Determination of atmospheric parameters and calculation of chemical composition

For understanding of an object at an advanced evolutionary stage, it is very important to know its metallicity and detailed chemical abundance pattern. Our echelle spectra provide such a possibility due to their large wavelengths coverage.

To study the chemical composition, we have used the plane-parallel homogeneous models generated by the MARCS program (Gustafsson et al.1975). It should be noted, however, that unstable and very extended atmospheres of supergiants probably require more advanced model atmospheres. Therefore, our results should be treated as only preliminary ones. For a chemical composition calculation by the model atmosphere method, one needs to know the values of the effective temperature ( $$\hbox{{<tex2html_image_mark\gt ...$ ), surface gravity (logg) and microturbulent velocity ( ${\rm \xi_t}$ ). Determination of $$\hbox{{<tex2html_image_mark\gt ...$ is problematic even for normal supergiants due to their extended atmospheres and significant non-LTE effects. In the case of so peculiar a supergiant as IRAS04296, for which the energy distribution is strongly distorted by interstellar and circumstellar extinction, determination of $$\hbox{{<tex2html_image_mark\gt ...$ is the most difficult problem. We cannot use for this purpose equivalent widths and profiles of HI lines (well known criteria of atmospheric conditions for normal supergiants), since these lines are strongly distorted in the spectrum of IRAS04296 as seen in Fig.1.

Therefore, we have applied the spectroscopic method for temperature determination of IRAS04296, forcing the abundance derived for each line to be independent on the lower excitation potential. We have estimated that $$\hbox{{<tex2html_image_mark\gt ...$ = 6300K with on internal uncertainty $\Delta$ $$\hbox{{<tex2html_image_mark\gt ...$ =250K. To check the realiability of our determination we have modelled the spectral energy distribution for this source (see Sect.4) and got a very similar temperature near 6500K. The surface gravity logg=0.0 was estimated through the ionization balance of the FeI and FeII abundances. The errors on the parameter logg is determined by forcing a maximum difference between ${\rm \epsilon\,(Fe\,I)}$ and ${\rm \epsilon\,(Fe\,II)}$ to be 0.1dex (where here and hereafter, ${\rm log\,\epsilon\,(X)\,=\,log\,N(X)-log\,N(H)}$ ). It should be noted that the hydrogen abundance ${\rm log\,N(H)}$ =12. Such a difference is achieved by varying the logg value by ${\rm \pm 0.2}$ keeping other parameters ( $$\hbox{{<tex2html_image_mark\gt ...$ and ${\rm \xi_t}$ ) constant. The microturbulent velocity value based on equivalent widths (W) of FeI and FeII lines is quite high, equal to 7km/s. This value is determined with an uncertainty of ${\rm \pm 1.0\,km/s}$ , which is typical for F, G-supergiants.

To illustrate the choice of model parameters for the object IRAS04296 in the Fig.6 are shown the excitation potential - abundance diagram and the equivalent width - abundance diagram for lines of neutral (dots) and ionized (crosses) iron atoms. As follows from this figure, there are not any essential dependences for values considered. The large dispersion is mainly explained by errors of measurement of equivalent widths of weak absorption lines for such a faint object as the IRAS04296 (see, for example, the similar dispersion on the Fig.1 in the paper by Decin et al. (1998) for the brighter object IRAS22223+4327, V=9.7).

We have checked the determination of IRAS04296 model parameters using weaker FeI and FeII lines and concluded that the parameters are steady within the erorr box up to ${\rm W}$ = 100-150mÅ. This can also be seen from Fig.6.

**Figure:** *Upper:* iron abundance FeI (circles) and FeII (crosses) calculated for IRAS04296+3429 with model parameters ${\rm T_{eff}=6300\,K}$ , ${\rm log\,g=0.0}$ and ${\rm \xi_t=7.0\,km/sec}$ using lines with different excitation potentials EP of a low level; *bottom:* the same as a function of the equivalent width W
$\begin{figure} \resizebox {\hsize}{!}{\includegraphics{IR04296fe1.ps}} \resizebox {\hsize}{!}{\includegraphics{IR04296fe2.ps}}\end{figure}$

It is well known that the plane-parallel static model atmosphere method does not give correct abundances for high luminosity stars (luminosity classes Ia, Ia+). The profiles of the spectral lines observed are broadened by non-thermal mechanisms whose influence may be variable at different levels in the atmosphere. Therefore, to obtain more reliable estimates of chemical element abundances we use weak lines with ${\rm W < }$ 250mÅ. The average values of the equivalent widths ${\rm \overline{W}}$ we used for the abundances calculations are also given in Table1. Only the BaII abundance was calculated using 3 very strong lines: ${\rm W(\lambda}$ 5853.67)=464mÅ, ${\rm W(\lambda}$ 6141.71)=679mÅ and ${\rm W(\lambda}$ 6496.90)=738mÅ, because the weaker lines of this element were not available. In general, the weak lines formed in deeper atmospheric layers are more correctly described by the standard static model. The limitation of equivalent width of lines used to ${\rm W < }$ 250mÅ significantly reduces the influence of uncertainty in the choice of ${\rm \xi_t}$ . Note, however, that the main factor in the abundance errors for most species remains the uncertainty of the $$\hbox{{<tex2html_image_mark\gt ...$ value. Therefore, we have checked our estimation of $$\hbox{{<tex2html_image_mark\gt ...$ by modelling of spectral energy distribution for IRAS04296.

Computed abundances of 26 chemical elements are presented in Table1. In the head of the Table1 parameters of the adopted model atmosphere are shown. The dependence of chemical composition determination on uncertanties of the model atmosphere parameters is discussed in Zacs et al. (1995). In the second column of Table1 derived abundances are given as ${\rm log\,\epsilon\,(X)}$ , while in the third column estimated uncertainties of ${\rm \sigma\,=\,\Delta\,log\,\epsilon\,(X)}$ are shown. In the next column, the number of spectral lines used for chemical composition calculation is indicated.

**Table:** Model atmosphere parameters adopted and abundances of chemical elements. Here, n is number of lines used for calculation, ${\sigma}$ - the standard deviation, ${\rm \overline{W}}$ - the average equivalent width, in ${\rm m\AA}$ , of lines used for the content calculation

	4c\|IRAS04296+3429	4c ${\rm\alpha\,Per}$
	4c\| $$\hbox{{<tex2html_image_mark\gt ...$ =6300K, logg=0.0, $\xi_t$ =7.0km/s	4c $$\hbox{{<tex2html_image_mark\gt ...$ =6500K, logg=1.0, $\xi_t$ =4.7km/s
	4c\|	4
Element	${\rm log\,\epsilon (X)}$	${\sigma}$	n	${\rm \overline{W}}$	${\rm log\,\epsilon (X)}$	${\sigma}$	n	${\rm \overline{W}}$
LiI	${\rm \ge2.70}$		1	32
CI	8.55	0.46	21	69	8.16	0.14	13	47
NI	7.96	0.10	4	99	8.35	0.10	4	127
OI	8.22	0.05	3	26	8.35	0.06	4	23
NaI	5.91	0.24	3	68	6.48	0.06	4	48
MgI					7.83	0.03	2	56
MgII	8.08	0.03	2	254
AlI	6.66	0.14	3	68	6.57	0.16	4	32
SiI	7.29	0.20	11	37	7.68	0.16	16	45
SiII	6.97		1	22	7.81		1	278
SI	6.80	0.21	7	30	7.53	0.23	2	187
CaI	5.71	0.30	19	98	6.41	0.22	14	122
ScII	2.51	0.28	10	164	2.72	0.07	6	119
TiII	3.91	0.33	5	184	4.78	0.08	4	47
VII	3.26	0.28	4	26	3.54	0.10	4	22
CrII	4.94	0.28	10	108	5.54	0.12	9	136
MnI					5.25	0.09	3	63
FeI	6.66	0.30	55	75	7.48	0.21	111	59
FeII	6.65	0.22	19	131	7.51	0.09	10	154
CuI	3.61		1	38	4.66		1	36
ZnI	3.84		1	9
YII	2.60	0.14	2	168	2.20	0.40	2	32
ZrI					3.38	0.10	4	6
ZrII	2.38		1	165
BaII	3.78	0.47	3	627	2.06		1	212
LaII	1.55	0.44	6	116	1.04	0.08	4	20
CeII	1.53	0.16	5	83
PrII	0.61		1	19
NdII	1.73	0.31	12	102	0.84	0.08	4	8
EuII	0.01	0.04	2	20	0.44	0.09	3	20

A lot of absorption lines of different elements (CNO-elements, light metals, iron group elements, Ce, Nd, Eu) have been reliably measured in the spectrum of IRAS04296. It is important that we have not found any dependence of the abundances of these species on the equivalent width or on the excitation potential. Therefore the microturbulent velocity does not vary between different chemical elements.

The gf-values for most of the spectral lines used for the abundance calculations were taken from the list used by Luck (1991). The S and CNO-abundances were determined by using the gf-data from Waelkens et al. (1991) and Giridhar et al. (1994). The list of lines with the adopted gf-values, excitation potentials of the lower level and equivalent widths we measured for the object IRAS04296 are available by e-mail (valenta@alba.sao.ru).

To verify the method of analysis we observed with the same spectral device the normal supergiant ${\alpha}$ Per. The same procedures for processing and the same list of lines were used for analysis of the ${\alpha}$ Per spectrum. This supergiant, whose parameters, ${\rm T_{eff}=6500\,K}$ , ${\rm log\,g=1.2}$ , ${\rm \xi_t=4.7\,km/sec}$ are very close to the object studied, is very convenient as a standard for the method testing because of its membership in the young open cluster ${\rm \alpha Per}$ which has solar chemical composition (Klochkova, Panchuk 1985; Boesgaard 1989). Using its membership of this cluster, we may predict that ${\rm\alpha\,Per}$ also has normal solar chemical composition (aside from the expected nonsolar CNO triad abundances relative to iron). As it is shown in Table1 ${\rm \alpha Per}$ has indeed the abundances of chemical elements close to solar ones, except for CNO and several elements whose abundances are calculated with a large uncertainity due to a small number of spectral lines used.