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Register a new userThe Tolman Surface Brightness Test for the Reality of the Expansion. II. The Effect of the Point-Spread Function and Galaxy Ellipticity on the Derived Photometric Parameters
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Lori M. Lubin
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To complete the Tolman surface brightness test on the reality of the expansion of the Universe, we need to measure accurately the surface brightness profiles of the high-redshift galaxy sample. We, therefore, investigate the effects of various sizes of point-spread-functions composed of telescope diffraction, CCD pixel resolutions, and ground-based seeing on the measurements of mean surface brightness. We have done the calculations using two synthetic galaxies of effective radii of 0.70 and 0.25 with point-spread functions of 0.1, 0.3, and 0.9 arcseconds. We have also compared actual observations of three high-redshift galaxies in the cluster Cl 1324 + 3011 (z = 0.76) made both with the Keck telescopes in seeing of about 0.9 and with HST which has a PSF that is approximately ten times smaller. The conclusion is that HST data can be used as far into the galaxy image as a Petrosian metric radius of eta = 1.3 magnitudes, whereas the ground-based data will have systematic errors of up to 2.9 magnitudes in the mean surface brightness at eta values of less than 2.2 magnitudes. In the final section, we compare the differences in derived average surface brightness for nearly circular galaxy images compared with highly flattened images. The comparison is made by using the two reduction procedures of (1) integrating the profile curves using circular apertures, and (2) approximating an ``equivalent circular galaxy that is highly elongated by using an ``effective radius of sqrt{ab}, where a and b are the semi-major and semi-minor axis, respectively, of the best-fitting ellipse. The conclusion is that the two methods of reduction give nearly identical results and that either method can be used to analyze the low and high-redshift galaxy samples used in the Tolman test.
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The extensive CCD photometry by Postman & Lauer (1995, ApJ, 440, 28) in the Cape/Cousins R photometric band for first ranked cluster elliptical and S0 galaxies in 118 low redshift clusters is analyzed for the correlations between average surface brightness, linear radius, and absolute magnitude. The purpose is to calibrate the correlations between these three parameters in the limit of zero redshift. These local correlations provide the comparisons to be made in Paper IV with the sample of early-type galaxies at high redshift in search of the Tolman surface brightness signal of (1 + z)^4 if the expansion is real. Surface brightness averages are calculated at various metric radii in each galaxy in the sample. The definition of such radii by Petrosian (1976, ApJ, 209, L1) uses ratios of observed surface photometric data. The observed surface brightnesses are listed for 118 first ranked cluster galaxies at Petrosian eta radii of 1.0, 1.3, 1.5, 1.7, 2.0, and 2.5 mag. The three local diagnostic correlation diagrams are defined and discussed. We review the Tolman test and show that, although recipes from the standard cosmological model that already have the Tolman signal incorporated are required to calculate linear radii and absolute magnitudes from the observed data, the test is nevertheless free from the hermeneutical circularity dilemma occasionally claimed in the literature. The reasons are the observed mean surface brightness (1) is independent of any assumptions of cosmological model, (2) does not depend on the existence of a Tolman signal because it is calculated directly from the data using only angular radii and apparent magnitudes, and (3) can be used to search for the Tolman signal because it carries the bulk of that signal.
We review a sample of the early literature in which the reality of the expansion is discussed, explain Hubbles reticence to accept the expansion as real, and contrast the Tolman surface brightness test with three other modern tests. We search for the Tolman surface brightness depression with redshift using the Hubble Space Telescope (HST) data from Paper III for 34 early-type galaxies from the three clusters Cl 1324+3011 (z=0.76), Cl 1604+4304 (z=0.90), and Cl 1604+4321 (z=0.92). Depressions of the surface brightness relative to the zero-redshift fiducial lines in the mean surface brightness, log linear radius diagrams of Paper I are found for all three clusters. Expressed as the exponent, n, in 2.5 log (1 + z)^n mag, the value of n for all three clusters is n = 2.59 +/- 0.17 in the R band and 3.37 +/- 0.13 in the I band for a q_o = 1/2 model. The sensitivity of the result to the assumed value of q_o is shown to be less than 23% between q_o = 0 and +1. For a true Tolman signal with n = 4, the luminosity evolution in the look-back time, expressed as the exponent in 2.5 log (1+z)^(4-n) mag, must then be between 1.72 to 1.19 in the R band and 0.94 to 0.45 in the I band. We show that this is precisely the range expected from the evolutionary models of Bruzual & Charlot. We conclude that the Tolman surface brightness test is consistent with the reality of the expansion. We have also used the high-redshift HST data to test the ``tired light speculation for a non-expansion model for the redshift. The HST data rule out the ``tired light model at a significance level of better than 10 sigma.
Photometric data for 34 early-type galaxies in the three high-redshift clusters Cl 1324+3011 (z = 0.76), Cl 1604+4304 (z = 0.90), and Cl 1604+4321 (z = 0.92), observed with the Hubble Space Telescope (HST) and with the Keck 10-meter telescopes by Oke, Postman & Lubin, are analyzed to obtain the photometric parameters of mean surface brightness, magnitudes for the growth curves, and angular radii at various Petrosian eta radii. The angular radii at eta = 1.3 mag for the program galaxies are all larger than 0.24. All of the galaxies are well resolved at this angular size using HST whose point-spread function is 0.05, half width at half maximum. The data for each of the program galaxies are listed at eta = 1.0, 1.3, 1.5, 1.7, and 2.0 mag. They are corrected by color equations and K terms for the effects of redshift to the rest-frame Cape/Cousins I for Cl 1324+3011 and Cl 1604+4304 and R for Cl 1604+4321. The K corrections are calculated from synthetic spectral energy distributions derived from evolving stellar population models of Bruzual & Charlot which have been fitted to the observed broad-band (BVRI) AB magnitudes of each program galaxy. The listed photometric data are independent of all cosmological parameters. They are the source data for the Tolman surface brightness test made in Paper IV.
We present measurements of the normalised redshift-space three-point correlation function (Q_z) of galaxies from the Sloan Digital Sky Survey (SDSS) main galaxy sample. We have applied our npt algorithm to both a volume-limited (36738 galaxies) and magnitude-limited sample (134741 galaxies) of SDSS galaxies, and find consistent results between the two samples, thus confirming the weak luminosity dependence of Q_z recently seen by other authors. We compare our results to other Q_z measurements in the literature and find it to be consistent within the full jack-knife error estimates. However, we find these errors are significantly increased by the presence of the ``Sloan Great Wall (at z ~ 0.08) within these two SDSS datasets, which changes the 3-point correlation function (3PCF) by 70% on large scales (s>=10h^-1 Mpc). If we exclude this supercluster, our observed Q_z is in better agreement with that obtained from the 2dFGRS by other authors, thus demonstrating the sensitivity of these higher-order correlation functions to large-scale structures in the Universe. This analysis highlights that the SDSS datasets used here are not ``fair samples of the Universe for the estimation of higher-order clustering statistics and larger volumes are required. We study the shape-dependence of Q_z(s,q,theta) as one expects this measurement to depend on scale if the large scale structure in the Universe has grown via gravitational instability from Gaussian initial conditions. On small scales (s <= 6h^-1 Mpc), we see some evidence for shape-dependence in Q_z, but at present our measurements are consistent with a constant within the errors (Q_z ~ 0.75 +/- 0.05). On scales >10h^-1 Mpc, we see considerable shape-dependence in Q_z.
Redshifts of an astronomical body measured at multiple epochs (e.g., separated by 10 years) are different due to the cosmic expansion. This so-called Sandage-Loeb test offers a direct measurement of the expansion rate of the Universe. However, acceleration in the motion of Solar System with respect to the cosmic microwave background also changes redshifts measured at multiple epochs. If not accounted for, it yields a biased cosmological inference. To address this, we calculate the acceleration of Solar System with respect to the Local Group of galaxies to quantify the change in the measured redshift due to local motion. Our study is motivated by the recent determination of the mass of Large Magellanic Cloud (LMC), which indicates a significant fraction of the Milky Way mass. We find that the acceleration towards the Galactic Center dominates, which gives a redshift change of 7 cm/s in 10 years, while the accelerations due to LMC and M31 cannot be ignored depending on lines of sight. We create all-sky maps of the expected change in redshift and the corresponding uncertainty, which can be used to correct for this effect.
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