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Astron. Astrophys. 360, 120-132 (2000)

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4. Atmospheric parameters

To derive effective temperatures, surface gravities and helium abundances we fitted the observed Balmer and helium lines with stellar model atmospheres. Beforehand we corrected the spectra for radial velocity shifts, derived from the positions of the Balmer and helium lines. The resulting heliocentric velocities are listed in Table 1. The error of the velocities (as estimated from the scatter of the velocities derived from individual lines) is about 40 km s-1. The spectra were then normalized by eye and are plotted in Figs. 2 and 3.

[FIGURE] Fig. 2. Normalized spectra of the programme stars that were observed at the ESO 1.52m telescope. The part shortward of 3900 Å was normalized by taking the highest flux point as continuum value. The HeI lines [FORMULA] 4026 Å, 4388 Å, 4471 Å, 4922 Å, and the MgII line 4481 Å are marked (if visible in the spectrum).

[FIGURE] Fig. 3. Normalized spectra of the programme stars that were observed at the NTT during 1997 and 1998. See Fig. 2 for details.

To establish the best fit we used the routines developed by Bergeron et al. (1992) and Saffer et al. (1994), which employ a [FORMULA] test. The [FORMULA] necessary for the calculation of [FORMULA] is estimated from the noise in the continuum regions of the spectra. The fit program normalizes model spectra and observed spectra using the same points for the continuum definition.

We computed model atmospheres using ATLAS9 (Kurucz 1991) and used Lemke's version 1 of the LINFOR program (developed originally by Holweger, Steffen, and Steenbock at Kiel University) to compute a grid of theoretical spectra which include the Balmer lines [FORMULA] to H22 and HeI lines. The grid covered the range 7,000 K [FORMULA] [FORMULA] [FORMULA] 35,000 K, 2.5 [FORMULA] [FORMULA] [FORMULA] 6.0, -3.0 [FORMULA] [FORMULA] [FORMULA] -1.0, at a metallicity of [M/H] = -1.5. In Table 2 we list the results obtained from fitting the Balmer lines [FORMULA] to H10 (excluding [FORMULA] to avoid the CaII  H line) and the HeI lines 4026 Å, 4388 Å, 4471 Å, and 4921 Å. The errors given are r.m.s. errors derived from the [FORMULA] fit (see Moehler et al. 1999b for more details). These errors are obtained under the assumption that the only error source is statistical noise (derived from the continuum of the spectrum). However, errors in the normalization of the spectrum, imperfections of flat field/sky background correction, variations in the resolution (e.g. due to seeing variations when using a rather large slit width) and other effects may produce systematic rather than statistic errors, which are not well represented by the error obtained from the fit routine. Systematic errors can only be quantified by comparing truly independent analyses of the same stars. As this is not possible here we use our experience with the analysis of similar stars and estimate the true errors to be about 10% in [FORMULA] and 0.15 dex in [FORMULA] (cf. Moehler et al. 1997b, 1998). Two stars show [FORMULA] colours that are significantly redder than expected from their effective temperatures (B 2697: [FORMULA] = [FORMULA], [FORMULA] = 15,700 K; B 3006: [FORMULA] = [FORMULA], [FORMULA] = 30,000 K), possibly indicating that the colours are affected by binarity or photometric blending with a cool star. While the spectra look quite normal, we will not include these stars in any statistical discussion below. To increase our data sample we reanalysed the NTT spectra described and analysed by Moehler et al. (1997b). We did not reanalyse the EFOSC1 data published in the same paper as they are of worse quality. We find that the atmospheric parameters determined by line profile fitting agree rather well with those published by Moehler et al. (1997b).


Table 2. Physical parameters, helium abundances, and masses for the target stars in NGC 6752 as derived using metal-poor model atmospheres. We used the photometry of Buonanno et al. (1986) to derive the masses.

The temperatures and gravities obtained from these metal-poor atmospheres are compared with the values predicted by canonical HB tracks in Fig. 4 (top panel). These tracks, which were computed for a main sequence mass of 0.805 [FORMULA], an initial helium abundance Y of 0.23 and a scaled-solar metallicity [M/H] of -1.54, define the locus of canonical HB models which lose varying amounts of mass during the RGB phase. According to the Reimers mass-loss formulation the value of the mass-loss parameter [FORMULA] would vary from [FORMULA]0.4 at the red end of the observed HB in NGC 6752 to [FORMULA]0.7 for the sdB stars, given the present composition parameters.

[FIGURE] Fig. 4a-c. Temperatures and gravities of the programme stars in NGC 6752. a determined using model atmospheres with cluster metallicity ([M/H] = -1.5), b adopting a solar metallicity ([M/H] = 0) for the model atmospheres, c adopting a super-solar metallicity ([M/H] = +0.5) for the model atmospheres (see Sect. 4.1 for details). The dashed lines mark the locus of the HB evolutionary tracks for [M/H] = -1.54, as computed with helium mixing for the indicated values of the Reimers mass-loss parameter [FORMULA] (see Sect. 4.2 for details). The solid lines mark the locus of canonical HB tracks for [M/H] = -1.54. These loci define the region within which the HB models spend 99 percent of their HB lifetime. Representative error bars are plotted.

One can see from Fig. 4 (top panel) that the HBB stars in NGC 6752 show the same effect as seen in other globular clusters, namely, an offset from the zero-age horizontal branch (ZAHB) towards lower surface gravities over the temperature range 4.05 [FORMULA] [FORMULA] [FORMULA] 4.30 (11,200 K [FORMULA] [FORMULA] [FORMULA] 20,000 K). At lower or higher temperatures the gravities agree with the locus of the canonical HB tracks.

4.1. Radiative levitation of heavy elements

As described in Moehler et al. (1999a, see also Fig. 5), we found evidence for iron enrichment in the spectra of the HBB stars obtained at the ESO 1.52m telescope, whereas the magnesium abundance appeared consistent with the cluster magnesium abundance. The actual iron abundances derived for these stars by fitting the iron lines in the ESO 1.52m spectra are listed in Table 4. The mean iron abundance turns out to be [Fe/H] = [FORMULA] (internal errors only, [FORMULA]) for stars hotter than about 11,500 K - in good agreement with the findings of Behr et al. (1999, 2000b) for HBB/HBA (horizontal branch A type) stars in M 13 and M 15 and Glaspey et al. (1989) for two HBB/HBA stars in NGC 6752. This iron abundance is a factor of 50 greater than that of the cluster, but still a factor of 3 smaller than that required to explain the Strömgren u-jump discussed by Grundahl et al. (1999, [FORMULA]). The mean magnesium abundance for the same stars is [Mg/H] = [FORMULA] (internal errors only), corresponding to [Mg/Fe] = +0.4 for [Fe/H] = -1.54. This value agrees well with the abundance [Mg/Fe] = [FORMULA] found by Norris & da Costa (1995b) for red giants in NGC 6752.

[FIGURE] Fig. 5a-c. Abundances of iron (a ), magnesium (b ), and helium (c ) for the programme stars in NGC 6752. The filled symbols mark stars which have been observed at higher resolution at the ESO 1.52m telescope, the open symbols mark stars observed at the NTT. Only the helium abundance could be derived for the NTT stars due to the low resolution of the data. The asterisk marks the results of Glaspey et al. (1989) for an HBB star in NGC 6752. Upper limits are marked by arrows.

The abundances are plotted versus temperature in Fig. 5. The trend of decreasing helium abundance with increasing temperature seen in the ESO 1.52m data (and also reported by Behr et al. 1999for HB stars in M 13) is not supported towards higher temperatures by the NTT data. This could be due to the lower resolution of the NTT data which may tend to overestimate abundances (Glaspey et al. 1989).

As iron is very important for the temperature stratification of stellar atmospheres we tried to take the increased iron abundance into account by computing model atmospheres for [M/H] = 0. Indeed a backwarming effect of 2-4% on the temperature structure was found in the formation region of the Balmer lines, when comparing solar composition models with the metal-poor models. We then repeated the fit to derive [FORMULA], [FORMULA], and [FORMULA] with these enriched model atmospheres. The resulting effective temperatures and gravities changed as displayed in Fig. 6. The results are listed in Table 3 and plotted in Fig. 4 (central panel). From Fig. 4 (central panel) it is clear that the use of solar-metallicity model atmospheres moves most stars closer to the canonical zero-age horizontal branch (ZAHB) due to a combination of lower [FORMULA] and/or higher [FORMULA]. The three stars between 10,000 K and 12,000 K, however, fall below the canonical ZAHB when fitted with enriched model atmospheres. This is plausible as the radiative levitation is supposed to start around 11,000 - 12,000 K (Grundahl et al. 1999) and the cooler stars therefore should have metal-poor atmospheres (see also Fig. 5, where the coolest analysed star shows no evidence of iron enrichment). This assumption is also supported by the results of Glaspey et al. (1985, NGC 6397; 1989, NGC 6752) and Behr et al. (1999, M 13; 2000b, M 15). Now the stars below 15,300 K scatter around the locus defined by the canonical HB tracks. The stars between 15,500 K and 19,000 K, however, still show offsets from the canonical locus while for the sdB stars not much is changed. Interestingly, 15,500 K is roughly the temperature 2at which the stars in NGC 6752 return to the ZAHB in ([FORMULA], u) of Grundahl et al. (1999). Grundahl et al. caution, however, that their faint photometry for NGC 6752 might be affected by poor seeing, and that in the Strömgren CMD of the better observed cluster, M13, the stars do not return to the ZAHB until a temperature of about 20,000 K.

[FIGURE] Fig. 6a-d. This plot shows the differences in effective temperature (a,c ) and surface gravity (b,d ) derived from fits with model atmospheres of different metallicity (solar-metal-poor [a,b ], metal-rich-metal-poor [c,d ]). It is obvious that an increase in the metallicity of the model atmospheres usually decreases the resulting temperatures and increases the resulting surface gravities.


Table 3. Physical parameters, helium abundances, and masses for the target stars in NGC 6752 as derived using solar metallicity model atmospheres.


Table 4. Helium, iron, and magnesium abundances of the HBB stars observed with the ESO 1.52m telescope (except B 3655, which has a too noisy spectrum). [Fe/H] and [Mg/H] are derived using solar abundances of [FORMULA] and [FORMULA]. The physical parameters and the helium abundances are taken from Table 3.

We next repeated the Balmer line profile fits by increasing the metal abundance of the model atmospheres to [M/H]=+0.5 (see Fig. 4, bottom panel, and Table 5), which did not significantly change the resulting values for [FORMULA] and [FORMULA]. In particular, note that especially the "deviant" stars (now between 15,300 K and 19,000 K) remain offset from the canonical ZAHB.


Table 5. Physical parameters, helium abundances, and masses for the target stars in NGC 6752 as derived using metal-rich model atmospheres.

4.2. Helium mixing

As outlined in Sect. 1, helium mixing during the RGB phase may also be able to explain the low gravities of the HBB stars. Under this scenario the mixing currents within the radiative zone below the base of the convective envelope of a red giant star are assumed to penetrate into the top of the hydrogen shell where helium is being produced by the hydrogen burning reactions. Ordinarily one would expect the gradient in the mean molecular weight µ to prevent any penetration of the mixing currents into the shell. If, however, the timescale for mixing were shorter than the timescale for nuclear burning, then the helium being produced at the top of the shell might be mixed outward into the envelope before a µ gradient is established. Under these circumstances a µ gradient would not inhibit deep mixing simply because such a gradient would not exist within the mixed region.

Since deep mixing is presumably driven by rotation, one would expect a more rapidly rotating red giant to show a larger increase in the envelope helium abundance. This, in turn, would lead to a brighter RGB tip luminosity and hence to greater mass loss. The progeny of the more rapidly rotating giants should therefore lie at higher effective temperatures along the HB than the progeny of the more slowly rotating giants. This predicted increase in the stellar rotational velocity with effective temperature along the HB has not, however, been confirmed by the recent observations of M13 by Behr et al. (2000a). These observations show that HB stars in M13 hotter than 11,000 K are, in fact, rotating slowly with [FORMULA] 10 km s-1 in contrast to the cooler HB stars where rotational velocities as high as 40 km s-1 are found (see also Peterson et al. 1995).

There are a couple of possible explanations for this apparent discrepancy. One possibility is that the greater mass loss suffered by the HBB stars might carry away so much angular momentum that the surface layers are spun down even though the core is still rotating rapidly. Alternatively Sills & Pinsonneault (2000) have suggested that the observed gravitational settling of helium in HBB stars might set up a µ gradient in the outer layers which inhibits the transfer of angular momentum from the rapidly rotating interior to the surface. Thus the surface rotational velocities may not necessarily be indicative of the interior rotation.

In order to explore the consequences of helium mixing for the HBB stars quantitatively, we evolved a set of 13 sequences up the RGB to the helium flash for varying amounts of helium mixing using the approach of Sweigart (1997a, 1997b). As in the case of the canonical models discussed previously, all of these mixed sequences had an initial helium abundance Y of 0.23 and a scaled-solar metallicity [M/H] of -1.54. The main-sequence mass was taken to be 0.805 [FORMULA], corresponding to an age at the tip of the RGB of 15 Gyr. The mixing depth, as defined by the parameter [FORMULA] of Sweigart (1997a, 1997b), ranged from 0.0 (canonical, unmixed case) to 0.24 in increments of 0.02. Mass loss via the Reimers formulation was included in the calculations with the mass-loss parameter [FORMULA] set equal to 0.40. This value for [FORMULA] was chosen so that a canonical, unmixed model would lie near the red end of the observed blue HB in NGC 6752. Both the mixing and mass loss were turned off once the models reached the core He flash at the tip of the RGB, and the subsequent evolution was then followed through the helium flash to the end of the HB phase using standard techniques.

We did not investigate the changes in the surface abundances of CNO, Na and Al caused by the helium mixing, since such a study was beyond the scope of the present paper. Rather, our objective was to determine how the mixing affected those quantities which impact on the HB evolution, i.e., envelope helium abundance and mass. We do note that the mixing in the more deeply mixed RGB models would have penetrated into regions of substantial Na and Al production according to the calculations of Cavallo et al. (1996, 1998). However, the resulting changes in the surface Na and Al abundances will depend on the assumed initial Ne and Mg isotopic abundances and on the adopted nuclear reaction rates, which in some cases are quite uncertain.

The locus of the above helium-mixed sequences in the [FORMULA] - [FORMULA] plane is indicated by the dashed lines in the top panel of Fig. 4. The red end of the mixed ZAHB in this panel, located at [FORMULA] = 3.93, is set by the canonical, unmixed sequence for the present set of model parameters. Since mixing increases the RGB mass loss, a mixed HB model will have a higher effective temperature than the corresponding canonical model. At the same time mixing increases the envelope helium abundance in the HB model, which, in turn, increases both the hydrogen-burning and surface luminosities. The net effect is to shift the mixed locus in Fig. 4 towards lower gravities with increasing [FORMULA] compared to the canonical locus, until a maximum offset is reached for 15,500 K [FORMULA] [FORMULA] [FORMULA] 19,000 K. At higher temperatures the mixed locus shifts back towards the canonical locus, as the contribution of the hydrogen shell to the surface luminosity declines due to the decreasing envelope mass. The predicted locus along the extreme HB (EHB) does not depend strongly on the extent of the mixing, since the luminosities and gravities of the EHB stars are primarily determined by the mass of the helium core, which is nearly the same for the mixed and canonical models. Overall the variation of [FORMULA] with [FORMULA] along the mixed locus in the top panel of Fig. 4 mimics the observed variation.

The results presented in Sect. 4.1 demonstrate that radiative levitation of heavy elements can account for a considerable fraction of the gravity offset along the HBB, especially for temperatures cooler than 15,100 K. Consequently the amount of helium mixing required to explain the remaining offset between 15,300 K and 19,000 K is much less than the amount required to explain the offsets found without accounting for radiative levitation (top panel of Fig. 4). In order to compare the gravities predicted by the helium-mixing scenario with those derived from the metal-enhanced atmospheres, we computed a second set of mixed sequences using the same approach as above but with a larger value of the mass-loss parameter [FORMULA], i.e., [FORMULA] = 0.45. The red end of the mixed ZAHB for these sequences is located at [FORMULA] = 4.01 and is therefore hotter than the red end of the mixed ZAHB for the sequences with [FORMULA] = 0.40. The HB stars cooler than this temperature in NGC 6752 would then be identified with unmixed stars which lost less mass along the RGB.

By increasing the mass loss efficiency we reduce the amount of mixing needed to populate the temperature range 15,300 K [FORMULA] [FORMULA] [FORMULA] 19,000 K and therefore the size of the resulting gravity offset. The locus of the mixed sequences with [FORMULA] = 0.45 is indicated by the dashed lines in the central panel of Fig. 4. The gravity offsets along this mixed locus seem to provide a reasonable fit to the gravities given by the model atmospheres with solar metallicity.

Finally we computed a third set of mixed sequences with the mass-loss parameter increased further to [FORMULA] = 0.50 for comparison with the gravities obtained from the atmospheres with super-solar metallicity in the bottom panel of Fig. 4. As expected, these mixed sequences show a smaller gravity offset in the temperature range 15,500 K [FORMULA] [FORMULA] [FORMULA] 19,000 K. Moreover, the red end of the mixed ZAHB shifts blueward to [FORMULA] = 4.08.

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© European Southern Observatory (ESO) 2000

Online publication: July 27, 2000