6 Discussion

In order to estimate the mass and the age of each of the program stars we have plotted them on the H-R diagram as can be seen in Fig. 5. The effective temperatures are those derived from the chemical analysis, and the luminosities were obtained from the above temperatures and the calibration of Schmidt-Kaler (1982); these quantities are listed in Table 2. Despite parallaxes do exist in the Hipparcos catalogue for some of the stars in our sample, we have preferred the above approach for the luminosity calculation for the following reasons. While a very respected version of the Period-Luminosity relation for cepheids has been calculated using Hipparcos parallaxes (Feast & Catchpole 1997) using the most well-known 26 cepheids as calibrators, individual parallaxes seem to be of little use. We have taken 21 cepheids such that the distances could be estimated without requiring the use of parallaxes. A straight comparison of distance moduli obtained from the Hipparcos parallaxes and from the P-L relation shows, in many cases, large differences. We have also noticed that Hipparcos parallaxes place some stars at unacceptable positions on the H-R diagram given the derived atmospheric parameters and elemental abundances. For example, for stars HD 172324 and HD 172481 the parallax data suggest values of log $(L/L_{\odot}) < 2.7$. The situation is further complicated by unknown circumstellar reddening, which could be substantial for some of the stars, given their high infrared fluxes. Therefore we decided not to use individual parallaxes in the present context.

All pre-AGB evolutionary model tracks plotted in Fig. 5 are those of Schaller et al. (1992), while the post-AGB models are from Blöcker (1995). All isochrones are from the work of Bertelli et al. (1994).

 

 

Table 14: Comparison of relevant [X/Fe] ratios for program stars and well known post-AGB stars

Star	[Fe/H]	[C/Fe]	[O/Fe]	[Mg/Fe]	[Si/Fe]	[S/Fe]	[Ca/Fe]	[s/Fe]	C/O	reference
HD 725	-0.29	-0.08		+0.12	+0.40	+0.20	+0.14	+0.27		1
HD 9167	-0.34			-0.04			+0.12	+0.12		1
HD 172324	-0.63	-0.68	+0.96	-0.02	+0.43	+0.42			+0.01	1
HD 173638	-0.08	-0.09		+0.03	+0.46		+0.09	+0.14		1
HD 218753	-0.19	-0.30	+0.05	-0.09	+0.23	+0.36	+0.11	+0.14	+0.21	1
HD 331319	-0.24	-0.09	+0.30	-0.01	+0.06	+0.53	-0.05	-0.30	+0.19	1
HD 158616	-0.57	+0.34	+0.04	+0.08	+0.56	+0.62	+0.21	+0.66	+0.95	1
HD 158616	-0.70	+0.64	-0.04		+0.68	+0.70	+0.71	+1.30	+1.90	2
HD 172481	-0.61	-0.01	+0.04	+0.51	+0.54	+0.58	+0.34	+0.52	+0.43	1
HR 7671	-1.10	-0.40	-0.30	+0.25	+0.40	+0.15	+0.32	+0.60	+0.38	6
HD 187785	-0.40	+1.00	+0.60	+0.67	+0.82	+0.57	+0.49	+1.30	+1.20	4
HD 187785	-0.60	+1.00	+0.70	+0.38		+0.26	+0.49	+1.10		11
HD 56126	-1.00	+1.08	+0.63	+0.97	+0.95	+0.63	+0.46	+1.78	+1.35	3
HD 56126	-1.00	+1.10	+0.80	+0.06		+0.40	-0.11	+1.50		11
IRAS 04296+3429	-0.60	+0.80			+0.79	+0.43	+0.18	+1.50		11
IRAS 05341+0852	-0.80	+1.00	+0.60		+0.59	+0.28	+0.08	+2.20		11
IRAS 22223+4237	-0.30	+0.30	-0.10		+0.29	+0.04	-0.17	+0.90		11
IRAS 23304+6147	-0.80	+0.90	+0.20		+0.79	+0.56	+0.29	+1.60		11
HR 4049	<-3.2	>+3.0	>+2.7	>+1.7	>+0.40	>+3.0	<-2.1		+0.95	5
HD 44179	-3.30	+3.30	+2.90	+1.2	+1.50	+3.00		+0.20	+1.20	2
HD 46703	-1.57	+0.98	+1.10	+0.09	-0.38	+1.20	+0.02	-0.49	+0.74	7, 8
HD 52961	-4.80	+4.40	+4.20			+3.80		+0.60	+0.76	2
HD 70379	-0.31	+0.42	+0.38	+0.01	+0.47	+0.34	-0.17	+0.20	+0.47	9
BD+39 4926	-2.85	+2.45	+2.75	+1.35	+1.15	+2.95	-0.75	+1.60	+0.25	10

References: 1 - This work, 2 - Van Winckel (1995) , 3 -Klochkova (1995), 4 - Van Winckel et al. (1996), 5 - Lambert et al. (1988), 6 - Luck et al. (1990), 7 - Luck & Bond (1984), 8 - Bond & Luck (1987), 9 - Reddy (1996), 10 - Kodaira (1973), 11 - Van Winckel & Reyniers (2000).

In terms of evolution, we could distinguish three groups among our sample stars. First, HD 158616, HD 172324, HD 172481, and HDE 341617 show clear indications of being post-AGB stars, these are shown in panel c of Fig. 5. The post-AGB model sequences of Blöcker (1995) suggest that all four stars had initial ZAMS masses larger than 7 $M_{\odot }$ and remnant or core mass of $\sim$ $1~M_{\odot}$. HD 158616 and HD 172481 might be starting their trajectory towards the white dwarfs region, i.e. they are near the zero age of central star evolution (Blöcker 1995), while HD 172324 is a bit more evolved. Since the evolution in this region of the H-R diagram is very fast, they are all expected to become planetary nebulae within a few hundreds of years. HDE 341617 has been found to be in the early stages of PN (Arkhipova et al. 1999; Parthasarathy et al. 2000). Our remnant mass estimate of $\sim$ $1~M_{\odot}$is substantially larger than 0.7 $M_{\odot }$ estimated by Arkhipova et al. (1999) from the rate of temperature evolutionary change and a comparison with the theoretical rates from Blöcker's (1995) models. Our value is a consequence of the spectroscopic determination of $T_{\rm eff} = 23\,000$ K and hence log $(L/L_{\odot}) = 4.6$ (Schmidt-Kaler 1982) as well as a comparison with the luminosities of Blöcker's (1995) models. While the Arkhipova et al. (1999) estimation is quite convincing the luminosity of the adopted model $(L/L_{\odot}) = 4.0$ seems too low as it would imply $T_{\rm eff}$ $\sim$ 18000 K for bright giant star of luminosity class II. Such low a temperature is not supported by the detailed spectroscopic analyses. Thus an independent estimate of the luminosity seems necessary to settle the core mass of this star.

In the second evolutionary group we include the stars HD 725, HD 218753 and HD 331319. These are all moderately iron-deficient but otherwise show nearly solar abundances. The heliocentric radial velocities for HD 218753 and HD 331319 are small. They are most likely young massive disk supergiants or bright giants that have gone through some nuclear processing. This is suggested by the C depletion and Na enhancement, indicating the effect of CN processing and post first dredge-up stage. HD 725 is an interesting star since three Y II and one Ba II lines indicate mild enhancement of s-process elements. Since we count on very scarce number of lines of s-process elements, we can only say that the star shows signs of evolution beyond RGB.

The tracks and isochrones in Figs. 5a and 5b suggest $M \sim 1.5-2.0~ M_{\odot}$ and age of 7.9   10⁸ yr for HD 218753 and $M \sim 11~ M_{\odot}$ and age of 2.2   10⁷ yr for HD 331319. From tracks in Fig. 5b we estimate a mass of $M \leq 9~ M_{\odot}$ and age of 2.5   10⁷ yr. Its rather large heliocentric radial velocity of -57 km s^-1 calls for attention, however, a calculation of the galactocentric motion indicates that the star moves on the galactic plane and has a mildly eccentrical galactic orbit. Its radial velocity could owe its origin to pulsations and/or orbital motions, although variability has not been reported.

The last two stars in our sample, HD 9167 and HD 173638, display, with few exceptions, solar abundances and no signs of nuclear processing. They are probably evolving very near the giant branch. The estimated masses and ages from Fig. 5b are respectively $M \sim 10~ M_{\odot}$ and 2.6  10⁷ yr and $M \sim 12~ M_{\odot}$ and 1.7   10⁷ yr. The only peculiarity of HD 9167 is its high radial velocity of -45.7 km s^-1 however, like HD 725, its galactocentric orbit seems to be on the galactic plane and mildly eccentric. Also the possibility, that their observed radial velocities are attained from pulsation and/or orbital motion cannot be discarded.

It should be noted that although HD 172481 and HD 158616 are post-AGB stars, they do not show the effect of selective removal of condensable elements such as Fe and Sc, observed in some well-known post-AGB stars like HR 4049, and HD 52961 and RV Tau stars of subclass B (Giridhar et al. 2000 and references therein). While studying a sample of RV Tau stars, these authors had noticed a strong dependence on temperature for the selective removal of refractory elements to occur. The effect is very prominent at temperature range 5500 to 6000 K and declines for lower temperatures. For stars cooler than 5000 K the effect was barely perceptible. At temperatures higher than 7000 K, we expect the effect to be larger. It is indeed true for HR 4049 (Lambert et al. 1988) which has $T_{\rm eff}$ = 7500 K, i.e. similar to HD 158616 and HD 172481. However, for these two stars we did not see any indication of dust condensation and subsequent removal of grain-forming elements. HD 158616 is a carbon-rich post-AGB star similar to HD 56126 (Klochkova 1995) and HD 187785 (Van Winckel et al. 1996) also showing significant enhancement of s-process elements.

Stars like HR 4049, HD 52961 and RV Tau stars of subclass B show C/O $\leq$ 1 and mild s-process enhancement. As a matter of fact, most stars showing abundance peculiarities caused by dust condensation have C/O $\leq$ 1. Stars HR 4049, HD 44179, HD 46703, HD 52961 and BD +39$^{\rm o}$ 4926 possibly belong to this subgroup. For these objects, since Fe gets locked in grains, [S/H] is considered a better indicator of metallicity. For these stars [S/H] ranges between +0.1 to -1.0 dex with a mean around -0.4 dex. In other words, they are mildly metal-deficient. Carbon-rich post-AGB stars with enhanced s-process elements, like HD 158616, HD 56126 and HD 187785 have [Fe/H] (which would be a true reflection of their metallicity since these stars are not affected by dust condensation) in the range -0.4 to -1.0 dex. These values are not radically different from those found for the subgroup having dust-grain condensation and C/O $\leq$ 1. We, therefore, do not visualize large differences in their ages though the O-rich phase in the AGB is expected to precede the C-rich phase.

The abundances of hot post-AGB stars studied by Conlon et al. (1993a) and McCausland et al. (1992) bear close resemblance to HD 172324. The hot post-AGB stars show strong deficiency of carbon and significant oxygen enrichment. These stars probably belong to a subgroup of post-AGB star that have evolved without experiencing third dredge-up. This carbon deficiency is also found in the proto-Planetary Nebula HDE 341617 (see Table 13). Caution is however needed with C II spectra since they are known to show large non-LTE effects (Eber & Butler 1988; Takeda & Takada-Hidai 1994). McCausland et al. (1992) have discussed at length two scenarios to explain the carbon deficiency. HBB occuring during interpulse phase could cause the production of ¹⁴N at the expense of ¹²C. However, overabundance of He like the one found in the SMC planetary nebula SMP 28 is not evident for HD 172324 and HD 341617 to make HBB the sole mechanism responsible for carbon deficiency. Another possibility suggested by McCausland et al. (1992) that the carbon deficiency might be inherent to the precursor itself is quite attractive. To substantiate their argument they pointed out the carbon-poor stars HR 4912 and HR 7671 as possible precursors to more evolved carbon-poor hot post-AGB stars. HR 4912 was included in our recent work and we found [C/H] = -1.27 (Giridhar et al. 1997) in good agreement with [C/H] of -1.15 found by Lambert et al. (1983). HR 7671 has [C/H] of -1.53 (Luck et al. 1990). It seems therefore that HD 172324 and HDE 341617 might form a special carbon-poor post-AGB stars evolutionary sequence. Search for carbon-poor objects in all temperature ranges may help in finding the precursors or successors of these objects.