Received 11th March 1998
Abstract.
We present the Near-IR
(K'-band, i.e.: λeq = 2.1 µm)
Tully-Fisher (TF) relation for 50 giant and dwarf late-type galaxies
of the Virgo cluster.
We find that L ∝ VMax4 for dwarf,
faint, slow rotators as well as for giant, bright, fast rotators.
The present slope is in agreement with the recent results
on the Near-IR Fundamental Plane for disk systems
and with the scenario of self-regulation of star formation in disks.
1. Introduction
The origin of the relation between the maximum rotational velocity
and the luminosity of giant high surface brightness
late-type galaxies (Tully & Fisher 1977) is still debated.
Aaronson et al. (1979) gave an ``a posteriori'' justification
of the Near-IR TF law (L ∝ VMax4),
based on the virial theorem and the three following assumptions:
- ``all galaxies have the same mass profiles and rotation curves
as a function of some dimensionless scale-length'';
- ``all galaxies have the same central mass surface density'';
- ``all galaxies have the same mean M/L''.
Some of the previous seminal ideas have been restated by Burstein et al.
(1997), who claimed that the Tully-Fisher relation is a projection
of the so-called κ-space three-dimensional parameter
system of the late-type galaxies.
However, Silk (1997) has proposed a scenario of self-regulated star formation
for disk systems explaining the (B-band) TF relation,
without any dynamical assumption.
In the present work we extend previous determinations
of the Near-IR (NIR) TF relation
to dwarf galaxies
and discuss the two hypotheses of its origin.
2. Results and Conclusions
K'-band imaging of a complete sample of 84 VCC
(Binggeli et al. 1985) member (Binggeli et al. 1993)
dwarf and giant galaxies later than S0a, with
BT≤16 mag,
was obtained by Boselli et al. (1997).
From the latter sample we selected 50 objects (24 with 1≤T≤8
and 26 with 9≤T≤11) according to the following criteria:
- 35°<i<80°;
- no interacting system;
- H I linewidths (W, i.e.: full width at 20%
level of I/Imax) with σW/W < 1/3
(see Pierini & Tuffs 1998 for H I references).
Near-IR magnitudes (at the isophotal diameter D25)
are taken from Boselli et al. (1997)
and corrected for Galactic and internal extinction.
The equation of the Tully-Fisher relation, obtained through a bivariate
least-squares fit algorithm, is:
K' = -9.82 (±0.13)·log(V)+30.06 (±0.25),
when turbulent and z-motion corrections are not applied
(Fig. 1).
We want to emphasize the following results:
- the linearity of the NIR TF relation seems to prevail over a range
of 8 magnitudes, for galaxies with different phenomenologies, structures,
and, perhaps, age and metallicities (see
Fig. 1);
- the present slope of -9.81±0.13 is fully consistent with the
derivations of the Near-IR TF relation for giant spiral galaxies in
the literature, e.g: Aaronson et al. (1979) (-9.67±0.24),
Kraan-Korteweg et al. (1988) (-9.81), Pierce & Tully (1988)
(-9.25±0.43), Peletier & Willner (1993) (-10.2±0.6).
[Click here to see Fig. 1!]
The existence of the L ∝ VMax4 law in
the Near-IR is confirmed by the distribution of galaxies within the NIR
(H-band, i.e.: λ = 1 µm)
κ2 - κ3 plane
(where κ2 ∝ log(M/L·Ieff3) and κ3 ∝ log(M/L)), shown in
Fig. 2
(see Pierini & Tuffs for its derivation).
However, the present slope is also consistent with the scenario of Silk (1997).
In fact, assuming that
LK'∝VMax4 and
LB ∝ VMax2.1
(Silk 1997), it follows that
ΣB∼0.5 ΣK'
(where Σ is for the mean surface brightness within D25),
as shown in Fig. 3 for our sample.
[Click here to see Figs. 2 and 3!]
On the basis of the present data, we cannot exclude the possibility
that the two building blocks for the physical basis of the Tully-Fisher
relation (dynamical equilibrium and self-regulated star formation) are
independent.
References
- Aaronson M., Huchra J., Mould J., 1979, ApJ 229, 1
- Binggeli B., Sandage A., Tammann G.A., 1985, AJ 90, 1681
- Binggeli B., Popescu C., Tammann G.A., 1993, A&AS 98, 275
- Boselli A., Tuffs R., Gavazzi G., Hippelein H., Pierini D., 1997,
A&AS 121, 507
- Burstein D., Bender R., Faber S.M., Nolthenius R., 1997,
AJ 114, 1365
- Kraan-Korteweg R.C., Cameron L.M., Tammann G.A., 1988, ApJ 331, 620
- Peletier R.F., Willner S.P., 1993, ApJ 418, 626
- Pierce M.J., Tully R.B., 1988, ApJ 330, 579
- Pierini D., Tuffs R., 1998, in preparation
- Silk J., 1997, ApJ 481, 703
- Tully B., Fisher J., 1977, A&A 54, 661
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| First version: | 02nd | August, | 1998
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| Last update: | 30th | September, | 1998
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Jochen M. Braun &
Tom Richtler
(E-Mail: jbraun|richtler@astro.uni-bonn.de)