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NASA NTRS1992

The Hubble constant

The Hubble constant is the constant of proportionality between recession velocity and distance in the expanding universe. It is a fundamental property of cosmology that sets both the scale and the expansion age of the universe. It is determined by measurement of galaxy radial velocities and distances. Although there has been considerable progress in the development of new techniques for the measurements of galaxy distances, both calibration uncertainties and debates over systematic errors remain. Current determinations still range over nearly a factor of 2; the higher values favored by most local measurements are not consistent with many theories of the origin of large-scale structure and stellar evolution.

Huchra, John P.↗
NASA NTRS1994

A new method for determining the Hubble constant from sub-TeV gamma-ray observations

The present uncertainty in the Hubble constant leaves unresolved questions regarding the age of the universe and related matters involving the amount and nature of the dark matter in the universe, consistency with the inflationary model of the universe, and the need for a cosmological constant. It is clear that a significantly precise determination of the Hubble constant by as many different methods as possible is crucial to our knowledge and understanding of the character of the universe. We propose here an entirely new method for determining the Hubble constant, based on measuring the extinction of high-energy gamma-rays emitted by detectable gamma-ray emitting blazars at various redshifts.

Salamon, M. H.↗
NASA NTRS1994

A measurement of the Hubble constant from the X-ray properties and the Sunyaev-Zel'dovich effect of Abell 2218

The distance of the cluster of galaxies Abell 2218, and hence the value of the Hubble constant, has been measured by comparing the X-ray properties and the Sunyaev-Zel'dovich effect of the cluster. The result for the Hubble constant is H(sub zero) = 65 +/- 25 km/s/MPC, where the error includes the random and systematic errors, combined in quadrature, and the largest contributions to the overall error come from systematic errors in the Sunyaev-Zel'dovich effect data and in the X-ray spectrum of the cluster. The X-ray and Sunyaev-Zel'dovich effect data are consistent with the same model for the intergalactic medium in Abell 2218 (an isothermal Beta-model with Beta is about 0.65 and cluster core radius about 1.0 min). A prevous report of a smaller Hubble constant, found by applying the same method on the same cluster, is shown to be based on a model for the cluster gas that is inconsistent with the Einstein IPC data. The present result for the Hubble constant is consistent with the value found earlier for the cluster Abell 665: by combining the results of the method for both clusters we conclude that the value of the Hubble constant is H(sub zero) = 55 +/- 17 km/s/MPC.

Birkinshaw, M.↗
NASA NTRS1982

Steps toward the Hubble constant. VIII - The global value

The problem of determining the global Hubble constant is approached by using two distance indicators whose dispersion in absolute magnitude is small, and hence which are virtually free of the Malmquist bias. New data are presented on the mean absolute-magnitude of the brightest individual red and blue supergiant stars in very nearby galaxies, calibrated relative to the Cepheids. The results are used to calibrate the maximum absolute blue magnitude for two well-observed Type I supernovae (SNe I). The velocity-relative distance diagram for 16 SNe I with known maximum apparent blue magnitudes is then calibrated using distances for IC 4182 and NGC 4214, with the result that the global Hubble constant equals 50 + or - 7 km per second per megaparsec. The result is compared with the known age of globular clusters in the Galaxy to show that the cosmological and the evolutionary time scales now closely agree.

Sandage, A.↗
NASA NTRS1991

A measurement of the value of the Hubble constant from the X-ray properties and the Sunyaev-Zel'dovich effect of Abell 665

A comparison of the X-ray properties and the Sunyaev-Zel'dovich (SZ) effect for a cluster of galaxies can be used to measure the distance of the cluster and hence the Hubble constant. This method was applied to the rich cluster Abell 665. The relative normalization of X-ray and SZ-effect data leads to an estimated Hubble constant of H sub 0 = 40 + or - 9 km/s Mpc if only the random errors are included. When the possible systematic errors are added in quadrature, the range of possible values of the Hubble constants expands to (40 to 50) + or - 12 km/s Mpc.

Birkinshaw, M.↗
NASA NTRS1985

On the use of measured time delays in gravitational lenses to determine the Hubble constant

Gravitational lenses are rare in the known samples of quasars, indicating that the conditions involved in their formation are unusual. In particular, the distribution of matter along the light rays from the observer through the deflector to the quasar may be very different from mean conditions. It is shown that reasonable deviations in the density of matter along the beams can significantly alter the relationship between time delays and the Hubble constant, and it is concluded that gravitational lenses are not promising estimators of this constant. However, should an independent, precise determination of the Hubble constant become available, gravitational lenses could be used to probe long-range density fluctuations.

Alcock, C.↗
NASA NTRS2012

Carnegie Hubble Program: A Mid-Infrared Calibration of the Hubble Constant

Using a mid-infrared calibration of the Cepheid distance scale based on recent observations at 3.6 micrometers with the Spitzer Space Telescope, we have obtained a new, high-accuracy calibration of the Hubble constant. We have established the mid-IR zero point of the Leavitt law (the Cepheid period-luminosity relation) using time-averaged 3.6 micrometers data for 10 high-metallicity, MilkyWay Cepheids having independently measured trigonometric parallaxes. We have adopted the slope of the PL relation using time-averaged 3.6micrometers data for 80 long-period Large Magellanic Cloud (LMC) Cepheids falling in the period range 0.8 < log(P) < 1.8.We find a new reddening-corrected distance to the LMC of 18.477 +/- 0.033 (systematic) mag. We re-examine the systematic uncertainties in H(sub 0), also taking into account new data over the past decade. In combination with the new Spitzer calibration, the systematic uncertainty in H(sub 0) over that obtained by the Hubble Space Telescope Key Project has decreased by over a factor of three. Applying the Spitzer calibration to the Key Project sample, we find a value of H(sub 0) = 74.3 with a systematic uncertainty of +/-2.1 (systematic) kilometers per second Mpc(sup −1), corresponding to a 2.8% systematic uncertainty in the Hubble constant. This result, in combination with WMAP7measurements of the cosmic microwave background anisotropies and assuming a flat universe, yields a value of the equation of state for dark energy, w(sub 0) = −1.09 +/- 0.10. Alternatively, relaxing the constraints on flatness and the numbers of relativistic species, and combining our results with those of WMAP7, Type Ia supernovae and baryon acoustic oscillations yield w(sub 0) = −1.08 +/- 0.10 and a value of N(sub eff) = 4.13 +/- 0.67, mildly consistent with the existence of a fourth neutrino species.

Program↗
NASA NTRS1994

The peak brightness of SN 1937C in IC 4182 and the Hubble constant

The light curve of the Type Ia supernova SN 1937C (in IC 4182) is important because Sandage et al. have measured a distance to the host galaxy by means of Cepheid variables and thus have derived the Hubble constant. However, the peak brightness of SN 1937C has only been derived with the relatively poor original comparison star brightnesses and without regard to a large body of data in the literature. In this paper, I will correct these and other procedural difficulties. I find that the late time photographic light curve appears to have a broken exponential decay with equivalent half-lives of 46 and 58 days with the break near 300 days after maximum. I also find that the peak B-magnitude was 8.71 +/- 0.14 on JD 2428770.0 +/- 1.0 at which time the B-V was -0.03 +/- 0.13. With these improved peak brightnesses, the distance modulus of Sandage et al., and peak absolute magnitudes in the center of the range of modern estimates, I derive the Hubble constant to be 50 km/s Mpc.

Schaefer, Bradley E.↗
NASA NTRS1996

The Compatibility of Friedmann Cosmological Models with Observed Properties of Gamma-Ray Bursts and a Large Hubble Constant

The distance scale to cosmic gamma-ray bursts (GRB's) is still uncertain by many orders of magnitude; however, one viable scenario places GRB's at cosmological distances, thereby permitting them to be used as tracers of the cosmological expansion over a significant range of redshifts zeta. Also, several recent measurements of the Hubble constant H(sub 0) appearing in the referred literature report values of 70-80 km/s /Mpc. Although there is significant debate regarding these measurements, we proceed here under the assumption that they are evidence of a large value for H(sub 0). This is done in order to investigate the additional constraints on cosmological models that can be obtained under this hypothesis when combined with the age of the universe and the brightness distribution of cosmological gamma-ray bursts. We show that the range of cosmological models that can be consistent with the GRB brightness distribution, a Hubble constant of 70-80 km/s/Mpc, and a minimum age of the universe of 13-15 Gyr is constrained significantly, largely independent of a wide range of assumptions regarding the evolutionary nature of the burst population. Low-density, Lambda greater than 0 cosmological models with deceleration parameter in the range -1 less than q(sub 0) less than 0 and density parameter sigma(sub 0) in the range approximately equals 0.10-0.25(Omega(sub 0) approximately equals 0.2-0.5) are strongly favored.

Horack, John M.↗
NASA NTRS1994

Measuring the Hubble constant and our Virgo-infall velocity independently

A sample of spiral galaxies with B(sub T) less than 14.5 located in two local volumes, one in the direction of, but behind, the Virgo Cluster (behind-Virgo volume (BV)) and the other in the opposite direction (anti-Virgo volume (AV)), were used via a Tully-Fisher (TF) relation to derive the following two parameters: H(sub AB), the mean Hubble ratio between AV and BV, and delta v(sub parallel), the peculiar velocity of the Local Group in the direction of the Virgo Cluster (VC) with respect to a uniformly expanding reference system defined by our AV and BV sub-samples. The two sampled volumes, separated by a velocity interval of 5600 km/s, form an antipodal pair. This particular geometry not only allows us to derive the two parameters independently but also reduces the dynamical effect of the Local Supercluster on H(sub AB) without increasing the Malmquist bias. By limiting our sample to spiral galaxies having large velocity widths W(sub R), we effectively reduce the TF scatter and Malmquist bias in our sample. The TF zero point and dispersion were then determined by further correcting for the small residual Malmquist bias. An additional sample of fainter galaxies was used to test for a non-Gaussian tail to the TF disperison. We found no evidence for such a tail and formally give an upper limit of about 18% for the fractional contribution of an unseen tail. The average intrinsic TF dispersion for the dominant Gaussian component is sigma(sub TF)(sup 0) approximately 0.33 mag for W(sub R) approximately equal to or greater than 180 km/s. Our numerical results are delta v(sub parallel) approximately equals 414 +/- 82 km/s and H(sub AB) approximately equals (84.0 +/- 2.4)(1 + epsilon) km/s Mpc, where (1 + epsilon) accounts for any systematic error between the calibrators and the sample galaxies. Various dynamical models were tested to explore the effect on H(sub AB) of the uncertainties in the local velocity field. Constrained by our observed delta v(sub parallel) as well as other observational quantities, we found that the rms deviation from unity of H(sub AB)/H(sub 0) (where H(sub 0) is the Hubble constant for each model) is 5%, making H(sub AB) a good indicator for H(sub 0). Taking this variation as an additional error, our formal estimate for the Hubble constant is H(sub 0) approximately equals (84 +/- 5)(1 + epsilon) km/s Mpc.

Lu, Nanyao Y.↗
NASA NTRS2021

A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo

This paper presents the gravitational-wave measurement of the Hubble constant (H(0)) using the detections from the first and second observing runs of the Advanced LIGO and Virgo detector network. The presence of the transient electromagnetic counterpart of the binary neutron star GW170817 led to the first standard-siren measurement of H(0). Here we additionally use binary black hole detections in conjunction with galaxy catalogs and report a joint measurement. Our updated measurement is H(0) = 69(+16,-8) km/s Mpc (68.3% of the highest density posterior interval with a flat-in-log prior) which is an improvement by a factor of 1.04 (about 4%) over the GW170817-only value of 6(+17,-8) km/s Mpc. A significant additional contribution currently comes from GW170814, a loud and well-localized detection from a part of the sky thoroughly covered by the Dark Energy Survey. With numerous detections anticipated over the upcoming years, an exhaustive understanding of other systematic effects are also going to become increasingly important. These results establish the path to cosmology using gravitational-wave observations with and without transient electromagnetic counterparts.

B. P. Abbott↗
NASA NTRS1998

Galaxy Cluster Shapes and Systematic Errors in the Hubble Constant as Determined by the Sunyaev-Zel'dovich Effect

Imaging of the Sunyaev-Zei'dovich (S-Z) effect in galaxy clusters combined with the cluster plasma x-ray diagnostics can measure the cosmic distance scale to high accuracy. However, projecting the inverse-Compton scattering and x-ray emission along the cluster line-of-sight will introduce systematic errors in the Hubble constant, H$-O$, because the true shape of the cluster is not known. This effect remains present for clusters that are otherwise chosen to avoid complications for the S-Z and x-ray analysis, such as plasma temperature variations, cluster substructure, or cluster dynamical evolution. In this paper we present a study of the systematic errors in the value of H$-0$, as determined by the x-ray and S-Z properties of a theoretical sample of triaxial isothermal 'beta-model' clusters, caused by projection effects and observer orientation relative to the model clusters' principal axes. The model clusters are not generated as ellipsoids of rotation, but have three independent 'core radii', as well as a random orientation to the plane of the sky.

Sulkanen, Martin E.↗
NASA NTRS1985

The infall velocity toward Virgo, the Hubble constant, and a search for motion toward the microwave background

The perturbation of the local velocity field due to the overdensity of the Virgo complex (VC) is investigated theoretically, using an idealized spherically symmetric Virgocentric flow model and testing for a correlation between cos theta (where theta is the angle from the VC direction to eight groups and clusters with velocity 800-2500 km/s) and the relevant velocity residuals. The data and results are presented in extensive tables, graphs, and a map in extragalactic coordinates. The infall of the Local Group (LG) toward the VC is estimated as 200 + or - 50 km/s, corresponding to a mean mass/light ratio M/L(B) = about 70 for a sphere centered at the VC core and extending to the LG. The rate of free expansion within the VC is estimated as 52 + or 2 km/s Mpc for a VC distance of 21.6 Mpc. It is pointed out that the LG infall toward the VC cannot account for observations of an apparent 630-km/s motion of the LG toward the microwave background.

Tammann, G. A.↗
NASA NTRS1992

A distance-independent calibration of the luminosity of type Ia supernovae and the Hubble constant

The absolute magnitude of SNe Ia at maximum is calibrated here using radioactive decay models for the light curve and a minimum of assumptions. The absolute magnitude parameter space is studied using explosion models and a range of rise times, and absolute B magnitudes at maximum are used to derive a range of the H0 and the distance to the Virgo Cluster from SNe Ia. Rigorous limits for H0 of 45 and 105 km/s/Mpc are derived.

Leibundgut, Bruno↗
NASA NTRS2008

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results

The Wilkinson Microwave Anisotropy Probe (WMAP) is a Medium-Class Explorer (MIDEX) satellite aimed at elucidating cosmology through full-sky observations of the cosmic microwave background (CMB). The WMAP full-sky maps of the temperature and polarization anisotropy in five frequency bands provide our most accurate view to date of conditions in the early universe. The multi-frequency data facilitate the separation of the CMB signal from foreground emission arising both from our Galaxy and from extragalactic sources. The CMB angular power spectrum derived from these maps exhibits a highly coherent acoustic peak structure which makes it possible to extract a wealth of information about the composition and history of the universe. as well as the processes that seeded the fluctuations. WMAP data have played a key role in establishing ACDM as the new standard model of cosmology (Bennett et al. 2003: Spergel et al. 2003; Hinshaw et al. 2007: Spergel et al. 2007): a flat universe dominated by dark energy, supplemented by dark matter and atoms with density fluctuations seeded by a Gaussian, adiabatic, nearly scale invariant process. The basic properties of this universe are determined by five numbers: the density of matter, the density of atoms. the age of the universe (or equivalently, the Hubble constant today), the amplitude of the initial fluctuations, and their scale dependence. By accurately measuring the first few peaks in the angular power spectrum, WMAP data have enabled the following accomplishments: Showing the dark matter must be non-baryonic and interact only weakly with atoms and radiation. The WMAP measurement of the dark matter density puts important constraints on supersymmetric dark matter models and on the properties of other dark matter candidates. With five years of data and a better determination of our beam response, this measurement has been significantly improved. Precise determination of the density of atoms in the universe. The agreement between the atomic density derived from WMAP and the density inferred from the deuterium abundance is an important test of the standard big bang model. Determination of the acoustic scale at redshift z = 1090. Similarly, the recent measurement of baryon acoustic oscillations (BAO) in the galaxy power spectrum (Eisenstein et al. 2005) has determined the acoustic scale at redshift z approx. 0.35. When combined, these standard rulers accurately measure the geometry of the universe and the properties of the dark energy. These data require a nearly flat universe dominated by dark energy consistent with a cosmological constant. Precise determination of the Hubble Constant, in conjunction with BAO observations. Even when allowing curvature (Omega(sub 0) does not equal 1) and a free dark energy equation of state (w does not equal -1), the acoustic data determine the Hubble constant to within 3%. The measured value is in excellent agreement with independent results from the Hubble Key Project (Freedman et al. 2001), providing yet another important consistency test for the standard model. Significant constraint of the basic properties of the primordial fluctuations. The anti-correlation seen in the temperature/polarization (TE) correlation spectrum on 4deg scales implies that the fluctuations are primarily adiabatic and rule out defect models and isocurvature models as the primary source of fluctuations (Peiris et al. 2003).

Weiland, J.L.↗