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King: One of the tightest correlations you showed was between Rmax and hR. What does Rmax mean, and is there any obvious reason for such a tight correlation?

van der Kruit: Rmax is the truncation radius. The tightness of the correlation results from the fact that over scalelengths in the range from 1 to 15 kpc or so, the truncation radius occurs at 3 - 4 scalelengths. I have commented on this in the paper above.

Byun: In the 1970 Freeman paper, disk galaxies were divided into two groups, type I and type II. Type II galaxies had exponential disks which do not continue into the centers. What are our current understandings of these type II galaxies?

van der Kruit: Although there still are some systems having profiles that were called type II, it appears that these no longer make up a substantial fraction of the observed profiles. The prime example, M83, is barred and the bar may be the cause of this behavior, but there are also galaxies that are unbarred and display the type II characteristic. But again it no longer is an important class in modern surface photometry profiles.

Fall: My impression is that realistic angular momentum distributions M(h) produced by hierarchical clustering do not have the sharp features that would lead to edges in the disks. My preferred explanation for the edges at Redge approx 4rdisk is in terms of local instabilities in the disks (Goldreich & Lynden-Bell and Toomre-type instabilities (2)). George Efstathiou and I showed these would give rise to Redge approx 4rdisk.

van der Kruit: I am aware of the Fall & Efstathiou (1980) explanation. Actually, in my third paper with Leonard Searle on edge-on galaxies (A&A, 110, 61, 1981) we refer to this and find that it predicts truncations at 0.8 ± 0.2 times the observed ones for our sample.

van der Kruit: After the session Mike Fall suggested that the conclusion that the maximum disk hypothesis does not apply to most galaxies using the disk flattening may be affected by underestimating the scaleheight due to the presence of stellar generations in the disks with a range in vertical velocity dispersions and scaleheights. The younger of these are brighter and their smaller dispersions lead to a lower scaleheight in the photometry than in the mass distribution. It is well-known that the observed diffusion of stellar random motions gives - according to observations in the solar neighborhood - a velocity dispersion proportional to sqrt[age] and Mike points out that the stellar generations therefore have a scaleheight proportional to age. I was urged by some participants to reply to this.
According to eq. (20) a systematic underestimate of the scaleheight hz results in an overestimate in the ratio Vmaxdisk / Vmax and allowing for it then takes the disks even further from maximum disk. However, the effect must also occur for the observed velocity disperions in face-on disks, so Bottema would systematically have underestimated the dispersions resulting in an underestimate of the coefficient in eq. (8) and (20). I have returned to some old notes to myself on this and updated these. In view of the potential importance of the effect I document this here.
The luminosity of a generation of stars as a function of age can be estimated in three ways. First look at the luminosity of the main sequence (MS) turn-off stars. The stellar MS luminosity is roughly proportional to M3 and MS lifetime tau to M-2. So luminosities LMS are roughly proportional to tau-3/2. Secondly, we may look at the giants only. I estimate from evolutionary tracks that at the tip of the giant branch the luminosity LGiant is crudely proportional to the mass on the MS (at least for stars between one and a few solar masses; MS lifetimes of 1 to 10 Gyr), so that LGiant propto tau-1/2. Finally, single burst models of photometric evolution can be used. A nice example is illustrated in Binney & Merrifield (Galactic Structure; Princeton Univ. Press, 1998) in Fig. 5.19 on page 318. The (M/L)B is proportional to age, so that the luminosity of a single burst LSB propto tau-1. This is -as expected- nicely in between LMS and LGiant.
To estimate the effect it is most practical to look at the integrated velocity dispersion in a face-on disk. The weighted velocity dispersion can then be estimated by integrating over the relevant ages tau in

Equation 22

To estimate the error this should then be compared to the case of equal weighing of the generations

Equation 23

We had sigma2 propto tau and may take for late type disks as a reasonable approximation a constant star formation rate SFR(tau).
In order to check the effect on the scaleheights the best approximation is to use LSB. The results depend on the range in tau we take to perform the integration. Since fits for hz are made above the dust lanes we need to ignore the youngest generations. As examples I take the integration from 2 and 3 to 10 Gyr ; this means ignoring generations in which the scaleheights are less than 0.2 and 0.3 times that of the oldest generations. The values for sqrt[<sigma>2] are then underestimated by respectively 9 and 6% and the scaleheights by 17 and 11%.
For the effect on the velocity dispersions we have to take LGiant, since thes are measured by comparing to a late-GIII or early-KIII template star. The galaxy spectra refer in practice for this mostly to interarm regions, so it is fair to take the lower limit in the integration now at 1 or 2 Gyr. Then sqrt[<sigma>2] is underestimated by respectively 8 and 4%. Even if the lower integration limit is set to zero (assuming red supergiants fit the luminosity class III template star), the error is only 18%.
So, the effects are small and furthermore in an application of eq. (20) we need to take the square root of the scaleheight, while the two effects work in opposite directions.

2 The references to the papers by Goldreich & Lynden-Bell (1965) and Toomre (1964) appear in Table 1 [PCvdK]. Back.

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