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Astron. Astrophys. 318, 841-869 (1997)

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10. An example: the model parameters for Procyon

Procyon is a very extensively studied star, which is very well suited to test the convection of the ATLAS9 model atmospheres owing to its spectral type F5 IV-V. In fact, the model parameters of Procyon lie in that part of the [FORMULA], [FORMULA] diagram that we found to be the most affected by the way convection is handled. Steffen (1985) summarized the physical parameters of Procyon. Owing to the binary nature of Procyon, and on the basis of several determinations of angular diameter and trigonometric parallax, its radius and mass are known. They are estimated to be [FORMULA] =2.11 [FORMULA] 0.1 and [FORMULA] =1.76 [FORMULA] 0.10. Therefore, the gravity [FORMULA] can be derived from the radius and the mass of the star. Values of [FORMULA] given in the literature range from 3.95 (Code, 1975) to 4.08 (Saxner & Hammarbäck, 1985). We assumed [FORMULA], as it is listed by Smalley and Dworetsky (1995). Several abundance analyses have shown that chemical composition of Procyon is almost solar (Steffen, 1985; Faraggiana et al., 1986, Edvardsson et al., 1993).

After having fixed both the gravity [FORMULA] and the solar chemical composition, values of [FORMULA] can be derived from colours, spectrophotometry, Balmer profiles, and ionization equilibria. A good model atmosphere of Procyon, together with high quality observations, must yield the same value for [FORMULA] from all these determinations.

10.1. [FORMULA] from colour indices

The first three rows of Table 7 show that the values of [FORMULA] derived from ([FORMULA]), ([FORMULA]), and ([FORMULA]) indices may differ up to 200 K when the COLK95 models are used and up to 50 K when the NOVER models are adopted. Observed indices were taken from the Steffen (1985) paper and from the Hauck & Mermilliod (1990) catalog. Because ([FORMULA]) index is the less affected by the "overshooting" option, we may assume that the Procyon model must have [FORMULA] included between 6657 K and 6634 K. Such a temperature well agrees with [FORMULA] from ([FORMULA]) and ([FORMULA]) indices when NOVER models are adopted.


[TABLE]

Table 7. Surface gravity of Procyon from c0 =0.532 and COLK95 and COLNOVER grids


10.2. [FORMULA] from spectrophotometry

The ultraviolet observed energy distribution is well fitted by a model with [FORMULA] =6650 K, as derived from the color indices, regardless of whether the "overshooting" option is switched on or off. Also the visual flux is rather well reproduced by this temperature, even if the slopes of the energy distributions from the K95 and the NOVER models are sligthly different. Fig. 26 compares the observed energy distribution normalized to 0 mag at 555.6 nm with that computed from a model with [FORMULA] =6650 K and [FORMULA]. Upper and lower plots are for the optical and ultraviolet regions respectively. Observed energy distributions are the data from Davis & Webb (1974) in the optical range and the IUE images SWP43428L, LWR9108L, and the S2/68 TD1 observations in the ultraviolet. Optical data were taken from the Breger (1976) Catalog; ultraviolet data were taken from IUE data base ULDA (Wamsteker et al., 1989) and from the S2/68 TD1 Catalog (Jamar et al. 1976). We tested that magnitudes of Procyon from different sources listed in the Breger Catalog do not differ significantly each from the other. The first tracings in the upper and lower plots compare energy distributions from the K95 (full line) and the NOVER (dashed line) models. The lower tracings compare observations (dots and dashed lines) with the computed energy distributions (full lines). The NOVER model is closer to the observations than the K95 model in the 400-450 nm region, but it is too hot longward [FORMULA], so that a model with [FORMULA] =6400 K would better fit the observations in this region. The K95 model well reproduces the flux longward [FORMULA], but it is too cool in the 400-450 nm region, so that [FORMULA] =6850 K would be more appropriate. Both models well reproduce the ultraviolet data. Fig. 27 is the analogous to Fig. 26, but for absolute fluxes obtained on the basis of the angular diameter of Procyon and of the Hayes & Latham (1975) absolute calibration of Vega at 555.6 nm. Both K95 and NOVER models with [FORMULA] =6650 K well reproduce the whole absolute flux, provided that the angular diameter is assumed to be [FORMULA] =5.25 milli arcsec. This value for the angular diameter is lower than all the measurements made up to now. In fact, according to Steffen (1985), the lowest value given in the literature is [FORMULA] =5.5 [FORMULA] 0.17 milli arcsec from Hanbury Brown et al. (1974). Larger values for the angular diameter would require models with [FORMULA] lower than 6650 K in order to fit the observed visual flux. Therefore values for [FORMULA] still larger than 6650 K become still more inconsistent with the angular diameter measurements.

[FIGURE] Fig. 26. Energy distribution of Procyon in the optical (upper plot) and ultraviolet (lower plot) regions, normalized to 0 mag at 555.6 nm. Upper plot from top to bottom: (1) Comparison of energy distributions computed from the K95 model (full line) and NOVER model having parameters [FORMULA] =6650 K, [FORMULA], [M/H]=0.0, [FORMULA] =2 km s-1. (2) Comparison between the observed energy distribution (points) and that computed from the K95 model with [FORMULA] =6650 K, [FORMULA], [M/H]=0.0, [FORMULA] =2 km s-1. (3) The same of (2), but for the NOVER model. Lower plot: The same as (1) and (3) in the upper plot, but for the ultraviolet region. In the lower tracing the points are S2/68 TD1 observations and the dashed line represents IUE data
[FIGURE] Fig. 27. The same as Fig. 26, but for absolute fluxes. For the observed fluxes absolute values have been obtained by means of the Hayes and Latham (1975) absolute calibration of Vega at 555.6 nm and an angular diameter [FORMULA] =5.25 milli arcsec

10.3. [FORMULA] from Balmer profiles

We compared the observed Balmer profiles given in the Procyon Atlas of Griffin & Griffin (1979) with profiles computed with the K95 and NOVER models.

We derived different temperatures from the K95 and the NOVER models in according to Fig. 24. The observed [FORMULA], [FORMULA], and [FORMULA] profiles are fitted by the K95 models for [FORMULA] =6700 K, 6850 K, and 6850 K respectively, and by the NOVER models for [FORMULA] =6500 K, 6550 K, and 6550 K respectively.

10.4. [FORMULA] from the ionization equilibria

We derived Fe I and Fe II abundances from the equivalent widths measured by Steffen (1985). Line data were taken from Kurucz (1993b) files, and most lines have [FORMULA] from laboratory measurements. For Fe I, the straight line fitting abundances versus equivalent widths has a minimum slope for a microturbulent velocity [FORMULA] =1.9 km s-1. Both K95 and NOVER models yield the same iron abundance from Fe I and Fe II lines for [FORMULA] =6650 K, but the abundances are slightly different, namely log ([FORMULA] / [FORMULA]) is equal to -4.36 [FORMULA] 0.25 and -4.44 [FORMULA] 0.25 for the K95 and the NOVER models respectively.

10.5. The final parameters of Procyon

Table 7 summarizes the values of [FORMULA] from K95 and NOVER models based on different methods. The average [FORMULA] from the K95 and NOVER models are 6744 [FORMULA] 94 K and 6593 [FORMULA] 91 K respectively. The difference is about 150 K. If we give more weight to [FORMULA] from the ([FORMULA]) index and from the ultraviolet flux which are almost unaffected by the "overshooting" option, we may conclude that NOVER models yield more consistent results, which also well agree with [FORMULA] based on the angular diameter measurements.

We may derive the gravity using the c1 Strömgren index. The observed c1 index from the Hauck & Mermilliod (1990) catalog is c1 =0.532. The star was found to be not reddened, so that c0 =c1. Table 8 lists gravities yielded by c0 for different [FORMULA] and derived from both the COLK95 and the COLNOVER synthetic colors grids.

The conclusion is that NOVER models yield both [FORMULA] and [FORMULA] more consistent with values derived from methods independent of models, which are [FORMULA] =6510 [FORMULA] 130 K, [FORMULA] according to Code (1975) and Code et al. (1976) or [FORMULA] =6560 [FORMULA] 130 K, [FORMULA] 0.06 according to Smalley & Dworetsky (1995).

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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