On surface brightness fluctuations: probabilistic and statistical bases I: Stellar population and theoretical SBF

This work aims to provide a theoretical formulation of Surface Brightness Fluctuations (SBF) in the framework of probabilistic synthesis models, and to distinguish between the different distributions involved in the SBF definition. RESULTS: We propose three definitions of SBF: (i) stellar population SBF, which can be computed from synthesis models and provide an intrinsic metric of fit for stellar population studies; (ii) theoretical SBF, which include the stellar population SBF plus an additional term that takes into account the distribution of the number of stars per resolution element psi(N); theoretical SBF coincide with Tonry & Schneider (1998) definition in the very particular case that psi(N) is assumed to be a Poisson distribution. However, the Poisson contribution to theoretical SBF is around 0.1% of the contribution due to the stellar population SBF, so there is no justification to include any reference to Poisson statistics in the SBF definition; (iii) observational SBF, which are those obtained in observations that are distributed around the theoretical SBF. Finally, we show alternative ways to compute SBF and extend the application of stellar population SBF to defining a metric of fitting for standard stellar population studies. CONCLUSIONS: We demostrate that SBF are observational evidence of a probabilistic paradigm in population synthesis, where integrated luminosities have an intrinsic distributed nature, and they rule out the commonly assumed deterministic paradigm of stellar population modeling.Comment: A&A accepte

Disentangling age and metallicity in distant unresolved stellar systems

We present some results of an observational and theoretical study on unresolved stellar systems based on the Surface Brightness Fluctuations (SBF) technique. It is shown that SBF magnitudes are a valuable tracer of stellar population properties, and a reliable distance indicator. SBF magnitudes, SBF-colors, and SBF-gradients can help to constrain within relatively narrow limits the metallicity and age of the dominant stellar component in distant stellar systems, especially if coupled with other spectro-photometric indicators.Comment: A contributed paper to the Cefalu' (Italy) "Probing Stellar Populations out to the Distant Universe", 4 pages. To appear as an AIP Conference Proceedin

New optical and near-infrared Surface Brightness Fluctuations models. A primary distance indicator ranging from Globular Clusters to distant galaxies?

We present new theoretical models for Surface Brightness Fluctuations (SBF) both for optical and near-infrared bands in standard ground-based and Hubble Space Telescope filter systems. Simple Stellar Population simulations are adopted. Models cover the age and metallicity ranges from $t=5$ to $15~Gyr$ and from $Z=0.0001$ to 0.04 respectively. Effects due to the variation of the Initial Mass Function and the stellar color-temperature relations are explored. Particular attention is devoted to very bright stars in the color-magnitude diagram and to investigate the effects of mass loss along the Red Giant Branch (RGB) and the Asymptotic Giant Branch (AGB). It is found that $U$ and $B$ bands SBF amplitudes are powerful diagnostics for the morphology of the Horizontal Branch and the Post-AGB stars population. We point out that a careful treatment of mass loss process along the RGB and AGB is fundamental in determining reliable SBF evaluations. The SBF measurements are used to give robust constraints on the evolution of AGB stars, suggesting that mass loss activity on AGB stars should be twice more efficient than on the RGB stars. Our models are able to reproduce the absolute SBF magnitudes of the Galactic Globular Clusters and of galaxies, and their integrated colors. New calibrations of absolute SBF magnitude in $V$, $R$, $I$, and $K$ photometric filters are provided, which appear reliable enough to directly gauge distances bypassing other distance indicators. The SBF technique is also used as stellar population tracer to derive age and metallicity of a selected sample of galaxies of known distances. Finally, {\it SBF color} versus {\it integrated color} diagrams are proposed as particularly useful in removing the well known {\it age-metallicity degeneracy} affecting our knowledge of remote stellar systems.Comment: AJ accepted, 46 pages, 21 figures, 10 tables, uses aastex.cl

The Distance to the Coma Cluster from Surface Brightness Fluctuations

We report on the first determination of the distance to the Coma Cluster based on surface brightness fluctuation (SBF) measurements obtained from Hubble Space Telescope WFPC2 observations of the bright E0 galaxy NGC 4881 in the Coma Cluster and ground-based observations of the standard E1 galaxy NGC 3379 in the Leo-I group. Relative distances based on the I-band fluctuation magnitude, I(SBF), are strongly dependent on metallicity and age of the stellar population. However, the radial changes in the stellar populations of the two giant ellipticals, NGC 3379 and NGC 4881, are well described by published Mg_2 gradients, and the ground-based measurements of I(SBF) at several radial points in NGC 3379 are used to calibrate I(SBF) in terms of the Mg_2 index. The distance to NGC 3379, assumed to be identical to the average SBF distance of the Leo-I group, is combined with the new SBF measurements of NGC 4881 to obtain a Coma Cluster distance of 102+-14 Mpc. Combining this distance with the cosmic recession velocity of Coma (7186+-428 km/s), we find the Hubble constant to be H_0 = 71+-11 km/s/Mpc.Comment: 12 pages, LaTex, includes aaspp4.sty and 3 eps figures. To appear in ApJ Letter

The SBF Survey of Galaxy Distances. I. Sample Selection, Photometric Calibration, and the Hubble Constant

We describe a program of surface brightness fluctuation (SBF) measurements for determining galaxy distances. This paper presents the photometric calibration of our sample and of SBF in general. Basing our zero point on observations of Cepheid variable stars, we find that the absolute SBF magnitude in the Kron-Cousins I band correlates well with the mean (V-I)o color of a galaxy according to M_Ibar = (-1.74 +/- 0.07) + (4.5 +/- 0.25) [ (V-I)o - 1.15 ] for 1.0 < (V-I) < 1.3. This agrees well with theoretical estimates from stellar population models. Comparisons between SBF distances and a variety of other estimators, including Cepheid variable stars, the Planetary Nebula Luminosity Function (PNLF), Tully-Fisher (TF), Dn-sigma, SNII, and SNIa, demonstrate that the calibration of SBF is universally valid and that SBF error estimates are accurate. The zero point given by Cepheids, PNLF, TF (both calibrated using Cepheids), and SNII is in units of Mpc; the zero point given by TF (referenced to a distant frame), Dn-sigma and SNIa is in terms of a Hubble expansion velocity expressed in km/s. Tying together these two zero points yields a Hubble constant of H_0 = 81 +/- 6 km/s/Mpc. As part of this analysis, we present SBF distances to 12 nearby groups of galaxies where Cepheids, SNII, and SNIa have been observed.Comment: 29 pages plus 8 figures; LaTeX (AASTeX) uses aaspp4.sty (included); To appear in The Astrophysical Journal, 1997 February 1 issue; Compressed PostScript available from ftp://mars.tuc.noao.edu/sbf

Entanglement, BEC, and superfluid-like behavior of two-mode photon systems

A system of two interacting photon modes, without constraints on the photon number, in the presence of a Kerr nonlinearity, exhibits BEC if the transfer amplitude is greater than the mode frequency. A symmetry-breaking field (SBF) can be introduced by taking into account a classical electron current. The ground state, in the limit of small nonlinearity, becomes a squeezed state, and thus the modes become entangled. The smaller is the SBF, the greater is entanglement. Superfluid-like behavior is observed in the study of entanglement growth from an initial coherent state, since in the short-time range the growth does not depend on the SBF amplitude, and on the initial state amplitude. On the other hand, the latter is the only parameter which determines entanglement in the absence of the SBF

Distance Measurements and Stellar Population Properties via Surface Brightness Fluctuations

Surface Brightness Fluctuations (SBFs) are one of the most powerful techniques to measure the distance and to constrain the unresolved stellar content of extragalactic systems. For a given bandpass, the absolute SBF magnitude \bar{M} depends on the properties of the underlying stellar population. Multi-band SBFs allow scientists to probe different stages of the stellar evolution: UV and blue wavelength band SBFs are sensitive to the evolution of stars within the hot Horizontal Branch (HB) and post-Asymptotic Giant Branch (post-AGB) phase, whereas optical SBF magnitudes explore the stars within the Red Giant Branch (RGB) and HB regime. Near- and Far-infrared SBF luminosities probe the important stellar evolution stage within the AGB and Thermally-Pulsating Asymptotic Giant Branch (TP-AGB) phase. Since the first successful application by Tonry and Schneider, a multiplicity of works have used this method to expand the distance scale up to 150 Mpc and beyond. This article gives a historical background of distance measurements, reviews the basic concepts of the SBF technique, presents a broad sample of these investigations and discusses possible selection effects, biases, and limitations of the method. In particular, exciting new developments and improvements in the field of stellar population synthesis are discussed that are essential to understand the physics and properties of the populations in unresolved stellar systems. Further, promising future directions of the SBF technique are presented. With new upcoming space-based satellites such as Gaia, the SBF method will remain as one of the most important tools to derive distances to galaxies with unprecedented accuracy and to give detailed insights into the stellar content of globular clusters and galaxies.Comment: 21 pages, 10 figures, 1 Table, accepted for publication in Publications of the Astronomical Society of Australia (PASA, CSIRO Publishing

K-band versus I-band Surface Brightness Fluctuations as distance indicators

We evaluate the method of optical and infrared Surface Brightness Fluctuations (SBF) as a distance indicator and its application on 8-m class telescopes, such as the Very Large Telescope (VLT). The novelty of our approach resides in the development of Monte Carlo simulations of SBF observations incorporating realistic elliptical galaxy stellar population models, the effects induced by globular clusters and background galaxies, instrumental noise, sky background and PSF blurring. We discuss, for each band and in different observational conditions, the errors on distance measurements arising from stellar population effects, data treatment and observational constraints. With 8-m class telescopes, one can extend I-band SBF measurements out to 6000-10000 km/s. Integration times in the K-band are too expensive from the ground, due to the high infrared background for large-scale distance determination projects. Nevertheless ground-based K-band measurements are necessary to understand stellar population effects on the SBF calibration, and to prepare future space-based observations, where this band is more efficient.Comment: A&A, in press, 17 pages, 10 figure

The SBF Survey of Galaxy Distances. IV. SBF Magnitudes, Colors, and Distances

We report data for $I$ band Surface Brightness Fluctuation (SBF) magnitudes, V-I colors, and distance moduli for 300 galaxies. The Survey contains E, S0 and early-type spiral galaxies in the proportions of 49:42:9, and is essentially complete for E galaxies to Hubble velocities of 2000 km/s, with a substantial sampling of E galaxies out to 4000 km/s. The median error in distance modulus is 0.22 mag. We also present two new results from the Survey. (1) We compare the mean peculiar flow velocity (bulk flow) implied by our distances with predictions of typical cold dark matter transfer functions as a function of scale, and find very good agreement with cold, dark matter cosmologies if the transfer function scale parameter $\Gamma$, and the power spectrum normalization $\sigma_8$ are related by $\sigma_8 \Gamma^{-0.5} \approx 2\pm0.5$. Derived directly from velocities, this result is independent of the distribution of galaxies or models for biasing. The modest bulk flow contradicts reports of large-scale, large-amplitude flows in the $\sim200$ Mpc diameter volume surrounding our Survey volume. (2) We present a distance-independent measure of absolute galaxy luminosity, \Nbar, and show how it correlates with galaxy properties such as color and velocity dispersion, demonstrating its utility for measuring galaxy distances through large and unknown extinction.Comment: Accepted for publication in ApJ (10 January 2001); 23 page

Theoretical Predictions for Surface Brightness Fluctuations and Implications for Stellar Populations of Elliptical Galaxies

(Abridged) We present new theoretical predictions for surface brightness fluctuations (SBFs) using models optimized for this purpose. Our predictions agree well with SBF data for globular clusters and elliptical galaxies. We provide refined theoretical calibrations and k-corrections needed to use SBFs as standard candles. We suggest that SBF distance measurements can be improved by using a filter around 1 micron and calibrating I-band SBFs with the integrated V-K galaxy color. We also show that current SBF data provide useful constraints on population synthesis models, and we suggest SBF-based tests for future models. The data favor specific choices of evolutionary tracks and spectra in the models among the several choices allowed by comparisons based on only integrated light. In addition, the tightness of the empirical I-band SBF calibration suggests that model uncertainties in post-main sequence lifetimes are less than +/-50% and that the IMF in ellipticals is not much steeper than that in the solar neighborhood. Finally, we analyze the potential of SBFs for probing unresolved stellar populations. We find that optical/near-IR SBFs are much more sensitive to metallicity than to age. Therefore, SBF magnitudes and colors are a valuable tool to break the age/metallicity degeneracy. Our initial results suggest that the most luminous stellar populations of bright cluster galaxies have roughly solar metallicities and about a factor of three spread in age.Comment: Astrophysical Journal, in press (uses Apr 20, 2000 version of emulateapj5.sty). Reposted version has a minor cosmetic change to Table