Astron. Astrophys. 345, 36-42 (1999)

3. The low-mass galaxy IC 2574

IC 2574 is a low-luminosity galaxy () (Hidalgo-Gámez & Olofsson 1998) classified as a SXS9 by de Vaucouleurs et al. (1991) and as 9X by Tully (1988). Although this galaxy is classified as a barred spiral in both catalogues, some authors have considered it as a blue compact/irregular dwarf (Masegosa et al. 1991; Miller & Hodge 1994). The spiral arms, if any, are small with almost no star-formation regions. From the HI synthesis observations (Martimbeau et al. 1994), the rotation curve rises slowly, reaching a maximum rotational velocity of 67 kms. The inclination is comfortably high (). Non-circular motions are the main source of uncertainties in the inner part.

The neutral interstellar medium of IC 2574 has been extensively studied by Walter & Brinks (1998) from observations with the NRAO Very Large Array with a spatial resolution of 70 pc. Although the HI velocity map is dominated by expanding holes and shells, Walter & Brinks (1998) have been able to infer a HI line-width of km/s by looking at quiescent regions and averaging several lines of sight. This value is very similar to those found for other galaxies (e.g. Puche et al. 1992; Dickey 1996; Olling 1996). Interestingly, the HI holes observed in the disc are circular in shape. This can be interpreted as a consequence of the solid-body rotation curve and the absence of strong spiral density waves (Walter et al. 1998).

We are now in a position to calculate the Toomre parameter for the gaseous component of this galaxy under MOND dynamics.

3.1. Local stability of IC 2574

Dwarf galaxies have received considerable attention because it is thought that features in the interstellar medium are longer lived than in spirals. In particular, the circular shape of the HI holes in IC 2574 would lead one to think that IC 2574 is presumably rather stable against large-scale gravitational perturbations.

In Fig. 1 and are plotted in the infinitesimally thin disc approximation, valid because of the relation with (Milgrom 1983). A distance to this galaxy of 3.0 Mpc has been adopted for a direct comparison with previous works. In the MOND case for the most galactocentric radii even with the high adopted of 10 km/s. From this figure it can be concluded that for the adopted distance, the interstellar medium would be very unstable and form rings which would produce catastrophic consequences for the survival of the HI disc.

Fig. 1. The Toomre parameter of the gas component of IC 2574 versus galactocentric radius at different adopted distances (h is the scale-length of the disc and km/s). For D = 3.0 Mpc in MOND (solid line) and in Newtonian dynamics (dashed line), and for D = 2.0 Mpc in MOND (dotted line).

The most unstable wavelength appears at

Thus, the unstable scale is so large that the dispersion relation should be modified to include curvature terms. Nevertheless, it is worthwhile keeping in mind that the WKB results for axisymmetric waves are reasonable for discs under Newtonian dynamics providing .

The corresponding growth time is

where is the orbit time and, for simplification, the superscript MO in has been suppressed. This time-scale for the development of instabilities is significantly shorter than the orbit time, so that the unstable region will respond stronger and faster to this instability than to any potential swing amplification sometimes called global instability. In a few orbit times a large open spiral or a large-scale asymmetry is expected to appear along the galaxy. The early stages of the instability described by the WKB approximation are not different from the case of a massive disc under Newtonian dynamics with the same value of (Milgrom 1989). The observational consequences of such a gravitational instability was discussed by Elmegreen (1996). The further evolution of the disc to these modes is a complicated task because it is non-linear and should be investigated with numerical simulations and the inclusion of star formation. In any case, the predicted distortions in the HI-disc discussed above are in contradiction with the general appearance of the HI distribution in IC 2574. Presumably, the circular shape of the holes reflects the level of stability of the disc. At the very least, this fact confirms the hypothesis that holes, shells and rims have their origin at small-scales and they have no any physical connection with the type of instability we are dealing with.

An important remark must be done at this stage. In calculating we used for the value at the equatorial plane, say , which is strictly valid provided that . The latter requisite is also needed in order to obtain the gravitational acceleration using only the radial component of Eq. (2). As far as we know, all MOND fits to rotation curves available in the literature have been carried out disregarding this point. In the case of IC 2574, the radial and vertical accelerations are comparable in magnitude and, therefore, both the fit to the rotation curve and the Toomre parameter should be recalculated. Nevertheless, it is straightforward to check that the Toomre parameter remains approximately the same. In fact, the ratio between the value of after solving Eq. (2) including the vertical acceleration and the value used here is approximately the same that the ratio between the respective surface densities. In the deep MOND limit, this ratio is

where are the radial and vertical accelerations, respectively.

3.2. Decreasing the distance to IC 2574

Different authors suggest different distance estimates to this galaxy. If IC 2574 is closer than the adopted distance ( Mpc), the contribution of the gas to the potential decreases. In this way, it is possible to increase simultaneously the Toomre parameter of the gaseous disc and the stellar mass-to-light ratio until the axisymmetric stability is achieved. From the independent measurements published in the last 15 years, 8 of them were retained here giving an average value of 3.3 0.8 Mpc. Except for the estimate suggested by Bottinelli et al. (1988), the values range between 2.7 and 4.1 Mpc. Moreover, there is strong evidence to believe that IC 2574 belongs to the M81 group which is at a distance of 3.63 0.84 Mpc.

In Fig. 1 the Toomre parameter is also plotted for the case of a significantly lower distance of, say Mpc. Then the gaseous disc becomes self-gravitating with . This is a conservative value if one considers that the observed is lower than 10 kms (for the inferred value of 7 km/s, IC 2574 would be marginally unstable even at Mpc) and that the circular shape of the HI holes is an indication of the degree of large-scale gravitational stability. The assumption 2.0 Mpc alleviates partially the stability problem of the gaseous disc but other concerns arise. In fact, it must be noticed that the needed distance is well outside the acceptable range. But additionally, since the density of the stellar mass must be increased to fit the observed rotation curve, the local stability of the combined gas plus star is suspect. An effective Q-parameter, , was suggested by Elmegreen (1995) when both stars and gas contribute.

For low-luminosity galaxies the parameter is problematic because of its dependence on the stellar velocity dispersion which has not been directly measured because of their low surface brightness. Nevertheless, the young stars borning in the disc from the gas must have the same velocity dispersion than the gas. The stellar velocity dispersion increases with time by dynamical heating mainly caused by scattering of the stars with spiral waves and with giant molecular clouds. Thereby, the stellar velocity dispersion of dynamically low-evolved discs, such as that of IC 2574, may not be appreciably different from the velocity dispersion of the gas component. Besides these arguments, it appears that, from a sample of 12 disc galaxies, the magnitude of the stellar velocity dispersion is proportional to the square root of the surface density, and that larger and more massive discs have larger velocity dispersions (Bottema 1993). An extrapolation of the observational data gives a typical stellar velocity dispersion at one scalelength of 12 5 kms for this galaxy. If such extrapolation is confirmed, for any distance D. More precisely, would be typically 0.6 at intermediate galactocentric radii even for Mpc. Molecular gas which is expected to be present in self-gravitating discs also contributes to increase the level of instability because of its low velocity dispersion. Generally speaking, the stability of IC 2574 under MOND dynamics is doubful at any D.

In Fig. 2 the best MOND fit for Mpc is plotted but the fit is not as good as for Mpc (see Sanders 1996). The need for decreasing the distance to gas-rich galaxies could have dramatic consequences to the attributed capacity of MOND to reproduce the fine structure of the rotation curves which was a good point in its favour (Begeman et al. 1991; Broeils 1992).

Fig. 2. The observed rotation curve for IC 2574 together with the best fit for an adapted distance of D = 2.0 Mpc ().

Errors in the adopted inclination, non-circular motions and the beam-smearing effect are the main sources of uncertainties in the HI rotation curve. Because of the high inclination of IC 2574, uncertainties on the inclination do not affect appreciably the inferred rotation curve. Of course, the abundant dust in gas-rich galaxies could hide the intrinsic axis ratio of the disc (de Grijs & van der Kruit 1996). Although this is an important point in general, reducing consequently the inclination to (Tully 1988) alleviates only partly the problem of stability. For the difference in is very small compared to the accuracy with which is estimated. This argument is also valid for other sources of uncertainties in the rotation curve.

Notice also that it is not possible to increase consistently by assuming a lower value of .

3.3. Magnetic support

It turns out that errors in the adopted distance cannot be invoked to reach more reasonable levels of stability. Given this situation it is important to find other routes for stability.

Large-scale azimuthal magnetic fields, , may contribute partly to stabilize radial perturbations. In the presence of such a magnetic fields, the Toomre parameter is

where is the Alfvén velocity. So that, we have

For the particular case of IC 2574 at Mpc, with M/pc² and for a relatively intense magnetic field of G, the Toomre parameter becomes 1.3 times higher. However, since IC 2574 is nearly pure gas in MOND, the one-fluid Q-parameter is a monotonic indicator for non-axisymmetric instabilities (Binney & Tremaine 1987) even though it was derived for axisymmetric instabilities. This means that although a strong azimuthal field can contribute to stabilize radial perturbations, it is not able to inhibit azimuthal instabilities.

© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999
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