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Astron. Astrophys. 322, 730-746 (1997)

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Kinematics of the Local Universe

V. The value of [FORMULA] from the Tully-Fisher B and log [FORMULA] relations for field galaxies

G. Theureau 1, M. Hanski 2, T. Ekholm 2, L. Bottinelli 1, 3, L. Gouguenheim 1, 3, G. Paturel 4 and P. Teerikorpi 2

1 Observatoire de Paris-Meudon, CNRS URA1757, F-92195 Meudon Principal Cedex, France
2 Tuorla Observatory, FIN-21500 Piikkiö, Finland
3 Université Paris-Sud, F-91405 Orsay, France
4 Observatoire de Lyon, F-69230 Saint-Genis Laval, France

Received 29 July 1996 / Accepted 9 December 1996


We have studied the value of the Hubble constant using the KLUN (Kinematics of the Local Universe) sample of 5171 spiral galaxies having isophotal diameters [FORMULA] (and partially B -magnitudes), H I line widths, and radial velocities. The sample is diameter-limited, complete down to [FORMULA] arcmin. As in the first similar study, where a much smaller magnitude-limited sample was used (Bottinelli et al. 1986), we pay special attention to the problem of Malmquist bias when photometric distances are derived by the Tully-Fisher diameter or magnitude relations. The bias is revealed and overcome by a more advanced version of the method of normalized distances, now taking into account, in addition to diameter and magnitude limits, also Hubble type effect, inclination effect, and variable galactic extinction.

Calibration of the Tully-Fisher relations is primarily performed using a sample of 15 galaxies with available Cepheid distances, mostly from the HST programmes. This sample does not show significant trends with distance and is concluded to be closely distance-limited.

Analysis of the [FORMULA] vs. [FORMULA] diagrams allows us to identify the "unbiased plateaus" for both the diameter and magnitude TF distances. A useful tool here introduced is the theoretical expectation of the bias in cumulative [FORMULA] as a function of the fraction of the sample accepted for the plateau. An iterative approach is utilized for determining the TF relations, the plateau, and the value of [FORMULA] therefrom.

Using the Peebles linear velocity field model with Virgo and our infall velocities equal to 980 km s-1 and 150 km s-1, respectively, we derived the following values of [FORMULA]:


from the magnitude relation, and


from the diameter relation.

The given [FORMULA] -errors refer to the statistical scatter around the adopted calibration, and the dispersion of the calibrator sample itself. These [FORMULA] values are not sensitive to reasonable changes in the kinematical parameters of the velocity field model, up to the extreme ones found in literature. This insensitivity is also expected from our numerical experiments. In the radial velocity space, the unbiased plateau extends up to about 6000 km s-1 and the value of [FORMULA] is in good agreement with the SNIa results by Sandage et al. (1996) which extend to still larger velocities. At present, the supernovae method and the KLUN TF-sample, both calibrated with Cepheid distances, provide complementary approaches to [FORMULA] in different, though overlapping, redshift ranges.

As an additional result, the normalized distance method provides a natural way to estimate the Local Group infall velocity by minimizing the [FORMULA] dispersion in the unbiased plateau. Using the diameter and the magnitude TF relations respectively, we obtained, as preliminary results, the following values:



These values are compatible with our standard value within [FORMULA] and agree particulary well with Sandage's preferred value [FORMULA] km s-1.

Key words: galaxies: spiral – galaxies: distances and redshifts – cosmology: distance scale

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998