The fundamental cosmic distance scale: state of the art and the Gaia perspective

In recent papers we had developed a unified picture of black hole entropy and curvature which was shown to lead to Hawking radiation. It was shown that for any black hole mass, holography implies a phase space of just one quantum associated with the interior of the black hole. Here we study extremal rotating and charged black holes and obtain unique values for ratios of angular momentum to entropy, charge to entropy, etc. It turns out that these ratios can be expressed in terms of fundamental constants in nature, having analogies with other physical systems, like in condensed matter physics.     

The cosmic distance scale

Summary The status of the cosmic distance scale problem in early 1989 is reviewed. Internally consistent distances to Local Group galaxies are given in Tables 5 and 6. Within the Local Group the distance scale is found to be 11±5% smaller than that previously adopted by Sandage and Tammann. Distances to nearby galaxies are used as stepping stones to the Virgo cluster. The interpretation of the Tully-Fisher observations of Virgo spirals is found to be ambiguous because it is not yet clear which spirals are cluster members and which are background objects. Distance estimates of the Virgo cluster obtained by different techniques are listed in Table 11. The distance modulus of the Virgo cluster is found to be 31.5±0.2, corresponding to a distance of 20±2 Mpc. The elliptical galaxies in the core of the Virgo cluster haveV ₀=1200±46 kms^–1, which corresponds toV _LG=1082±48 km s^–1. With an infall velocity of 250±50 km s^–1 this yields a cosmological redshiftV=1332±69 km s^–1, from which a Hubble parameter H₀=67±8 km s^–1 Mpc^–1 is obtained. Space Telescope observations of distant Cepheids, Tully-Fisher observations of spirals in the Hercules eluster, and interference filter observations of Virgo planetary nebulae in the light of [O_III], should soon result in a major improvement in the accuracy with which H₀ is known.     

Hipparcos trigonometric parallaxes and the distance scale for open star clusters

Hipparcos trigonometric parallaxes are used to estimate the distances to the maximum possible number of open star clusters (OSC); distance moduli are estimated for 45 clusters with maximum heliocentric distances of about 1000 pc. The latter value can serve as an estimate of the limit to which it still makes sense to use Hipparcos trigonometric parallaxes to determine the distances to small groups composed of 6–10 sufficiently bright stars. A systematic correction to the distance moduli of clusters from the homogeneous catalog of OSC parameters (Loktin et al. 1997, 2000) is estimated, which turns out to be independent of the cluster age.     

The Gaia Data Release 1 parallaxes and the distance scale of Galactic planetary nebulae

In this paper we gauge the potentiality of Gaia in the distance scale calibration of planetary nebulae (PNe) by assessing the impact of DR1 parallaxes of central stars of Galactic PNe (CSPNe) against known physical relations. For selected PNe targets with state-of-the-art data on angular sizes and fluxes, we derive the distance-dependent parameters of the classical distance scales, i.e., physical radii and ionized masses, from DR1 parallaxes; we propagate the uncertainties in the estimated quantities and evaluate their statistical properties in the presence of large relative parallax errors; we populate the statistical distance scale diagrams with this sample and discuss its significance in light of existing data and current calibrations. We glean from DR1 parallaxes 8 CSPNe with S/N> 1. We show that this set of potential calibrators doubles the number of extant trigonometric parallaxes (from HST and ground-based), and increases by two orders of magnitude the domain of physical parameters probed previously. We then use the combined sample of suitable trigonometric parallaxes to fit the physical-radius-to-surface-brightness relation. This distance scale calibration, although preliminary, appears solid on statistical grounds, and suggestive of new PNe physics. With the tenfold improvement in PNe number statistics and astrometric accuracy expected from future Gaia releases the new distance scale, already very intriguing, will be definitively constrained.     

Anchors for the cosmic distance scale: the Cepheid QZ Normae in the open cluster NGC 6067

Cepheids are key to establishing the cosmic distance scale. Therefore it’s important to assess the viability of QZ Nor, V340 Nor, and GU Nor as calibrators for Leavitt’s law via their purported membership in the open cluster NGC 6067. The following suite of evidence confirms that QZ Nor and V340 Nor are members of NGC 6067, whereas GU Nor likely lies in the foreground: (i) existing radial velocities for QZ Nor and V340 Nor agree with that established for the cluster ( $-39.4\pm0.2(\sigma_{\bar {x}}) \pm1.2 (\sigma)~\mbox{km/s}$ ) to within 1 km/s, whereas GU Nor exhibits a markedly smaller value; (ii) a steep velocity-distance gradient characterizes the sight-line toward NGC 6067, thus implying that objects sharing common velocities are nearly equidistant; (iii) a radial profile constructed for NGC 6067 indicates that QZ Nor is within the cluster bounds, despite being 20′ from the cluster center; (iv) new BVJH photometry for NGC 6067 confirms the cluster lies d=1.75±0.10 kpc distant, a result that matches Wesenheit distances computed for QZ Nor/V340 Nor using the Benedict et al. (Astron. J. 133:1810, 2007, HST parallaxes) calibration. QZ Nor is a cluster Cepheid that should be employed as a calibrator for the cosmic distance scale.     

Standard candles from the Gaia perspective

The ESA Gaia mission will bring a new era to the domain of standard candles. Progresses in this domain will be achieved thanks to unprecedented astrometric precision, whole-sky coverage and the combination of photometric, spectrophotometric and spectroscopic measurements. The fundamental outcome of the mission will be the Gaia catalogue produced by the Gaia Data Analysis and Processing Consortium (DPAC), which will contain a variable source classification and specific properties for stars of specific variability types. We review what will be produced for Cepheids, RR Lyrae, Long Period Variable stars and eclipsing binaries.     

Deriving the GRB distance scale

We describe a method to address the burster origin problem by determining their distance scale. We show that this can be easily carried out at soft X-ray wavelengths by measuring the effective column densities of a representative sample of burst spectra. We demonstrate the effectiveness of the technique by simulating the performance of a small CATSAT-type mission (Forrestet al., 1995).     

Mira kinematics from Hipparcos data: a Galactic bar to beyond the Solar circle

The space motions of Mira variables are derived from radial velocities, Hipparcos proper motions and a period–luminosity relation. The previously known dependence of Mira kinematics on the period of pulsation is confirmed and refined. In addition, it is found that Miras with periods in the range 145–200 d in the general Solar neighbourhood have a net radial outward motion from the Galactic Centre of 75±18 km s⁻¹. This, together with a lag behind the circular velocity of Galactic rotation of 98±19 km s⁻¹, is interpreted as evidence for an elongation of their orbits, with their major axes aligned at an angle of ∼17° with the Sun–Galactic Centre line, towards positive Galactic longitudes. This concentration seems to be a continuation to the Solar circle and beyond of the bar-like structure of the Galactic bulge, with the orbits of some local Miras probably penetrating into the bulge. These conclusions are not sensitive to the distance scale adopted. A further analysis is given of the short-period (SP) red group of Miras discussed in companion papers in this series. In Appendix A the mean radial velocities and other data for 842 oxygen-rich Mira-like variables are tabulated. These velocities were derived from published optical and radio observations.     

New periodic variables from the Hipparcos epoch photometry

Two selection statistics are used to extract new candidate periodic variables from the epoch photometry of the Hipparcos catalogue. The primary selection criterion is a signal-to-noise ratio. The dependence of this statistic on the number of observations is calibrated using about 30 000 randomly permuted Hipparcos data sets. A significance level of 0.1 per cent is used to extract a first batch of candidate variables. The second criterion requires that the optimal frequency be unaffected if the data are de-trended by low-order polynomials. We find 2675 new candidate periodic variables, of which the majority (2082) are from the Hipparcos 'unsolved' variables. Potential problems with the interpretation of the data (e.g. aliasing) are discussed.     

Bright bursts and the GRB distance scale

We discuss the use of selected characteristics of the burster population (e.g. the distribution of peak fluxes, or durations) to derive the GRB distance scale within the framework of cosmological models. The effects of the cosmological expansion on GRBs are briefly noted and it is shown that intrinsic GRB properties may strongly complicate the search for (and the interpretation of) purely cosmological effects. In this context, bright GRBs provide a sample of reference; they are almost free of cosmological influences and they have been studied for a long time. We also emphasize the need for a GRB distance indicator which could be used for individual events; several recent studies suggest that such a quantity may exist.     

The Gaia Mission: Expected Applications to Asteroid Science

According to current plans of the European space agency, Gaia will be launched in 2011. By performing a systematic survey of the whole sky down to magnitude V = 20, this mission will provide a fundamental contribution in practically all branches of modern Astrophysics. Gaia will be able to survey with repeated observations spanning over 5 years several 100,000 s asteroids. It will directly measure sizes of about 1,000 objects, obtain the masses of about 100 of them, derive spin properties and overall shapes of more than 10,000 objects, yield much improved orbits and taxonomic classification for most of the observed sources. The final harvest will very likely include new discoveries of objects orbiting at heliocentric distances less than 1 AU. At the end of the mission, we will know average densities of about 100 objects belonging to all the major taxonomic classes, have a much more precise knowledge of the inventory and size and spin distributions of the population, of the distribution of taxonomic classes as a function of heliocentric distance, and of the dynamical and physical properties of dynamical families.     

On the determination of absolute magnitude zero-points from Hipparcos parallaxes

The period–luminosity (PL) relation zero-point determination from Hipparcos trigonometric parallaxes of Cepheids is contentious. It is shown that the method used by Feast &38; Catchpole is equivalent to a standard minimization of sum of squares, and that it is free of Lutz–Kelker bias. The same technique is applied to RR Lyrae and field HB star data, the PL relation being replaced by a luminosity–metallicity relation.     

The Large Magellanic Cloud and the distance scale

The Magellanic Clouds, especially the Large Magellanic Cloud, are places where multiple distance indicators can be compared with each other in a straight-forward manner at considerable precision. We here review the distances derived from Cepheids, Red Variables, RR Lyraes, Red Clump Stars and Eclipsing Binaries, and show that the results from these distance indicators generally agree to within their errors, and the distance modulus to the Large Magellanic Cloud appears to be defined to ±3% with a mean value (m−M)₀=18.48 mag, corresponding to 49.7 kpc. The utility of the Magellanic Clouds in constructing and testing the distance scale will remain as we move into the era of Gaia.     

Stellar models and Hyades: the Hipparcos test

We compare theoretical stellar models for main sequence (MS) stars with the Hipparcos data base for the Hyades cluster to give a warning against the uncritical use of available theoretical scenarios and to show how formal MS fittings can be fortuitous if not fictitious. Moreover, we find that none of the current theoretical scenarios appears able to account for an observed mismatch between theoretical predictions and observations of the coolest Hyades MS stars. Finally, we show that current theoretical models probably give too faint He burning luminosities unlike the case of less massive He burning models, with degenerate progenitors, which have been suggested to suffer the opposite discrepancy.     

Harmonizing the RR Lyrae and clump distance scales – stretching the short distance scale to intermediate ranges?

I explore the consequences of making the RR Lyrae and clump giant distance scales consistent in the solar neighbourhood, Galactic bulge and Large Magellanic Cloud (LMC). I employ two major assumptions: (i) that the absolute magnitude–metallicity, M _V (RR)–[Fe/H], relation for RR Lyrae stars is universal, and (ii) that absolute I magnitudes of clump giants, M _I (RC), in Baade's Window are known (e.g. can be inferred from the local Hipparcos -based calibration or theoretical modelling). A comparison between the solar neighbourhood and Baade's Window sets M _V (RR) at [Fe/H]=−1.6 in the range (0.59±0.05, 0.70±0.05), somewhat brighter than the statistical parallax solution. More luminous RR Lyrae stars imply younger globular clusters, which would be in better agreement with the conclusions from the currently favoured stellar evolution and cosmological models. A comparison between Baade's Window and the LMC sets M ^LMC(RC) _I in the range (−0.33±0.09,−0.53±0.09). The distance modulus to the LMC is μ ^LMC∈(18.24±0.08,18.44±0.07). Unlike M ^LMC(RC) _I , this range in μ ^LMC does not depend on the adopted value of the dereddened LMC clump magnitude, I ^LMC(RC)₀. I argue that the currently available information is insufficient to select the correct distance scale with high confidence.