8 Comparison of $\vec{T}_\mathsf{eff}$ and log$\vec{g}$ with other determinations and with the evolutionary models

In order to have an idea whether the gravities we derived from the ultraviolet energy distribution are more reliable than those we derived from the visible region in the case of stars cooler than about 8700 K, we have compared our determinations with those from other sources and with the evolutionary models plotted in the $T_{\rm eff}$, $\log\,g$ plane.

8.1 Comparison with other sources

Table 8 compares the parameters derived by us from the ultraviolet energy distribution (Cols. 4, 5) and from the visible energy distribution (Cols. 6, 7) with the parameters from Wilhelm et al. (1999) (WBG) (Cols. 9, 10) and with those from Gray et al. (1996) (GCP) (Cols. 13, 14). The parameters from WBG are based on both UBV photometry and a spectroscopic index D_0.2, related with the width of the H$_{\gamma }$ and H$_{\delta}$ Balmer profiles, which were measured by WBG on medium-resolution spectra. The parameters from GCP are based on both Strömgren photometry and the index D_0.2, which was measured by GCP on 2.8 Å resolution spectra.

The comparison of the parameters derived by us with those from WBG is shown in Fig. 8, where the stars are plotted in the $T_{\rm eff}$, $\log\,g$ plane. The upper panel in Fig. 8 indicates that the parameters from WBG (full points) and the parameters derived by us from the ultraviolet energy distribution (open triangles) agree quite well, with only one exception, HD 180903. The lower panel of Fig. 8 shows that the gravities derived by us from the visible energy distributions (open triangles) are larger than the gravities derived by WBG (full points).

Figure 8: Comparison of the parameters from Wilhelm et al. (1999) (WBG) (full points) with the parameters from this paper (CC) (open triangles) from the ultraviolet energy distribution (upper panel) and from the visible energy distribution (lower panel).

Figure 9: Comparison of the parameters from Gray et al. (1996) (GCP) (full points) with the parameters from this paper (CC) (open triangles) from the ultraviolet energy distribution (upper plot) and from the visible energy distribution (lower panel).

Figure 9 compares the parameters derived by us with those derived by GCP. In this case, the upper plot of Fig. 9 shows poor agreement between the parameters derived by us from the IUE spectra (open triangles) and those from GCP (full points), in the sense that the gravities derived from the ultraviolet energy distributions are systematically lower. Vice versa, the lower panel of Fig. 9 shows that the gravities derived by us from the visible region well agree with those from GCP.

In conclusion, the comparison of the parameters derived by us with those from WBG and GCP has not helped solving the question whether the gravities from the ultraviolet energy distributions are more reliable than those from the visible energy distributions.

8.2 The comparison with the evolutionary models

The parameters derived for our target stars from the IUE spectra and the new-ODF models (Cols. 5 and 6 of Table 3) are compared in Fig. 10 with ZAHB models at metallicity Z=0.002 and primordial helium content Y = 0.23, 0.33 and 0.43. These models are discussed in Sect. 3.1 of Sweigart & Catelan (1998), and were kindly made available to us by Catelan (2001, private communication). The stars BD+32 2188 and BD+00 145 are not shown in Fig. 10 as they are not BHB stars.

 

 

Table 7: The effect of different choices of $\xi$, [M/H], and $L/H_{\rm p}$on model parameters derived from UV (1200-1978 Å) and from the visible (3400-700 Å) energy distribution for HD 2857 when E(B-V)=0.022, and for HD 86986 when E(B-V)=0.022.

$\xi$	[M/H]	$L/H_{\rm p}$	$T_{\rm eff}$	$\log\,g$	$T_{\rm eff}$	$\log\,g$	$\xi$	[M/H]	$L/H_{\rm p}$	$T_{\rm eff}$	$\log\,g$	$T_{\rm eff}$	$\log\,g$
			HD 2857							HD 86986
			UV		visible					UV		visible
different $\xi$
2	[-1.75a]	1.25	7650	2.5	7550	3.0	2	[-1.75a]	1.25	8100	2.7	8000	3.2
4	[-1.75a]	1.25	7650	2.5	7550	3.0	4	[-1.75a]	1.25	8100	2.8	8000	3.3
different [M/H]
4	[-1.75a]	1.25	7650	2.5	7550	3.0	2	[-1.75a]	1.25	8100	2.7	8000	3.2
4	[-1.50a]	1.25	7700	2.5	7600	3.1	2	[-1.50a]	1.25	8150	2.7	8050	3.3
4	[-1.50]	1.25	7650	2.6	7600	3.1	2	[-1.50]	1.25	8100	2.8	8050	3.3
4	[-2.00a]	1.25	7800	2.8	7750	3.2	2	[-2.00a]	1.25	8050	2.8	8000	3.2
different $L/H_{\rm p}$
4	[-1.75a]	1.25	7650	2.5	7550	3.0	2	[-1.75a]	1.25	8100	2.7	8000	3.2
4	[-1.75a]	0.00	7650	2.5	7500	3.1	2	[-1.75a]	0.00	8100	2.7	7950	3.3

 

 

Table 8: Comparison between parameters from this paper and those from Wilhelm et al. (1999) (WBG) and from Gray et al. (1996) (GCP).

Star	E(B-V)	[M/H]	$T_{\rm eff}$	$\log\,g$	$T_{\rm eff}$	$\log\,g$	[M/H]	$T_{\rm eff}$	$\log\,g$	E(B-V)	[M/H]	$T_{\rm eff}$	$\log\,g$
			UV		vis.		WBG			GCP
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
HD 2857	0.022	[-1.75a]	7600	2.8	7700	3.2	[-1.62]	7663	2.92	0.044	[-1.5]	7700	3.1
HD 4850	0.009	[-1.25a]	8450	2.7			[-1.84]	8006	2.94
HD 13780	0.000	[-1.50a]	7900	2.7			[-1.81]	7684	2.62
HD 14829	0.018	[-2.00a]	8900	3.1	9000	3.1	[-2.42]	8519	3.05	0.015	[-2.0]	8700	3.3
HD 31943	0.006	[-1.00a]	7850	3.1			[-1.65]	7624	2.63
HD 60778	0.028	[-1.50a]	8250	2.9	8050	3.1				0.067	[-1.0]	8600	3.3
HD 74721	0.012	[-1.50a]	8800	3.2	8850	3.3	[-2.22]	8181	2.82	0.000	[-1.5]	8600	3.3
HD 86986	0.022	[-1.75a]	8100	2.8	8050	3.3	[-2.01]	7930	3.04	0.035	[-1.5]	8050	3.2
HD 87047	0.006	[-2.50a]	7900	2.8			[-2.11]	7985	2.93	0.001	[-1.5]	8300	3.2
HD 87112	0.003	[-1.50a]	9700	3.6			[-1.88]	9386	3.37
HD 93329	0.014	[-1.50a]	8250	2.9			[-1.85]	7949	2.99
HD 109995	0.010	[-1.75a]	8500	3.0	8450	3.4	[-2.11]	8103	2.96
HD 117880	0.077	[-1.50a]	9350	3.3	9400	2.8	[-2.53]	8684	3.08	0.067	[-1.5]	9200	3.4
HD 130095	0.072	[-2.00a]	9100	3.2	9050	3.4	[-2.34]	8845	3.20	0.064	[-1.5]	8950	3.4
HD 139961	0.051	[-1.75a]	8600	2.8			[-1.68]	8519	3.10
HD 161817	0.000	[-1.50a]	7600	2.7	7600	3.1	[-1.67]	7593	2.60	0.020	[-1.2]	7650	3.1
HD 167105	0.024	[-1.50a]	9000	3.1			[-1.95]	9498	3.12
HD 180903	0.098	[-1.50a]	7800	2.9			[-1.44]	7772	3.53
HD 202759	0.072	[-2.00a]	7500	2.8	7400	3.0	[-2.37]	7431	2.90
BD+42 2309	0.013	[-1.75a]	8750	3.0	9100	(2.4)				0.001	[-1.5]	8400	3.3

This comparison shows that, with the exception of the few stars hotter than about 9500 K, the gravities that we derive would be appropriate for models with a (unrealistically) high content of primordial helium. Other mechanisms of helium enhancement, such as those proposed by Sweigart (1999) and related to non-canonical mixing, are not relevant here because no significant mixing is expected to occur in field stars, and in any case i) it would affect the hotter stars rather than the cooler ones; and ii) it would produce abundance anomalies that are not observed in our sample.

This result leads us to conclude that determinations of gravity, as difficult as they may be in any wavelength range, are particularly uncertain and unreliable in the UV range especially for stars cooler than about 8700 K.

Figure 10: The parameters for the BHB stars derived from the UV energy distributions and new-ODF models (dots) are compared with the ZAHB evolutionary tracks for Z=0.002 and primordial helium abundances Y=0.23, 0.33 and 0.43 (Catelan 2001, private communication).