Observational Evidence Favors a Static Universe - Journal of ...

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4.1.1 Surface brightness in BB The obvious candidates for surface brightness tests are elliptic and S0 galaxies which have minimal projection effects compared to spiral galaxies . The major problem is that surface brightness measurements are intrinsically difficult due to the strong intensity gradients across their images. In a series of papers Sandage & Lubin (2001); Lubin & Sandage (2001a,b,c) (hereafter SL01) have investigated the Tolman surface brightness test for elliptical and S0 galaxies. More recently Sandage (2010) has done a more comprehensive analysis but since he came to the same conclusion as the earlier papers and since the earlier papers are better known this analysis will concentrate on them. The observational difficulties are thoroughly discussed by Sandage & Lubin (2001) with the conclusion that the use of Petrosian metric radii helps solve many of the problems. Petrosian (1976); Djorgovski & Spinrad (1981); Sandage & Perelmuter (1990) showed that if the ratio of the average surface brightness within a radius is equal to η times the surface brightness at that radius then that defines the Petrosian metric radius, η. The procedure is to examine an image and to vary the angular radius until the specified Petrosian radius is achieved. Thus, the aim is to measure the mean surface brightness for each galaxy at the same value of η. The choice of Petrosian radii greatly diminishes the differences in surface brightness due to the luminosity distribution across the galaxies. However, there still is a dependence of the surface brightness on the size of the galaxy which is the Kormendy relationship (Kormendy, 1977). The purpose of the preliminary analysis done by SL01 is not only to determine the low redshift absolute luminosity but also to determine the surface brightness verses linear size relationship that can be used to correct for effects of size 17
Table 3: Galactic properties for Petrosian radius η = 2.0 Cluster N log(S BB) SB M BB Nearby 74 4.69 (0.28) 22.56 (0.84) -23.84 (0.66) 1324+3011 11 3.99 (0.21) 22.87 (0.75) -23.28 (0.65) 1604+4304 6 4.05 (0.17) 22.34 (0.60) -23.51 (0.68) 1604+4321 13 4.00 (0.15) 22.35 (0.78) -23.33 (0.64) variation in distant galaxies. The data on the nearby galaxies used by SL01 was taken from Postman & Lauer (1995) and consists of extensive data on the brightest cluster galaxies (BCG) from 119 nearby Abell clusters. All magnitudes for these galaxies are in the R C (Cape/Landolt) system. Since the results for different Petrosian radii are highly correlated the analysis repeated here using similar procedures will use only the Petrosian η = 2 radius. Although the actual value used for h does not alter any significant results here it is set to h = 0.5 for numerical consistency. A minor difference is that the angular radius used here is provided by equation (4) whereas they used the older Mattig equation. The higher z data also comes from SL01. They made Hubble Space Telescope observations of galaxies in three clusters and measured their surface brightness and radii. The names and redshifts of these clusters are given in Table 3 which also shows the number of galaxies in each cluster, N, the logarithm of the average metric radius in kpc, log(S BB), and the average absolute magnitude. Note that the original magnitudes for Cl 1324+3011 and Cl 1604+4304 were observed in the I band. The bracketed numbers are the root-mean-square (rms) values for each vari- able. In order to get a reference surface brightness at z = 0 all the surface 18
Page 1 and 2: The Journal of Cosmology Journal of
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Page 5 and 6: premise that the most constant char
Page 7 and 8: (λ0/λ−1) where λ0 is the obser
Page 9 and 10: cosmic gas (i.e. inter-galactic gas
Page 11 and 12: For this geometry the area of a thr
Page 13 and 14: 3 Theoretical Table 2: Comparison o
Page 15: characteristics would constitute se
Page 19 and 20: Table 4: Fitted exponents for dista
Page 21 and 22: Table 5: Radii and fitted exponents
Page 23 and 24: used 393 galaxies with redshift ran
Page 25 and 26: likelihood estimate of ˆ S is ˆSe
Page 27 and 28: can be compared with β = 2.28 give
Page 29 and 30: Figure 1: Width of supernovae type
Page 31 and 32: 4.3.2 Supernovae in CC Since the re
Page 33 and 34: Figure 2: Absolute magnitudes, M CC
Page 35 and 36: the peak luminosity will be proport
Page 37 and 38: that is M0, is −19.070 ± 0.042.
Page 39 and 40: evidence for strong luminosity sele
Page 41 and 42: Table 8: M ∗ CC for SED Type 1 ga
Page 43 and 44: volume and ρ is the quasar density
Page 45 and 46: this region which not only produces
Page 47 and 48: S would be constant. It has the fur
Page 49 and 50: Table 9: Origin of radio source-cou
Page 51 and 52: Clearly, the model satisfies the ba
Page 53 and 54: e more precise fB is the fraction t
Page 55 and 56: where σi is the uncertainty in yi,
Page 57 and 58: Buchalter, A., Helfand, D.J., Becke
Page 59 and 60: Djorgovski, S.G. & Spinrad H., (198
Page 61 and 62: Hogg D.W., (1999). Distance measure
Page 63 and 64: Liddle, A.E. & Lyth, D.H., 2000, Co
Page 65 and 66: Peacock, J.A., (1999), Cosmological
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Sloan Digital Sky Survey Quasar Sur
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Schneider, D. P., Hall, P. B., Rich
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Good Standard Candles in the Near I
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