A&A 375, 963-976 (2001)
DOI: 10.1051/0004-6361:20010894

New results of magnetic field diagnosis in HgMn stars and normal late B-type stars

S. Hubrig1 - F. Castelli 2

1 - European Southern Observatory, Casilla 19001, Santiago 19, Chile

2 - CNR-Gruppo Nazionale Astronomia and Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, 34131 Trieste, Italy

Received 2 February 2001 / Accepted 18 June 2001

We suggested in a previous paper that three HgMn stars, HD 175640, HD 178065, and HD 186122, may be suspected to possess a magnetic field that could be larger than 2 kG. We report here new observations of these three stars, three more HgMn stars, and four normal late B-type stars. The search was carried out by measuring the equivalent width of the Fe  $\scriptstyle {\rm II}$ $\lambda\,6147.7$ Å line relative to the equivalent width of the Fe  $\scriptstyle {\rm II}$ $\lambda\,6149.2$ Å line. The observed relative differences between the equivalent widths of these Fe  $\scriptstyle {\rm II}$ lines are compared with those derived from synthetic spectra computed by neglecting magnetic field effects. To investigate the effect of oscillator strength uncertainties on the results, we computed equivalent widths by using both Fe  $\scriptstyle {\rm II}$ $\log~gf$-values taken from Kurucz & Bell (1995) and Fe  $\scriptstyle {\rm II}$ $\log~gf$-values taken from Raassen & Uylings (2000). The comparison of the computed and observed equivalent widths based on the Kurucz & Bell (1995) atomic data leads us to conclude that all the stars of our sample, except HD 175640, are very likely to possess a magnetic field. On the other hand, the comparison of the computed and observed equivalent widths based on the Raassen & Uylings (2000) $\log~gf$-values suggests the possible presence of magnetic fields only in three stars, the HgMn star HD 16717 and the two normal B-type stars HD 179761 and HD 186568. The latter two are those in the sample with the largest $v\sin i$ (15 km s-1 and 18 km s-1, respectively), so that the results for them are the most uncertain ones.

Key words: stars: abundances - stars: atmospheres - stars: chemically peculiar - stars: magnetic fields

1 Introduction

HgMn stars constitute a well-defined sub-group of chemically peculiar (CP) stars of B spectral type in the temperature range 10000-14000 K. These stars exhibit marked abundance anomalies of several elements: e.g., overabundances of Hg, Mn, Ga, Y, Cu, Be, P, Bi, Sr, Zr, and deficiencies of He, Al, Zn, Ni, Co. The HgMn stars differ from the classical Bp stars, which share the same temperature range, because they generally have neither extreme overabundances of rare earths, nor significant overabundances of Si. In fact, the excess of Si is the most obvious anomaly in classical Bp stars. The He-weak stars constitute another group of peculiar stars which overlap in temperature the hottest HgMn stars, in that their $T_{\rm eff}$ ranges from about 13000 K to about 17000 K. The He-weak stars are defined as stars having abnormally weak helium lines. In analogy with the HgMn stars they may show enhanced lines of Mn and Hg.

In contrast with Bp and He-weak stars, the HgMn stars do not show conspicuous intensity variations of the spectral lines. Large-scaled organized magnetic fields were measured in both classical Bp and He-weak stars, while they have not been definitely detected in HgMn stars. Although Babcock (1958) had reported about weak longitudinal fields in some HgMn stars, this finding was never confirmed in later studies (e.g., Conti 1970; Landstreet 1992). However, weak magnetic fields, with a longitudinal component less than a few hundred Gauss, or complex in structure, can not be excluded a priori for HgMn stars, owing to the limitations of the usual spectropolarimetric techniques.

We have shown in a previous paper (Hubrig et al. 1999, Paper I) that three HgMn stars, HD 175640, HD 178065, and HD 186122, were suspected to possess a magnetic field with complex and/or toroidal structure. To detect magnetic fields we have applied a simple method introduced by Mathys (1990) which uses the relative magnetic intensification $\Delta$W/ $\overline {W}$ of the two Fe  $\scriptstyle {\rm II}$ lines of mult. 74, $\lambda\,6147.7$ Å and $\lambda\,6149.2$ Å. $\Delta$W/ $\overline {W}$ is defined as the ratio of the difference of the equivalent widths of the two Fe  $\scriptstyle {\rm II}$ lines to the average of the two equivalent widths. The two Fe  $\scriptstyle {\rm II}$ transitions have approximately the same intensity under normal conditions and observations of normal A-type stars have shown that the equivalent widths of the two lines do not differ in these stars more than 2.5% (Mathys & Lanz 1990). Differences larger than 10% in the equivalent widths were observed in magnetic Ap and Bp stars by Mathys (1990). They were explained by Takeda (1991) as due to magnetic intensification produced by different magnetic desaturations induced by different Zeeman-split components. Takeda (1991) also showed that the relative intensification is roughly correlated with the strength of the magnetic field, so that it is potentially a powerful tool for detecting magnetic fields which have a complex structure and are difficult to detect by polarization measurements.

The method was successively applied by Lanz & Mathys (1993) to detect magnetic fields in Am stars, after Mathys & Lanz (1990) measured a relative intensification of 5.2% in the Am star o Peg. Among the 18 Am stars examined, they found two stars affected by magnetic fields according to their measured $\Delta W/\overline {W}$, whose values were larger by 0.03-0.04 than the predicted ones.

The same method was used in this paper with the aim to continue the search for magnetic fields in HgMn stars performed in Paper I. In the previous study we examined nine HgMn stars. All the stars except one (HD 141556) were observed on a single occasion. In order to confirm the results from Paper I and/or assess the possible variability of magnetic fields, we have reobserved four HgMn stars. We added two new HgMn stars, and five normal late B-type stars to be used as comparison stars. All the spectra analyzed in this paper were obtained on one night in August 1999 at the CFHT with the high-resolution coudè spectrograph (Gecko) and have a higher S/N ratio than the spectra adopted for Paper I, which were taken at ESO with the 1.4 m CAT telescope.

\par\includegraphics[width=11cm]{fig1ab.ps}\end{figure} Figure 1: The observed spectra normalized to the continuum. For HD 175640, HD 178065, HD 186122, HD 193452, and HD 196426, the CFHT spectra (full lines) are compared with the CAT spectra (dashed lines) used in Paper I. The vertical scale is reduced by one half for HD 186122 and HD 193452. Absorption lines are Cr  $\scriptstyle {\rm II}$ mult. 105 at 6147.154 Å, Fe  $\scriptstyle {\rm II}$ mult. 74 at 6147.741 Å together with Fe  $\scriptstyle {\rm II}$ at 6147.775 Å, Fe  $\scriptstyle {\rm II}$ mult. 74 at 6149.258 Å, and Hg  $\scriptstyle {\rm II}$ at 6149.5 Å.
Open with DEXTER

\end{figure} Figure 1: continued.
Open with DEXTER

Because the Mathys method can be applied only to stars having $v\sin i$ low enough to avoid blends of the two Fe  $\scriptstyle {\rm II}$ lines at 6147.7 Å and 6149.2 Å each other and with other components, we observed only sharp-lined stars. As mentioned in Paper I, the line Fe  $\scriptstyle {\rm II}$ $\lambda\,6149.248$ Å is severely blended in HgMn stars with the line Hg  $\scriptstyle {\rm II}$ at $\lambda\,6149.475$ Å and therefore the applied method can provide a satisfactory diagnosis only for very slowly rotating HgMn stars observed at high resolution, so that the Fe  $\scriptstyle {\rm II}$ and the Hg  $\scriptstyle {\rm II}$ features are not blended. All the HgMn stars in our sample (HD 16727, HD 27295, HD 175640, HD 178065, HD 186122, and HD 193452) are slowly rotating stars with $v\sin i$ $\leq$ 5 km s-1 and they are not known to be spectroscopic binaries.

Five late B-type stars, HD 179761, HD 186568, HD 196426, HD 209459, and HD 219927, were observed as comparison stars because they have a sharp-lined spectrum and were not found to show chemical peculiarities and magnetic fields (Cowley 1972; Cowley & Aikman 1980). Three out of the five stars (HD 179761, HD 196426 and HD 209459) have been frequently used as comparison standards in other studies (e.g., Smith & Dworetsky 1993; Dworetsky & Budaj 2000). The Hg  $\scriptstyle {\rm II}$ line is not a problem for the normal B-type stars. Mercury abundances $\le$2.5 dex were derived by Smith (1997) in normal late B-type stars from the analyis of Hg  $\scriptstyle {\rm II}$ at 1942 Å observed in co-added IUE spectra. We verified by computing synthetic spectra for log $\epsilon\rm (Hg)=2.5$ that no Hg  $\scriptstyle {\rm II}$ line at $\lambda\,6149.475$ Å is predicted in late B-type stars for this mercury abundance.

2 Observations

The observations were made on 1999 August 29 at the CFHT with the GECKO spectrograph at a resolving power of $R = 125\,000$ and grating settings corresponding to the wavelength interval 6105-6190 Å. Programme stars are listed in Table 1, where we give the HD number and other identifiers in Cols. 1-3, the V magnitude and the spectral type (both from the catalog of Renson 1991) in Cols. 4 and 5. The spectra were reduced with the help of D. A. Bohlender. A set of IRAF macros written by Bohlender et al. (1998) was used. Special care was taken in order to eliminate the scattered light from the spectra.

The achieved signal-to-noise ratios in the continuum are given in Col. 6 of Table 1. They were measured after reduction in portions of the spectrum apparently devoid of lines: accordingly the derived values must be regarded as upper limits of the S/N ratio actually obtained. The typical value of the signal-to-noise ratio of our spectra is larger than 300.


Table 1: Journal of observations.
HD HR Other id. V Sp. type S/N
HgMn stars
 16727 785 11 Per 5.7 B7 HgMn 320
 27295 1339 53 Tau 5.5 B9 HgMn 250
1756401 7143   6.2 B9 HgMn 390
1780651 7245   6.6 B9 HgMn 375
1861221 7493 46 Aql 6.3 B9 MnHg 360
1934521 7775   6.1 B9 HgMn 350
Superficially normal stars
1964261 7878   6.2 B8 III 460
209459 8404 21 Peg 5.8 B9.5 V 380
Normal stars
179761 7287 21 Aql 5.1 B8 II-III 370
186568 7512   6.1 B9 II 420
219927 8873   6.3 B8 III 320

1 Stars studied also in Hubrig et al. (1999) (Paper I).

The spectra, normalized to the continuum, are shown in Fig. 1 for the region 6146-6150 Å. The CFHT spectra of HD 175640, HD 178065, HD 186122, HD 193452, and HD 196426 are compared with the spectra observed at CAT and used in Paper I. The larger noise of the CAT spectra is evident in the figure. The superficially normal late B-type star HD 196426, used in Paper I as a comparison star, turned out to be a spectroscopic binary. Both Fe  $\scriptstyle {\rm II}$ lines show very asymmetric profiles in the CFHT spectrum, with red wings much steeper than blue wings. As a consequence, this star was not used in this paper.

3 The method

The analysis was performed as in Paper I. We searched for a possible intensification of the line Fe  $\scriptstyle {\rm II}$ 6147.7 Å relative to the line Fe  $\scriptstyle {\rm II}$ 6149.2 Å by measuring the equivalent widths of the two absorption profiles. Then, we derived an intensification index in according to Mathys (1990):

\begin{displaymath}{\Delta W}/{\overline{W}}=\frac{{W(6147.7)-W(6149.2)}}{{ 0.5 (W(6147.7)+W(6149.2))}}\cdot

Because Fe  $\scriptstyle {\rm II}$ 6147.741 Å may be blended with Fe  $\scriptstyle {\rm II}$ 6147.775 Å, the measured intensification could be due to the blend of the two Fe  $\scriptstyle {\rm II}$ lines at 6147.7 Å rather than to the effect af a magnetic field. We therefore simulated the observed spectrum with synthetic spectra which consider all the possible predicted contributions to Fe  $\scriptstyle {\rm II}$ 6147.741 Å. Then we measured the equivalent widths of the computed profiles at 6147.7 Å and at 6149.2 Å and we derived the computed intensification index. The difference between the observed and computed $\Delta W/\overline {W}$ ratios yields the amount of the intensification of Fe  $\scriptstyle {\rm II}$ 6147.7 Å over Fe  $\scriptstyle {\rm II}$ 6149.2 Å due to the magnetic field.

4 The measured equivalent widths and the measured $\Delta W/\overline {W}$ ratio

The equivalent widths W of the Fe  $\scriptstyle {\rm II}$ lines at 6147.7 Å and 6149.2 Å were measured both by Gaussian fitting and by direct integration of the line profiles using the IRAF package. For the most rapidly rotating stars, HD 179761 and HD 186568, we kept only the measurements performed by direct integration, because of the non-Gaussian form of the rotational broadening function.

In the spectra examined with IRAF any preselected continuum disappears, so that it may be differently fixed each time a line is measured. Therefore, we also used a code written by F.C., which keeps the preselected continuum and yields equivalent widths measured by direct integration. A further shortcoming affecting the measurement of the equivalent widths is the requirement that the width of the profile has to be fixed at the level of the continuum. Owing to the spectral noise, the choice of the blue end and of the red end of a profile may be a difficult decision especially when very accurate equivalent widths are required. Since the CFHT spectra are taken at high S/N ratio, Fig. 1 shows that this is not a serious problem for some stars in our sample. However, for other stars, such as HD 178065, HD 209459, and HD 186568, the fixing of the width of the profiles is a completely subjective decision. A further uncertainty occurs in HgMn stars for the equivalent width of Fe  $\scriptstyle {\rm II}$ 6149.25 Å, when the line is blended with Hg  $\scriptstyle {\rm II}$ 6149.48 Å.

To be more definitive about uncertainties in the equivalent widths, the measurements were performed independently by each author. Table 2 lists the measured equivalent widths: ( $W_{\rm g,c}$) and ( $W_{\rm g,h}$) are the equivalent widths from the fit to Gaussians measured by F.C. and S.H. respectively; ( $W_{\rm i,c}$) and ( $W_{\rm i,h }$) are the equivalent widths measured by direct integration by F.C. and S.H. respectively; ( $W_{\rm i,c1}$) indicates the equivalent widths measured by F.C. by direct integration by means of her code. The average of all five determinations together with the rms values for W(6147) and W(6149) are given in Cols. 12 and 13. Finally, Col. 14 shows the ratio ( $\Delta W/\overline {W}$) $_{\rm obs}$ with the associated uncertainties. The equivalent widths in Table 2 are given in mÅ.

HD 27295 yields an example of the uncertainty in $\Delta W/\overline {W}$related with different placements of the continuum. This star exhibits the faintest Fe  $\scriptstyle {\rm II}$ lines. Equivalent widths which differ more than 1.0 mÅ were measured by F.C. and S.H., respectively. In Table 2, the first row for HD 27295 lists all the measured equivalent widths and their average, while the two successive rows list the separate measurements and show that systematic differences in the placement of the continuum may lead to differences on the order of 0.02 for the $\Delta W/\overline {W}$ ratio. If we exclude HD 27295, the uncertainty on $\Delta W/\overline {W}$ is less than 0.03. The typical difference between several measurements of the equivalent widths in the same spectrum with the same continuum is on the order of 0.3-0.4 mÅ.

Unfortunately, all the spectra were obtained during a single night, and we do not have several spectra for any star to verify the noise statistics across the measured lines. On the other hand, we have already shown (Paper I) for the star HD 141556 that the ratio $\Delta W/\overline {W}$ derived from the repeated observations is almost the same, differing by only 0.003 when the direct integration method was used.

For nine out of the ten stars examined the equivalent width of Fe  $\scriptstyle {\rm II}$  $\lambda\,6147.7$ Å is larger than that of Fe  $\scriptstyle {\rm II}$  $\lambda\,6149.2$ Å. This behaviour is similar, even if less conspicuous, to that observed by Mathys & Lanz (1992) for the magnetic Ap stars. Only for the HgMn star HD 175640, the equivalent width of Fe  $\scriptstyle {\rm II}$  $\lambda\,6149.2$ Å is larger by 0.1 mÅ than that of Fe  $\scriptstyle {\rm II}$  $\lambda\,6147.7$ Å. In Paper I this star was suspected to possess a magnetic field. Figure 1 shows that the profiles in the CAT spectrum are slightly stronger than those in the CFHT spectrum. The difference is reduced if the continuum in the CAT spectrum is lowered. The slightly higher continuum placement and the rather strong noise are probably the cause of the larger measured equivalent widths in the CAT spectrum. The results from Paper I are compared in more detail with those from this paper in Sect. 7.

5 The computed quantities

5.1 Model parameters

The model parameters $T_{\rm eff}$ and $\log g$ were derived from observed Strömgren indices and also from spectrophotometry, when available.

Observed Strömgren indices were taken from the catalog of Hauck & Mermilliod (1998) and were dereddened by means of the UVBYLIST code of Moon (1985), which yields E(b-y), and therefore (b-y)0=(b-y)-E(b-y), m0= m1+ 0.33E(b-y), and c0= c1 - 0.19E(b-y); the last two relations, as well as E(B-V)=E(b-y)/0.724 for RV=3.1, are taken from Crawford & Mandwewala (1976). The reddening E(B-V) was used for dereddening the spectrophotometric observations, which are available for HD 27295 (Adelman & Pyper 1979), HD 209459 (Adelman & Pyper 1983), HD 179761 (Adelman 1978), and HD 219927 (Breger 1976). For each star of the sample, Table 3 lists the observed Strömgren indices, the reddening E(b-y), and the reddening E(B-V).


Table 2: Measured equivalent widths in mÅ and the $\Delta W/\overline {W}$ ratio.

$W_{\rm g,c}$ $W_{\rm i,c}$ $W_{\rm i,c1}$ $W_{\rm g,h}$ $W_{\rm i,h }$ $W_{\rm g,c}$ $W_{\rm i,c}$ $W_{\rm i,c1}$ $W_{\rm g,h}$ $W_{\rm i,h }$ $\overline {W}_{\rm obs}$ $\overline {W}_{\rm obs}$ ( $\Delta W/\overline{W})_{\rm obs}$
      6147         6149     6147 6149  

HgMn stars
16727 15.6 15.4 15.2 15.3 15.1 14.1 13.3 13.7 13.4 13.0 $15.32\pm0.09$ $13.50\pm0.19$ $0.126\pm0.015$
27295 4.8 4.7 4.8 6.1 6.0 4.5 4.5 4.5 5.6 5.6 $5.28\pm0.33$ $4.94\pm0.28$ $0.066\pm0.081$
  4.8 4.7 4.8     4.5 4.5 4.5     $4.77\pm0.00$ $4.50\pm0.00$ $0.058\pm0.007$
        6.1 6.0       5.6 5.6 $6.05\pm0.05$ $5.6\pm0.00$ $0.077\pm0.008$
175640 10.3 10.4 10.5 10.3 10.3 10.4 10.5 10.7 10.2 10.2 $10.36\pm0.04$ $10.40\pm0.09$ - $0.004\pm0.010$
178065 19.9 20.1 20.3 20.1 20.2 19.3 19.3 19.6 19.2 19.4 $20.12\pm0.07$ $19.36\pm0.07$ $0.039\pm0.005$
186122 38.1 38.2 38.4 37.8 38.1 36.7 36.4 36.9 36.4 36.1 $38.12\pm0.10$ $36.50\pm0.14$ $0.043\pm0.005$
193452 33.7 34.0 35.1 33.6 34.4 33.5 33.0 33.5 32.5 32.6 $34.16\pm0.27$ $33.02\pm0.21$ $0.034\pm0.010$
Normal stars
209459 24.4 24.2 24.5 25.1 25.1 24.1 24.1 23.9 24.0 24.0 $24.66\pm0.19$ $24.02\pm0.04$ $0.026\pm0.008$
179761   16.0 16.3   16.4   14.7 14.6   14.9 $16.23\pm0.12$ $14.73\pm0.09$ $0.097\pm0.009$
186568   24.2 24.4   23.9   21.6 21.9   21.3 $24.17\pm0.14$ $21.60\pm0.17$ $0.112\pm0.002$
219927 18.3 18.4 19.5 19.6 19.8 17.6 17.6 17.8 18.2 18.4 $19.12\pm0.32$ $17.92\pm0.16$ $0.066\pm0.019$

Because our spectra have too few lines in order to derive the microturbulent velocity $\xi$, we searched for it in the literature. The available $\xi$ and the corresponding source are given in Cols. 8 and 9 of Table 3. All the microturbulent velocities are lower than 2 km s-1, in agreement with Adelman & Rayle (2000), who stated that "Trends in recent elemental abundances studies indicate for normal main sequence band stars with $T_{\rm eff}\ge10\,500$ K that their microturbulence is 0 km s-1...'' and in agreement with Adelman (1994) who showed that most HgMn stars have little or no microturbulent velocity. We investigated the effect of the microturbulent velocity on the stellar parameters by deriving them from fluxes and colors based on two different grids of models, namely AP00K0NOVER and AP00K2NOVER. The first grid was computed for $\xi=0.0$ km s-1, while the second grid was computed for $\xi=2.0$ km s-1. The metallicity is $\rm [M/H]=0.0$ for both grids. The grids are available at the Kurucz website[*] in the subdirectory "gridp00nover'' of the directory "grids of model atmospheres''. The models in the grids were obtained by merging the models computed by Castelli for $T_{\rm eff}\le8750$ K with the models computed by Kurucz for $T_{\rm eff}> 8750$ K. More details about these grids are given by Castelli (1999). The grids of fluxes and the grids of synthetic Strömgren colors used for this paper were computed from the above models and are available in the same directories of the grids of models. The grids of fluxes are FP00K0NOVER (for $\xi=0.0$ km s-1) and FP00K2NOVER (for $\xi=2.0$ km s-1), while the grids of synthetic Strömgren colors are UVBYBETAP00K0NOVER (for $\xi=0.0$ km s-1) and UVBYBETAP00K2NOVER (for $\xi=2.0$ km s-1). The synthetic $uvby\beta$ indices were computed according to Lester et al. (1986) except for the normalization: instead of using five stars ($\gamma$ Gem, $\alpha$ CMi, $\beta$ Leo, $\eta$ UMa, and Vega) for the normalization of the indices as did Lester et al. (1986), the uvby indices were normalized using only Vega, while the $\beta$ indices were normalized by using both Vega and the Sun. The possible problems due to the use of $\eta$ UMa to normalize the indices are discussed by Castelli (1991).

Parameters $T_{\rm eff}$ and $\log~g$ from Strömgren photometry were derived by interpolating the dereddened observed indices in the grids of synthetic indices. Those for $\xi=0$ km s-1 are given in Cols. 2 and 3 of Table 4, while those for $\xi=2$ km s-1 are listed in Cols. 4 and 5. The largest difference in $T_{\rm eff}$ is 77 K for HD 16727, while the largest difference in $\log~g$ is 0.02 dex for HD 209459. Column 9 in Table 4 specifies which indices were used to obtain $T_{\rm eff}$ and $\log g$. The errors associated with the parameters were derived by assuming an uncertainty of $\pm$0.015 mag for all the observed indices (Relyea & Kurucz 1978), except for $\beta$, for which an error of $\pm$ 0.016 mag was adopted. It is the largest error in $\beta$ for the sample of stars. In fact, errors in $\beta$, as taken from the catalog of Hauck & Mermilliod (1998), range from 0.001 mag for HD 219927 to 0.016 mag for HD 175640, while, for all the stars, the errors in c are less than the error adopted by us.

Parameters for HD 27295, HD 209459, HD 179761, and HD 219927 were also derived by fitting the dereddened spectrophotometric observations to the grids of synthetic fluxes FP00K0NOVER and FP00K2NOVER. The fitting procedure is based on that described by Lane & Lester (1984). The search for the minimum rms difference between the observed and computed energy distributions is made by interpolating in the grids of computed fluxes. The computed fluxes are sampled in steps of 50 K in $T_{\rm eff}$ and in steps of 0.1 dex in $\log~g$, so the finer sampling was obtained by linear interpolation. Columns 7 and 8 of Table 4 show the parameters derived from the spectrophotometry by using fluxes computed for $\xi=0$ km s-1. For the four stars, the temperature derived from fluxes computed for $\xi=2.0$ km s-1 is 50 K lower than $T_{\rm eff}$ derived from fluxes computed for $\xi=0.0$ km s-1, while the gravity does not change. Temperatures from Strömgren indices and from the spectrophotometry corresponding to $\xi=0$ km s-1 differ no more than 104 K (HD 209459), while the differences in $\log~g$ are as large as 0.4 dex (HD 27295). The adopted parameters for the sample of stars are given in Cols. 9 and 10 of Table 4. They approximate the determinations listed in Cols. 2-5, 7, and 8.

The last two columns of Table 4 list, for comparison, the parameters derived by Smith & Dworetsky (1993) for the stars in common and which were derived by them from Strömgren photometry, Geneva photometry, spectrophotometric scans, and H$_{\gamma}$ profiles. The agreement with our determinations from Strömgren photometry is very good.


Table 3: Strömgren indices, reddening, microturbulent velocity, and rotational velocity.

(b-y) m1 c1 $\beta$ E(b-y) E(B-V) $\xi$ Ref. $v\sin i$

HgMn stars
16727 -0.050 0.114 0.471 2.729 0.016 0.022 -   4.50
27295 -0.036 0.129 0.738 2.799 0.004 0.055 0.0 (1) 5.00
175640 +0.001 0.103 0.747 2.771 0.044 0.061 1.0 (2) 2.50
178065 +0.073 0.077 0.729 2.718 0.119 0.164 -   1.70
186122 -0.019 0.094 0.641 2.729 0.035 0.048 0.0 (2) 0.00
193452 -0.007 0.138 0.909 2.845 0.017 0.023 0.0 (2) 0.75
Normal stars    
209459 -0.011 0.112 1.023 0.796 0.008 0.011 0.5 (2) 3.70
179761 -0.010 0.084 0.629 2.700 0.046 0.063 0.0 (3) 15.00
186568 -0.008 0.088 0.814 2.724 0.032 0.044 -   18.00
219927 -0.008 0.095 0.637 2.718 0.045 0.062 -   5.00

References for $\xi$: (1) Adelman & Pyper (1979); (2) Smith & Dworetsky (1993); (3) Adelman (1984).


Table 4: Stellar parameters $T_{\rm eff}$(K) and $\log~g$.

                                1 SD: Smith & Dworetsky (1993).
                                2 The definition of the indices a and r* can be found in Strömgren (1966) and in Moon & Dworetsky (1985).

5.2 The synthetic Fe9pt11ptII profiles

The iron abundance needed for computing the synthetic Fe  $\scriptstyle {\rm II}$ profiles was derived for each star from the measured equivalent width of the line Fe  $\scriptstyle {\rm II}$ $\lambda\,6149.2$ Å and from the ATLAS9 (Kurucz 1993a) model computed for $\xi=0.0$ km s-1, solar metallicity, and parameters given in Cols. 9 and 10 of Table 4. The WIDTH code of Kurucz (1993a) was used to obtain the iron abundance.

The line Fe  $\scriptstyle {\rm II}$ $\lambda\,6149.2$ Å was assumed as unblended in all the stars, although this hypothesis could be questionable for HD 179761 and HD 186568, the most rapidly rotating stars of the sample ( $v\sin i=15$ km s-1 and $v\sin i=18$ km s-1, respectively). However, if some unpredicted line contributes to the equivalent width of Fe  $\scriptstyle {\rm II}$ at 6149.2 Å, the actual magnetic intensification should be larger than that measured by us and listed in Table 2 (i.e. a blend with Fe  $\scriptstyle {\rm II}$ $\lambda\,6149.2$ Å serves to reduce $\Delta W/\overline {W}$).

For each star, the same atmosphere model used in WIDTH and the iron abundance obtained from WIDTH were then used in the SYNTHE code of Kurucz (1993b) to compute a synthetic spectrum at $1.2\times10^{6}$ resolution. As in Paper I, the lines of the gf0800.100 line list from Kurucz & Bell (1995) were adopted, except for the Hg  $\scriptstyle {\rm II}$ line at 6149.47 Å, which was replaced by the Hg  $\scriptstyle {\rm II}$ isotopic components given in Paper I and reported here in Table 5. The $\Delta W/\overline {W}$ ratios were computed by assuming solar abundances for all the elements except for iron.

The synthetic profiles were broadened for an instrumental resolution of 125000 and for the rotational velocity $v\sin i$ listed in the last column of Table 3. For each star, the rotational velocity is that which best reproduces the observed Fe  $\scriptstyle {\rm II}$ $\lambda\,6149.2$ Å profile, when the synthetic profile is computed by using the adopted model parameters given in Table 4 and the corresponding iron abundance listed in Table 6.

The wavelength sampling in the synthetic spectra corresponding to the resolution of $1.2\times10^{6}$ was selected in order to provide accurate equivalent widths from the synthetic profiles integrated by means of a simple Simpson rule for a constant step-size. The computed equivalent widths in WIDTH are obtained by a generalized Simpson rule for a step-size which increases with the increasing of the distance from the line center. The two different integration methods give differences in the computed equivalent widths on the order of 0.1 mÅ. Because the computed profiles are free from any noise, the equivalent widths obtained by direct integration are not affected by the uncertainty related to the choice of the blue and red ends of the profile as in the case of the equivalent widths measured on the observed profiles, provided that the stars have low $v\sin i$. In fact, for the two most rapidly rotating stars of the sample, HD 179761 and HD 186568, the predicted lines of Ni  $\scriptstyle {\rm II}$ at 6148.246 Å, Ni  $\scriptstyle {\rm II}$ at 6148.674 Å, and Fe  $\scriptstyle {\rm II}$ at 6148.848 Å cause a lowering of the continuum on the order of 0.1% in the region 6148.20-6148.85 Å, so that it is impossible to know where exactly the red wing of the 6147.7 Å line ends and where the blue wing of the 6149.2 Å line starts. By looking at the numbers giving the residual flux, we assumed for HD 179761 that the blue wing of Fe  $\scriptstyle {\rm II}$ 6147.7 Å ends at 6148.1899 Å and that the red wing of Fe  $\scriptstyle {\rm II}$ 6149.2 Å starts at 6148.8384 Å. The corresponding equivalent widths are 15.55 mÅ and 14.82 mÅ. For the same star, we derived slightly different wavelength limits from the visual inspection of the plotted profiles, corresponding to equivalent widths of 15.37 mÅ and 14.80 mÅ. The $\Delta W/\overline {W}$ ratios corresponding to two cases are 0.048 and 0.038, respectively. They are both much lower than the observed ratio 0.097.

For HD 186568, the equivalent widths derived by fixing the limits of the profiles by looking at values of the residual flux are 22.57 mÅ for Fe  $\scriptstyle {\rm II}$ 6147.7 Å and 21.85 mÅ for Fe  $\scriptstyle {\rm II}$ 6149.2 Å. When the limits of the profiles were fixed from the visual inspection of their shape we derived 22.23 mÅ and 21.68 mÅ for the two Fe  $\scriptstyle {\rm II}$ lines. The $\Delta W/\overline {W}$ ratios corresponding to the two measurements are 0.032 and 0.025, respectively. Both values are lower than the observed ratio 0.112.

The lines of the region 6147-6150 Å which have a computed residual flux at the line center equal or less than 0.999 are listed in Col. 3 of Table 5. They are taken from the Kurucz & Bell (1995) line list. The $\log~gf=-2.519$ adopted in Paper I for Fe  $\scriptstyle {\rm II}$ 6147.775 Å is replaced in this paper by $\log~gf=-0.819$ from Kurucz & Bell (1995). The $\log~gf$ adopted in Paper I was fixed from the requirement that the difference between the computed equivalent widths of Fe  $\scriptstyle {\rm II}$ 6147.741 Å and Fe  $\scriptstyle {\rm II}$ 6149.258 Å be not larger than 0.1 mÅ for HD 196426, in agreement with the measured equivalent widths. The computed contribution of Fe  $\scriptstyle {\rm II}$ 6147.775 Å to Fe  $\scriptstyle {\rm II}$ 6147.741 Å was suppressed when $\log~gf(6147.775)=-2.519$ was adopted. In Paper I, HD 196426 was considered to be a normal B-type star, therefore free from any magnetic intensification. For this reason, it was adopted as a comparison star for the sample of HgMn stars. The finding that HD 196426 is very likely a spectroscopic binary makes now the lowering of the $\log~gf$ value very arbitrary, all the more so, as Table 2 shows, that the measured equivalent widths of the profiles at 6147.7 Å and 6149.2 Å are different also in normal B-type stars.

In order to investigate the effect on the computed equivalent widths of Fe  $\scriptstyle {\rm II}$ $\log~gf$-values different from those of Kurucz & Bell (1995), we also used the Fe  $\scriptstyle {\rm II}$ oscillator strengths from Raassen & Uylings (2000). They are listed in the fourth column of Table 5.

In all the stars, Fe  $\scriptstyle {\rm II}$ at 6147.741 Å is blended with Fe  $\scriptstyle {\rm II}$ 6147.775 Å, whichever is the source of the Fe  $\scriptstyle {\rm II}$ $\log~gf$-values, Kurucz & Bell (1995) or Raassen & Uylings (2000). In HD 193452 and in HD 209459, Fe  $\scriptstyle {\rm II}$ 6147.741 Å is also blended with Fe  $\scriptstyle {\rm I}$ 6147.829 Å. The residual flux at the line center of the unbroadened Fe  $\scriptstyle {\rm I}$ profile is 0.995 for HD 193452 and 0.997 for HD 209450, when $\log~gf$-values from Kurucz & Bell (1995) are considered; it is 0.996 and 0.998 when $\log~gf$-values from Raassen & Uylings (2000) are adopted. The Fe  $\scriptstyle {\rm II}$ line at 6149.258 Å is unblended in all the stars, except in HD 186568 when the Kurucz & Bell (1995) $\log~gf$-values are used. In this case, the Fe  $\scriptstyle {\rm II}$ line at 6148.848 Å contributes to the Fe  $\scriptstyle {\rm II}$ 6149.258 Å with a residual flux at the line center equal to 0.997. The contribution of Fe  $\scriptstyle {\rm II}$ 6148.848 Å disappears when the Raassen & Uylings (2000) data are used.


Table 5: Lines in the 6147-6150 Å region which produce a predicted residual flux at the line center $F_{\lambda }/F_{\rm c}\le 0.999$.
Ion $\lambda$(Å) $\log g\!f$(KB)1 $\log g\!f$(RU)2 $E_{\rm low}$ (cm-1) $E_{\rm up}$ (cm-1) isotope
Cr  $\scriptstyle {\rm II}$ 6147.154 -2.843   38362.430 54625.620  
Fe  $\scriptstyle {\rm II}$ 6147.741 -2.721 -2.827 31364.440 47626.076  
Fe  $\scriptstyle {\rm II}$ 6147.775 -0.819 -0.974 90638.822 106900.379  
Fe  $\scriptstyle {\rm I}$ 6147.829 -1.700   32873.619 49135.022  
Ni  $\scriptstyle {\rm II}$ 6148.246 0.173   103653.030 119913.330  
Ni  $\scriptstyle {\rm II}$ 6148.674 0.143   105439.850 121699.020  
Fe  $\scriptstyle {\rm II}$ 6148.848 -1.496 -4.037 88614.520 104873.230  
Fe  $\scriptstyle {\rm II}$ 6149.258 -2.724 -2.841 31368.450 47626.076  
Hg  $\scriptstyle {\rm II}$ 6149.419 -1.047   95714.408 111971.460 199
Hg  $\scriptstyle {\rm II}$ 6149.451 -0.757       201
Hg  $\scriptstyle {\rm II}$ 6149.461 -0.680       204
Hg  $\scriptstyle {\rm II}$ 6149.469 -0.042       202
Hg  $\scriptstyle {\rm II}$ 6149.477 -0.153       200
Hg  $\scriptstyle {\rm II}$ 6149.483 -0.518       198
Hg  $\scriptstyle {\rm II}$ 6149.504 -0.570       199
Hg  $\scriptstyle {\rm II}$ 6149.513 -0.978       201

                                                                1 KB: $\log~gf$ from Kurucz & Bell (1995), except for Hg  $\scriptstyle {\rm II}$ (see text).
                                                                2 RU: $\log~gf$ from Raassen & Uylings (2000).

5.3 The computed $\mathsfsl{\Delta W/ \overline{W}_{calc}}$ ratios

Five different computed intensification indices ( $\Delta W/\overline {W})_{\rm calc}$, based on the Kurucz & Bell (1995) $\log~gf$-values, are listed for each star in Col. 8 of Table 6. The first one is computed from synthetic profiles corresponding to the adopted model parameters (Cols. 9 and 10 of Table 4). The other four ( $\Delta W/\overline {W})_{\rm calc}$ ratios are computed by assuming errors in the model parameters on the order of $\pm$500 K in $T_{\rm eff}$ and $\pm$0.5 dex in $\log~g$. For all the stars these errors are much larger than those estimated in Sect. 5.1.


Table 6: The ( $\Delta W/\overline {W})_{\rm calc}$ ratios computed by using the Kurucz & Bell (1995) $\log~gf$-values.

$\overline {W}_{\rm obs}$(6149) $T_{\rm eff}$ $\log~g$ $\log(N$(Fe)/ $N_{\rm tot}$) $W(6147)_{\rm calc}$ $W(6149)_{\rm calc}$ ( $\Delta W/\overline {W})_{\rm calc}$ ( $\Delta W/\overline{W})_{\rm obs}$

HgMn stars
HD 16727 13.50 14 050 4.25 -4.342 14.10 13.39 0.052 $0.126\pm0.015$
    14 550 4.25 -4.231 14.24 13.41 0.060  
    13 550 4.25 -4.437 14.02 13.42 0.044  
    14 050 3.75 -4.371 14.12 13.41 0.052  
    14 050 4.75 -4.271 14.14 13.42 0.052  
HD 272951 4.50 11 950 4.00 -5.251 4.61 4.48 0.029 $0.058\pm0.007$
    12 450 4.00 -5.208 4.63 4.48 0.033  
    11 450 4.00 -5.281 4.60 4.48 0.026  
    11 950 3.50 -5.387 4.61 4.48 0.029  
    11 950 4.50 -5.098 4.62 4.48 0.031  
HD 272952 5.60 11 950 4.00 -5.146 5.74 5.58 0.028 $0.077\pm0.008$
    12 450 4.00 -5.103 5.77 5.58 0.033  
    11 450 4.00 -5.176 5.72 5.57 0.027  
    11 950 3.50 -5.282 5.74 5.58 0.028  
    11 950 4.50 -4.993 5.75 5.57 0.032  
HD 175640 10.40 12 000 3.95 -4.842 10.65 10.35 0.029 $-0.004\pm0.010$
    12 500 3.95 -4.795 10.70 10.35 0.033  
    11 500 3.95 -4.873 10.62 10.35 0.026  
    12 000 3.45 -4.974 10.65 10.36 0.028  
    12 000 4.45 -4.690 10.67 10.35 0.030  
HD 178065 19.36 12 250 3.55 -4.552 19.79 19.26 0.027 $0.039\pm0.005$
    12 750 3.55 -4.468 19.85 19.24 0.031  
    11 750 3.55 -4.608 19.71 19.25 0.024  
    12 250 3.05 -4.635 19.78 19.26 0.027  
    12 250 4.05 -4.425 19.79 19.24 0.028  
HD 186122 36.50 12 750 3.80 -3.889 37.42 36.37 0.028 $0.043\pm0.005$
    13 250 3.80 -3.793 37.59 36.37 0.033  
    12 250 3.80 -3.957 37.30 36.38 0.025  
    12 750 3.30 -3.960 37.40 36.38 0.028  
    12 750 4.30 -3.772 37.49 36.38 0.030  
HD 193452 33.02 10 800 4.10 -4.083 33.57 32.90 0.020 $0.034\pm0.010$
    11 300 4.10 -4.038 33.62 32.92 0.021  
    10 300 4.10 -4.160 33.60 32.92 0.020  
    10 800 3.60 -4.409 33.43 32.92 0.015  
    10 800 4.60 -3.964 33.71 32.89 0.024  
Normal stars  
HD 209459 24.02 10 450 3.60 -4.527 24.31 23.90 0.017 $0.026\pm0.008$
    10 950 3.60 -4.489 24.34 23.90 0.018  
    9950 3.60 -4.599 24.31 23.91 0.017  
    10 450 3.10 -4.673 24.27 23.90 0.015  
    10 450 4.10 -4.400 24.37 23.90 0.019  
HD 179761 14.73 12 900 3.70 -4.588 15.55 14.82 0.048 $0.097\pm0.009$
    13 400 3.70 -4.483 15.55 14.82 0.048  
    12 400 3.70 -4.670 15.48 14.79 0.045  
    12 000 3.20 -4.636 15.53 14.81 0.047  
    12 900 4.20 -4.492 15.81 15.04 0.050  

Table 6: continued.

$\overline {W}_{\rm obs}$(6149) $T_{\rm eff}$ $\log~g$ $\log(N$(Fe)/ $N_{\rm tot}$) $W(6147)_{\rm calc}$ $W(6149)_{\rm calc}$ ( $\Delta W/\overline {W})_{\rm calc}$ ( $\Delta W/\overline{W})_{\rm obs}$

HD 186568

21.6 11600 3.40 -4.587 22.57 21.85 0.032 $0.112\pm0.002$
    12100 3.40 -4.530 22.58 21.86 0.032  
    11100 3.40 -4.621 22.60 21.78 0.037  
    11600 2.90 -4.707 22.57 21.85 0.032  
    11600 3.90 -4.438 22.45 21.80 0.029  
HD 219927 17.92 12800 3.70 -4.486 18.41 17.81 0.033 $0.066\pm0.019$
    13300 3.70 -4.384 18.51 17.81 0.038  
    12300 3.70 -4.562 18.33 17.82 0.028  
    12300 3.20 -4.541 18.41 17.82 0.033  
    12300 4.20 -4.382 18.42 17.81 0.034  

                                                       1 ( $\Delta W/\overline{W})_{\rm obs}$ and ( $\Delta W/\overline {W})_{\rm calc}$ are based on the equivalent widths measured by F.C.
                                                       2 ( $\Delta W/\overline{W})_{\rm obs}$ and ( $\Delta W/\overline {W})_{\rm calc}$ are based on the equivalent widths measured by S.H.

Column 2 in Table 6 lists the average measured equivalent width $\overline {W}_{\rm obs}$(6149) of the observed line at $\lambda\,6149.2$ taken from Table 2; Cols. 3 and 4 list the model parameters, Col. 5 gives the corresponding iron abundance $\log(N_{\rm elem}/N_{\rm tot}$) derived with the WIDTH code. The adopted hydrogen abundance, needed for the conversion on the scale where $\log\epsilon$(H) = 12.00, is $N_{\rm H}/N_{\rm tot}=0.911$. The next two columns list the equivalent widths of the two Fe  $\scriptstyle {\rm II}$ synthetic profiles at 6147.7 Å and 6149.2 Å, corresponding to the iron abundance given in col. 5. We point out that the computed ratios ( $\Delta W/\overline {W})_{\rm calc}$ given in Col. 8 do not include magnetic field contributions, so that they should correspond to those observed in non-magnetic stars having similar stellar parameters. The last column of Table 6 lists for comparison the observed ratios ( $\Delta W/\overline{W})_{\rm obs}$ taken from Table 2.

As mentioned in Sect. 4, the star HD 27295 shows the largest uncertainty in ( $\Delta W/\overline{W})_{\rm obs}$ related with different placements of the continuum. The fractional errors of the equivalent widths $\overline {W}_{\rm obs}$(6147) and $\overline {W}_{\rm obs}$(6149) derived by averaging all the five measurements available for each line are so large that they indicate the meaninglessness of averaging equivalent widths based on very different continua. We therefore considered the separate measurements performed for this star. The two different sets of data for HD 27295 given in Table 6 correspond to the meaurements made by F.C. and to the measurements made by S.H, respectively. Both separate measurements show evidence of relative intensification.

Table 6 indicates that the computed intensification indices depend only marginally on $T_{\rm eff}$ and $\log~g$, so that large errors in the adopted parameters do not affect the results in a significant way.

Table 7 lists the intensification indices computed for the adopted model parameters when the Fe  $\scriptstyle {\rm II}$ profiles are computed by using $\log~gf$-values from Raassen & Uylings (2000).


Table 7: The ( $\Delta W/\overline {W})_{\rm calc}$ ratios computed by using the Fe  $\scriptstyle {\rm II}$ $\log~gf$-values from Raassen & Uylings (2000).

$\overline {W}_{\rm obs}$(6149) $T_{\rm eff}$ $\log~g$ $\log(N$(Fe)/ $N_{\rm tot}$) $W(6147)_{\rm calc}$ $W(6149)_{\rm calc}$ ( $\Delta W/\overline {W})_{\rm calc}$ ( $\Delta W/\overline{W})_{\rm obs}$

HgMn stars
HD 16727 13.50 14050 4.25 -4.220 14.42 13.51 0.065 $0.126\pm0.015$
HD 272951 4.50 11950 4.00 -5.134 4.71 4.48 0.050 $0.058\pm0.007$
HD 272952 5.60 11950 4.00 -5.029 5.86 5.57 0.051 $0.077\pm0.008$
HD 175640 10.40 12000 3.95 -4.725 10.85 10.35 0.047 $-0.004\pm0.010$
HD 178065 19.36 12250 3.55 -4.435 20.07 19.26 0.041 $0.039\pm0.005$
HD 186122 36.50 12750 3.80 -3.772 37.71 36.37 0.036 $0.043\pm0.005$
HD 193452 33.02 10800 4.10 -3.966 32.92 31.88 0.032 $0.034\pm0.010$
HD 209459 24.02 10450 3.60 -4.410 24.66 23.90 0.031 $0.026\pm0.008$
HD 179761 14.73 12900 3.70 -4.471 15.79 14.73 0.069 $0.097\pm0.009$
HD 186568 21.6 11600 3.40 -4.470 22.88 21.62 0.057 $0.112\pm0.002$
HD 219927 17.92 12800 3.70 -4.369 18.67 17.81 0.047 $0.066\pm0.019$

                                                       1 ( $\Delta W/\overline{W})_{\rm obs}$ and ( $\Delta W/\overline {W})_{\rm calc}$ are based on the equivalent widths measured by F.C.
                                                       2 ( $\Delta W/\overline{W})_{\rm obs}$ and ( $\Delta W/\overline {W})_{\rm calc}$ are based on the equivalent widths measured by S.H.

6 Comparison between the observed and computed ( $\Delta W/\overline {W}$) ratios

The observed and computed ( $\Delta W/\overline {W}$) ratios listed in Table 6 are compared in Fig. 2, where the full black symbols show the computed intensification indices as function of $T_{\rm eff}$ and the white open symbols show the observed ( $\Delta W/\overline{W})_{\rm obs}$ratios together with the estimated errors. The two separate ( $\Delta W/\overline{W})_{\rm obs}$ ratios for HD 27295 are plotted, while only one ( $\Delta W/\overline {W})_{\rm calc}$ ratio is shown, owing to the negligible differences between the two separated computed intensification factors.

The computed intensification indices plotted in Fig. 2 are those given in the first row of Table 5 for each star, while the small error bars indicate the $\Delta W/\overline {W}$ ratios derived from models computed for gravities which differ by $\pm$0.5 dex from the adopted $\log~g$. These are given in Table 6 for each star in the fourth and fifth rows. An error of -0.5 dex in $\log~g$ does not change the value of the intensification index for most stars, so that there is no error bar in Fig. 2 for $\Delta$logg=-0.5.

The ( $\Delta W/\overline {W})_{\rm calc}$ ratios corresponding to errors of $\pm$500 K in $T_{\rm eff}$and listed for each star in Col. 8 of Table 6, in the second and thirth rows, are so close to those computed for the adopted parameters that Fig. 2 does not change in a significant way if models with $T_{\rm eff}$ increased or decreased by 500 K are used.

The full line plotted in Fig. 2 shows the computed intensification index as function of $T_{\rm eff}$, when $\Delta W/\overline {W}$ is computed from unbroadened profiles predicted for $T_{\rm eff}$ ranging, at steps of 500 K, from 10000 K to 15000 K, $\log~g$ = 3.5 and solar iron abundance ( $\log~N_{\rm Fe}/N_{\rm tot}=-4.54$). A gravity change from $\log~g$ = 3.5 to $\log~g$ = 4.0 gives a maximum difference of 0.003 in ( $\Delta W/\overline {W})_{\rm calc}$. A change of microturbulent velocity from 0 km s-1 to 2 km s-1 gives a maximum difference of 0.002 in ( $\Delta W/\overline {W})_{\rm calc}$.

Figure 3 shows the same comparison plotted in Fig. 2, but, in this case, all the computations, which are listed in Table 7, are based on the Fe  $\scriptstyle {\rm II}$ $\log~gf$-values taken from Raassen & Uylings (2000). The sample of stars showing magnetic intensification consists now only of three stars instead of nine stars, as we obtained when we used the Kurucz & Bell (1995) Fe  $\scriptstyle {\rm II}$ $\log~gf$-values. The three stars are the HgMn star HD 16727 and the two normal stars HD 179761 and HD 186568. We note that the two normal stars are those of the sample having the highest rotational velocity.

\par\includegraphics[width=8cm]{1101f2.eps}\end{figure} Figure 2: Comparison of the observed intensification indices (open circles and open squares) with those computed by using the Kurucz & Bell (1995) $\log~gf$-values (full circles and full squares). The correspondence of each number to each star is: 1 = HD 16727, 2 = HD 27295, 3 = HD 175640, 4 = HD 178065, 5 = HD 186122, 6 = HD 193452, 7 = HD 209459, 8 = HD 179761, 9 = HD 186568, 10 = HD 219927. The full line shows the computed intensification index derived from unbroadened Fe  $\scriptstyle {\rm II}$ lines computed for $\log~g=3.5$, zero microturbulent velocity, and solar iron abundance.
Open with DEXTER

\par\includegraphics[width=8cm]{1101f3.eps}\end{figure} Figure 3: Comparison of the observed intensification indices (open circles and open squares) with those computed by using the Raassen & Uylings (2000) $\log~gf$-values for Fe  $\scriptstyle {\rm II}$ (full circles and full squares). The correspondence of each number to each star is: 1 = HD 16727, 2 = HD 27295, 3 = HD 175640, 4 = HD 178065, 5 = HD 186122, 6 = HD 193452, 7 = HD 209459, 8 = HD 179761, 9 = HD 186568, 10 = HD 219927. The full line shows the computed intensification index derived from unbroadened Fe  $\scriptstyle {\rm II}$ lines computed for $\log~g=3.5$, zero microturbulent velocity, and solar iron abundance.
Open with DEXTER

7 The mercury abundance and some comparisons with Paper I

There are five stars in our sample in common with the stars analyzed in Paper I. For the normal B-type star HD 196426 we already pointed out in Sect. 2 that the spectrum taken at ESO is so different from that taken at CFHT, that the star is suspected to be binary.

All the HgMn stars of our sample, except HD 27295, show a moderately strong line at 6149.45 Å, which we identified as Hg  $\scriptstyle {\rm II}$. Table 8 compares the mercury abundance of the four HgMn stars analyzed both in Paper I and in this paper and gives also the mercury abundance for HD 16727 obtained in this study. The mercury abundance was derived from the comparison of the observed profiles with profiles computed taking into account the isotopic composition, which was discussed in Paper I. The model parameters are those adopted for the stars and given in Cols. 9 and 10 of Table 4; the rotational velocities $v\sin i$ used for computing the synthetic profiles are given in the last two columns of Table 8. There is an excellent agreement between the $v\sin i$ values from this paper and Paper I.

The mercury abundances derived in this paper, and listed in Col. 2 of Table 8, are lower than those derived in Paper I, which are given in the third column of Table 7. The difference is about 0.2-0.4 dex, except for HD 186122. In fact, in Paper I we estimated as a pure noise the signal observed in the CAT spectrum of HD 186122, so that we assumed meteoritic abundance for this star.


Table 8: The mercury abundance and the rotational velocity $v\sin i$ from this paper (II) and Paper I (I).

$\log(N_{\rm Hg}/N_{\rm tot}$) $v\sin i$
  (II) (I) (II) (I)

-7.25 - 4.50 -
175640 -6.75 -6.50 2.50 2.50
178065 -7.05 -6.85 1.70 1.50
186122 -7.45 -10.95 0.00 0.00
193452 -5.70 -5.31 0.75 0.75

Table 9 compares results for iron from Paper I and from this paper for the four HgMn stars analyzed in both studies. In particular, it compares the measured equivalent widths of Fe  $\scriptstyle {\rm II}$ 6149.2 Å, the corresponding iron abundances $\log(N_{\rm Fe}/N_{\rm tot}$), the computed equivalent widths $W(6147)_{\rm calc}$ and $W(6149)_{\rm calc}$ of Fe  $\scriptstyle {\rm II}$ 6147.7 Å and Fe  $\scriptstyle {\rm II}$ 6149.2 Å, respectively, and the computed and measured intensification factors ( $\Delta W/\overline {W})_{\rm calc}$ and ( $\Delta W/\overline{W})_{\rm obs}$. Computations performed in this paper by using both the Kurucz & Bell (1995) (KB) $\log~gf$-values and the Fe  $\scriptstyle {\rm II}$ $\log~gf$-values from Raassen & Uylings (2000) (RU) are considered.

For three stars (HD 175640, HD 178065, and HD 193452) the equivalent widths of Fe  $\scriptstyle {\rm II}$ $\lambda\,6149.258$ Å are systematically smaller in the CFHT spectra than in the ESO spectra taken at the higher spectral resolution ( $R = 135\,000$). The opposite is true for HD 186122.

A few factors could be responsible for the different intensity of the Hg  $\scriptstyle {\rm II}$ and Fe  $\scriptstyle {\rm II}$ profiles observed in the CAT and CFHT spectra (see Fig. 1): for instance, the different spectral resolution, the placing of the continuum, or the residual scattered light in the Gecko spectrograph, which could have been not completely removed. The lower Fe  $\scriptstyle {\rm II}$ equivalent widths measured in this paper could be also due to the more accurate measuraments performed in this second analysis. In fact, in Paper I, the equivalent widths used to derive the iron abundance were measured only by gaussian fitting, whereas for the present paper we used the average of five measurements.

For all the four HgMn stars, the measured intensification factors are lower in this paper than those obtained in Paper I and they are very close to the intensification factors computed by using the Raassen & Uylings (2000) $\log~gf$-values for Fe  $\scriptstyle {\rm II}$, so that the suggestion of the presence of a magnetic field for HD 175640, HD 178065, and HD 186122 can not be confirmed by the present results.


Table 9: Comparison of results from Paper I (I) and this paper (II) for Fe  $\scriptstyle {\rm II}$ and for the computed and measured intensification indices $\Delta W/\overline {W}$: (KB) are the results obtained by using the Kurucz & Bell $\log~gf$-values for Fe  $\scriptstyle {\rm II}$; (RU) are the results related with the Raassen & Uylings (2000) $\log~gf$-values for Fe  $\scriptstyle {\rm II}$.
  Paper HD 175640 HD178065 HD 186122 HD 193452

$W(6149)_{\rm obs}$
I 10.7 20.4 35.2 33.6
  II $10.40\pm0.09$ $19.36\pm0.07$ $36.50\pm0.14$ $33.02\pm0.21$
$\log(N_{\rm Fe}/N_{\rm tot}$) I -4.82 -4.53 -3.93 -4.07
  II (KB) -4.84 -4.55 -3.89 -4.08
  II (RU) -4.73 -4.44 -3.77 -3.97
$W(6147)_{\rm calc}$ I 11.06 20.89 36.17 34.30
  II (KB) 10.65 19.79 37.42 33.57
  II (RU) 10.85 20.07 37.71 32.92
$W(6149)_{\rm calc}$ I 10.76 20.35 35.17 33.64
  II (KB) 10.35 19.26 36.37 32.90
  II (RU) 10.35 19.26 36.37 31.88
$(\Delta W/\overline{W})_{\rm calc}$ I 0.027 0.026 0.028 0.019
  II(KB) 0.029 0.027 0.028 0.020
  II(RU) 0.047 0.041 0.036 0.032
$(\Delta W/\overline{W})_{\rm obs}$ I 0.090 0.067 0.086 0.041
  II $-0.004\pm0.010$ $0.039\pm0.005$ $0.043\pm0.005$ $0.034\pm0.010$

8 Discussion

Table 6 and Fig. 2 show that the intensification indices computed by using $\log~gf$-values from Kurucz & Bell (1995) are lower than the observed intensification indices for all the stars in our sample, except HD 175640. For HD 193452 and HD 209459 the differences lie within the error limits, but for five stars, HD 16727, HD 27295, HD 179761, HD 186568 and HD 219927, the differences are larger even when the observational and computational uncertainties discussed in the previous sections are taken into account. Especially striking is the outcome of measurements in the star HD 186568 with the largest value of $v\sin i$. The difference between the equivalent widths of Fe  $\scriptstyle {\rm II}$ 6147.7 Å and Fe  $\scriptstyle {\rm II}$ 6149.2 Å is expected to be 0.72 mÅ, whereas we have measured 2.57 mÅ.

Our calculations show that large errors in the adopted parameter $T_{\rm eff}$ and $\log~g$ do not affect the results in a significant way. However, if Fe  $\scriptstyle {\rm II}$ $\log~gf$-values from Raassen & Uylings (2000) are used to compute the Fe  $\scriptstyle {\rm II}$ profiles, the intensification indices become by about 2% higher and the comparison between the calculated and observed $\Delta W/\overline {W}$ ratios suggests the possible presence of magnetic fields in only three stars, the HgMn star HD 16727 and the two normal late B-type stars HD 179761 and HD 186568.

We must deduce from the above results that the used diagnosis method heavly depends on uncertainties of the atomic data. Karlsson et al. (2001) demonstrated that experimental $\log~gf$-values of Fe  $\scriptstyle {\rm II}$ better agree with the $\log~gf$-values computed by Raassen & Uylings (2000) than with those computed by Kurucz & Bell (1995), and recommend the use of the Raassen & Uylings (2000) data. As a consequence, we have to conclude that our claim for magnetic field detection can be held only for few stars. In particular, we can not confirm any magnetic field for the three stars studied in Paper I, HD 175640, HD 178065, and HD 186122.

The differences between the measurements made in this paper and those from Paper I could be related with instrumental effects and data reduction problems, as we discussed in Sect. 7. However, we can not exclude a priori the presence of weak magnetic fields of complex structure which change with time. They could be responsible for the differences in the observed intensification indices and for the small differences in the measured equivalent widths of Fe  $\scriptstyle {\rm II}$ and Hg  $\scriptstyle {\rm II}$ of the stars observed both at CAT and at CFHT, in particular of HD 175640 (Tables 8 and 9). In fact, Takeda (1991) shows that the magnetic intensification may become negative for particular magnetic field configurations.

The most intriguing result would have been to recognize the presence of magnetic fields in normal late B-type stars that have been selected by us as standards on the basis of previous studies on their nature. Whereas the observed and computed intensification indices agree within the estimated errors for the normal stars HD 209459 and HD 219927, the other two normal stars, HD 179761 and HD 186568, show rather high observed relative differences between the equivalent widths of the two Fe  $\scriptstyle {\rm II}$ lines compared with those derived from synthetic spectra. However, the rather high rotational velocity of HD 179761 (15 km s-1) and HD 186568 (18 km s-1) makes the results from the Mathys method somewhat uncertain. In fact, as we discussed in Sect. 5.2, it is difficult to compute accurate equivalent widths for the rotationally broadened profiles, owing to the depressed continuum in the range 6148.20-6148.85 Å, due to the presence of very weak lines (Table 5).

No large-scale magnetic fields were ever detected for normal upper-main-sequence stars (O9.5-F6)(Landstreet 1982). There is only a little information in the literature about the normal late B-type stars studied in this paper. Previous studies of the four normal stars in our sample revealed only very mild peculiarities and the possibility that they may be regarded as superficially normal stars is still viable. In particular, Babcock (1958) observed the star HD 186568 photographically, but no magnetic field was found.

Bohlender & Landstreet (1990) searched for magnetic field in the star HD 209459 with the H$\beta$ Zeeman analyser technique. Measurement errors have been typically few hundred Gauss and no definite field detections have emerged. Sadakane (1981) determined abundances of 15 elements in this star and found that the metal abundances are nearly solar or slightly underabundant except for Mn, Y and Ba, which may be overabundant. Cowley (1980) mentioned a weakness of Sc  $\scriptstyle {\rm II}$ relative to lines of other ions and suggested that HD 209459 may be related to hot Am stars.

Cowley(1980) also studied the star HD 219927 and describes it as nearly normal. No search for magnetic field has been carried out for this star.

The star HD 179761 is one of the hottest stars for which Babcock (1958) has found a longitudinal field. Three out of four measurements performed by him revealed a magnetic field ranging from -500 to -600 Gauss at the level of 3.5$\sigma$ to 5$\sigma$. No peculiar elements have been detected in our spectrum. However, Cowley (1972) noticed that the character of the hydrogen wings suggests that this star could be similar to HgMn stars. No variation of radial velocity $V_{\rm r}$ has been reported for the stars HD 186568 and HD 209459. Our measurement of radial velocity of the star HD 186568 ($V_{\rm r}$ = -8.4 km s-1) agrees well with the value measured by Morse et al. (1991) ( $V_{\rm r}=
-8.6$ km s-1). The stars HD 179761 and HD 219927 show variable $V_{\rm r}$ and they are probably spectroscopic binaries. However, only very few radial velocity measurements are available at the moment for them. For HD 179761 Morse et al. (1991) measured $V_{\rm r}= -5.0$ km s-1 whereas we measured $V_{\rm r} = -19.6$ km s-1. Wolff (1978) found that the radial velocity of HD 219927 varies from -3.1 km s-1 to 4.9 km s-1. We measured for this star $V_{\rm r}$ = -11.4 km s-1. Spectral lines from the companions have not been detected in our data.

HgMn stars still remain interesting objects for future studies on the presence of magnetic fields for them. Further high resolution and high signal-to-noise ratio spectra are needed to state whether the equivalent width variations and the intensification indices found for both HgMn and normal late B-type stars are due to weak variable magnetic fields or are rather due to instrumental effects and measurement techniques. For instance, in addition to the two Fe  $\scriptstyle {\rm II}$ lines of mult. 74 used in this paper, other pairs of magnetically sensitive lines could be observed and analyzed. Takeda (1991) pointed out the existence of another pair of Fe  $\scriptstyle {\rm II}$ lines at 4416.8 Å and 4385.4 Å with the same Zeeman patterns. Among the other elements different from iron, there is a pair of Cr  $\scriptstyle {\rm II}$ lines at 5620.918 Å and 5622.468 Å, which have identical patterns.

Other independent approaches to study weak magnetic fields in normal late B-type stars and HgMn stars would be the moment technique in order to look for possible differential broadening of spectral lines having different magnetic sensitivities (Mathys 1995; Mathys & Hubrig 1997), or the multi-line Stenflo-Lindegren (1977) technique, which can be very powerful if it is applied to a suitable sample of spectral lines. Magnetic field detections might also be valuably attempted through the observation of linear polarization in spectral lines. To our knowledge, such observations have never been done for normal late B-type stars and HgMn stars.


We would like to thank J. Matthews for assistance during the CFHT observations and D. A. Bohlender for help with the data reduction. We thank the referee G. Wade for the constructive comments and discussions which have helped us to improve the paper in a substantial way. S. H. thanks the DFG for travel funds to the CFHT.


Copyright ESO 2001