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1 1 COROT and the onset of deep convection 1 F. D'Antona and J. Montalban based on work in collaboration with: Ulrike Heiter and Friedrich Kupka (Wien Observatory), P. Ventura (Universita di Roma La Sapienza), Italo Mazzitelli and Vittoria Caloi (IAS CNR, Roma), E. Antonello (Milan). Collaboration is welcome. 1 Summary We show the results of our new models for the evolution of stars from 1 to 2M, obtained by using both in the atmospheres, computed in Wien with a modied version of the Kurucz ATLAS program, and in the interiors the Full Spectrum of Turbulence convection model by Canuto Goldman and Mazzitelli (1996). These models conrm that the transition between structures which are convective only in the surface layers, and structures which show a well developped convection also in the interior is very sharp in the HR diagram (or in the T e gravity plane). This sharp transition occurs cooler than the red edge of the Scuti instability strip, problably close to the (uncertain) red edge of the Doradus instability strip from ground based observations, and we speculate that it harbors dierent modalities of stellar oscillation patterns, as the excitation of modes can be very dierent for stars having so dierent convective structure. In particular, it could represent the dividing line between coherent pulsations and solar-type oscillations. We suggest to work out wheter this dierence can be experimentally detected in the framework of COROT exploratory program. 2 `Philosophy' in modeling turbulent convection We summarize the status of convection computation: modeling turbulence in stars for a variety of masses and evolutionary phases is today possible by using two main models: - MLT (Mixing Length Theory), by Bohm-Vitense 1958 and following; - FST (Full Spectrum of Turbulence) modeling (Canuto and Mazzitelli 1991 and following) The attempts to overcome local models are the Large Eddy Simulations (LES), which are not yet able to deal with enough scales to be considered a viable general alternative model, and much hope resides today in the recent non local models by Kupka (1999, see also Kupka and Montgomery 2001) which however can not yet fully deal with extended convective regions. The hegemony of the MLT as a model to treat turbulent convection is due both to its simplicity and, perhaps more importantly, to the lack of observational data that unequivocally show its limitations. In these years, however, the recent advances in stellar data have shown the necessity of changing the eciency of convection [by changing the ratio = l=h p ], not only for dierent evolutionary phases or stellar populations, but even at dierent levels inside each one stellar structure. The best example is certainly the following: the t of the solar radius requires globally ' 1:6? 1:8, but the t of Balmer lines proles in the Sun and cool stars requires a much smaller ' 0:5, as shown by Fuhrmann et al It is interesting to notice that the FST model obtains this result ecient convection in the interior; much lower eciency in the atmospheric layers quite naturally (Bernkopf, 1998). As an example of what can be done to overcome this diculty in the case of MLT models, Weiss and Schlattl (1998) have built solar models by adopting model atmospheres having = 0:5 down to optical depth = 20 as boundary conditions, and a smooth transition of to a nal larger value in the inner layers. A convection model of very low eciency in the atmospheric layers is better apt to reproduce the colors and line proles also for other main sequence structures: Smalley and Kupka (1997) have shown that the FST model provides better uvby colors for AF-F and G main sequence stars, than the solar tuned MLT. Based also on the work by van't 1 Presented at the COROT week, Vienna, 17{21 September 2001

2 log P Figure 1: The log T versus log P stratication along the main sequence of out new stellar models. Left: models are shown for masses in mass steps of 0.1M. The dot{dashed (red) lines are the Wien model atmospheres down to = 100. The stellar interior stratication starts from = 10 and the superposition between these two optical depths shows the consistency of atmospheric and stellar models. Right: here the models from 1.4 to 1.45M are given in mass{steps of 0.01M. The structures at M 1:42 have their convective regions limited to the most external layers, while the models at M 1:41 show a well developped stellar convection. Veer-Menneret & Megessier(1996), Gardiner et al. (1999), recently Kupka and his coworkers at Wien University have resorted to compute convection in the atmospheric models, to be used in the interpretation of stellar spectra, either with MLT and a very low value of = 0:5, or with the FST. On the other hand, there are other examples that whole stellar models require ecient convection in the interior. Recently, it became clear that, e.g., t of the MS and Giant Branch in Globular Clusters requires 2:2, if the `long' distance scale, corresponding to ages 12Gyr for the metal poor GCs, is adopted. In a totally dierent context, understanding of the Hot Bottom Burning which leads to achieve Lithium production in the upper AGB also requires very large. We conclude that the MLT is useful for stellar structure calculations until only bolometric (integrated) properties are considered, but it has a very poor performance in low eciency region. Therefore, if one wishes to use this theory, the mixing length must be tuned model by model (and even layer by layer), losing any possibility of predictive power. On the contrary, the FST model can not be innitely tuned and, as such, it may provide hints on the stellar structure which are necessarily washed out when we adopt an MLT tuned to the structure we need to investigate at the moment. In fact by now we think that the best and main use of FST is to TEST the stellar structure in a dierent way than with the simpler and more parametric MLT, without necessarily believing that what we get is \the nal solution" or \the truth". It is easier to understand that we are not obtaining the truth, when we are not able to perfectly t observations. The FST however joins the observationally necessary very low eciency in the surface regions and the very high eciency in the deeper stellar regions, and as such it may be used as a tool to test stellar models, particularly in the region in which we expect that convection changes from being highly inecient to become highly ecient. Thus we

3 3 Figure 2: The general HR diagram of the computed tracks, which extend from the pre Main Sequence (MS) to the MS and then to the Giant Branch. The right gure shows an enlargement including only the tracks of 1.2, 1.4, 1.45, 1.5, 1.55, 1.6, 1.65M. The open squares indicate the location of models 418, 429 and 443 along the 1.5M track. The diagonal (green) arrow shows schematically the separation line between higly convective structures on the right and structures with convection limited to the atmosphere (on the left). The diagonal dotted (black) line indicates the observational red edge of the Scuti instability strip, according to Pamyatnykh (2000). The two dash{dotted (red) lines indicate the observational boundaries of the Dor strip (Zerbi, 2000). The MS at 10 8 yr age is also shown. can use FST models to ask whether we expect any `qualitatively important' global behaviour these models, which can allow us to make prediction which might be tested by the COROT observations. Notice that, although Helio-seismological studies show that the residual between the theoretical and observed solar oscillation frequences as a function of, at large 's are much closer to zero in the FST solar model than in the MLT model (see, e.g., Canuto and Christensen Dalsgaard 1998), asteroseismological mission will give information only on the global modes of oscillation, and so we can not expect tests of the convection along this line. Mazzitelli and D'Antona (1993) had noticed that the way in which convection becomes deeper in the envelope depends on the convection model adopted. FST models show a very sharp transition from `radiative' envelopes (in which convection is limited only to the atmospheric layers) and `convective' envelopes. Here we show that our new models including the FST Wien model atmospheres show this behaviour even more strikingly: a well dened line separates (for solar chemistry) the models which are convective only in the atmosphere from those with deep convection, and we suggest that this may hide a dierent qualitative oscillatory behaviour. 3 New Stellar Models F. Kupka and U. Heiter have provided a huge grid of model atmospheres computed in the framework of the ATLAS9 Kurucz' program, but including the FST convection modelling by Canuto et al. (1996). This grid has two main advantages if we wish to use it for the boundary conditions for full stellar models: rst of all, we may fully exploit FST convection, without having to deal with model atmospheres computed with MLT, a procedure which we have

4 4 Figure 3: Right: the radiative (black), adiabatic (red) and superadiabatic (blue) gradient r? r ad in the external layers of the selected models along the 1.5Mevolution, versus the logarithm of the pressure. The rst and third model have their convection region limited to the atmospheric layers, while the second one shows an extension of convection down to log P 9, well inside the envelope. The transition occurs for a very small variation of the physical parameters, and is mainly due to the high ineciency of the FST model in the atmospheric regions. Left: MS at 10 8 yr for the present models, in which the masses are indicated. From top to bottom they go from 1.1 to 1.75Min mass steps of 0.05M, but the masses from 1.40 to 1.45Mhave mass step of 0.01M. The dashed line shows the MS of grey FST models (from Ventura et al. 2001). MLT models with = 1:6 which ts the Solar location have an even smoother transition (Mazzitelli and D'Antona 1993). shown to be very unsafe (Montalban et al. 2001); second, these model atmosphere are computed bown to = 100 as usually done, but they include a factor four more layers (288) than the normal atmospheric grids (72 layers). This allows a more precise computation of the structure below = 1, which is not very important if the models are used to derive spectral synthesis of lines, but is crucial if we wish to use them as boundary conditions for full stellar models (Montalban et al., in preparation). We then take the pressure and temperature of this grid of models at = 10 as boundary conditions for our full stellar structure computation. The resulting full stratications in the plane log T versus log P are shown in gures 1 for main sequence models of age 100Myr. The left gure shows that the merging between the interior and the atmosphere is very good. The right gure shows the whole structures. It is very impressive how the structure changes rapidly from having a very small convective region limited to the atmosphere (1.42M) to a structure with a wide convective envelope (1.41M). This behaviour also occurs along the evolutionary tracks. Figures 2 show on the left the whole set of tracks computed, and on the right an enlargement of the HR diagram at masses around the transition between radiative and convective envelopes. The (green) arrow shows the separation between the two regions. Three models are highlighted along the 1.5M track, and their behaviour in terms of temperature gradient is shown in gure 3. The transition is well known to produce a change of slope in the MS in the HR diagram: this occurs with any treatment of overadiabatic convection, but is more sharp in the FST models. In addition, the non{grey modelling of the atmosphere makes this change of slope even sharper, as illustrated in the right part of gure 3, which compares the MS shape in the present models (full line) with the MS by Ventura et al. (2001), having the same convection

5 5 treatment but grey atmospheric integration. Figure 4 shows a comparison with the Hyades: we show that the hotter `Bohm Vitense gap' (Bohm Vitense 1970, Bohm Vitense and Canterna 1974) occurs precisely where, increasing T e, the models become mostly radiative: a simulation of the expected stellar population (right gure) shows that a statistically signicant gap may occur. In fact, due to the sharp onset of convection, the stellar models are not distributed evenly in T e at the transition between radiative and convective structures. This example might be an indication that actually such a sharp transition occurs in nature, and we are compelled to look for other possible observational tests. In particular, does this structure dierence lead to any dierences in the oscillatory stellar behaviour? In gure 3 we also show the observational red edge of the Scuti instability strip, which runs parallel to our dividing line, but it is some 500K hotter. The intermediate region is populated by Doradus g{type pulsators, which are also in part found mixed with the Scuti variables (e.g. Zerbi 2000). We suggest that, at the right of our new dividing line, damping in the much larger convective region does not allow any longer coherent pulsations of the Dor type, and possibly only solar type oscillations will be found. What we wish to do now? It seems important to understand rst of all whether the COROT exploratory program will eciently cover this transition region of the HR diagram with enough stellar objects. From a theoretical point of view, we must investigate the onset of deep convection as a function of the metallicity and helium initial stellar content. Further, gure 4 shows that the `Lithium dip' (Boesgaard and Tripicco 1986) occurs at this borderline too: this means that we must also take into account diusion in the stellar models. The possible modes of oscillation must be computed: we expect to collaborate e.g. with our Catania colleagues for this aim. The excitation of modes in these structures must be investigated. We are open to any collaboration on this project. References [Bernkopf(1998)] Bernkopf, J. 1998, A&A, 332, 127 [Boesgaard & Tripicco (1986)] Boesgaard, A.M., & Tripicco, M.J. 1986, ApJ, 302, L49 [Bohm-Vitense 1958] Bohm-Vitense, E. 1958, Z. Astrophys., 46, 108 [Bohm-Vitense(1970)] Bohm-Vitense, E. 1970, A&A, 8, 283 [Bohm-Vitense & Canterna(1974)] Bohm-Vitense, E. & Canterna, R. 1974, ApJ, 194, 629 [Canuto & Mazzitelli(1991)] Canuto, V. M. & Mazzitelli, I. 1991, ApJ, 370, 295 [Canuto, Goldman, & Mazzitelli(1996)] Canuto, V. M., Goldman, I., & Mazzitelli, I. 1996, ApJ, 473, 550 [] Canuto, V.M. & Christensen Dalsgaard, J. 1998, Ann. Rev. Fluid Mech. 30, 167 [1] Castelli, F. 1999, A&A, 346, 564 [de Bruijne, Hoogerwerf, & de Zeeuw(2001)] de Bruijne, J. H. J., Hoogerwerf, R., & de Zeeuw, P. T. 2001, A&A, 367, 111 [de Bruijne, Hoogerwerf, & de Zeeuw(2000)] de Bruijne, J. H. J., Hoogerwerf, R., & de Zeeuw, P. T. 2000, ApJ, 544, L65 [Fuhrmann, Axer, & Gehren(1993)] Fuhrmann, K., Axer, M., & Gehren, T. 1993, A&A, 271, 451 [Gardiner, Kupka, & Smalley(1999)] Gardiner, R. B., Kupka, F., & Smalley, B. 1999, A&A, 347, 876 [Kupka(1999)] Kupka, F. 1999, ApJ, 526, L45 [KM] Kupka, F. & Montgomery, M.H. 2001, COROT/SWG/Milestone 2000, eds. E. Michel & A. Hui-Bon-Hoa

6 6 [Mazzitelli(1993)] Mazzitelli, I., & D'Antona, F. 1993, in Inside the stars; Proceedings of the 137th IAU Colloquium, Univ. of Vienna, Austria, Apr , 1992, p. 457 [Montalban, Kupka, D'Antona, & Schmidt(2001)] Montalban, J., Kupka, F., D'Antona, F., & Schmidt, W. 2001, A&A, 370, 982 [Pamyatnykh (2000)] Pamyatnykh, A.A. 2000, in \Delta Scuti and Related Stars", eds. M. Breger and M.H. Montgomery, ASP Conf. Series 210, 215 [Smalley & Kupka(1997)] Smalley, B. & Kupka, F. 1997, A&A, 328, 349 [van't Veer-Menneret & Megessier(1996)] van't Veer-Menneret, C. & Megessier, C. 1996, A&A, 309, 879 [] Ventura, P., D'Antona, F., Mazzitelli, I. 2001, in preparation [] Zerbi, F.M. 2000, in \Delta Scuti and Related Stars", eds. M. Breger and M.H. Montgomery, ASP Conf. Series 210, 332 [Weiss & Schlattl(1998)] Weiss, A. & Schlattl, H. 1998, A&A, 332, 215

7 N*= < M < Salpeter s IMF Figure 4: On the right we see the HR diagram of the Hyades from Hipparcos data (de Brujine et al. 2001) together with an isochrone of 600Myr from grey models including overshooting (Ventura et al. 2001), which correctly ts the location of the clump stars as core helium burning stars. The colors of this isochrone have been obtained by using Castelli (1999) model atmosphere. The non grey present models are shown in black. The colors are given by the grid of FST model atmosphere, so they are consistent with the atmospheric boundary conditions employed, and with the FST convection. We see that the dierences between the non grey and grey colors are not very important. Notice, as already pointed out several times in the recent literature, that the colors of the upper main sequence are not well reproduced by these model atmosphere. This must be taken into account when the same model atmospehres are used to derive the physical properties (T e and gravity) of the stars to be observed in COROT. The variation of the fractional mass in the convective region (log M ce, scale on the right) is also shown as a function fo the B-V; the Lithium abundance of several stars, dening the so called `Boesgaard Lithium dip' is also shown as an insert. It is evident that the lithium dip is linked to the convective behaviour of the envelope, as already well known. The MS of the Hyades show two \Bohm Vitense" gaps, which are generally interpreted as `color' gaps, due to the atmosphere granulation, whose treatment is not included in Kurucz type colors. Nevertheless, we show on the right a simulation of the population of the MS predicted by our models, on the basis of a Salpeter mass function for masses between 1 and 2M: a gap in T e is predicted by our new models, and it is due to the sharp transition between radiative and convective envelopes. In fact, the T e (and B-V) distribution of masses in this region is not monotonic in our models: these cluster at `cooler' T e, until, very suddenly, convection becomes very inecient and the structure become hotter. We then expect a (statistical) gap at T e just above the onset of deep convection.