence of the magnetic field strength on black hole mass., Comment: 12 pages, 12 figures, 5 tables

Beam power is a fundamental parameter that describes, in part, the state of a supermassive black hole system. Determining the beam powers of powerful classical double radio sources requires substantial observing time, so it would be useful to determine the relationship between beam power and radio power so that radio power could be used as a proxy for beam power. A sample of 31 powerful classical double radio sources with previously determined beam and radio powers are studied; the sources have redshifts between about 0.056 and 1.8. It is found that the relationship between beam power, Lj, and radio power, P, is well described by Log(Lj) = 0.84 Log(P) + 2.15, where both L_j and P are in units of 10^(44) erg/s. This indicates that beam power is converted to radio power with an efficiency of about 0.7%. The ratio of beam power to radio power is studied as a function of redshift; there is no significant evidence for redshift evolution of this ratio over the redshift range studied. The relationship is consistent with empirical results obtained by Cavagnolo et al. (2010) for radio sources in gas rich environments, which are primarily FRI sources, and with the theoretical predictions of Willott et al. (1999)., Comment: 6 pages, 2 figures, 2 tables; accepted for publication in MNRAS

Studies of black hole spin and other parameters as a function of redshift provide information about the physical state and merger and accretion histories of the systems. One way that black hole spin may be estimated is through observations of extended radio sources. These sources, powered by outflows from an AGN, allow the beam power and total outflow energy to be studied. In a broad class of models, the beam power of the outflow is related to the spin of the black hole. This relationship is used to estimate black hole spins for 55 radio sources. The samples studied include 7 FRII quasars and 19 FRII radio galaxies with redshifts between 0.056 and 1.79, and 29 radio sources associated with CD galaxies with redshifts between 0.0035 and 0.291. The FRII sources studied have estimated spin values of between about 0.2 and 1; there is a range of values at a given redshift, and the values tend to increase with increasing redshift. Results obtained for FRII quasars are very similar to those obtained for FRII galaxies. A broader range of spin values are obtained for the sample of radio sources associated with CD galaxies studied. The fraction of the spin energy extracted per outflow event is estimated and ranges from about 0.03 to 0.5 for FRII sources and 0.002 to about 1 for radio sources associated with CD galaxies; the data are consistent with this fraction being independent of redshift though the uncertainties are large. The results obtained are consistent with those predicted by numerical simulations that track the merger and accretion history of AGN, supporting the idea that, for AGN with powerful large-scale outflows, beam power is directly related to black hole spin., Comment: 13 pages; to appear in MNRAS

Radio lobes of a sample of eleven very powerful classical double radio galaxies were studied. Each source was rotated so that the symmetry axis of the source was horizontal, and vertical cross-sectional cuts were taken across the source at intervals of one beam size. These were used to study the cross-sectional surface brightness profiles, the width of each slice, radio emissivity as a function of position across each slice, the first and second moments, and the average surface brightness, minimum energy magnetic field strength, and pressure of each slice. A Gaussian provides a good description of the surface brightness profile of cross-sectional slices. The Gaussian FWHM as a function of distance from the hot spot first increases and then decreases with distance from the hot spot. The width as a function of distance from the hot spot is highly symmetric on each side of the source. The radio emissivity is often close to flat across a slice, indicating a roughly constant emissivity and pressure for that slice. Some slices show variations in radio emissivity that indicate an ``edge-peaked'' pressure profile for that slice; these often occur in slices near the local maxima of the bridge width. The emissivity does not exhibit any signature of emission from a jet. The first moment is generally quite close to zero indicating only small excursions of the ridge line from the symmetry axis of the source. The second moment indicates the same source shape as is found using the Gaussian FWHM. The average magnetic field strength and pressure decrease with increasing distance from the hot spot, reaching a roughly constant value at a location that is typically just before the location of a local maximum of the bridge width. These results are interpreted in terms of a heuristic model for the radio lobes., Comment: 102 pages, 136 figures, accepted for publication in ApJ Supplement Series

Beam powers and black hole masses of 48 extended radio sources are combined to obtain lower bounds on the spins and magnetic field strengths of supermassive black holes. This is done in the context of the models of Blandford & Znajek (1977) (the 'BZ' model) and Meier (1999); a parameterization for bounds in the context of other models is suggested. The bounds obtained for very powerful classical double radio sources in the BZ model are consistent with black hole spins of order unity for sources at high redshift. The black hole spins are largest for the highest redshift sources and decrease for sources at lower redshift; the sources studied have redshifts between zero and two. Lower power radio sources associated with central dominant galaxies may have black hole spins that are significantly less than one. Combining this analysis with other results suggests that the maximum values of black hole spin associated with powerful radio galaxies decline from values of order unity at a redshift of 2 to values of order 0.7 at a redshift of zero, while lower power radio sources have spin values that range from about 0.1 to 0.8. These black hole spin values decrease if the data are considered in the context of the Meier model rather than the BZ model., Comment: Accepted for publication in ApJL

The years 1998 to 2008 were very exciting years for cosmology. It was a pleasure to accept this invitation to describe my contributions to the development of our knowledge and understanding of the universe over the course of the past decade. Here, I begin by describing some of my work on radio galaxies as a modified standard yardstick and go on to describe model-independent studies of the accelerating universe and the properties of the dark energy. During the course of these studies, I came upon interesting ways to study the spin and other properties of supermassive black holes, some of which are briefly mentioned., Comment: Proceedings of the 2008 UCLA Conference "Dark Matter and Dark Energy in the Universe," submitted to AIP Conference Proceedings, 6 pages

A new approach to constraining or determining the spin of a massive black hole is proposed. A key parameter in the analysis is the dimensionless ratio, r, of the energy released to the mass of the hole. It is shown that the black hole spin, j, may be written as a function of the dimensionless ratio of the black hole spin energy to the black hole mass. When extraction of the black hole spin energy powers an outflow from the hole, the ratio r provides an indication of the black hole spin. The method is applied to a sample of 19 very powerful classical double radio galaxies with a range of size and redshift. The sources are found to have remarkably similar values of r and j, implying that the sources have very similar physical conditions at the time the outflow is generated. A sample of 29 central dominant galaxies is also studied; most of these sources have amorphous or FRI radio structure. The sources have a broad range of ratios r, and correspondingly broad range of black hole spins. The broad range probably results from the fact that each source is observed at a different stage in its lifetime. The intrinsic range of parameters could be as tight as it is for the powerful classical double radio galaxies., Comment: To appear in ApJ Letters

We estimate ages and physical properties of powerful radio galaxies. An analysis of new multi-wavelength VLA observations of eleven very powerful classical double (FRIIb) radio galaxies with redshifts between 0.4 and 1.3 is presented. We estimate ages and velocities for each side of each source. The eleven new sources are combined with previously studied samples and the characteristics of the full sample of 31 sources are studied; the full sample includes sources with redshifts between 0.056 and 1.79, and core-hot spot sizes of about 30 to 400 kpc. The velocities are independent of core-hotspot separation, suggesting the rate of growth of a given source is roughly constant over the source lifetime. We combine the rate of growth, width, and pressure of a source to study the beam power, lifetime, energy, and ambient gas density using standard methods previously applied to smaller samples. Typical beam powers are in the range from 1E44 to 1E46 erg/s; we show that this quantity is insensitive to assumptions regarding minimum energy conditions. The beam powers are independent of core-hotspot separation suggesting that the beam power of a given source is roughly constant over the source lifetime. Typical total source lifetimes are found to be about a few E6 to E7 years, and typical total outflow energies (E/c^2) are found to be about 5(E5 - E6) solar masses. Ambient gas densities are found to decrease with increasing core-hotspot distance, but have no redshift dependence. Overall, the results obtained with the sample of 31 sources studied here are consistent with those obtained earlier with smaller samples., Comment: Astronomy and Astrophysics, accepted

The model-independent method of using type Ia supernovae proposed and developed by Daly and Djorgovski (2003, 2004) has been applied to the Riess et al. (2007) supernovae sample. Assuming only a Robertson-Walker metric, we find that the universe is accelerating today. This result is purely kinematic, is independent of the contents of the universe, and does not require that a theory of gravity be specified. Our model-independent method allows a determination of q(z) for a particular value of space curvature. When q(z) transitions from negative to positive values, the universe transitions from an accelerating to a decelerating state. For zero space curvature, we find that the universe transitions from acceleration to deceleration at a zedshift of about = 0.35 for the Riess et al. (2007) sample. If a theory of gravity is specified, the supernovae data can be used to determine the pressure, energy density, and equation of state of the dark energy, and the potential and kinetic energy density of a dark energy scalar field as functions of redshift. The relevant equations from General Relativity are applied, and these functions are obtained. The results are consistent with predictions in the standard Lambda Cold Dark Matter model at about the two sigma level., Comment: To appear in "Supernova 1987A: 20 Years After: Supernovae and Gamma-Ray Bursters," AIP, New York, eds. S. Immler, K. W. Weiler, and R. McCray

We extend and apply a model-independent analysis method developed earlier by Daly & Djorgovski to new samples of supernova standard candles, radio galaxy and cluster standard rulers, and use it to constrain physical properties of the dark energy as functions of redshift. Similar results are obtained for the radio galaxy and supernova data sets. The first and second derivatives of the distance are compared directly with predictions in a standard model based on General Relativity. The good agreement indicates that General Relativity provides an accurate description of the data on look-back time scales of about ten billion years. The first and second derivatives are combined to obtain the acceleration parameter, assuming only the validity of the Robertson-Walker metric, independent of a theory of gravity and of the physical nature of the dark energy. The acceleration of the universe at the current epoch is indicated by the analysis. The effect of non-zero space curvature on q(z) is explored. We solve for the pressure, energy density, equation of state, and potential and kinetic energy of the dark energy as functions of redshift assuming that General Relativity is the correct theory of gravity, and the results indicate that a cosmological constant in a spatially flat universe provides a good description of each of these quantities over the redshift range from zero to about one. We define a new function, the dark energy indicator, in terms of the first and second derivatives of the coordinate distance and show how this can be used to measure deviations of w from -1 and to obtain a new and independent measure of Omega., Comment: 46 pages, submitted for publication

Physical sizes of extended radio galaxies can be employed as a cosmological "standard ruler", using a previously developed method. Eleven new radio galaxies are added to our previous sample of nineteen sources, forming a sample of thirty objects with redshifts between 0 and 1.8. This sample of radio galaxies are used to obtain the best fit cosmological parameters in a quintessence model in a spatially flat universe, a cosmological constant model that allows for non-zero space curvature, and a rolling scalar field model in a spatially flat universe. Results obtained with radio galaxies are compared with those obtained with different supernova samples, and with combined radio galaxy and supernova samples. Results obtained with different samples are consistent, suggesting that neither method is seriously affected by systematic errors. Best fit radio galaxy and supernovae model parameters determined in the different cosmological models are nearly identical, and are used to determine dimensionless coordinate distances to supernovae and radio galaxies, and distance moduli to the radio galaxies. The distance moduli to the radio galaxies can be combined with supernovae samples to increase the number of sources, particularly high-redshift sources, in the samples. The constraints obtained here with the combined radio galaxy plus supernovae data set in the rolling scalar field model are quite strong. The best fit parameter values suggest a value of omega is less than about 0.35, and the model parameter alpha is close to zero; that is, a cosmological constant provides a good description of the data. We also obtain new constraints on the physics of engines that power the large-scale radio emission., Comment: 32 pages. Accepted for publication in the Astrophysical Journal

The properties of a sample of 31 very powerful classical double radio galaxies with redshifts between zero and 1.8 are studied. The source velocities, beam powers, ambient gas densities, total lifetimes, and total outflow energies are presented and discussed. The rate of growth of each side of each source were obtained using a spectral aging analysis. The beam power and ambient gas density were obtained by applying the strong shock jump conditions to the ends of each side of the source. The total outflow lifetime was obtained by applying the power-law relationship between the beam power and the total source lifetime derived elsewhere for sources of this type, and the total outflow energy was obtained by combining the beam power and the total source lifetime. Composite profiles were constructed by combining results obtained from each side of each source. The composite profiles indicate that the ambient gas density falls with distance from the central engine. The source velocities, beam powers, total lifetimes, and total energies seem to be independent of radio source size. This is consistent with the standard model in which each source grows at a roughly constant rate during which time the central engine puts out a roughly constant beam power. The fact that the total source lifetimes and energies are independent of radio source size indicates that the sources are being sampled at random times during their lifetimes., Comment: 7 pages, 5 figures, to appear in "Extragalactic Jets: Theory and Observation from Radio to Gamma Ray", eds. T. A. Rector and D. S. De Young, ASP conference series, Replaced version has minor textual corrections

Understanding the acceleration of the universe and its cause is one of the key problems in physics and cosmology today, and is best studied using a variety of mutually complementary approaches. Daly and Djorgovski (2003, 2004) proposed a model independent approach to determine the expansion and acceleration history of the universe and a number of important physical parameters of the dark energy as functions of redshift directly from the data. Here, we apply the method to explicitly determine the first and second derivatives of the coordinate distance with respect to redshift and combine them to solve for the acceleration of the universe and the kinetic and potential energy density of the dark energy as functions of redshift. A data set of 228 supernova and 20 radio galaxy measurements with redshifts from zero to 1.79 is used for this study. The values we obtain are shown to be consistent with the values expected in a standard Lambda Cold Dark Matter model., Comment: 5 pages, 8 figures

Understanding the physical nature of the dark energy which appears to drive the accelerated expansion of the unvierse is one of the key problems in physics and cosmology today. This important problem is best studied using a variety of mutually complementary approaches. Daly and Djorgovski (2003, 2004) proposed a model independent approach to determine a number of important physical parameters of the dark energy as functions of redshift directly from the data. Here, we expand this method to include the determinations of its potential and kinetic energy as functions of redshift. We show that the dark energy potential and kinetic energy may be written as combinations of the first and second derivatives of the coordinate distance with respect to redshift. We expand the data set to include new supernova measurements, and now use a total of 248 coordinate distances that span the redshift range from zero to 1.79. First and second derivatives of the coordinate distance are obtained as functions of redshift, and these are combined to determine the potential and kinetic energy of the dark energy as functions of redshift. An update on the redshift behavior of the dimensionless expansion rate E(z), the acceleration rate q(z), and the dark energy pressure p(z), energy density f(z), and equation of state w(z) is also presented. We find that the standard Omega = 0.3 and Lambda = 0.7 model is in an excellent agreement with the data. We also show tentative evidence that the Cardassian and Chaplygin gas models in a spatially flat universe do not fit the data as well., Comment: 10 pages, 20 figures, submitted for publication

We describe a method to derive the expansion and acceleration rates directly from the data, without the need for the specification of a theory of gravity, and without adopting an a priori parameterization of the form or redshift evolution of the dark energy. If one also specifies a theory of gravity we can also determine the pressure, energy density, and equation of state of the dark energy as functions of redshift. We then apply this methodology on a modern data set of distances to Supernovae and to radio galaxies. We find that the universe transitions from deceleration to acceleration at a redshift of about 0.4, and the present value of deceleration parameter is -0.35 +/- 0.15. The standard ``concordance model'' provides a reasonably good fit to the dimensionless expansion rate as a function of redshift, though it fits the dimensionless acceleration rate as a function of redshift less well. Adopting General Relativity as the theory of gravity, we obtain the redshift trends for the pressure, energy density, and equation of state of the dark energy out to a redshift of about one. They are generally consistent with the concordance model, at least out to a redshift of about 0.5, but the existing data preclude any stronger conclusions at this point., Comment: 11 pages, 8 figures, invited presentation from the Observing Dark Energy NOAO Workshop in Tucson

One of the goals of current cosmological studies is the determination of the expansion and acceleration rates of the universe as functions of redshift, and the determination of the properties of the dark energy that can explain these observations. Here the expansion and acceleration rates are determined directly from the data, without the need for the specification of a theory of gravity, and without adopting an a priori parameterization of the form or redshift evolution of the dark energy. We use the latest set of distances to SN standard candles from Riess et al. (2004), supplemented by data on radio galaxy standard ruler sizes, as described by Daly and Djorgovski (2003, 2004). We find that the universe transitions from acceleration to deceleration at a redshift of about 0.4. The standard "concordance model" provides a reasonably good fit to the dimensionless expansion rate as a function of redshift, though it fits the dimensionless acceleration rate as a function of redshift less well. The expansion and acceleration rates are then combined with a theory of gravity to determine the pressure, energy density, and equation of state of the dark energy as functions of redshift. Adopting General Relativity as the correct theory of gravity, the redshift trends for the pressure, energy density, and equation of state of the dark energy out to redshifts of about one are determined, and are found to be generally consistent with the concordance model., Comment: 8 pages, 5 figures. Invited presentation at Coral Gables 2003

Understanding of the nature of dark energy, which appears to drive the expansion of the universe, is one of the central problems of physical cosmology today. In an earlier paper [Daly & Djorgovski (2003)] we proposed a novel method to determine the expansion rate and the deceleration parameter in a largely model-independent way, directly from the data on coordinate distances. Here we expand this methodology to include measurements of the pressure of dark energy, its normalized energy density, and the equation of state parameter as functions of redshift. We then apply this methodology to a new, combined data set of distances to supernovae and radio galaxies., Comment: 27 pages, 8 figures. Will appear in the Astrophysical Journal, v612, September 10, 2004

Determination of the expansion and acceleration history of the universe is one of the fundamental goals of cosmology. Detailed measurements of these rates as a function of redshift can provide new physical insights into the nature and evolution of the dark energy, which apparently dominates the global dynamics of the universe at the present epoch. We present here dimensionless coordinate distances y(z) to twenty radio galaxies reaching out to z of about 1.8, the redshift range currently not covered by Supernova standard candle observations. We develop a simple numerical method for a direct determination of the expansion and acceleration rates, E(z) and q(z), from the data, which makes no assumptions about the underlying cosmological model or the equation of state parameter w. This differential method is in contrast to the traditional cosmological tests, where particular model equations are integrated and then compared with the observations. The new model-independent method is applied to currently available Supernova data and the data on radio galaxies presented here. We derive the expansion rate of the universe as a function of redshift, E(z), and for the first time obtain a direct estimate of the acceleration rate of the universe as a function of redshift, q(z), in a way that is independent of assumptions regarding the dark energy and its redshift evolution. The current observations indicate that the universe transitions from acceleration to deceleration at a redshift greater than 0.3, with a best fit estimate of about 0.45; this transition redshift and our determinations of E(z) are broadly in agreement with the currently popular Friedmann-Lemaitre cosmology with Omega = 0.3, and Lambda = 0.7, even though no model assumptions are made in deriving the fits for E(z) and q(z)., Comment: 30 pages, 9 figures, to appear in ApJ, v597, Nov. 1, 2003

Radio galaxies provide a means to determine the coordinate distance,the luminosity distance, the dimensionless luminosity distance, or the angular size distance to sources with redshifts as large as two. Dimensionless coodinate distances for 55 supernovae and 20 radio galaxies are presented and discussed here. The radio galaxy results are consistent with those obtained using supernovae, suggesting that neither method is plagued by unknown systematic errors. The acceleration parameter q(z) and the expansion rate H(z) or dimensionless expansion rate E(z) can be determined directly from the data without having to make assumptions regarding the nature or evolution of the ``dark energy.'' The expansion rate E(z) can be determined from the first derivative of the dimensionless coordinate distance, and the acceleration parameter can be determined from a combination of the first and second derivatives of the dimensionless coordinate distance. A model-independent determination of E(z) will allow the properties and redshift evolution of the ``dark energy'' to be determined, and a model-independent determination of q(z) will allow the redshift at which the universe transitions from acceleration to deceleration to be determined directly. Determination of E(z) and q(z) may also elucidate possible systematic errors in the determinations of the dimensionless coordinate distances., Comment: 9 pages, 3 figures, uses cospar.sty, presented at the 2002 Cospar Meeting

We present new Chandra Observatory observations with archival HST and radio observations of 3C254, a radio quasara at z=0.734, and 3C280, a radio galaxy at z=0.996. We report the detection of X-ray and possible HST optical counterparts to the radio hot spots in 3C280 and of an X-ray counterpart to the radio hot spot in 3C254. We present constraints on the presence of X-ray clusters and on the magnetic field strengths in and around the radio hot spots. The spatial resolution of Chandra allows us to show that these sources are not in hot, massive clusters. The extended emission seen in ROSAT observations is resolved into point sources. The IGM around these sources is demonstrably not dense and hot. We conclude that radio sources are not reliable signposts of massive clusters at moderate redshifts. X-ray synchrotron emission could explain the radio, optical, and X-ray hot spot fluxes in 3C280, but it would require continuous acceleration of electrons to high Lorentz factors, since the synchrotron lifetime required to produce the X-ray emission is of order a human lifetime. SSC with or without IC scattering of the CMB can also explain the X-ray emission, but not the optical. We review all of the physical mechanisms and summarize our current constraints on the magnetic field strengths in andaround the hot spots of 3C254 and 3C280., Comment: accepted, ApJ, Feb 20, 2003 publication date estimated

Fanaroff-Riley type IIb (FR IIb) radio galaxies provide a modified standard yardstick that allows constraints to be placed on global cosmological parameters. A sample of 20 FR IIb radio galaxies with redshifts between 0 and 2 are compared with the parent population of 70 radio galaxies to determine the coordinate distance to each source. The coordinate-distance determinations are used to constrain the current mean mass-energy density of quintessence $\Omega_q$, the equation of state of the quintessence w, and the current mean mass-energy density of nonrelativistic matter $\Omega_m$; zero space curvature is assumed. Radio galaxies alone indicate that the universe is currently accelerating in its expansion (with 84% confidence); most of the allowed parameter space falls within the accelerating universe region on the $\Omega_m$-w plane. This provides verification of the acceleration of the universe indicated by high-redshift supernovae and suggests that neither method is plagued by systematic errors. It is found that $\Omega_m$ must be less than about 0.5 and the equation of state w of the quintessence must lie between -0.25 and -2.5 at about 90% confidence. Fits of the radio galaxy data constrain the model parameter $\beta$, which describes a relation between the beam power of the active galactic nucleus (AGN) and the total energy expelled through large-scale jets. It is shown that the empirically determined model parameter is consistent with models in which the outflow results from the electromagnetic extraction of rotational energy from the central compact object. A specific relation between the strength of the magnetic field near the AGN and the spin angular momentum per unit mass of the central compact object is predicted.

We use FRIIb radio galaxy redshift-angular size data to constrain cosmological parameters in a dark energy scalar field model. The derived constraints are consistent with but weaker than those determined using Type Ia supernova redshift-magnitude data., Comment: ApJ, in press, expanded discussion

There are many different approaches to using observations to constrain or determine the global cosmological parameters that describe our universe. Methods that rely upon a determination of the coordinate distance to high-redshift sources are particularly useful because they do not involve assumptions about the clustering properties of matter, or the evolution of this clustering. Two of the methods currently being used to determine the coordinate distance to high-redshift sources are the radio galaxy method and the supernova method. These methods are similar in their dependence on the coordinate distance. Here, the radio galaxy method is briefly described and results are presented. One of the underlying assumptions of the method is explored. In addition, the method is compared and contrasted to the supernova method. The constraints imposed on global cosmological parameters by radio galaxies are consistent with those imposed by supernovae. For a universe that is spatially flat with mean mass density $\Omega_m$ in non-relativistic matter and mean mass density 1- $\Omega_m$ in quintessence, radio galaxies alone indicate at 84 % confidence that the expansion of the universe is accelerating at the current epoch. And, independent of whether or not the universe is spatially flat, radio galaxies alone indicate at 95 % confidence that $\Omega_m$ must be less than 0.6 at the current epoch., Comment: 8 pages

FRIIb radio galaxies provide a tool to determine the coordinate distance to sources out to redshifts of two. The coordinate distance depends on the present values of global cosmological parameters, quintessence, and the equation of state of quintessence, and provides one of the cleanest determinations of global cosmological parameters because it does not depend on the clustering properties of any mass-energy components. The modified standard candle method (using type Ia supernove) of determining the coordinate distance is compared in detail with the modified standard yardstick method (using FRIIb radio galaxies); the methods are found to be complementary. The most significant difference between the methods is that the radio galaxy method is completely independent of the local distance scale and the properties of local sources, while the supernovae method is very closely tied to the local distance scale and the properties of local sources. FRIIb radio galaxies provide one of the very few reliable probes of the coordinate distance to sources with redshifts out to two. The method indicates that the current value of the density parameter in non-relativistic matter must be low irrespective of whether the universe is spatially flat, and of whether a significant cosmological constant or quintessence pervades the universe at the present epoch. FRIIb radio galaxies indicate that the universe is currently accelerating in its expansion if the primary components of the universe at the present epoch are non-relativistic matter and quintessence, and the universe is spatially flat., Comment: 19 pages, and 19 figures, Contribution STSCI Conference Proceeding ``The Dark Universe: Matter, Energy, and Gravity''

Multi-frequency radio observations of the radio bridge of a powerful classical double radio source can be used to determine: the beam power of the jets emanating from the AGN; the total time the source will actively produce jets that power large-scale radio emission; the thermal pressure of the medium in the vicinity of the radio source; and the total mass, including dark matter, of the galaxy or cluster of galaxies traced by the ambient gas that surrounds the radio source. Empirical determinations of each of these quantities are obtained and analyzed for 22 radio sources. Typical beam powers are about $10^{45} {erg s}^{-1}$. The characteristic or total time the AGN will actively produce a collimated outflow is estimated. Typical total lifetimes are $\sim (10^7$ to $10^8$) years. Total masses, and mass-density profiles, similar to those of low-redshift clusters of galaxies are obtained. Thus, some clusters of galaxies, or cores of clusters, exist at redshifts of one to two. A new method of estimating the thermal pressure of the ambient gas in the vicinity of a powerful classical double radio source is presented. This new estimate is independent of synchrotron and inverse Compton aging arguments, and depends only upon the properties of the radio lobe and the shape of the radio bridge. Thermal pressures on the order of $10^{-10} {dyne cm}^{-2}$, typical of gas in low-redshift clusters of galaxies, are found for the environments of the sources studied here. It is shown that appreciable amounts of cosmic microwave background diminution (the Sunyaev-Zel'dovich effect) are expected from many of these clusters. This could be detected at high frequency where the emission from the radio sources is weak., Comment: 53 pages, includes 13 figures, accepted by ApJ

A sample of 20 powerful extended radio galaxies with redshifts between zero and two were used to determine constraints on global cosmological parameters. Data for six radio sources were obtained from the VLA archive, analyzed, and combined with the sample of 14 radio galaxies used previously by Guerra & Daly to determine cosmological parameters. The results are consistent with our previous results, and indicate that the current value of the mean mass density of the universe is significantly less than the critical value. A universe with $\Omega_m$ of unity is ruled out at 99.0% confidence, and the best fitting values of $\Omega_m$ in matter are $0.10^{+0.25}_{-0.10}$ and $-0.25^{+0.35}_{-0.25}$ assuming zero space curvature and zero cosmological constant, respectively. Note that identical results obtain when the low redshift bin, which includes Cygnus A, is excluded; these results are independent of whether the radio source Cygnus A is included. The method does not rely on a zero-redshift normalization. The radio properties of each source are also used to determine the density of the gas in the vicinity of the source, and the beam power of the source. The six new radio sources have physical characteristics similar to those found for the original 14 sources. The density of the gas around these radio sources is typical of gas in present day clusters of galaxies. The beam powers are typically about $10^{45} \hbox{erg s}^{-1}$., Comment: 39 pages includes 21 figures, accepted to ApJ

Multi-frequency radio observations of the radio bridge of powerful classical double radio sources can be used to determine: the beam power of the jets emanating from the AGN; the total time the source will actively produce jets that power large-scale radio emission; the thermal pressure of the medium in the vicinity of the radio source; and the total mass, including dark matter, of the galaxy or cluster of galaxies traced by the ambient gas that surrounds the radio source. The theoretical constructs that allow a determination of each of these quantities using radio observations are presented and discussed. Empirical determinations of each of these quantities are obtained and analyzed. A sample of 14 radio galaxies and 8 radio loud quasars with redshifts between zero and two for which there is enough radio information to be able to determine the physical parameters listed above was studied in detail. (abridged), Comment: Submitted to ApJ, LaTex, 26 total pages of text which includes captions & two tables, plus 13 EPS figures & 1 table

A sample of 20 powerful extended radio galaxies with redshifts between zero and two were used to determine constraints on global cosmological parameters. Data for six radio sources were obtained from the VLA archive, analyzed, and combined with the sample of 14 radio galaxies used previously by Guerra & Daly to determine cosmological parameters. The new results are consistent with our previous results, and indicate that the current value of the mean mass density of the universe is significantly less than the critical value. A universe with $\Omega_m$ in matter of unity is ruled out at 99.0% confidence, and the best fitting values of $\Omega_m$ in matter are $0.10^{+0.25}_{-0.10}$ and $-0.25^{+0.35}_{-0.25}$ assuming zero space curvature and zero cosmological constant, respectively. The radio properties of each source are also used to determine the density of the gas in the vicinity of the source, and the beam power of the source. The six new radio sources have physical characteristics similar to those found for the original 14 sources. The density of the gas around these radio sources is typical of gas in present day clusters of galaxies. The beam powers are typically about $10^{45} {erg s}^{-1}$., Comment: Submitted to ApJ, LaTex, 10 pages of text, plus 4 tables and 5 figures in document

Fourteen classical double radio galaxies with redshifts between zero and two were used to determine the cosmological parameters $\Omega_m$, $\Omega_{\Lambda}$, and $\Omega_k$, where these are the normalized values of the mean mass density, cosmological constant, and space curvature at the present epoch. A low value of $\Omega_m$ is obtained, and $\Omega_m = 1$ is ruled out with 97.5% confidence. The low value of $\Omega_m$ determined using the radio source method described here is also indicated by several independent tests. Thus, it appears that either a cosmological constant, or space curvature, is significant at the present epoch. This means that the universe is undergoing, or has recently undergone, a transition away from a state of matter domination and into a state where either a cosmological constant or space curvature is determining the expansion rate of the universe. The low value of $\Omega_m$ presented here and by Guerra & Daly (1998) means that we can state with 97.5 % confidence that the universe will continue to expand forever., Comment: To appear in "Fundamental Parameters in Cosmology", The proceedings of the XXXIIIrd Rencontres de Moriond, eds. J. Tr\^an Thanh V\^an & Y. Giraud-Heraud, (Paris, France: Editions Frontieres)

Outflow angles and bulk Lorentz factors for 43 sources that have proper motions compiled by Vermeulen & Cohen (1994) are computed on the basis of Doppler factors and observed apparent motions in the plane of the sky. These estimates of outflow angles and bulk Lorentz factors are discussed along with their agreement with orientation unified models of AGN. Intrinsic (i.e. rest frame) brightness temperatures computed by using the inverse Compton and equipartition Doppler factor are discussed along with their relevance to the ``Inverse Compton catastrophe''. Intrinsic luminosity densities and luminosities are presented, and the role of systematic errors is discussed. These studies are carried out using a sample of 100 compact radio sources compiled by Ghisellini et al. (1993). Error estimates for previously computed inverse Compton Doppler factors and equipartition Doppler factors are presented for these sources, along with a few updates of these Doppler factor estimates., Comment: 30 pages, Latex, uses AAS Latex macros v4.0 (aaspp4.sty), 6 seperate table files tb*.tex, 33 postscript file figures. Postscript version available at http://pulsar.princeton.edu/~eddie/preprint.html Accepted to The Astrophysical Journal

Powerful extended radio galaxies in the 3CR survey are observed out to redshifts of about 2. For redshifts greater than about 0.3, the average lobe-lobe size of the sources decreases monotonically with redshift for all reasonable cosmological parameter choices. This suggests that the characteristic time for which an AGN produces a highly collimated outflow that powers the radio emission is shorter for the high-redshift sources than it is for low-redshift sources. The fact that the characteristic time for which an AGN produces a collimated outflow decreases with redshift implies that the physical mechanism that gives rise to the large scale jets is not Eddington limited. Higher redshift sources have higher radio powers due the flux limit of the sample, and sources with higher radio powers have higher beam powers relative to lower redshift sources. Both the beam power and active lifetime of the AGN are controlled by processes occurring at the heart of the AGN, and may be related for non-Eddington limited processes. The relation between the active lifetime, $t_*$, and the beam power, $L_j$, of powerful extended radio galaxies is investigated here and found to be $t_*\proptoL_j^{-2/3}$. A comparison of the redshift evolution of the characteristic source sizes with that of the average lobe-lobe size for the 3CR sample of radio galaxies could be used to constrain cosmology., Comment: revised version accepted to ApJ, in press, Vol 493

The radio properties of powerful extended radio sources may be used to estimate the ambient gas density in the vicinity of radio lobes. A sample of 27 radio lobes from 14 radio galaxies and of 14 radio lobes from 8 radio loud quasars was constructed using sources from the published literature with sufficient radio information to allow an estimate of the ambient gas density. The ambient gas density as a function of separation of the lobe from the center of the parent galaxy indicates a composite density profile, where Cygnus A plays the key role of determining the normalization for the ambient gas density. The composite density profile of the galaxies and quasars studied here is similar to the density profile of gas in low-redshift clusters of galaxies, which confirms the result obtained by Daly [1] using a somewhat smaller sample of radio sources. The data presented here allow an estimate of the core gas density, core radius, and slope of the density profile assuming that the gas density can be fit by a King model. The data suggest that the core gas density decreases as the redshift of the source increases, and is consistent with either a roughly constant core radius, or a core radius that increases with increasing source redshift. Thus, our results are completely consistent with observations indicating negative evolution of the cluster X-ray luminosity function. (truncated to <24 lines), Comment: 8 pages, uuencoded compressed postscript. To appear in the Procedings of the Cygnus A Workshop, May 1-4, Green Bank, WV

Measurements of the width of the radio bridge at several locations along the bridge for each of four powerful extended radio sources are presented. Adopting a few simple assumptions, these measurements may be used to predict the radio surface brightness as a function of position across the radio bridge. The predicted and observed surface brightnesses across the bridges are compared and found to agree fairly well. The results are consistent with a simple picture in which the radio power and size of the radio lobe at the forward edge of the radio bridge are roughly time-independent for a given source, and the expansion of the bridge in the lateral direction is adiabatic. There is no indication that reacceleration or energy transport is important in the bridges of these sources. The rate of lateral expansion of the bridge just behind the radio lobe and hotspot in terms of the rate of forward propagation is compared with that predicted, and found to be in good agreement with the predicted value., Comment: 7 pages, uuencoded compressed postscript. To appear in the Proceding of the Cygnus A workshop, May 1-4, Green Bank, WV

A sample of FRII radio sources in rich clusters of galaxies, both at high (z$\sim$0.5) and low (z$\sim$0) redshift, has been constructed to study the effect of environment on radio sources. Comparisons are made between the properties of FRII sources in cluster and non-cluster environments, and between X-ray clusters with and without FRII sources. The principal results are the following: 1. Most low-redshift FRII sources in clusters appear to be similar to FRII sources in group or field environments in terms of radio power, optical properties of the host galaxy, and nonthermal pressure of the radio bridge. Most low-redshift clusters with FRII sources tend to lie at the lower end of cluster X-ray luminosity distribution, some having $L_x$ comparable to FRII sources in non-cluster environments. 2. High-redshift FRII sources are all quite similar to each other irrespective of their environments. The nonthermal pressures of their radio bridges appear to be similar to those of low-redshift FRII's. 3. The nonthermal pressures of the bridges of FRII sources appear to be similar to the thermal pressures of the ICM around them. This result would allow FRII sources to be used as probes of their gaseous environments. The current data imply that the evolution in the clustering strength around FRII sources toward high-redshift is likely to be closely linked to an evolution of the state of the intracluster medium., Comment: 8 pages, 3 figures in text, uuencoded compressed postscript file. To appear in the proceedings of the Cygnus A Workshop, May 1-4, Green Bank, WV

Powerful extended radio galaxies like Cygnus A can be used for cosmological tests. The characteristic, time-independent length $D_*$ for several radio sources is calculated and compared to the average physical length for a sample of radio galaxies. The ratio of these two lengths as a function of redshift is used to constrain cosmological parameters. Cygnus A is the only low-redshift ($z<0.5$) radio galaxy for which we have an estimate for $D_*$. We comment on the sensitivity to this one low-redshift point, and results including and excluding Cygnus A are shown. A low density universe is favored, and the one free model parameter is relatively well constrained., Comment: 8 pages, 6 figures in text, uuencoded compressed postscript file. To appear in the proceedings of the Cygnus A Workshop