Kapteyn Institute

Thesis Summary

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This thesis consists of two main parts. The first part presents a series of theoretical and interpretative studies on the subject of the Tully-Fisher relation. We mainly focus on a better understanding of the physical basis of the Tully-Fisher relation. The second parts of the thesis presents the results of the new Westerbork HI observations of spiral galaxies. We study the HI properties and the Tully-Fisher relation of spiral and irregular galaxies based on these observations.

In the first part, we first analyse the dependence of the luminous mass-to-light ratio of spiral galaxies on the present star formation rate, and find that galaxies with high present star formation rates have low luminous mass-to-light ratios, presumably as a result of the enhanced luminosity. On this basis we argue that variations in the stellar content of galaxies result in a major source of intrinsic scatter in the Tully-Fisher relation. We have also analysed the relation between the (maximum) luminous mass and circular velocity, and find it to have small scatter. We therefore propose that the physical basis of the Tully-Fisher relation lies in a relationship between the luminous mass and circular velocity, in combination with a `well-behaved' relation between luminous and dark matter (Chapter 2).

We show that the errors in the Tully-Fisher relation are intercorrelated through inclination corrections, resulting in a lower combined scatter than the individual errors. Ignoring this effect could result in an underestimation of the intrinsic scatter in the Tully-Fisher relation. We discuss a compensation effect between luminosity enhancement due to stellar activity and luminosity dimming due to dust, which could result in a small apparent scatter in the TF relation because high star formation activity is associated with high dust content. We argue that the Tully-Fisher relation for the low surface brightness galaxies and IRAS mini-survey galaxies could also be the results of some compensation effect. We try to explain why the K-band Tully-Fisher relation does not show substantial improvement over the I-band Tully-Fisher relation by means of the error correlation and the compensation effect (Chapter 3).

We analyse the results of mass models derived from the HI rotation curves of spiral galaxies and find that the slope of the luminous mass-circular velocity relation is close to 4. The luminous mass-circular velocity relation with the slope of about 4 can be explained by an anti-correlation between the mass surface density of luminous matter and the mass ratio of the dark and luminous components. We also argue that the conspiracy between luminous and dark matter exists in a local sense (producing a flat or smooth rotation curve) and in a global sense (affecting the mass ratio of the dark and luminous matter), maintaining the luminous mass-circular velocity relation with the slope of about 4. We confirm our earlier proposal that the physical basis of the Tully-Fisher relation lies in the luminous mass-circular velocity relation (Chapter 4).

These results imply that the Tully-Fisher relation is a combination of two independent relations: (i) a relation between luminosity and (luminous) mass, based mainly on the star formation history in galaxies, and (ii) a relation between mass and rotation velocity, which is the outcome of the process of galaxy formation.

We analyse the shape of rotation curves by means of Principal Component Analysis and find that the first principal component accounts for about 80-90% of the total variance in rotation curve shapes. The first principal component behaves in a similar way at all positions within galaxies. The second principal component explains about 5-15% of the total variance, and mainly describes the variations of the central rotation curve: in case of a rise of the circular velocity in the central part of a galaxy, the outer part of the rotation curve falls. We have compared the principal components with the physical properties of the sample of galaxies and found that the first principal component is clearly related to the size parameters like the luminous mass of the galaxy and the second principal component is most likely related to the luminous mass density. We conclude that the first two principal components largely determine the shape of the rotation curve. We have constructed synthetic rotation curves based on the principal components: they are objective, comprehensive and widely applicable (Chapter 5).

In the second part, we first present new observational results from short HI observations of 60 late-type spiral galaxies with the Westerbork Synthesis Radio Telescope (WSRT). We present several HI properties, including the radial surface density distributions of HI and position-velocity maps. When possible these are compared to those measured from single-dish observations. We confirm earlier results that there is no serious systematic difference between the WSRT and single-dish observations in total flux and linewidths (Chapter 6).

We analyse HI properties of 108 galaxies based on the short HI observations with the WSRT and find that the HI diameter defined at 1 M_sun/pc^2 is larger than the optical diameter defined at the 25 mag/arcsec^2. The HI-to-optical-diameter ratio does not depend on morphological type or luminosity. The strongest correlation found is the one between the total HI mass and HI diameter with a slope of 2, implying constant mean HI surface density. The radial HI surface density profiles are studied using Principal Component Analysis. We find that about 82% of the variation in the density profiles of galaxies can be explained by two dimensions. The most dominant component can be related to `scale' and the second principal component accounts for the variance in the behaviour of the radial profile in the central parts of galaxies. The third component is most likely responsible for bumps and wiggles in the observed density profiles (Chapter 7).

We determine the rotation velocities of 108 spiral and irregular galaxies (XV- Sample) obtained from the first-order rotation curves from the position-velocity maps. To investigate the size of the random motion corrections, we compare the HI linewidths and the rotation velocities, obtained from the full HI synthesis observations for a sample of 28 galaxies (RC-Sample) and find that the most frequently used random-motion correction formulae (Tully & Fouqué, 1985, ApJS 58, 67) are not very satisfactory. We show that the rotation velocity parameters derived with these corrections may be statistically equal to the true rotation velocity but in individual cases the differences can be large. We analyse the Tully-Fisher relation for the different definitions of the rotation velocity parameters and inclinations, and find a significant reduction of the scatter in the Tully-Fisher relation for RC-Sample when the rotation velocities and kinematical inclinations derived from rotation curves are used instead of the random-motion corrected HI linewidths and optical inclinations. No such reduction in the scatter is seen for XV-Sample. The reduction of the scatter seems to be related to the use of two-dimensional velocity information: accurate rotation velocity and kinematical inclination (Chapter 8).

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