5 Discussion

We have determined the central velocity dispersion in 34 spiral galaxies. For 32 of them, we have presented profiles of the projected rotation velocity and velocity dispersion, along at least one main axis. Our data significantly increase the very limited amount already available in the literature: the compilations of McElroy (1995) and Prugniel & Simien (1996) indicate that the central velocity dispersion was so far published for 16 of these objects, and a rotation curve for only nine.

At variance with SP, we have not listed in Table 1 a maximum velocity of rotation $V_{\rm max}$. Knowledge of the maximum rotation velocity of the central bulge would be valuable as a constraint on its mass and dynamical status, but the influence of the disk is (in most cases) important, and even when a conspicuous inner "plateau'' is visible in the rotation curve, it cannot be connected to the bulge $V_{\rm max}$ in a dependable way. As for the disk maximum rotation, few of our spectra are deep enough to determine it (a small but significant difference with the gas rotation should be present).

Although applications to both bulges and disks can be considered, the present data are clearly biased toward the formers. It is thus relevant to ask the following question: How is $\sigma_0$ related to the kinematics of the bulge population? The answer is not straightforward, and several aspects of the problem have to be detailed, as below.

To begin with, a typical bulge is a fast rotator, compared to bright ellipticals; for our observations at intermediate or high inclination, at the very center, resolution effects (integration due to pixel and slit dimensions, atmospheric smearing) tend to widen the apparent line-of-sight velocity distribution (the LOSVD), thus increasing $\sigma_0$. The light from the colder disk, when superimposed on the bulge in sufficient quantity, has the opposite effect on $\sigma_0$. The resulting balance can be accurately determined if: a) a bulge+disk photometric decomposition is performed, b) a dynamical model is applied and integrated along the line of sight, and c) comparison to the observations is made with proper attention to the fact that the LOSVD of the model is likely non-Gaussian, since the two components, locally, show different rotational velocities as well as velocity dispersions.

This has recently been applied, for example, to edge-on S0 galaxies (Loyer et al. 1998), and this elaborate modeling is beyond the scope of the present paper. Instead, we have limited ourselves to a simpler estimate of the resolution and disk-contamination effects on the central bulge kinematics (see Appendix); as a result, we list in Col. (12) of Table 1 a factor $f_{\rm bulge}$ by which the bulge velocity dispersion, averaged within a tenth of its effective radius ($0.1 r_{\rm e}$), has been modified to give the observed $\sigma_0$. We note that $f_{\rm bulge}$ is close to unity, and that the correction is, for most bulges, marginal compared to the error bars of the present data.

We now stress two more points: first, although $\sigma_0/f_{\rm bulge}$ is intended to represent a physical kinematical parameter, it scales only a part of the total kinetic energy; from Binney (1978), and Prugniel & Simien (1994), we can estimate to $\simeq$ 20% the ratio of the rotational to the random kinetic energy for bulges of spiral galaxies. Second, detailed individual models can be significantly complicated by a barred or triaxial geometry; for most of these galaxies, isophote parameters can be found in HS96 for a previous check.

We will present in the near future similar data for a complementary sample of more recent observations, together with comparisons to other sources (Héraudeau & Simien, in preparation); we also plan to study relevant correlations and detailed kinematical modeling.

Acknowledgements

We are endebted to the telescope operators at the Observatoire de Haute-Provence for their help in collecting the data. We thank an anonymous referee for valuable comments on previous versions of the manuscript. We have made use of the Lyon-Meudon Extragalactic Database operated by the LEDA team.