6. Determination of atmospheric parameters: non-standard approach
Microturbulent velocity in this case has been found using only lines (see Fig. 5), which are not suspected to be strongly affected by the NLTE effects. It is not surprising that with this microturbulent velocity ( 3.4 km s-1, which is 0.5 km s-1 greater than that determined by analysing only lines), the lines give a progressively lower abundance. We believe, that in this case more or less realistic iron abundance based on lines should be refered to equivalent width W = 0 mÅ. formally extrapolated abundance from the sample of neutral iron lines must then be compared with the mean result from all investigated lines in order to specify the value.
It is clear, that with a higher value, the mean iron abundance derived from lines will be lower and / ionization balance will take place at greater gravity than it is expected from the standard analysis. Using this method, we have found that falls in the region 2.0-2.2 dex for Cep. Results of and determination for different phases are given in Table 1 with the mark "NS" (non-standard approach).
It is worth estimating an independent value from the combination of empirical "mass-period" calibration (Turner 1996):
that was obtained for cluster Cepheids using B stars of well-known masses, and the "period-luminosity" relation (Gieren et al. 1998):
Using the following formula:
we calculated physical gravity values for different phases (see the fifth column of Table 1) supposing that Cep has a mass . While using the expression for the physical gravity, we have taken into account the luminosity variation during the pulsation. The luminosity values for the phases of interest were found using the mean value (Eq. 2), corresponding values (Kiss 1998) and bolometrical corrections calculated for different effective temperatures at the different phases ( are taken from Straizys 1982).
At the present time, Cepheid masses are probably known with uncertainty not greater than 1 . If so, then the gravity is uncertain by about 0.1 dex for . This estimate shows that for Cep the difference between physical value and spectroscopically determined (in the standard approach) ph -sp = 0.5 is significant, i.e. exceeds the probable errors of both gravity values.
It is also important to take into account the correction to physical gravity caused by dynamical effects in Cep atmosphere. In this case the effective gravity value can deviate from that estimated with the help of Eq. (3). In fact, correction for Cep is small (about -0.06 dex) for the time interval 0.15-0.70 P, but can achieve significant value (more than +0.15 dex) between = 0.8-1.0 (note that we do not have any observations relevant to this phase interval).
At present we cannot answer the question whether the changes in the physical gravity value caused by the additional dynamic acceleration in the pulsating atmosphere can be detected by spectroscopic analysis similar to that performed in this work. We suppose that this problem requires a special consideration using high-resolution spectra spaced with small time steps within the pulsational period.
Breitfellner & Gillet (1993) obtained the surface gravity variation for Cep using very precise radial velocity curve and angular diameter variation determined by Fernley et al. (1989). They found that varies from 2.01 to 2.12 reaching the maximum at the phase 0.9. The mean gravity value (assuming the mean radius of Cep estimated by Fernley et al. 1989, i.e, 37.28 ) is 2.05. Even with Turner's (1988) radius estimate 43 one has = 1.93 for 5.7 (this mass value was adopted by Breitfellner & Gillet).
As one can see, the result of Breitfellner & Gillet (1993) is very close to our estimate based on the non-standard approach. Note also, that according to Breitfellner & Gillet the amplitude of gravity variation is really small (about 0.1 dex). Therefore, any reported variations within the range more than 0.2, in fact, do not reflect the real pulsational radius changes, but rather testify to problems of the standard spectroscopic analysis.
© European Southern Observatory (ESO) 1999
Online publication: November 3, 1999