*Astron. Astrophys. 322, 730-746 (1997)*
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## Kinematics of the Local Universe
### V. The value of from the Tully-Fisher
*B* and log 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*
**Abstract**
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 (and partially
*B* -magnitudes), H I line widths, and radial
velocities. The sample is diameter-limited, complete down to
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 vs.
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
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
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 :
from the magnitude relation, and
from the diameter relation.
The given -errors refer to the statistical
scatter around the adopted calibration, and the dispersion of the
calibrator sample itself. These 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 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 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 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
and agree particulary well with Sandage's
preferred value km s^{-1}.
**Key words:** galaxies:
spiral
galaxies: distances and
redshifts
cosmology: distance scale
© European Southern Observatory (ESO) 1997
Online publication: June 5, 1998
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