sign in sign up
<<
Home , Distance modulus, Malmquist bias

Proc. Natl. Acad. Sci. USA Vol. 90, pp. 4811-4813, June 1993 Colloquium Paper

This paper was presented at a colloquium entitled "Physical ," organized by a committee chaired by David N. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA.

Tests of the long and short extragalactic distance scales

G. DE VAUCOULEURS Department of , University of Texas, Austin, TX 78712

ABSTRACT Distances on the short and long scales of 12 2.5 - nearby , one group, and three clusters are compared with recent estimates by independent methods and researchers. All comparisons show a close agreement [within 0.3 2 S (mag) in the (DM)] between the short-scale moduli and the new estimates by others at all distances from the 0 [A (distance) = 0.05 megaparsec 1.5 1- (Mpc); 1 pc = 3.09 x 1016 mI to the Coma cluster (A = 83 Mpc). 0 The mean systematic difference (short - others) is only -0.04 0 mag no a ii with evidence for significant in the S Cl) 1 short scale. The long scale differs systematically from all the c others by about +0.25 mag within the Local Group (DM < 26) 0 and by +1.1 outside (26 < DM < 35). Accidental errors are also 0 much larger in the long-scale moduli (0.5 mag) than in the other .5 S 0 two scales (0.1 mag). The mean value of the Hubble expansion 4 0 ratio for the test objects is (H) = 86 1 km sec'1 Mpc' . - S S 0 Until such time that unequivocal determinations ofthe global Hubble constant, Ho, over long distances [A > 100 megapar- = x sec (Mpc); 1 pc 3.09 1016 m] by two or more independent -.5 - - methods (e.g., gravitational lenses, supernovae, . . . ) be- 20 25 30 35 come available, we must still rely on estimates of the Hubble DM(XYZ) ratio, cz/A, in the relatively nearby region (A < 100 Mpc) where available indicators of distance, A, can be used. The FIG. 1. Modulus difference ST - XYZ versus DM(XYZ). Note persistent dichotomy between the distance scales of large systematic and accidental differences, particularly at DM > 26. Sandage, Tammann, and collaborators (the long scale) on the I have assembled some 300 such determinations for 12 one hand and of myself and collaborators (the short scale) on individual galaxies and four groups or clusters, ranging from the other has been puzzling astronomers for 16 years. It is not the Large Magellanic Cloud [distance modulus (DM) = 18.4, necessary to review here the pros and cons of both sides as A = 0.05 Mpc] to the Coma cluster (DM = 35.6, A = 83 they have been extensively discussed in the past (e.g., for a Mpc), a distance interval to a test good account, see ref. 1 and references therein). large enough provide significant zero scales. It has been frequently asserted that a progressive of both the point and linearity of the competing Malmquist bias in magnitude-limited samples is the main Details will appear elsewhere in 1993 (8). Tables 1 and 2 cause of systematic error in my scale and the same argument summarizing the comparisons for all 16 objects show that has been used against others who also favor the short scale within the Local Group (DM < 26), the long scale (ST) has [e.g., Aaronson et al. (2), Tully et al. (ref. 3 and this a zero point error of about +0.3 magnitude (mag) relative to symposium), van den Bergh (this symposium), and Pierce both the short scale (GV) and all "others" (XYZ), but that the (4)]. In recent years, however, new methods have arisen, discrepancy jumps to about +1.1 mag outside the Local such as fits of the functions of planetary nebulae Group (DM > 26) and is practically independent of distance (PNLF) or ofglobular clusters (GCLF) and the power spectra in the interval 1.5 < A < 83 Mpc (Fig. 1). On the contrary, of luminosity fluctuations in elliptical galaxies and in the the short scale shows no significant progressive departure spheroidal components of lenticular and early-type spirals, from the others scale over the whole interval 0.05 < A < 83 which are apparently immune to Malmquist bias. Also, some Mpc and a barely significant, constant zero-point error of classical indicators, such as cepheids, novae, and the bright- -0.04 mag both inside and outside the Local Group (Fig. 2). est red and blue supergiants, have recently been applied to The conclusion seems unavoidable that the main cause of more distant galaxies than hitherto. There is now a large the dichotomy between the short and long scales is not so enough body of distance determinations based on different much a large progressive Malmquist bias in the short scale methods used by separate groups of astronomers to allow than a large zero-point error in the long scale, with an objective tests of the distances previously estimated on the unexplained discontinuity between galaxies inside and out- long- and short-distance scales. side the Local Group. Further, for individual galaxies at DM > 26, the standard deviations from the means are large between the long and short scales (0.46 mag) and between the The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact. Abbreviations: pc, ; mag, magnitude. 4811 Downloaded by guest on September 29, 2021 4812 Colloquium Paper: de Vaucouleurs Proc. Natl. Acad. Sci. USA 90 (1993) Table 1. Comparison of mean distance moduli ST (n) GV (n) XYZ (n) ST-GV ST-XYZ GV-XYZ LMC 18.69 (2) 18.32 (5) 18.38 (55) +0.37 +0.31 -0.06 M 31 24.33 (3) 24.12 (5) 24.27 (13) +0.21 +0.06 -0.15 M 33 24.80 (4) 24.46 (8) 24.43 (15) +0.34 +0.37 +0.03 N3109 26.0 (1) 25.69 (1) 25.74 (2) +0.31 +0.26 -0.05 N 300 28.33 (1) 26.56 (8) 26.22 (11) +1.77 +2.11 +0.34 14182 28.3 (2) 26.95 (2) 27.0 (2) +1.35 +1.3 -0.05 N2403 27.66 (3) 27.18 (6) 27.29 (4) +0.48 +0.37 -0.11 N5128 29.30 (4) 27.62 (4) 27.61 (6) +1.68 +1.69 +0.01 M 81 28.70 (1) 27.82 (7) 27.72 (4) +0.88 +0.98 +0.10 M 101 29.20 (4) 28.40 (7) 28.67 (8) +0.80 +0.53 -0.27 M 104 31.21 (1) 30.02 (5) 29.97 (3) +1.19 +1.24 +0.05 Leo 31.14 (2) 29.98 (1) 30.00 (3) +1.16 +1.14 -0.02 N4571 31.70 30.93 (2) 30.90 (2) +0.77 +0.80 +0.03 Vir I 31.70 30.81 (14) 30.99 (23) +0.89 +0.71 -0.18 For I 31.86 (2) 30.88 (2) 30.76 (6) +0.98 +1.10 +0.12 Coma 35.60 (3) 34.31 (2) 34.58 (5) +1.28 +1.02 -0.27 ST, long scale; GV, short scale; XYZ, others scale; LMC, Large Magellanic Cloud; n, number of estimates.

Table 2. Unweighted means of mean and (median) DM differences Unweighted means and mean errors ST-GV ST-XYZ GV - XYZ Unweighted mean (DM < 26, n = 4) +0.31 (+0.27) +0.25 (+0.15) -0.06 (-0.07) Standard deviation 0.07 (0.07) 0.13 (0.13) 0.07 (0.06) Mean error of mean 0.04 (0.04) 0.07 (0.07) 0.05 (0.03) Unweighted mean (DM > 26, n = 12) +1.10 (+1.11) +1.08 (+1.08) -0.02 (-0.03) Standard deviation 0.38 (0.41) 0.48 (0.46) 0.17 (0.11) Mean error of mean 0.11 (0.12) 0.14 (0.13) 0.05 (0.03) Eight galaxies (26 < DM < 31) +1.12 (+1.12) +1.13 (+1.13) +0.01 (+0.01) Standard deviation 0.46 (0.50) 0.58 (0.55) 0.18 (0.09) Mean error of mean 0.16 (0.18) 0.20 (0.19) 0.08 (0.03) Four groups and clusters (30 < DM < 35) +1.09 (+1.07) +0.99 (+0.98) -0.09 (-0.10) Standard deviation 0.18 (0.18) 0.19 (0.21) 0.17 (0.12) Mean error of mean 0.09 (0.09) 0.10 (0.10) 0.09 (0.06) ST, long scale; GV, short scale; XYZ, others scale.

2.5 - -

2

1.5

1

a 4000

.5

0~~~ 0 - *.*% a 0 l -

-.5 III - 20 25 30 35 DM(XYZ) 0 20 40 60 80 100 FIG. 2. Modulus difference GV - XYZ versus DM(XYZ). Distance (Mpc) Note good agreement, small systematic and accidental differences, and absence of trend (i.e., Malmquist bias) over the 16 mag range FIG. 3. Velocity-distance correlation for 13 test objects in the from the Large Magellanic Cloud to the Coma cluster (0.05 < A < 83 interval 1.5-83 Mpc (Coma cluster at upper right). The straight line Mpc). corresponds to a mean Hubble ratio (H) = 86 km-sec-1Mpc-1. Downloaded by guest on September 29, 2021 Colloquium Paper: de Vaucouleurs Proc. Natl. Acad. Sci. USA 90 (1993) 4813

long scale and the others scale (0.58 mag), while the scatter 2. Aaronson, M. & Mould, J. (1983) Astrophys. J. 265, 1-17. between the short scale and the others scale is quite small 3. Tully, R. B. (1988) in The Extragalactic Distance Scale, eds. (0.16 mag), implying for the latter two scales remarkably Van den Berg, S. & Pritchet, C. J. (Astron. Soc. of the Pacific, small accidental errors (=0.1 mag) contrasting with much San Francisco), Vol. 4, pp. 318-328. larger errors (~=0.5 mag) for the long-scale values. 4. Pierce, M. J. & Tully, R. B. (1988) Astrophys. J. 330, 579- The mean Hubble ratio for 13 test objects in the interval 26 595. < DM < 35 is (H) = 86 ± 1 (internal m.e.) km sec-l Mpc-1 5. de Vaucouleurs, G. (1977) Nature (London) 266, 126-129. with no indication of departure from linearity (Fig. 3). This 6. de Vaucouleurs, G. (1977) Colloq. Int. Astron. Union 37, 301- agrees closely with values first reported 16 years ago (6-8). 307. 7. de Vaucouleurs, G. (1977) C.R. Seances Acad. Sci. Ser. B 284, 1. Rowan-Robinson, M. (1985) The Cosmological Distance Ladder 227-229. (Freeman, New York). 8. de Vaucouleurs, G. (1993) Astrophys. J., in press. Downloaded by guest on September 29, 2021