Received 13th March 1998
Abstract.
Although Milgrom's modified dynamics (MOND) can reproduce the rotation curves
for a large sample of spiral galaxies without invoking dark matter,
catastrophic ring instabilities could arise in the gaseous disc of rich-gas
dwarf galaxies, causing severe observational consequences.
Errors in the adopted distance and inclination corrections are unlikely
to account for this discrepancy.
1. Introduction
The modified Newtonian gravity (MOND) proposed by Milgrom (1983) to account
for the rotation curves of spiral galaxies continues without a definitive
observational contradiction.
On the contrary, MOND can match the shape and magnitude of more than 50
rotation curves.
This fact is surprising if one considers that for nearby dwarf galaxies,
MOND is able to reproduce the detailed rotation curve better than dark-halo
models for which this fine structure is diluted.
However, these analysis are restricted to fit the rotation curve regardless
of the stability of the gas.
In the present work, the MOND Toomre parameter for the gaseous component of
the low-mass galaxy IC 2574 is calculated.
Since Qg<1, catastrophic ring instabilities should arise
in the gas disc, destroying the smoothness of the H I
distribution and triggering star formation.
The exact value of Qg depends on the adopted distance.
However, it is shown that the disc is marginally stable only for the unlikely
distance of D < 2.0 Mpc.
2. The M/L ratio of the stellar disc
From Sanders (1996) the M/L required in the MOND fit for the nearby
(Sanders used D = 3 Mpc, see Sect. 4) gas-rich galaxy
IC 2574 is 0.13 (gas-dominated disc).
This value is only possible in an extreme starburst.
However, apart from the Halpha images of IC 2574 which
show clearly that the star formation is restricted almost to the northern
part of the bar, another evidence for the non-starburst condition is that
the star formation rate has been constant during the last 14 Gyr,
according to the calculation by Miller & Hodge (1994).
This length time for the star formation is not typical of starburst galaxies.
Therefore the MOND value of M/L for IC 2574 seems rather low.
3. The Toomre parameter in MOND
The MOND force, 
,
is related to the Newtonian force, 
through:
with µ (x) → 1 for g>>a0
and µ (x) → x for g<<a0.
For analytical purposes, it is usual to adopt the functional dependence
µ (x) = x (1 + x2)-1/2.
Milgrom (1989) deduced the Toomre condition for local stability of gaseous
discs, QgMO>1, where
QgMO is given by:
where κ is the epicyclic frequency, σg
the velocity dispersion of the gas, Σ the gas density and L
the logaritmic derivative of µ.
In Fig. 1 we plot
QgMO and QgNE
(in Newtonian dynamics) for the quite high value of σg
= 10 km s-1 (Σ and the rotation curve from
Martimbeau et al. 1994).
In the MOND case and for the adopted distance of 3.0 Mpc,
QgMO<1 at any galactocentric radius.
For that distance, either QgMO and
(M/L)MO are uncomfortable.
Due to the squared dependence with the distance of the gas mass,
it is possible to increase both values decreasing the adopted distance
to the galaxy.
D has been reduced systematically until stability is achieved in
the whole radius range.
This condition is fulfilled only if this galaxy is closer than 2 Mpc.
Then, the best MOND-fit requires M/Lsim;1.1 (see
Fig. 2).
Although M/L is in agreement with the estimates from the population
synthesis models of Larson & Tinsley (Miller & Hodge 1994), the
needed distance is outside the acceptable range.
[Click here to see Fig. 1 - 2!]
4. Distance estimate
No definitive distance to this galaxy has been obtained yet.
We have revised the independent measurements published in the last 15 years,
but none of them is based on a definitive method.
Anyhow, we count 8 measurements giving an average value of
3.3±0.8 Mpc.
In addition, there are strong evidence that IC 2574 belongs to M 81
group which is at a distance of 3.63±0.84 Mpc.
Therefore, the required distance for stability is not plausible.
5. Conclusions
In modified Newtonian dynamics most of the dwarf gas-rich galaxies might be
very unstable against axisymmetric local perturbations in the gaseous
component.
The general trend in the MOND theory of arbitrarily lowering the distance
to these galaxies to recover stability and more plausible values of the
stellar mass-to-light ratios is not satisfactory.
Acknowledgments.
One of us, A.M.H.G., thanks to Dr. N. Bergvall for financing her attendance to
this workshop.
This research made used of the NASA/IPAC Extragalactic Database (NED) which is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration.
A.M.H.G. is financially supported by NOTSA.
References
- Martimbeau N., Carignan C., Roy J.-R., 1994, AJ 107, 543
- Milgrom M., 1983, ApJ 270, 371
- Milgrom M., 1989, ApJ 338, 121
- Miller B.W., Hodge P., 1994, ApJ 427, 656
- Sanders R.H., 1996, ApJ 473, 117
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| First version: | 06th | 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)