3.2. Inner slope values : astrophysical issues
The determination of the kinematical center, and the influence of non-circular motions on the rotation curves are also debated.
The rather irregular nature of some of the dwarf or LSB galaxies studied, and the faintness of particularly the near-infrared images makes the determination of the center of such galaxies difficult. Interestingly, HST data on central star clusters in late type spirals is available for a number of the galaxies used in the core/cusp studies, and comparison of these positions and the centers of the inner disks show agreement to within 1 - 2 arcsec (Böker et al. 2002).
For the galaxy IC 2574, I reanalyzed the HI data obtained by Walter & Brinks (1999), and deliberately varied the position of the center. In some cases I also carved up the galaxy into annuli, and allowed the center of each annulus to vary with respect to the next one. Despite the variation of the center positions with an r.m.s. scatter of about 250 pc, the determined slopes still come out to be -0.15 ± 0.38, well away from the fiducial NFW slope of -1.0.
Bars could contribute to non-circular motions in the inner parts, and thus lead to a poor quality rotation curve when long slit data are used, or when a two-dimensional velocity field is not properly analyzed. Swaters et al. (2003a) assert that bars in their long slit data sample predominantly have shallow slopes, but inspection shows that UGC 2259, UGC 4499, and UGC 5721, as well as F568-3 are also barred, in addition to the galaxies they identify as such. For the remaining unbarred galaxies, there is a wide variety of slopes. Swaters et al. (2003b) observed the galaxy DDO 39 with an integral field spectrograph yielding a twodimensional velocity field, which shows that the inner parts of this galaxy are affected by non-circular motion caused by a bar-like distortion. Several other studies of twodimensional H velocity fields are underway. Garrido et al. (2002) report on data obtained with a Fabry-Pérot instrument, and Bolatto (this meeting, see Simon et al. 2003) report on data obtained with an integral field spectrograph, combined with CO data obtained with BIMA. The results sofar for NGC 4605 and NGC 2976 are that the inner slopes are rather shallow, and that the non-circular motions are mainly in the inner parts.
One can look at bars in LSB galaxies in two ways: 1) they could be similar to bars in HSB galaxies, or 2) they could be just the response to the expected triaxiality of the dark halo. Since the reported non-circular motions are stronger in the inner parts for DDO 39 and NGC 2976, it seems likely that those galaxies behave like HSB's, where the disk is dynamically important in the inner parts. Yet it cannot be excluded that whole disks are elongated due to the triaxial halo. One way to study this further is to look at results of a Fourier analysis of velocity fields of a number of galaxies, performed by Schoenmakers (1999). From his work, I have collected the results on disk elongation in Figure 4a, which shows that the scatter in pot sin is larger for galaxies with smaller maximum rotation velocity. Thus disks in small galaxies could be globally elongated due to the forcing of a triaxial halo. Interestingly, the small galaxy with no elongation, NGC 247, was declared in Van den Bosch et al. (2000) "the only galaxy found [sofar] capable of limiting the slope of the dark matter profile". True enough, its slope is -1.02, close the the NFW slope, but perusal of Schoenmakers's results and a near infrared image show the presence of a bar, and a strong lopsidedness.
Figure 4. a) Disk elongation as function of Vmax, data extracted from Schoenmakers (1999) b) Disk mass fraction as function of Vmax, data from Kranz et al. (2003) with N4123 (left) and N1365 added. Faster rotators seem to have rounder disks, which are more self-gravitating.
In future, the effort will thus shift towards evaluating the importance of the disc component in LSB galaxies, using near-infrared surface photometry, and twodimensional velocity fields at high spatial resolution. Meanwhile, some evaluation of the importance of non-circular motions can be had by studying bars in HSB galaxies. Disk elongation can be constrained using the Tully-Fisher relation (Franx & de Zeeuw 1992). Early work on the barred spiral NGC 5383 (Athanassoula 1984) shows that the viewing angle is important : some angles are more favourable than others. Neither the mean rotation curve, nor the position velocity cut along the major axis can be trusted as a good representation of the true rotation curve, but the deviations scale with the strength of the bar. For the weak bars in LSB galaxies, it is not obvious how strong these effects are.