N. R. Tanvir
Institute of Astronomy, University of Cambridge, Madingley Road,
Cambridge, CB3 0HA, United Kingdom.
inferred (Tanvir et al. 1995).
Soon, Cepheid results will be available for two other
probable members of the Leo-I group, thus refining the distance
estimate.
Here we consider the
various secondary indicators which can be used
to step from the Leo-I group to more remote clusters
in order to determine 
.
Keywords: Hubble constant, Cepheids, Leo-I group
The long-running debate over the value of the Hubble constant has centered largely on the calibration and use of secondary and tertiary distance indicators. Such indicators are required to extend the distance ladder to a regime where peculiar velocities are small compared to recession velocities. By greatly increasing the range of Cepheid distance determination, HST is beginning to provide much more secure calibration of the secondary indicators.
The Leo-I group is the nearest group containing a mix of early- and late-type galaxies and is, therefore, a good location to set about the calibration of the various early-type galaxy distance indicators. It is relatively compact, has a small range in velocity and is at high galactic latitude. Most importantly, it contains a unique ring of intergalactic HI gas which is orbiting the central two E/S0 galaxies (NGC3379 and NGC3384) and exhibits a tidal tail apparently due to the passage of the spiral galaxy M96 (Schneider 1989). This fortuitous circumstance provides good evidence that M96 is indeed near the center of the group, and gives confidence that its distance can be taken to apply to the group as a whole.
To date, three Leo-I spirals have been studied
for Cepheids. The result for M96 itself gave a distance
modulus of 
mag (Tanvir et al. 1995; hereafter TSFR).
In passing we note that
this is somewhat higher than the 30.07 mag and 29.90 mag
inferred from Ciardullo, Jacoby & Tonry (1993; hereafter CJT)
for the PNLF and SBF methods, respectively, when calibrated
consistently in the M31 system, but is in excellent agreement with the new
SBF distance to NGC3379 of 
mag determined by
Sodemann & Thomsen (1996).
The other two spirals being studied for Cepheids are UGC5889, a small
galaxy close to NGC3377 (Tanvir et al. 1996, in prep.)
and M95 which is being observed as part of the HST distance
scale key-project (Freedman, this volume, p. 
).
Between them, these galaxies should provide an extremely
good distance to the group, with some indication
of the depth of the late-type members.
Figure: This flow diagram shows all the steps used by TSFR in deriving 
.
Each box represents a difference in distance modulus
between particular objects, shown as ellipses.
The two routes from Leo-I to Coma rely mainly on various early-type
galaxy distance indicators, namely the surface brightness fluctuation
(SBF), planetary nebula luminosity function (PNLF), globular cluster
luminosity function (GCLF), color-magnitude relation (CMR)
and 
methods.
Although the formal error on the weighted mean
in the Leo-I to Virgo step is
only 
2% TSFR allowed a larger uncertainty
to account for possible systematic effects.
such as those described in section 2.2.
The Coma cluster is assumed to be sufficiently remote
that the corrections to its velocity for peculiar motions
are small.
The reader is referred to TSFR for bibliographic details of
each indicator.
Stepping from Leo-I to Coma, TSFR infer a value for 
of 
(see figure 1).
A detailed discussion of the Cepheid photometry is the
subject another paper (Tanvir et al. 1996, in prep.).
Here we consider some of the
issues concerning the secondary indicators
which can be calibrated in the
Leo-I group.
The peculiar velocity of the Leo-I group is difficult
to determine, so to evaluate 
we must use secondary
distance indicators to step to more remote clusters.
Various secondary indicators can be calibrated in the Leo-I
group.
TSFR considered five secondary indicators based on early-type
galaxies, as is illustrated in figure 1.
The argument for using only the early-type galaxies as secondary
calibrators is that to use the
Leo-I spirals, other than M96, requires us to face again the difficulty
of assigning group membership to the late-type galaxies.
Early-type galaxies being more highly
clustered suffer much less from background
and foreground contamination,
and in the particular case of the Leo-I group there is
independent evidence placing
at least NGC3379, NGC3377 and NGC3384 at a common
distance (Ciardullo, Jacoby, & Ford 1989, Tonry, Ahjar,
& Luppino 1990).
Of course, M96 is itself another calibrator of
the Tully-Fisher relations.
Below we consider in more detail some of the issues
concerning type Ia supernovae, which TSFR did not
use, and the surface brightness fluctuation (SBF)
and planetary nebula luminosity function (PNLF)
methods, which they did.
Normal type Ia supernovae have been observed in two galaxies in
the Leo-I region, namely SN1967C in NGC3389 and SN1989B in NGC3627.
The estimated peak, extinction-corrected V-band magnitudes of these
supernovae are very different being 13.3 and 10.84,
respectively, (Leibundgut et al. 1991, Wells et al. 1994).
Even considering the large, and therefore
uncertain, extinction correction
in the case of SN1989B, of 
, the difference
between peak magnitudes alone shows
that both galaxies are not at the
same distance.
In fact, while both have been classed as group members
in some previous surveys of the region, neither galaxy
is in the set of ``high-confidence''
Leo-I members used by TSFR, as listed in Tanvir (1996).
Let us consider the evidence for and against the group membership of each galaxy:
This galaxy is located very close on the sky to the center of the
Leo-I group,
forming a tight triplet with the central
two E/S0 galaxies, NGC3379 and NGC3384.
Its heliocentric velocity is
v=1270
compared with
for the average of NGC3379 and
NGC3384 (data from de Vaucouleurs et al. 1991).
Some catalogues (e.g., Huchra & Geller 1982)
have included NGC3389 as a Leo-I group member
but latterly it is generally thought to be in
the background (e.g., Garcia 1993).
In fact, if NGC3389 were a group member then
SN1967C would have to have been underluminous by
mag for any reasonable SNe Ia calibration.
This galaxy forms a well known triplet,
with NGC3623 and NGC3628, some 
on the sky from the center of the Leo-I group.
Tully (1987) distinguishes the two groups,
calling them the `M66 group' and `M96 cluster',
respectively, and suggests they form part
of a larger, more amorphous structure
dubbed the Leo Spur.
Branch, Romanishin & Baron (preprint)
have noted that if NGC3627 is assumed to be at the
TSFR Leo-I distance, then the magnitude of SN1989B
agrees very well with the current Sandage et al. \
SNe Ia calibration (e.g., Sandage 1995, Tammann, this volume, p.
).
However, using the Tully-Fisher relation distances
given by Bottinelli et al. (1984) we
find the M66 group to be 
% closer
than the Leo-I/M96 group, although the uncertainties
are such that the possibility of both groups
being at the same distance is not ruled out.
For the present, then, we suggest that SN1989B only be used as a SNe Ia
calibrator with some degree of caution.
These two methods, suited primarily to application in
early-type (gE/S0) galaxies, are claimed to
be of very high precision, and hence are highly
weighted in the TSFR 
determination.
The PNLF method is based on measuring the bright end cut off
in the planetary nebula luminosity function, which
is assumed to be universal.
The SBF method relies on the measurement of fluctuations
in brightness across the face of elliptical galaxies
which are due to the counting statistics of individual
stars in each resolution element.
The evidence for high precision is based
on the good internal agreement of each indicator
for galaxies within groups and clusters
(Jacoby, Ciardullo & Ford 1990, Tonry 1991).
Both methods were also claimed to agree well with each other,
when calibrated in the M31/M32 system (CJT), but
more recent work places this calibration in doubt
(Méndez et al. 1993, Sodemann & Thomsen 1996).
However, Bottinelli et al. (1991) have pointed out that there is even a
small but significant difference between the two indicators
in their measurement of the distance ratio between the Leo-I group
and the Virgo cluster.
They suggest that this reflects a dependence of PNLF distances
on parent galaxy luminosity, which, if accounted for empirically,
changes the relative Leo-I to Virgo distance to
.
Bottinelli et al. argue that such an effect could be produced by a high luminosity tail
to the PNLF, however, CJT counter that this should actually
produce a dependence on surveyed luminosity rather than
total luminosity of the parent galaxy, something which is not seen.
In fact, because the PNLF galaxies in Virgo all have brighter absolute magnitudes
than those in the Leo-I sample, there is an equally good correlation
between 
and SBF distance.
Such a bias could be the result of problems in determining
the completeness level for the very faint PNe in Virgo.
Both possibilities are illustrated in figure 2.
We note that any problem is rather less likely to be with
the SBF distances, since the SBF method has been shown
to agree fairly well with other indicators out to higher
redshifts (Jacoby et al. 1992).
It is worrisome that such a discrepancy should arise in
galaxies of the same type (i.e., giant E/S0) and in the same
distance regime, however, we note that both
correlations are reduced somewhat if the three Fornax cluster
galaxies (CJT) are added.
Clearly further observations are necessary to resolve this conflict.
Figure: Comparison of SBF and PNLF distances
to individual E/S0
galaxies in the Leo-I group (closed symbols) and
the Virgo cluster (open symbols)
taken from results
compiled by Ciardullo, Jacoby & Tonry (1993).
The PNLF method finds the Leo-I to
Virgo distance to be systematically less than the SBF method.
The discrepancy is significant at
the 97% level given the quoted errors.
Empirical correlations are seen with
(a) parent galaxy magnitude (assuming SBF distances),
as previously noticed by Bottinelli et al. (1991), and (b)
SBF distance modulus. Distinguishing which of these effects, if either,
is fundamental requires more data.
We have argued that
the Leo-I group offers a particularly good stepping stone
to 
, by allowing calibration of the E/S0 galaxy secondary
distance indicators.
In general, the E/S0 indicators agree well with each other and benefit
from the predominance of early-type galaxies in cluster cores.
TSFR have used the HST Cepheid distance to M96 in the Leo-I
group to obtain 
.
Further, HST observations of Cepheids in another two Leo-I
galaxies will refine this estimate further.
There are some outstanding problems with the SBF/PNLF indicators, in that they appear to give small but significant differences in the Leo-I to Virgo relative distance. This discrepancy is important for the Leo-I group and also the wider distance scale controversy, but should be resolved by further observations. Finally, we urge caution in using SN1989B as a calibrator for the SNe Ia, given the line of sight uncertainty in the position of its parent galaxy NGC3627 relative to the core of the Leo-I group.
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