CONCATENATED DISCUSSIONS %========= Sylvia Becker \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Puls:} When I see the beautiful results which Ivan has presented, I ask myself -- since I have to code all this at some time [laughter] -- what is the advantage of your very detailed input with respect to his `packing' of the levels? He had very nice results in respect of the profiles. \noindent{\bf SB:} I think he uses the packed levels for his structure calculations, and he needs the full data for his spectral synthesis..? [Turning to Hubeny.] \noindent{\bf Hubeny:} No, the nice point is that there's no difference between structure and line formation; everything's done together. The reason I have to use ODFs is that, even with ODFs, there are already 18\,000 frequency points. \noindent{\bf Puls:} But in non-LTE you had 30 levels or so, isn't that right? The inversion of 30 levels is much easier than the inversion of 800 levels! \noindent{\bf SB} [showing impenetrably dense Grotrian diagram]: It will be possible to pack these levels -- in fact I have the packed levels -- but for the line-formation step, in {\sc detail} as it is, I have to be a bit more careful how I go about it. \noindent{\bf Puls:} But apart from this, you see no advantages in using the full data? \noindent{\bf SB:} Not necessarily. \noindent{\bf Hubeny:} The general question is not so much should you pack levels -- there has always been some sort of packing, even in C\,{\sc iv} you always pack fine-structure levels anyway, so it's not something new -- but how you treat individual lines. Opacity {\it sampling}\/ is a bit tricky because the doppler width is so small, and unless you had a very large turbulent velocity you'd have to use something like 0.01{\AA} resolution instead of 0.1{\AA}. I'd also like to ask, do you think titanium might be important for the structure? Why did you choose Ti\,{\sc ii}? \noindent{\bf SB:} Because when I'd modelled all the Fe\,{\sc ii} lines in my spectra, everything that was left was Ti\,{\sc ii}! And Fe\,{\sc i}, which is the other important spectrum to look at, is more or less done. \noindent{\bf Prinja:} How did you constrain the velocity fields? \noindent{\bf SB:} At the moment, the velocity-field structure is an input, provided by Adi's models. \noindent{\bf Kudritzki:} It's possible to analyse the H$\alpha$ profile for this. Particularly for the A~supergiants which have well-pronounced P-Cygni profiles, you can get information about both $v_{\infty}$ and the $\beta$ index. %========= Bruce Bohannan \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Langer:} Bruce, I remember from playing with those mass-loss formulae that there's a dependence on chemical composition; and we know that the slash stars are extremely helium rich. Did you take that into account when you calculated the mass-loss rates? \noindent{\bf BB:} We did, and moreover the slash stars aren't significantly more helium rich than the peculiar O-type supergiants that we're using as comparisons. Together with the WN9ha stars, they're something like five times solar. \noindent{\bf Maeder:} Ignoring rotation, ignoring mass loss, it's very clear that the helium enrichment alone implies an overluminosity. Either mass loss or rotation could bring that about; do we have any evidence concerning the rotation of the slash stars? \noindent{\bf BB:} Well, we don't see the photospheres, so we have absolutely no idea about that. But let me return to the point that these stars are no more helium enriched than some types of O~star; so whatever happened in their evolution brought them to the same effective temperature, the same luminosity, and the same helium abundance, but quite different terminal velocities and hence {\it quite different masses.} \noindent{\bf Schmutz:} You're probably aware that Claus [Leitherer] and I played the same game when we were in Boulder, not for so many stars but for a few of them, and we got out these low masses. And then, of course, I ran my wind model to see if I could get the winds; but as soon as your wind model is better than the old CAK model, you realise that you can't start these winds -- basically, you run into the old Wolf-Rayet problem. So I think these results don't have any significance, because we don't understand the winds well enough to make these inferences from them. \noindent{\bf BB:} Well, let me go back to the basic physics: the fundamental point is that the terminal velocity is related to the escape velocity, which scales with $M/R$. Doesn't the low terminal velocity then imply a lower mass than the other WN9 stars? [Several responses of ``Not necessarily''.] \noindent{\bf Walborn:} I think the idea that you can get a mass from wind parameters rests on the assumption that for a given mass you have a unique wind structure, and that's not true. My understanding is that the terminal velocity is lower for a denser wind. Now suppose a star of given mass could have two different wind states; the denser one would give a lower terminal velocity, and you'd infer from that too low a mass. This may be related to the `bistability' mechanism in objects like P~Cygni. HD~152408 and 151804 are examples of stars with low terminal velocities from which you'd get too low a mass. \noindent{\bf Kudritzki} [to Walborn]: I think I disagree here. Although the bistability mechanism can have the effects you describe, the fact that the terminal velocities shown in Table~XXX are {\it that}\/ low can {\it only}\/ be explained if you have objects close to the Eddington limit; and if you then compare with objects of similar temperature and luminosity the only explanation is that the masses are much lower. [Turning to Schmutz.] And you say that you were unable to reproduce these winds with your models, but we heard the talk yesterday by Uwe [Springmann], and using the same method as you he is now able to get these winds. \noindent{\bf Schmutz:} No no, he was not able to show he could reproduce these winds; he was playing some games, and he has only shown that with those games he can do it. \noindent{\bf Kudritzki:} Well, I'm pretty sure that the method works; there's obviously a discrepancy between your older results and Uwe's results, and it has to be resolved why you were not able to reproduce these winds and he is. I wouldn't stand here and say that just because I wasn't able to get a wind for this kind of object in '93, it isn't possible -- there's always a chance that something was wrong with your calculations. The fact that these objects in general have such small terminal velocities makes me think that, well, of course the masses are less; I would buy this interpretation. \noindent{\bf Schmutz:} The basic mistake is to assume you have a line-driven wind here. If you have such a line-driven wind then your remarks apply; but my {\it new}\/ models can't produce these winds, so what I'm saying is that the wind isn't started in the line-driven regime. If we have a different physics to start the wind, the $v_{\rm esc}/v_\infty$ relation doesn't apply any more. \noindent{\bf Kudritzki:} Well, I understand what you're saying, of course; you can say it's a god-driven wind{\ldots} \noindent{\bf Schmutz:} You can say it's probably a {\it continuum}\/-driven wind. \noindent{\bf Nota} [as Chair]: I think this will be a very interesting discussion -- over lunch! [Laughter.] %========= Peter Conti \centerline{\rm Discussion}\medskip \noindent{\bf Kudritzki:} What's the minimum useful spectral resolution? \noindent{\bf PSC:} 1\,200 is a sort of `optimimum minimum'; 800--900 is pretty marginal, but of course if you can go higher, so much the better. And the S/N needs to be at least 70, even with $R\simeq 10^3$ -- 30 isn't going to do it. \noindent{\bf Langer:} Does this work provide some clues for the theory of the formation of O stars? \noindent{\bf PSC:} Yes, it ought to. To remind you, in M17 we found 5 stars that have CO emission, which almost certainly means a disk. Those stars have luminosities corresponding to a mass range of late-O to early-B ($\sim$10--20$M_\odot$; we didn't go much below about 10$M_\odot$). Now, we found a bunch of early O~stars that don't have any evidence of disks, so it {\it appears}\/ that the earliest, most massive O~stars have the disk phenomenon behind them (or possibly it didn't happen, although I think that's less likely). We also have 4 objects with no lines, which we also interpret as having disks but no CO emission; just about all these stars have IR excesses. \noindent{\bf Langer:} What about radio emission? I always though about O~stars being labelled as these ultracompact H$\;${\sc ii} regions\dots \noindent{\bf PSC:} I think in M17 we're after the ultracompact phase. Margaret [Hanson] will talk about the ultracompacts. \noindent{\bf Kudritzki:} Are you able to say something about rotational velocities? \noindent{\bf PSC:} No, we'd like to do that but we really need higher spectral resolution -- it would take $R\simeq3\,000$--4\,000. \noindent{\bf Najarro:} What is the longest wavelength you're reaching? \noindent{\bf PSC:} Some of the things we were getting were down towards 2.3$\mu$m. \noindent{\bf Najarro:} Okay, you're getting the N$\;${\sc iii} line at 2.2\dots2.25. [XXX Unintelligible sentence concerning various lines.] \noindent{\bf PSC:} What's the wavelength of it? \noindent{\bf Najarro:} [Cautiously] Two point {\dots}four{\dots}seven or so; well, 2.5. %========= Paul Crowther \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Kudritzki:} When considering emission-line strengths in nebulae around WRs, stellar models which include line blanketing fix some problems, but, as your Table~2 shows, still leave some helium lines in error by more than a factor of 10. \noindent{\bf PAC:} Yes, that's a known problem{\dots}Linda, do you want to comment? \noindent{\bf Smith:} The electron temperature of a given nebula is known, and in some cases indicates that most of the helium is neutral and unobservable. The helium abundance then becomes a free parameter, and you can get agreement just by adjusting the abundance until the He\,{\sc i} line intensities are correctly reproduced. This hasn't been done for the table that Paul showed. \noindent{\bf Schmutz:} Paul, in Bali I pointed out that there's always a problem with the 1.0124-$\mu$m He\,{\sc ii} line. Has this gone away, or is it still there? \noindent{\bf PAC:} Still there. As you mentioned in Bali, it's not there for the very hot WNE stars, but it is for the cooler WN stars. \noindent{\bf Gies:} Alex Fullerton has shown that He\,{\sc i}~5876{\AA} shows huge variations in HD~152408. When you modelled that star, did you use just a single spectrum? \noindent{\bf PAC:} `Fraid so! We're trying to get more observations. \noindent{\bf Owocki:} Another TAC problem! %========= Alex de Koter \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Crowther:} I think we need to be very careful when we talk about `Wolf-Rayet' and `Wolf-Rayet-like' stars. If we observe something to have a Wolf-Rayet spectrum shouldn't we call it a Wolf-Rayet star, and not rely on evolutionary definitions? \noindent{\bf AdK:} Yes{\ldots}just to clarify, this isn't a WR star from the point of evolution. \noindent{\bf Maeder:} Would it be possible to know where on your empirical isochrone you have an N/C ratio enhanced with respect to cosmic? This would be a very strong constraint on models{\ldots}I know when people present data like yours there is always someone asking for more\ldots [laughter]. \noindent{\bf AdK:} The method of using O\,{\sc v} to determine the temperature clearly also depends on the abundance. With increasing initial mass, at some point you would expect to see oxygen depletion and nitrogen enrichment. I think you can see that by looking at the O\,{\sc iv} and O\,{\sc v} lines at the same time. I can always fit the O\,{\sc v} line, obviously, just by changing the temperature, but I also have to fit O\,{\sc iv}. It always works out for these stars, except for the most massive ones, when I predict too-strong O\,{\sc iv}, which implies that in reality oxygen is being depleted. So for about 60 or 65$M_\odot$, at 2~million years, there may be some depletion. \noindent{\bf Langer:} The abundances are related to mixing, and there is an interesting point here, which is that if we consider stellar-evolution models which include rotational mixing we would not expect isochrones to be single lines any more, but rather we expect some scatter corresponding to scatter in the original rotation rates of the stars. When you showed you HR diagram you didn't show any error bars; can you say whether the scatter you see is `serious', or is it just observational error? \noindent{\bf AdK:} The uncertainty in temperature is around 2\,000$\;$K; the scatter is therefore mostly just observational error. \noindent{\bf Becker:} When you get a fit to the oxygen lines, the silicon doesn't seem to fit at all\ldots{?} \noindent{\bf AdK:} It's interstellar. \noindent{\bf Kudritzki:} Just a comment concerning the results on mass-loss rates; these are not especilly well suited to comparison with theory, as they depend on how well you have determined the stellar parameters. If you use wind {\it momentum,}\/ that depends on luminosity only. Therefore it's better to compare the wind momentum, rather than mass-loss rate, with the predictions of theory; then you take out details of sensitivity to gravity determination, for instance. \noindent{\bf Walborn:} I think it might be useful to point out (since I know what's coming in Massey's paper) that, in terms of ultraviolet wind morphology, if you see an O\,{\sc v} line, then you have an O3 star. So what you've found, from the UV features alone, is that they're all O3 stars. %========= Janet Drew \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Owocki:} I'd like to ask a little bit more about the actual driving mechanism. The radiation is coming off the disk itself? \noindent{\bf JED:} No, the disk luminosity generated by accretion isn't enough by itself to do the trick. We're using a simple algorithm which turns the {\it stellar}\/ radiation incident on the disk into a reprocessed luminosity, and that gives the disk wind. \noindent{\bf Owocki:} Okay{\ldots}na\"{\i}vely at least, I'd expect the inner disk to lose mass after a while, just because that's where most of the wind is coming from; is it resupplied? \noindent{\bf JED:} Yes, it's an active disk in the sense that it has an accretion rate. \noindent{\bf Owocki:} Then don't you need to match things up pretty nicely at the disk/star boundary? \noindent{\bf JED:} No, the accretion luminosity is relatively minor, so the disk is `passive' in that sense. Also, the disk accretion rate exceeds the disk-wind mass-loss rate by something like two orders of magnitude. \noindent{\bf Conti:} Janet, you mentioned that high-mass YSOs don't have jets. What's the evidence on that? Or is it a lack of evidence? \noindent{\bf JED:} Essentially, lack of evidence -- any good jet you care to mention will be associated with a low-mass object\ldots \noindent{\bf Hanson:} DR21? \noindent{\bf JED:} {\ldots}with the exception of DR21. [Laughter.] And it's not really certain what the luminosity of that object is. There's also a distinction between a really collimated jet and some vague outflow; you don't get the former in high-mass objects (with the possible exception of DR21). %========= Philip Dufton \noindent{\bf Jeffery:} Before I invite questions, I have an announcement: this is a special occasion for Philip, being his 50th birthday. [Applause, shamefully mingled with whoops of derision.] \noindent{\bf Kaper:} LS~4825 is well below the Galactic plane -- about 12~kpc? How does it get there? \noindent{\bf PLD:} That's not actually a problem, and LS~4825 isn't unique in this respect. The most likely mechanism is ejection from the Galactic disk, either from a cluster (following momentum transfer through a collision) or by evolving a massive close binary to a supernova stage (when the companion gets a `kick'). There are a number of normal, young B-type stars in the solar neighbourhood which are 2, 3, even up to $\sim$10~kpc from the sun. \noindent{\bf Gies:} Is there any velocity information on 4825 that would help, and is there a UV spectrum from which the wind terminal velocity could be measured? Ebbets and others have shown that the escape velocity can be estimated from $v_{\infty}$. \noindent{\bf PLD:} The radial-velocity information is consistent with the star corotating with the plane, if it's at 20~kpc. Of course, it would then be in the halo, with the implication of a significant ejection velocity, but we have no information on the transverse velocity. We've tried to use the $v_\infty/v_{\rm esc}$ method for several stars, and always end up with ambiguous results. %========= Achim Feldmeier \noindent{\bf Kaper:} At what depth in your model does the wind become optically thick to soft X-rays? \noindent{\bf AF:} 3--4$R_*$ for intermediate energies ($\sim$1~keV), and the effective X-ray photosphere is at 2--3$R_*$. For all the examples I showed, the X-ray photosphere is below the cloud--cloud collisions. \noindent{\bf Owocki:} Surely that must depend on the mass-loss rate; I seem to remember from Hillier that at 1~keV the X-ray photosphere for $\zeta$~Pup was at $10R_*$? \noindent{\bf AF:} Yes, that's a very strange point; in Hillier's model, nearly all the X-rays are re-absorbed. Leon Lucy also asked me to make a comparison between my results and his model, and I found that in his model also 99.9{\%} of X-rays should be re-absorbed in the wind, whereas in our models the figure is only 90{\%}. I asked Ralf Palsa, who analysed our Rosat dataset of 42 O-type stars, what number he got, and it's remarkable how close it usually is to 90{\%}. So, I think the Hillier case was exceptional because he had helium recombining in the wind, and $\zeta$~Pup is one of very few stars where this occurs. I would make the claim that, in general, X-ray absorption in stellar winds has previously been overestimated. \noindent{\bf Owocki:} Okay, but I thought that in the Hillier model the non-helium absorption at $10R_*$ was still considerable at 1~keV? \noindent{\bf AF:} No, it was was mostly helium. It's also true that the present model would not work for $\zeta$~Pup. %========= Alex Fullerton \centerline{\bf Discussion}\medskip \noindent{\bf Drew:} What has this instrument got that other systems available since the 1980s, which seemed to be limited by seeing changes? \noindent{\bf AWF:} I think the clever thing about this one is that it uses phase modulation instead of a rotating chopper to deal with atmospheric scintillation. Also, sky removal is facilitated by automatic beam-switching between the twin detectors; even in the thermal IR there is no problem. \noindent{\bf Hanson:} I wanted to make a general comment that TAGs concerned with IR spectroscopy have historically tended to be supportive of studies of relatively low-mass stars at the expense of high-mass stars. When Peter and I started on my thesis work it took years to get past the TAGs. \noindent{\bf AWF:} That's a fair comment. Of course, it's our job to swing TAGs! \noindent{\bf Barlow:} FTS has many advantages, but a disadvantage is in the thermal infrared, longwards of about 2.3$\mu$m, you get the background from the entire bandpass -- with a grating you just get the background in that resolution element. \noindent{\bf AWF:} Exactly, but subtracting the background as you go helps. %========= Doug Gies \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Dufton:} I thought that the theoretical prediction was that about 50{\%} of close binaries should survive supernova explosions. If that's the case, do your results imply that most runaways have, rather, been ejected from clusters? \noindent{\bf DRG:} That's a good point; I think the answer is that what happens when a supernova explodes in a binary is very controversial now. Originally, based on work by Blaauw, and later by Ed van den Heuvel and the Dutch school, you would've expected that the progenitor would have lost about half its mass through stellar winds and perhaps other processes, so that when it exploded as a supernova it would not disprupt the system. On the other hand, we now know, from work by Lynne and others, that pulsars have very high random velocities, and it's thought that the reason for that is that there is some asymmetry in the supernova explosion. If you put that in, it may well be that many more systems are disrupted; on the other hand, we observe massive X-ray binaries, so clearly some do survive. \noindent{\bf Venn:} With the CHARA array, have you thought of searching for planets as well? \noindent{\bf DRG:} Yes, we've looked at that quite closely; we're very interested to see if we can detect astrometric perturbations in a binary-star system. When you're looking at a very small area of sky, usually much less than one arc-second, you need some sort of fiducial point to refer everything to; when you have a binary, you can use the stellar orbit to provide that frame of reference. \noindent{\bf Langer:} Can you say something about the distribution of eccentricities, and whether there's a trend with the period? \noindent{\bf Gies:} I haven't yet made that comparison. Unfortunately, for the visual binaries, where presumably the eccentricities are very high, there are only two catalogued orbits; one of them has a 1\,500-year period and the other has a 200-year period. \noindent{\bf Hilditch:} I think the general result among detached systems is that eccentricities tend to go to zero at periods below something like 6--8~days, and then the eccentricities can increase substantially at longer periods. For the interacting systems you have two effects: tidal forces circularize the orbits, but supernova explosions can make them very eccentric again, because we do see that in [XXX unintelligible] \noindent{\bf Jeffery:} What sort of initial masses do you expect for the components of $\phi$~Per? If they're low, does that suggest another mechanism for generating O~stars? \noindent{\bf DRG:} That's an excellent question -- to be honest, I haven't thought about that too seriously. My main impression comes from a discussion with Dany Venbeveren at Brussels; he modelled $\phi$~Per as a system that started with a mass ratio very close to unity, which went through lobe overflow, and the big question is, how conservative was that process? At the moment the system is about $10M_\odot$, so it could possibly have started as a pair of $5M_\odot$ B~stars, where one essentially went to nothing. On the other hand, if the overflow was a very messy process, it could've started as a pair of O~stars that lost a lot of mass to the surroundings. But you're right, if you started with two B~stars and dumped enough material over, you could end with an O~star -- the primary of $\phi$~Per is B0.5, so it's nearly there. Incidentally, the HIPPARCOS distance is about 210~pc, and if it's believed then this is a truly overluminous for its mass. %========= Margaret Hanson \centerline{Discussion}\medskip \noindent{\bf Kaper:} I'm interested in the bow shocks; I have a colleague at ESO who models these with hydro codes, and he gets a shock as soon as you have an O-star wind blowing against a molecular cloud. If you add some relative velocity you create a bow shock. How do you think you get such a shock? \noindent{\bf MH:} You just described it! But there's always been this problem of how you get ultracompacts to live as long as the statistics suggest. About 5 years ago one of the best suggestions, by McKee and Van Buren, was that if you simply move the star relative to the cloud you'll retain a high-density environment much longer, even though the cocoon may've blown away. Now I think that's actually happening in some situations, but it certainly doesn't explain all of them. \noindent{\bf Kaper:} But then it doesn't necessarily put a constraint on the age of the stars? \noindent{\bf MH:} I agree; I can't say anything about the age of a star. The only thing you can say now is, what is the timescale for it to leave the cloud? That's probably on the order of millions of years. \noindent{\bf Drew:} There's an alternative view, the `blister/champagne' model. Recent high-resolution work by Stuart Lumsden and Melvin Hoare has, if anything, come down in favour of this, rather than bow shocks. \noindent{\bf MH:} Yes, there the density's not quite the same all the way round, and you get blow-out on one side. In fact, my co-author in this work believes in `champagne'. Since I don't work on the models myself, I have to accept what the bow-shock people say, which is that the velocities they get from radio recombination lines are in better agreement with that model than with `champagne' -- I guess it hasn't been sorted out yet. Thanks for bringing that up. \noindent{\bf Najarro:} Some of the shapes you've shown look very much like the `pistol' feature at the Galactic Centre, and most of us think that that nebula is the result of an LBV which erupted around a million years ago. What is the mass of you nebulosity? At the Galactic Centre there's around 10$M_\odot$. Can you measure the recombination-line radial velocities and compare them with the radial velocity of the star? \noindent{\bf MH:} The velocities range from 85 to 115 km$\;$s$^{-1}$ across the region. Those velocities `smear' spatially across the nebula, which is what supports the idea of a bow shock. \noindent{\bf Maeder:} You've been speaking about the accretion rate. There are {\it two}\/ accretion rates: one from the molecular cloud onto the desk, and the second from the disk onto the star. It's not clear which one you're observing, and they're not necessarily the same, as there can be a long delay between accretion onto the disk and accretion onto the star. \noindent{\bf MH:} What I'm told is that the situation is very unstable if the disk is much more massive than the central star. Over longer timescales, therefore, at least half the (disk) accreted mass has to be going onto the star -- you can't build up lots of mass into the disk with a substantially smaller accretion onto the star. The rates therefore have to be more or less the same. %========= Tim Harries \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Langer:} It's very unlikely that you'll find any systems in case~B mass transfer, because that phase lasts only a few $10^4$~years, while case~A mass transfer lasts for several {\it million}\/ years. \noindent{\bf Hilditch} [to Langer]: Yes, but these are semi-detached {\it post}\/ mass-transfer systems. \noindent{\bf Langer:} Semi-detached? That means one star fills its Roche lobe, doesn't it? \noindent{\bf Hilditch:} Yes; the lobe-filling star is the mass loser, and is overluminous for its mass. \noindent{\bf Langer:} But if it fills its Roche lobe at present then it's still losing mass? \noindent{\bf Hilditch:} Yes; what I meant was that these systems have already gone through the phase of {\it rapid}\/ mass transfer. \noindent{\bf Crowther:} Just a comment on the calibrations you've used: in astronomy we know there's scatter everywhere, and at a given spectral type there's no such thing as a single value for temperature, or $M_V$, or whatever -- you're probably looking at a spread of a few thousand in temperature, or several tenths in $M_V$, at any spectral type. \noindent{\bf Conti:} I was a little concerned about fiddling with the temperature scale, but, you know, it could be; but it depends fairly heavily on the spectral types that are assigned to DH~Cep, for example. It could be that there's something off in the spectral types you take for a close binary. Does Nolan have anything to say on that [looking round]? \noindent{\bf Howarth} He stepped out just a moment ago, but if he were here I'm sure he'd point out that there's no such thing as an `O9.3' star [laughter]. \noindent{\bf Hilditch:} People {\it say}\/ that there are such things O9.3 stars; we're not spectral-type experts. \noindent{\bf Kudritizki:} I wouldn't be surprised if the effective-temperature scale had to be revised to slightly cooler values, because all the temperatures we've determined in the past have been from unblanketed non-LTE models. I think a shift by as much as 2\,000$\;$K is very possible with blanketing, so if you find this empirically, I think that's okay. \noindent{\bf TJH:} Sure; and if you take DH~Cephei out of the equation I think the argument that you need to reduce the temperatures at early spectral types still remains valid. \noindent{\bf Hubeny:} Just a comment that the calibrations you use are based on non-LTE hydrogen/helium models; you can get very different results if you use Kurucz line-blanketed LTE, where you get just the reverse effect, an {\it increase}\/ in temperatures, compared to line-blanketed non-LTE. [XXXTape is noisy - check] This is just the point you're making, of course, that there are differences between the calibrations. %========= Artemio Herrero \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Dufton:} You talked about microturbulence in OB stars, and mentioned Neil McErlean's paper; as with most `hot' projects (sorry!), a number of people have worked independently on this topic, and Keith Smith has a very nice poster paper discussing the importance of microturbulence in late-O supergiants, which everyone should try to look at. \noindent{\bf Gies:} Could you comment on the state of the `mass discrepancy' which you identified in your 1992 paper? \noindent{\bf AH:} Well, at the beginning we were really convinced that this was an effect of the wind on the spectroscopic analysis. However, it now seems that this only goes half-way to giving the answer. Allowing for rotation in the evolutionary tracks can explain another little bit of the discrepancy, so I think that, when you consider the errors, the problem is now more or less solved. \noindent{\bf Kaper:} On the basis of your 1992 results, Blaauw suggested that helium enrichment and rapid rotation might be related with the fact that the rapid rotators are OB-runaway stars. Then the helium overabundance and the rapid rotation might be the result of binary evolution; mass transfer from the initially more massive star supplies both enriched material and angular momentum. \noindent{\bf Howarth:} I've been carrying out some analyses of the most rapidly rotating O~stars, taking into account the equator-to-pole variations in temperature and gravity. Preliminary results for HD~191423, which is the most rapidly rotating near-main-sequence O-star known, show clearly that it has enhanced helium, and also that it is, in fact, an ON star. Two other well-known rapid rotators, HD~93521 and HD~149757, are clearly {\it not}\/ ON stars, although the helium analysis is not yet complete. \noindent{\bf Kudritzki} [to Howarth]: Did you check if you can remove the helium overabundance by using microturbulence? \noindent{\bf Howarth:} Yes; microturbulence has no important effect on the analysis of 191423. %========= Ivan Hubeny \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Herrero:} Did you find anything out about the helium abundance? \noindent{\bf IH:} My purpose here wasn't really to do a specific analysis, just to show what errors you make using different methods. So I used solar helium, actually; and you can see, it fits perfectly. \noindent{\bf Walborn:} Just an incidental comment about the parallaxes: I've seen a preprint by Henny Lamers and, according to HIPPARCOS, 10~Lac has an $M_V$ of $-3$. From the cluster distance you'd assume $-4.3$, and that's an anchor point in the absolute-magnitude calibration for O9$\;$V, so{\ldots}I hope the HIPPARCOS results are wrong! [Laughter.] \noindent{\bf Kudritzki:} The paper says that the absolute magnitudes of O-type stars as a function of spectral type are correlated with rotation, in the sense that the slow rotators are always much fainter than the fast rotators. One could study that independently of HIPPARCOS if you just looked at clusters. \noindent{\bf Harries:} So you're saying that the inclusion of line blanketing reduces the inferred temperature by 2\,000$\;$K in the example you've discussed? How would that vary with spectral type? \noindent{\IH:} Well, for hotter stars it will be more, but it's always more or less around 10{\%}. For BDXXX it was 6\,000 out of 58\,000K. \noindent{\bf Puls:} If you were to play the same game with your reduced iron and nickel atoms, what would be the effect? Would it take you more or less than half-way to this 2\,000$\;$K change? \noindent{\bf IH:} In this case it is less than half-way. %========= Lex Kaper \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Conti:} Can you remind me, what is the numerical definition of a `runaway' velocity? \noindent{\bf LK:} Well, it was originally a 3-$\sigma$ detection, so, if the average space velocity is 10~km$\;$s$^{-1}$, that's $\sim$30~km$\;$s$^{-1}$. In that sense, not all the stars I listed are `official' runaways. \noindent{\bf Owocki:} I'm not sure I followed the full logic{\ldots}in the press release I saw(!){\ldots}you're saying that this actually proves the supernova-ejection scenario for Vela~X-1? Or could it be a coincidence, that the system was ejected from a cluster through dynamical interactions, and then subsequently the supernova went off? \noindent{\bf LK:} Well, that's possible, of course; but then it would've been ejected as a binary, and there are only about 3 such binary runaways. Here you also have the originating OB association identified -- that doesn't rule out a dynamical interaction, but we do know for sure that a supernova has gone off in the system. \noindent{\bf Dufton:} Don't the simulations show that you very rarely get binaries ejected from clusters through dynamical interactions? \noindent{\bf LK:} Yes, and that seems to be supported by the observations. \noindent{\bf Maeder:} It's remarkable that these runaway stars very often have high rotational velocities. The idea is that matter coming from the supernova imparts angular momentum, and at the same time enriches the companion's surface helium? Then it would be very interesting to look for other elements coming from the supernova. \noindent{\bf LK:} No, only a {\it very}\/ small fraction of the supernova mass is intercepted by the companion. It is the mass-transfer process just {\it before}\/ the eruption that is important. The mass donor at that stage could be helium rich. \noindent{\bf Gies:} Peter Leonard wrote a paper, I think in Monthly Notices, where he said that some binary--binary dynamical interactions could involve actual collisions, and he proposed that this could lead to some additional angular-momentum transfer and perhaps extra mixing. So the dynamical model might lead to high rotational velocities and surface helium abundances, as well as Blaauw's traditional supernova model. I think there's now good evidence for both scenarios. Your work with Vela X-1 has beautifully shown that at least some of these X-ray binaries are clearly runaway objects, but there are also runaway binaries, such as Y~Cyg and HD~1337, and it's very hard to see how you could get those in the supernova scenario. Clearly, Nature lets both mechanisms operate. \noindent{\bf Langer:} Looking at the space velocities, they're not all that impressive. Are they consistent with simple mechanical arguments of the momentum transfer in supernova explosions? \noindent{\bf LK:} Well, you expect to get something that's about the orbital velocity. Most of the systems here are Be-type X-ray binaries, so you might expect lower runaway velocities than for the high-mass, OB X-ray binaries. \noindent{\bf Conti:} Just looking at that old binary-evolution scenario you showed at the beginning, I wondered what sort of supernova is produced by a massive helium star? \noindent{\bf LK:} Do you mind if I just rephrase your question a little bit? Because a very interesting point is what happens if a black hole is formed; then a lot of material that might otherwise be lost is caught by the black hole. Cygnus~X-1 really seems to be a runaway system, and tells us something about what must happen to the supernova. %========= Rolf Kudritzki \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Owocki:} There's the question of what happens when there are rapid jumps in line-force parameters near critical temperatures, like the bistability temperature. I didn't notice that showing up in your plots -- could you comment on that? Also, is the curvature, or departure from a simple power-law dependence of the force multipliers, in the right sense to help increase the mass-loss rates in WR-star models? \noindent{\bf RPK:} The critical temperatures just correspond to points at which the dominant ions of the most important elements change; that's in the input data, of course. I haven't shown plots of the parameters against temperature, but if I had then you would've seen corresponding features. The sense of curvature also depends on temperature, so there's no simple answer to the second part of your question. \noindent{\bf Maeder:} Some time ago you made calculations showing the dependence of mass-loss rates on metallicity. Do you expect very different results with your new parameterization? \noindent{\bf RKP:} Not {\it very}\/ different. The old calculations told you that the wind momentum goes with metallicity to some power which is a function of the force-multiplier parameters, and which is in the range of something like 0.6 to 0.8. I would have to reinvestigate this analytically with the new parameterization, but of course we can look to the detailed numerical models by Joachim Puls and Adi Pauldrach, where the force is calculated point by point. Then I think the exponent is the same -- around 0.6--0.8. The advantage of the analytical approach is first that it helps you understand the numerical models, which is not something we should forget, of course; and secondly that you can cover a very wide range of the HR diagram with a fast calculation, which you could incorporate into stellar-evolution models, for example. As an illustration, I could easily model mass loss in the post-AGB stage of evolution. \noindent{\bf Becker:} The overall slope of the power laws must depend on the number of weak lines you include, particularly at the lower end, where you seem to get the biggest differences from a linear model. Is there any problem of completeness? \noindent{\bf RPK:} It's possible to calculate, analytically, the weakest lines that have to be included. In this regard, I think we are complete, although of course one can never be truly complete in the sense of including every line. \noindent{\bf Schaerer:} If I understood correctly, you seem to show that your parameterization changes completely when you go to cooler temperatures? \noindent{\bf RPK:} Yes. For the O stars the old parameterization is not so bad; but still, you would not be able to explain the difference bewteen main-sequence and supergiants at the same temperature. \noindent{\bf Schaerer:} My question, really, is in regard to the B and A stars. Babel has shown that, qualitatively, the winds behave very differently in that regime, and that you have to take into account photospheric shadowing and things like that\ldots \noindent{\bf RPK:} He was looking at main-sequence objects, whose winds are very weak, and there are a number of effects at lower luminosities. Babel has shown one, and additionally Joachim Puls has found that the use of the Sobolev approximation is no longer useful for such stars. I'm not aiming at these objects, only at stars where the winds are really strong, like supergiants. In those the winds are strong enough to modify stellar evolution, and also I can observe them at large distances with instruments like the Keck HIRES. \noindent{\bf Langer:} Do you have a general understanding of where in the HR diagram CAK theory breaks down at low temperatures? F stars, G stars? \noindent{\bf RPK:} One always has to be careful about critical-point solutions in stars with very extensive photospheres. Leaving that aside for the moment, I think that as soon as hydrogen stops being ionized, then you can't apply CAK any more. Winds in F~stars, for example, may still be ionized, because the density is so low. %========= Norbert Langer \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Kudritzki:} I have a very simple question: if the radius increases through stellar evolution, how can you have constant rotational velocity? Shouldn't the velocity become smaller as soon as the star starts to expand? \noindent{\bf NTL:} The reason is that the core contracts at the same time, and spins up, and so you develop a large gradient in angular velocity, which leads to a redistribution of angular momentum from the core to the surface. That helps the surface to keep this rotation rate. \noindent{\bf Venn:} Are you suggesting that all O and B stars that hit this Eddington limit and spin down go through an LBV phase? \noindent{\bf NTL:} Classically, we had the idea that we obtain LBVs from stars that hit the Humphreys-Davidson limit, basically. My idea is that we should replace it by the $\Omega$ limit, which of course depends on the rotation rate, and is not a constant for all stars. So we have LBVs well below the Humphreys-Davidson limit, which could not be explained with the classical Eddington limit, but which might be rapidly rotating stars; a slowly-rotating star could just go smoothly through the same region of the HR diagram and become a red supergiant. \noindent{\bf Owocki:} Well, Norbert and I have talked about this an awful lot, but I just wanted to make a comment for the record. I think one has to distinguish between two possible kinds of mass loss from the star. Norbert says that, from an interiors point of view, it is necessary for the star to lose a certain amount of angular momentum. We automatically think of mass loss as a mechanism -- the Sun is a good example of that -- and then we maybe think of a wind; but another way for a star to lose angular momentum is to shed a disk. So an alternative to the scenario put forward by Norbert is that, when a star gets close to its critical rotation rate it does indeed inflate up at the equaotor, but as it does so it gets harder and harder to maintain the radiative driving there, because it's harder for the photons to make their way out along the major axis. The key question is, can you then maintain rigid rotation as the equator extends. If you can, then at some point the outer part effectively goes into orbit, and maybe then you shed a disk. So the actual mass loss wouldn't be in the classical wind that we normal think of, but through some sort of decretion disk. \noindent{\bf NTL:} Let me just say, I don't want to be rude, but this is {\it your}\/ problem! [Laughter.] The star has to get rid of some mass, otherwise it would hit the $\Omega$ limit, and I said here that the mass loss I need is a factor of 10 above the rate given by the theory of radiation-driven winds; so there are maybe other things going on. I don't say that the mass has to be taken away to infinity, it can stay somewhere in the environment -- it just has to come off the star. \noindent{\bf Owocki:} Okay, one way we can distinguish these two things is to look at the nebulae carefully. \noindent{\bf Gies:} There has recently been some extensive work on projected rotational velocities of O stars -- there's a paper by Howarth et al. in 1997 and one by Laura Penny in 1996. Laura made a very interesting plot of $v_{\rm e}\sin{i}$ against mass, and there's a large empty area in that diagram where there are no stars of high mass that are rapid rotators. So this might tie in with the idea that the more massive stars, which evolve rapidly, tend to slow down their rotation rather quickly. \noindent{\bf NTL:} Thanks for pointing that out; I'm eager to compare my results with observations. %========= Andre Maeder \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Langer:} If the rotation is transporting angular momentum inwards, doesn't that mean that the amount of differential rotation is increasing, and that therefore the shear instability becomes larger, opposing this effect? \noindent{\bf AM:} Exactly! You have meridional circulation {\it increasing}\/ differential rotation, but at the same time time you have more shear, and that moves angular momentum outside. So we look for an equilibrium betwee these two effects, called by Zahn the `asymptotic solution', and as a matter of fact there is no equilibrium, so this asymptotic solution cannot be applied. At the same time, $\mu$ is increasing in the centre, and so, by local angular-momentum conservation, the centre is rotating faster. \noindent{\bf Kudritzki:} What is the role of mass loss in this business? It should take away angular momentum. \noindent{\bf AM:} Yes, this is an important point. Certainly in low-mass stars, like the Sun, there is some magnetic connection between the star and the mass lost. Thus a certain amount of mass is removing much more angular momentum than it started with. In massive stars, we don't really know much about magnetic fields, but if there is no magnetic field -- and the usual treatments assume that -- then the matter moving away carries only its own angular momentum, without depleting the angular momentum of the interior. \noindent{\bf Townsend:} Do you think that vibrational instability due to a $\delta$-mechanism in the semiconvective zone could have any effect on your results for the shear instability? \noindent{\bf AM:} These problems, such as the transport of angular momentum by waves, are being considered by Schatzmann. In principle, for the massive stars we should have some vibrational instability, but current results suggest that the timescale for this instability to grow large enough to be significant is the same as the timescale for stellar evolution, so it should be unimportant. \noindent{\bf Owocki:} How important is the meridional circulation for energy transport, and can that modify the standard von~Zeipel picture for gravity darkening? \noindent{\bf AM:} I think the von~Zeipel theorem is something like the statue of King George\footnote{A larger-than-life equestrian statue of George$\;$III, the reigning monarch at the time of the declaration of independence of the American colonies from Britain, stands a short walk from Cumberland Lodge.}; we have to have a careful look at it [laughter]. The fact that there is a thermal imbalance with meridional circulation could certainly lead to a revision of von~Zeipel. \noindent{\bf Owocki:} That hasn't been worked out yet? \noindent{\bf AM:} I think at least 20 years ago Lucy looked at how the von~Zeipel theorem is modified if there is convection in the outer layers, but not so many people have worked on that. It's certainly a point to re-examine. %========= Derck Massa \centerline{\bf Discussion}\medskip \noindent{\bf Drew:} There is a problem with parallaxes, the so-called Lutz-Kelker corrections, which is well understood in the astrometry community but less well known outside. Put crudely, just ignore any results which are poorer than 5$\sigma$ -- with Hipparcos, most things beyond 150~pc. \noindent{\bf Kudritzki:} I was very happy to find out that $\kappa$~Ori is half the distance of $\epsilon$~Ori. If you put them at the same distance, then they should have more or less the same luminosity, but $\epsilon$~Ori has H$\alpha$ emission and $\kappa$~Ori has H$\alpha$ absorption, and $\kappa$ just did not fit the wind-momentum/luminosity relationship. For me, now, the problem is solved! %========= Phil Massey [PSC] \centerline{\bf Discussion}\medskip \noindent{\bf PSC:} Although I've presented the talk, I reserve the right not to answer any questions! \noindent{\bf Crowther:} NGC~3603 is a Galactic counterpart to R136, and at last week's Herstmonceux Conference in Cambridge results were presented which also show a normal Salpeter IMF. \noindent{\bf Hilditch:} Could the problem you have of some stars being to the left of the ZAMS be solved by lowering the temperature scale? Later in the conference Tim Harries will be presenting evidence that such a reduction is indicated by binary-star studies, where the temperatures implied by Geneva models from the measured masses and radii are generally lower than those assigned spectroscopically. \noindent{\bf Conti:} Are you saying that some O3 stars have lower temperatures? \noindent{\bf Hilditch:} Well, we don't have any O3 stars, unfortunately; but the late O stars are cooler. \noindent{\bf Maeder:} Do you know if the O3 stars are concentrated to the centre of the cluster? Because in some very old clusters the most massive stars are found at the centre, and it cannot be a dynamical effect. \noindent{\bf Bohannan:} Peter, just put up the diagram showing the stars that were observed. Two-thirds -- 40 out of 60 -- are O3. \noindent{\bf Conti:} [Showing viewgraph] Right, this is the inner part, but there isn't any obvious central concentration. \noindent{\bf Nota:} I just want to mention our poster, where we measure the IMF down to 0.8$M_\odot$ (by summing everything that was available in the HST archive) and we find a turn-over at 1.5$M_\odot$. \noindent{\bf Conti:} Hmm, for that mass the formation time is something like the cluster age, a few million years{\ldots}interesting. %========= Jim McCarthy \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Schmutz:} I was very interested in your remarks about the electron-scattering wings. In my experience with WR stars, as soon as you introduce electron scattering you find that the model profiles don't fit unless you also introduce clumping. You didn't mention this, so I guess the electron-scattering wings fit okay from the outset, which I find surprising. \noindent{\bf JMcC:} Well, we didn't need to use clumping, although of course we could be misled if clumping does exist. Do you want to comment, Rolf? \noindent{\bf Kudritzki} [to Schmutz]: You assume that all the electron scattering takes place in the wind, which is not true for these objects; it's a {\it photospheric}\/ effect. \noindent{\bf Schmutz:} But in the hotter stars, when you introduce electron-scattering you find that it does not fit\ldots \noindent{\bf Kudritzki:} My problem is, it fits! [Laughter.] I'm sorry! But the point is that these wings are not formed in the wind but in the photosphere. \noindent{\bf Puls:} I think there are two things which can be confused here. We are not speaking of coherent scattering, which occurs in your Wolf-Rayet winds and which I agree is a real problem, but the non-coherent redistribution of photons from underpopulated $n=2$ levels in the photosphere. \noindent{\bf Harries:} I'm amazed that you can get a unique solution when you have so many free parameters. Do you construct a grid of models and find a $\chi^2$ minimum? \noindent{\bf JMcC:} The different parameters affect the profile in different ways, and at our resolution we can constrain each parameter uniquely. I forgot to mention in my talk that $T_{\rm eff},$ $\log{g},$ and the abundances are all separately determined before we undertake the H$\alpha$ analysis. \noindent{\bf Harries:} The rotation velocity looks quite low. \noindent{\bf JMcC:} From the metal lines, certainly less than 50~km$\;$s$^{-1}$. \noindent{\bf Kudritzki:} Thirty. %========= Georges Meynet \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Kudritzki:} I wanted to draw attention to a paper by Henny Lamers, with me and a couple of other authors, just submitted to \aap as a Letter. From HIPPARCOS data, we find slow rotators on the main sequence are fainter than rapid rotators. It would be extremely interesting to see if you could explain this quantitatively. \noindent{\bf GM:} You mean on the zero-age main sequence? \noindent{\bf Kudritzki:} No, not {\it zero\/}-age main sequence; but stars classified as dwarfs. \noindent{\bf GM:} Qualitatively, I'd expect fast-rotating stars to have higher luminosities than slow-rotating ones. \noindent{\bf Howarth:} I believe I understood your mechanism for moving angular momentum about: the circulation first transports material from the core to the surface along the polar axis; the material then moves across the surface to the equator, picking up angular momentum along the way, and finally transports that momentum inwards along the equatorial plane. \noindent{\bf GM:} That's right. \noindent{\bf Howarth:} So that carries angular momentum from the outside in{\ldots}but I understood Norbert to say that, in his picture, as the core shrank and the outside got bigger, angular momentum was transported {\it outwards,}\/ to maintain the rotation rate. I don't understand how these two things fit together. \noindent{\bf GM:} You have two mechanisms: one which tends to reduce the radial gradient in angular velocity, and another which, most of the time, tends to strengthen it. Only models expressly including both can say whether we have an equilibrium situation or not, and which mechanism will overcome the other. In our models, the effect of meridional currents overcomes the effect of shear turbulence. \noindent{\bf Howarth:} Is that something specific to these models, or something we can expect to be generally true? \noindent{\bf GM:} I think that if the physics we've included is right, it must be like this. There is no fine-tuning; we've just put in the equations, and we look at what happens. \noindent{\bf Howarth:} What does Norbert say? \noindent{\bf Langer:} Well, I've included both processes as well, and get something rather close to rigid rotation{\ldots}we have to check to see what the differences are. \noindent{\bf GM:} I don't know if you [Langer] do this, but one difference could be that many people include meridional circulation through a diffusion equation, and my experience is that you can't model it well in this way; the diffusion approach always tend to smooth any gradients, and suppresses any mechanism which steepens the angular-momentum gradients. But of course we will have to examine this. \noindent{\bf Conti:} I'm very excited to hear about a new Wolf-Rayet channel being opened, although obviously there are other things going on at the same time and you've got a lot of work to do. What I was wondering about is what role would magnetic fields play -- of course, they haven't yet been discovered [laughter]{\ldots}but if this channel is correct, there can't be any magnetic fields, because stars will obviously brake themselves very quickly with a stellar wind {\it and}\/ a magnetic field. \noindent{\bf GM:} I think maybe this is for the next generation! \noindent{\bf Crowther:} I just wanted to comment on the assumed main-sequence mass-loss rates of these very massive stars. I think you're using mass-loss rates based on the de~Jager prescription for rates across the HR diagram, and it seems that if you look in detail at the very massive stars then you find that the factor of~2 enhancement over the de~Jager rates that you assume actually gives much better agreement with the momentum relationship. \noindent{\bf GM:} Yes, we believe that the enhanced rates are better in the sense that, with them, our models reproduce many observations; so we provide an independent confirmation of these higher rates. %========= Illu Monteverde \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Barlow:} How luminous are your targets? Could CNO-processed material be exposed at the surfaces, depressing the observed oxygen abundances? \noindent{\bf Dufton:} Changes in oxygen are relatively small. \noindent{\bf IMV:} The apparent magnitudes are around 16\ldots \noindent{\bf Kudritzki:} {\ldots}so with a distance modulus of 24, the absolute magnitudes are around $-8$. These are very luminous stars, so there could be contamination, but oxygen is the last element to respond in CNO processing. My guess would be that you'd see effects in the carbon and nitrogen lines first. %========= Paco Najarro \centerline{\bf Discussion}\medskip \noindent{\bf Langer:} You seem to get very large values for the acceleration parameter, $\beta$, in the B hypergiants. Is that something you expect from radiation-pressure theory? \noindent{\bf PN:} We carried out an investigation for P~Cygni, with Adi Pauldrach's code, and the velocity structure I was getting from the spectroscopic analysis was more or less the same as he was getting from the multi-line models. It's a pretty flat velocity law, and can be approximated with such a $\beta$~value. \noindent{\bf Kudritzki:} When you include the ISO infra-red, it goes the other way round; the exponent becomes smaller than you might expect from wind models \noindent{\bf PN:} Yes, in the case of P~Cyg. But when you use Adi's models you get very similar results. \noindent{\bf Kaper:} It looks like not only $\beta$, but also $v_0$ has decreased dramatically, from something like 80~km$\;$s$^{-1}$ if you use only optical data? \noindent{\bf PN:} The reason for that large value was the high members of the Paschen series, which were observed to have high-velocity absorption dips. One way to explain that was to have the high transition velocity between wind and photosphere. \noindent{\bf Walborn:} With regard to $\lambda$~Cep, the reason for the classification that you quote, O(n)fp, was exactly for the reason of the peculiar profiles; $\zeta$~Pup is another example. Those stars have reverse $\lambda$4686 (the class Conti called Oef); also, as a class they have broadened absorption lines -- rapid rotation. Additionally, the profiles tend to vary, so the timing of your observations may be important. \noindent{\bf PN:} Yes, that's true. As far as I remember, it's only ever been observed once that the red peak was higher than the blue peak in $\lambda$4686 for $\lambda$~Cep. \noindent{\bf Owocki:} These models are still one-dimensional, right? You haven't been able to investigate rotational effects? \noindent{\bf PN:} That's right. %========= Sally Oey \noindent{\bf Crowther:} The WR stars in the inner region of 30~Dor contribute around 15{\%} of the ionizing flux -- slightly higher than you assume. \noindent{\bf MSO:} Okay, thanks{\ldots}clearly, the relative numbers of WR:O stars depends on the ages. \noindent{\bf Barlow:} Wolf-Rayets are also a lot harder to miss than O~stars, and may therefore tend to be over-represented. \noindent{\bf Aufdenberg:} Regarding `leaking' photons, we may be able to measure this quantity directly in $\beta$~CMa. We now have a very nice model fit to the EUV, shown in my paper [p.~XXX], and we also have a measured column, so we actually measure the EUV flux. Using a simple {\sc cloudy}-type model you can then get a direct measure of the leakage. It turns out to be very small -- about a half per cent. \noindent{\bf MSO:} The former discrepancy between observed and modelled fluxes has been resolved? \noindent{\bf Aufdenberg:} Our line-blanketed models give better temperature structures. %========= Stan Owocki \noindent{\bf Kudritzki:} You could easily include the $\delta$-dependence (that is, the density dependence) in the force multiplier; you should do this, because it might well change the results again. \noindent{\bf SPO:} I didn't mean to say that I ignore it completely; in the simple argument I was making about the change in mass-loss rate from pole to equator I neglected it for clarity, but it's in all the numerical calculations. I normally give this talk to non-hot-star people, and it's hard enough for them to follow even the simple arguments! \noindent{\bf Puls:} I have a question concerning your explanation of equator-to-pole changes in outflow. What I think you have assumed is that the major effect is, more or less, the difference in $\alpha$, the power-law index of the force multiplier, whereas your overall scaling parameter, $K$, you kept constant. [XXXCorrect interpretation of question?] I think the main idea by Adi Pauldrach, and also Lamers and maybe myself, in respect of P~Cygni, where this bistability idea came from, was that the effect that due just because with different density and temperature structures you change the ionization, which means you change the effective number of driving lines, which in terms of the model turns out to be much more important. \noindent{\bf SPO:} Well, yes, I agree with you, except that the parameter $K$ is actually a {\it mixture}\/ of $\alpha$ and the overall normalization, so unfortunately it varies even if you keep the total number of lines constant but vary $\alpha$. The argument I'd like to make is that Ken Gayley's ${\bar Q}$ parameterization will tend to be much more constant. The key point is that the way to change the total number of driving lines most easily is to shift the slope of the distribution, $\alpha$. I need to talk to you guys off-line about how true it is that this ${\bar Q}$ parameter stays constant as you move across a bistability line. %========= Anna Pasquali \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Owocki:} I think that the evidence among many types of rapidly-rotating stars for equatorial density enhancements, probably even disks, is very strong. In a way that's a real puzzle, given the results I showed yesterday [p.~XXX], because you don't seem to be able to get that in the natural way everyone thought possible with the `wind-compressed disk' model; although I would like to comment that there may be many ways to get a disk -- what we saw on Monday [p.~XXX], for example, where you have an equatorial accretion disk modified by radiation. As a theoretician, what I'd like to ask the observers is this: is it possible that when we see a slash star we are viewing a star, which might otherwise appear more normal, at some special orientation? Rolf's argument about the terminal velocity being tied to the escape velocity, for example; that assumes more-or-less spherically symmetric, steady-state outflow. If you were accelerating a wind from the inner part of a disk, for example, where the escape velocity would be very small, you could get a very low terminal velocity. Could you use this to explain the slash stars? \noindent{\bf AP:} Well, my opinion is that for slash stars we have to go to spectropolarimetry to test what I've presented; and we're doing that. \noindent{\bf Bohannan} [to Owocki]: There are only ten slash stars known, and there are only three of the related O\,Iafpe stars in the Galaxy, so we're not looking at large numbers. There's only one of the slash stars that's like R99, and making up three groups out of ten stars{\ldots}what I'm saying is that this isn't something that's common in stellar evolution. Your point is well taken that we have to be careful about making generalities about stellar evolution from these stars. \noindent{\bf Nota:} LBVs are the same. \noindent{\bf Harries:} As a general point, if you use spherically-symmetric models to fit emission-line profiles from winds with large-scale asymmetries, then you {\it over}\/-estimate the mass-loss rates, because any asymmetry increases the line emission over the spherically-symmetric case. \noindent{\bf Najarro:} If you forget about $\lambda$4686 and go to fit H$\alpha$, or the He\,{\sc i} lines, what parameters would you get? \noindent{\bf AP:} Oh, we didn't check that. \noindent{\bf Walborn:} Just to add an historical comment, back in the '30s or '40s Struve found XXX$\lambda$3089{\AA} in HD~152408, which he considered unidentified because it was a `detached', very blue-shifted component. This problem was later discussed by Hutchings; $\lambda\lambda$3089, 10830, and to some extent $\lambda$5876 are metastable or quasi-metastable lines that are very sensitive to dilute structure, and may need special consideration because of that. You could imagine that the detached dip in Fig.~XXX, for example, might arise from a spherically symmetric structure with some sort of high-velocity structure in the line of sight. \noindent{\bf AP:} But then how would you explain the red wing, which is present not only in He\,{\sc ii} $\lambda$4686 but also $\lambda$1640? \noindent{\bf Walborn:} Well, I really just wanted to point out that it would be interesting to try to take into account these metastable effects. \noindent{\bf Conti:} It looks like we're now going in the direction of non-spherical situations, as has happened for Wolf-Rayet stars. Presumbly the stars involved are those with high rotation, so it's interesting to look at that. This brings up a couple of puzzles in my mind, one of which is that it's curious that the high rotation manifests itself once the star has evolved away from zero age, where the radius has got larger and, if anything, you'd imagine rotation to be {\it less}\/ important. The second thing is, presumably we're concerned with the high-velocity tail of the $v_{\rm e}\sin{i}$ distribution, and then the question is what is happening to those stars when they're on the main sequence; maybe they're the Oe stars, and have disks already on the main sequence. \noindent{\bf Crowther:} Can I just re-emphasize that R99 really is unique; I don't think it should really be associated with the rest of the slash stars. \noindent{\bf Owocki:} I think that the evidence among many types of rapidly-rotating stars for equatorial density enhancements, probably even disks, is very strong. In a way that's a real puzzle, given the results I showed yesterday [p.~XXX], because you don't seem to be able to get that in the natural way everyone thought possible with the `wind-compressed disk' model; although I would like to comment that there may be many ways to get a disk -- what we saw on Monday [p.~XXX], for example, where you have an equatorial accretion disk modified by radiation. As a theoretician, what I'd like to ask the observers is this: is it possible that when we see a slash star we are viewing a star, which might otherwise appear more normal, at some special orientation? Rolf's argument about the terminal velocity being tied to the escape velocity, for example; that assumes more-or-less spherically symmetric, steady-state outflow. If you were accelerating a wind from the inner part of a disk, for example, where the escape velocity would be very small, you could get a very low terminal velocity. Could you use this to explain the slash stars? \noindent{\bf AP:} Well, my opinion is that for slash stars we have to go to spectropolarimetry to test what I've presented; and we're doing that. \noindent{\bf Bohannan} [to Owocki]: There are only ten slash stars known, and there are only three of the related O\,Iafpe stars in the Galaxy, so we're not looking at large numbers. There's only one of the slash stars that's like R99, and making up three groups out of ten stars{\ldots}what I'm saying is that this isn't something that's common in stellar evolution. Your point is well taken that we have to be careful about making generalities about stellar evolution from these stars. \noindent{\bf Nota:} LBVs are the same. \noindent{\bf Harries:} As a general point, if you use spherically-symmetric models to fit emission-line profiles from winds with large-scale asymmetries, then you {\it over}\/-estimate the mass-loss rates, because any asymmetry increases the line emission over the spherically-symmetric case. \noindent{\bf Najarro:} If you forget about $\lambda$4686 and go to fit H$\alpha$, or the He\,{\sc i} lines, what parameters would you get? \noindent{\bf AP:} Oh, we didn't check that. \noindent{\bf Walborn:} Just to add an historical comment, back in the '30s or '40s Struve found XXX$\lambda$3089{\AA} in HD~152408, which he considered unidentified because it was a `detached', very blue-shifted component. This problem was later discussed by Hutchings; $\lambda\lambda$3089, 10830, and to some extent $\lambda$5876 are metastable or quasi-metastable lines that are very sensitive to dilute structure, and may need special consideration because of that. You could imagine that the detached dip in Fig.~XXX, for example, might arise from a spherically symmetric structure with some sort of high-velocity structure in the line of sight. \noindent{\bf AP:} But then how would you explain the red wing, which is present not only in He\,{\sc ii} $\lambda$4686 but also $\lambda$1640? \noindent{\bf Walborn:} Well, I really just wanted to point out that it would be interesting to try to take into account these metastable effects. \noindent{\bf Conti:} It looks like we're now going in the direction of non-spherical situations, as has happened for Wolf-Rayet stars. Presumbly the stars involved are those with high rotation, so it's interesting to look at that. This brings up a couple of puzzles in my mind, one of which is that it's curious that the high rotation manifests itself once the star has evolved away from zero age, where the radius has got larger and, if anything, you'd imagine rotation to be {\it less}\/ important. The second thing is, presumably we're concerned with the high-velocity tail of the $v_{\rm e}\sin{i}$ distribution, and then the question is what is happening to those stars when they're on the main sequence; maybe they're the Oe stars, and have disks already on the main sequence. \noindent{\bf Crowther:} Can I just re-emphasize that R99 really is unique; I don't think it should really be associated with the rest of the slash stars. %========= Adi Pauldrach \centerline{\bf Discussion} \medskip \noindent{\bf Gies:} What difference does line-blanketing make to the effective temperature you would estimate for a given stars? \noindent{\bf AWP:} It depends whether you have a dwarf or a supergiant; in the case of a 50kK supergiant it's about 12{\%} in the flux, which I would say corresponds to 4--5kK. \noindent{\bf Gies:} How does this relate to the wind blanketing discussed by Abbott and Hummer? \noindent{\bf AWP:} The effect I showed is due to wind blanketing, and not photospheric line blanketing. \noindent{\bf Crowther:} Your models seem to be in line with the Kurucz model distributions in terms of ionizing fluxes for the very hot O~stars, whereas I thought Daniel Schaerer and Alex de~Koter got quite large differences? \noindent{\bf AWP:} I think this is the case, but perhaps Schaerer should comment? \noindent{\bf Schaerer:} I will discuss this when I give my talk tomorrow. \noindent{\bf Kudritzki:} Could you say something about the effect of shocks in the wind? \noindent{\bf AWP:} Yes, we include shocks but I didn't have time to discuss this. We use an approximate description of the emission coefficient, using a filling factor and a cooling function for the shocks. So we have two free parameters: a filling factor (which is fixed by an integration over the emergent flux in Rosat observations), and the jump velocity, which determines the immediate post-shock temperature and hence the cooling function. For the jump velocity we found a proportionality to the terminal velocity. As an example, the model for $\zeta$~Pup fits the Rosat observation very well. %========= Laura Penny \bigskip\centerline{\bf Discussion}\medskip \noindent{\bf Langer:} In one system you showed, the mass lost was as much as some tens of solar masses. I want to pick up Stan's argument here, that it's not always easy to drive matter to infinity, at least with radiation (and we don't have any other mechanism); so my question is, is there any evidence for circumstellar matter here? If I can't drive it to infinity the lost mass might still be around. \noindent{\bf LP:} Well, this is an eccentric orbit; I don't really know, but I guess it's pretty hard to `catch' this material when you're moving away from it{\ldots} \noindent{\bf Owocki:} The basic point is, what is the total potential that you have to move the material out of? You have the potential of both stars here, and it's not an easy problem. You have to ask where's the energy to get the material out to infinity, compared to the binding energy of the system. \noindent{\bf LP:} Okay{\ldots}these are both O7 supergiants, so there's tremendous radiation pressure. \noindent{\bf Hilditch:} In binary-evolution models there's a parameter `$\beta$', unrelated to the usual velocity-law exponent, which is the fraction of mass that is conserved in mass transfer, with the remainder lost from the system. A typical guesstimate is $\beta \simeq 0.5$, and we can get agreement between observations and models with that value. Of course, an unknown is the initial mass ratio, which you don't know. \noindent{\bf Schaerer:} For the system where you have the O3+O8 dwarfs, and a discrepancy with the mass ratio, do you also have rotational velocities? \noindent{\bf LP:} I have $v_{\rm e}\sin{i}$, but not the rotation; the primary's 107 and the secondary is XXX6. \noindent{\bf Harries:} I just wanted to clarify the DH~Cephei situation -- I only saw your paper [XXX] the day before coming to the meeting. We had another look at our light-curve, and I've plotted $\chi^2$ as a function of inclination [showing viewgraph]; I think you'll agree there's a clear minimum there at 47$^\circ$, although I admit that the errors we gave in our MN paper were too small. \noindent{\bf LP:} The main difference between our inclinations arises because we've put some weight into the absolute magnitude from the cluster membership, which, with the reddenning, gives a radius that you need to match. \noindent{\bf Harries:} Well, even if membership is certain, the cluster distance might have an uncertainty of half a magnitude. %========= Raman Prinja \noindent{\bf Kudritzki:} My original ambition was to come here with a new calibration of $v_{\infinty}/v_{\rm esc}$, but of course I ran out of time\ldots \noindent{\bf RKP:} Well, I look forward to seeing it soon! %========= Joachim Puls \centerline{\bf Discussion} \medskip \noindent{\bf Owocki:} One of the things you didn't have time to mention is that another corollary to the fact that the source function dips down at the sonic point is that it dips below the level necessary for the line-drag effect to suppress the instability there. Therefore, unlike O~stars, where the instability really doesn't take hold until you get to maybe a half a stellar radius or so above the star, the prediction for B~stars is that the instability will go right down to the basement. %========= Daniel Schaerer \bigskip \centerline{\bf Discussion} \medskip \noindent{\bf Najarro:} Daniel, have you tested for any difference if you treat CNO with Sobolev or in the comoving frame? \noindent{\bf DS:} Not specifically; the code has been extensively tested for differences between Sobolev and comoving frame, but only for hydrogen and helium. \noindent{\bf Najarro:} It could be very important just close to the edges. \noindent{\bf Pauldrach:} So you found a difference with respect to your old models by including CNO elements in the analysis; would you expect that including iron would make further changes? \noindent{\bf DS:} It is difficult to say; we have to understand the physical reason why we get the differences in this wavelength range. As I said, I think the important test is to look at the implications of what these model spectra give you, so if we combine the nebular analysis with the classical spectral range we can learn more about the ionizing fluxes. \noindent{\bf Kudritzki:} I agree that one of the most important tests is to make this sort of comparison with the observations. On the other hand, we have two codes, yours and Adi's, and they give significant differences for exactly the same input parameters. Both codes make a lot of approximations, and it may be that some of them are crucial and simply bad. Maybe one of the codes will give better agreement with observations -- but you can always be right for the wrong reason. So I think it's very important to try to understand the physical reasons for the differences in the two codes. \noindent{\bf DS:} Yes, that's why I'm pleased we now have results so we can really make a comparison. \noindent{\bf Conti:} Is it premature to say anything about the $\lambda$4686 nebular emission that's found in some of these starburst galaxies, and which up to now is unexplained? \noindent{\bf DS:} Well, you know I like these objects, but I think there's definitely no hope that the O~stars are responsible for this ionization. In the best case you can only get to $10^{-3}$--$10^{-4}$ of the observed flux with O~stars. As you know, with WC stars and hot WN stars, if you believe in the ionizing fluxes in the literature, you can do it reasonably well. Even in the lowest-metallicity objects, like 1318(XXX?), you find WC stars, and so there's a very good hope that they can produce this ionization. \noindent{\bf Kudritzki:} You know there is a paper by Gabler et~al., in `92, which says for extreme O~stars, with high mass-loss rates, very close to the Eddington limit, you might get enough ionization. These were only hydrogen/helium models, so can you confirm their result, or..? \noindent{\bf DS:} We got agreement with the Gabler results, but just for the regular O~stars. I haven't pushed my models as far, but in any case I don't think these stars will do it, simply because if you want to explain the fluxes you need a huge number of stars. \noindent{\bf Hanson:} I just wanted to point out that the star I discussed on Monday, which is the ionizing source for G29, was studied by the SimpsonXXX group, and they get an upper limit to $T_{\rm eff}$ of 37\,000$\;$K. When you apply your numbers to \hbox{S\,{\sc ii}/O\,{\sc ii},} you get about the same; but when you look at the {\it star,}\/ the minimum temperature is probably 40\,000$\;$K. So I think there are still some problems, even in a case like that where you have a fairly simple ultracompact H\,{\sc ii} region. \noindent{\bf DS:} We haven't really starting compiling lists of objects where detailed testing can be done, so it's good to have at least one. %========= Werner Schmutz \bigskip\centerline{\bf Discussion}\medskip\noindent {\bf Walborn:} I'm not sure that I understand completely, but I think that there may be some confusion here about the relationship between spectral type and temperature. You showed a constant $T_{\rm eff}$ for a given spectral type as a function of luminosity? \noindent{\bf WS:} Let me explain this diagram a little bit more carefully: I plot contour lines of the ratio 4471/4545. Then I plot what Mathys assigns as borders between spectral types. Of course, there is always a problem in plotting more than two parameters, and here there is also the gravity parameter, and metallicity and so on, so the borders can move around a little bit. \noindent{\bf Walborn:} In previous calibrations, at a given spectral type there was a decrease in $T_{\rm eff}$ with increasing luminosity, simply because of the gravity dependence of the line ratios. \noindent{\bf WS:} Sure, that's here too. \noindent{\bf Walborn:} But you're saying that the reason for that is due to mass-loss rather than gravity? \noindent{\bf WS:} Yes; well, both are are important! But mass-loss rate is {\it more}\/ important. \noindent{\bf Puls:} With respect to this photon-loss factor, I studied your paper, and my interpretation of it comes down to the following: what you are doing, in effect, is changing the local escape probability. So really it is no surprise that by putting in the photon-loss factor in thin lines, in O~stars, you really get no effect, since the photon-loss factor is much smaller than the escape probability. \noindent{\WS:} Yes, that's basically correct. \noindent{\bf Puls:} Okay, good. But what we really want to do is suppress the source function, and there's another way to do that, namely, not to change the denominator, but to change the numerator -- that is, the incident intensity (normally the irradiation field). Is it not possible that the real effect which is decreasing the source function is not so much the increase of the local escape probability, but the decrease of the incident radiation? That is, that you underestimate line blocking? \noindent{\bf WS:} This point has also been raised by Leon Lucy, actually. The answer is, for the O~stars, that probably is the dominant effect. For the Wolf-Rayet stars, I don't believe it makes a difference, because the helium line is so immensely optically thick that the incident radiation is basically unimportant. Since photon loss has an important effect, even though it's very very small, only around $10^{-4}$, that's a clear sign that the line `feeds' on itself, and only on itself. \noindent{\bf Puls:} Yes, but it's big with respect to the escape probability, which is $10^{-6}$. \noindent{\bf WS:} But as soon as you have something else influencing the level populations, low lines will react more. This is the basic reason why no other lines are affected; they are embedded in a rate scheme that is much more robust. You have to isolate this transition from everything else, otherwise it will not respond to a small photon loss. The rates between $n=1$ and 2 are so huge that if you do a little bit they don't care -- unless the line is isolated. But if the radiation field is generated just by the line, then it's very sensitive to a little disturbance. \noindent{\bf Najarro:} Werner, you suggest that this photon-loss mechanism is through iron. For the Wolf-Rayets, where photon loss is important, have you been able to correlate this with difference between SMC and Galactic objects? \noindent{\bf WS:} Actually, for Wolf-Rayets, it's not so much the iron lines as Ca\,{\sc v}, but it's not just one line. But it doesn't much matter how strong the line is, just where it is in the helium-line profile. Of course, if you take it away completely, that's important, but as long as there is a line, and it's comparable in opacity with the wings of the He\,{\sc ii}, then it will work. \noindent{\bf Najarro:} But the branching ratios will be different; shouldn't you see that in the photon-loss factor? \noindent{\bf WS:} Not really. Let me put it this way: the photon loss is actually quite complicated, but the {\it capture}\/ factor is just a question of where the line sits in the wings. Of course, if you take away the line completely, it will not work, so maybe there would be a problem in the SMC; but in the Galaxy and the LMC it will be the same. \noindent{\bf Kudritzki:} I guess we could have endless discussion about this, but what it really comes down to is that correct treatment of the multiline effects around the resonance line is crucial. I want to draw attention to the fact that this isn't the only resonance line which is important in Wolf-Rayets; the {\it neutral}\/ helium line at 504{\AA} is also terribly important. \noindent{\bf WS:} Yes; it depends on the temperature range you're working at.