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Astron. Astrophys. 342, 773-784 (1999)

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3. The stars with oxygen-type SEDs

3.1. Introduction

A few stars catalogued in Stephenson (1989) are not analysed in terms of the HC and CV-groups we introduced for carbon stars. Their SEDs are typically those of hot stars. Some of them are also Ba II stars. They can be analysed making use of the oxygen-type SEDs we adopted for Ba II stars (Bergeat & Knapik 1997). We have also studied a sample of well-documented RCB stars, the RV Tauri-type carbon star AC Her and V345 Her a carbon Cepheid. The results are given in Table 5. Most of these SEDs can be interpreted with oxygen-type SEDs of giants (g for class III) or supergiants (sg for class Ib). Six RCB stars made exception (1 HC0, 4 HC1 and 1 HC3) which are nevertheless included here. Obviously, they represent the cool end in our sample of RCB stars. The SEDs of hot RCBs are classified F-G while cooler stars in the K- range do have SEDs of the HC-type. This is the well-known junction at G-types, between SEDs of carbon-rich and oxygen-rich stars. The derived oxygen-type group is very often close to the spectral type and luminosity class from spectroscopy. Both may well be variable in a few objects like C 3533 = V553 Cen, a type II-Cepheid (see GCVS). We find again the fact that the SEDs of the hottest carbon-rich stars tend to oxygen-type SEDs. This was already noted by Goldsmith et al. (1987) for carbon-rich yellow supergiants.


[TABLE]

Table 5. Stars with oxygen-type SEDs and HC-groups including RCB variables. Their C-entries from Stephenson (1989), or number in the HD-catalogue, or variable star name in the GCVS, are given. The spectral types, peculiarities and variability types are collected in column 2. Our SED-group and colour excess are given in column 3, while the values from maps can be found in column 4 together with additional information such as alternative name or spectral classification; also quoted, the occurrence of an infrared excess relative to our solution from a specified filter (J, H, K..) or not (no).


3.2. The interstellar extinctions

With the exception of C3982 = RS Tel at minimum light and C4098 = V CrA at an intermediary phase, our values of E(B-V) are found to be close to those from maps in the literature (see Table 5). The former two analyses are discussed in Sect. 3.4. as an illustration of CS extinction. We conclude that the remaining 25 SEDs (22 stars) in Table 5 show, at the corresponding epochs, no selective circumstellar extinction on the line of sight. This is the case of the RCB variables or AC Her then at maximum light. We thus attribute the corresponding colour excess to the interstellar extinction on the line of sight to the star. As mentioned in the notes of Table 5, near IR excesses are however observed. Those near IR excesses, characteristic of dust at an equivalent blackbody temperature of [FORMULA], are a general feature of the RCB-class (Feast & Glass 1973). The only possible exception in our Table 5 is [FORMULA] Cas. We show in Fig. 5 the plot of the data from the maps in the literature (see Refs. in Sect. 2.3.) against our results. The linear fit obtained for oxygen-types SEDs:

[EQUATION]

is also shown, with a correlation coefficient of 0.989 (see Eq. 6 of Paper I for a definition). The standard deviation of the slope is 0.026 while it is 0.016 on a single ordinate estimate. The first bisector is thus within the error domain in this diagram, which is quite satisfactory. We attribute to selective CS extinction the extra [FORMULA] of C 3982 at minimum light and [FORMULA] of C 4098 at an intermediary phase.

[FIGURE] Fig. 5. A comparison of E(B-V) excesses from the maps and graphs of Neckel & Klare (1980, NK80) and Burstein & Heiles (1982, BH82) with values from the present paper (KB) for stars with oxygen-type SEDs. The regression line (5) is also shown.

3.3. The RV Tauri-type star AC Her

We have applied our method (see Fig. 6) to the nearly simultaneous data on AC Her (within 40 min..; at JD 2446248,47 i.e. [FORMULA]=0.66) published by Goldsmith et al. (1987). A good fit is obtained (G0g, [FORMULA] internal error) with six points from U (extreme right) to J leftwards. An increasing IR excess is then observed at H, K and L with respect to the model. This is consistent with the analysis of Goldsmith et al. as shown by their Fig. 2b. The excess is still larger in the IRAS-bandpasses (for instance 6.3 mag at [12] and 8.1 mag at [25]; the IRAS Point Source Catalogue 1988; AC Her = IRAS 18281+2149). The silicate emission at 10 [FORMULA] and 18 [FORMULA] is obvious in its LRS Spectrum. Due to the scale of Fig. 6 the corresponding points cannot be displayed: the stellar photons are outnumbered by circumstellar photons. The field interstellar colour excess is found to be less or equal to 0.19-0.21 from the published maps (see Refs. in Sect. 2.2.), while Goldsmith et al. quoted [FORMULA] in their Table 3. Clearly no room is left for a substantial contribution of selective CS extinction on the line of sight (Goldsmith et al. concluded to [FORMULA] which appears here as an upper limit). Concerning the CS extinction, we are left with the same two possible conclusions as in Sect. 2.4., viz.:

  • it is essentially wavelength-independent at least up to [FORMULA] = 1.25 [FORMULA] which points to large grains (radii [FORMULA] or even larger),

  • and/or it is strongly non-spherical in distribution (e.g. a disc or torus seen at a large inclination angle nearly pole on) or even patchy.

[FIGURE] Fig. 6. The plot of y vs. r illustrating Eqs. (1) and (2) in the case of AC Her (G0g, E(B-V) = 0.17). The slope is A(J) the extinction at [FORMULA] and the intercept is [FORMULA] the dereddened magnitude at [FORMULA]. The IR excess starts from r=0.62 (H-filter). See Sect. 3.3. for details.

As we did for HD 100764, we favour the second hypothesis. Since AC Her is a RV Tau-a star, i.e. it has a constant mean light, we suggest that no CS dust is present on the lines of sight to those stars. Conversely, intervening CS dust on the line of sight of a RV Tau-b star would be responsible for their redder colours and cyclical variations of mean lights. It is plausible that mass loss proceeds more or less sporadically in RV Tau stars (Lloyd Evans 1985, Goldsmith et al. 1987). Recently Van Winckel et al. (1998) have confirmed that AC Her is in fact member of a wide binary system. These authors favour the existence of a long-lived disc in the system, the gas-dust separation accounting for the depletion pattern of refractory elements.

Finally, we briefly discuss the type of the adopted SED, i.e. G0g. Apart from Rp and C0,0 classifications, the quoted spectral types from various catalogues available at CDS are F2pIb-K4e, F4IbP var, and F8. The nearest of our photometric groups should be F5sg, F8sg and G0sg. They yield solutions ranging from less good (F5sg) to very bad (F8sg and G0sg). The observed HIPPARCOS parallax of [FORMULA] seems to preclude the class III but not the class II, and of course also Ib. We have tried to exploit some additional non-simultaneous SEDs. The solutions ranged from G0g, E(B-V)=0.14 to F8sg, E(B-V)=0.3, but none was as good as the one adopted above (G0g, E(B-V)=0.17). Clearly, we need more simultaneous data obtained on the whole spectral range at various phases.

3.4. The R Coronae Borealis variables

3.4.1. Introduction

We display in Fig. 7 the diagram of y vs. r for R CrB, the prototype of its class. The solution is F8sg, E(B-V)=0.0. For the same reasons we mentioned in Sect. 2.4., we favour the absence of both interstellar and circumstellar extinctions on the line of sight, at the time of the observations. Large IR excesses are seen which can be attributed to dust outside the line of sight. The RCB-stars are evolved variable objects (usually hydrogen-poor and carbon-rich) often classified as F-G supergiants. They show large amplitude variations with deep minimas attributed to strong extinction on the line of sight (e.g. Feast et al. 1997and references therein). It was shown from simple geometrical considerations that the dust condensates close to the star in patchy puffs. Then clearing occurs while they expand and/or leave the line of sight. The calculated dust temperatures (3000 K in the vicinity of a 6000 K star) are however by far too high for known species to condense and survive. Following Goeres & Sedlmayr (1992), the condensation temperature depends on the local density in a range of 1200 K to 1600 K which is reached at distances larger than 10 stellar radii in standard models of pulsating atmospheres. However, dust formed at 20 stellar radii cannot explain the fast recovery times because the dissipation time is too long (e.g. Clayton, 1996). Woitke et al. (1996) have studied the thermal balance, chemistry and nucleation in fluid elements of CS envelopes around RCB stars, periodically hit by strong shock waves due to pulsation (periods of 40-50 days). Non-LTE radiative heating and cooling via various processes are taken into account. After compression and heating, the element radiates and re-expands with adiabatic cooling. Abundant polar molecules (like possibly the carbon monoxide CO) should play a substantial role in the cooling process. Gas temperatures lower than estimated from radiative equilibrium are reached, e.g. 1500 K at 1.5 to 3 stellar radii (Woitke et al. 1996). Carbon dust can form from chains or clusters, in "puffs" then ejected by radiation pressure. The conditions might still be improved in puffs formed above giant convective cells (Wdowiak 1975). As noted by Feast (1997), it is not clear however whether all RCB stars undergo significant pulsation or whether optical variability outside obscuration minimas occurs which could be attributed to randomly occurring convective cells.

[FIGURE] Fig. 7. Same as Fig. 6 for R CrB: strong IR excesses are noted for [FORMULA] (K-filter and beyond) when compared to the extrapolated dashed line.

The optical properties and temperatures of the grains depend on their nature. Zubko (1997) analysed the extinction curves available for some RCB stars, making use of the method of regularization for solution of ill-posed problems. The best solutions were obtained making use of graphite with a [FORMULA] size distribution, similar in separate forming clouds. The calculated extinction law is selective. A similar range of glassy or amorphous carbon particles [FORMULA] was already deduced by Hecht et al. (1984), the graphite bump at [FORMULA] being absent from RCB spectra. They concluded to the possibility of larger particles forming initially, and being replaced gradually by a broad distribution of smaller grains. The mechanism could be particle collisions producing a MRN type distribution in a red giant outflow as proposed by Biermann & Harwit (1980).

3.4.2. Analyses of variations in two RCB stars

The main results and data we obtained for RCB variables can be found in Sect. 3 and Table 5. Two stars are considered hereafter which we found documented at two epochs, namely V CrA and RS Tel. We present the two studied SEDs of V CrA in Fig. 8. The solution F9g with E(B-V)=0.13 is derived at maximum light (JD 2447390). This colour excess being consistent with maps values, we consider this is the amount of interstellar extinction on the line of sight. The other solution F9g and E(B-V)=0.23 is obtained at JD 2446597.5, on a rising branch of the light curve. The extra [FORMULA] is attributed to CS dust, no difference between the CS and interstellar laws being detected at the wavelengths we used. We also note that the dereddened magnitudes in Fig. 8 are [FORMULA] and [FORMULA] respectively, i.e. practically the same value within the internal errors. This is consistent with extinction on the line of sight being responsible of the variations, the star variations remaining negligible. Small grains are indicated here with a selective law similar to the one for the interstellar extinction.

[FIGURE] Fig. 8. Same as Fig. 6 for V CrA: strong IR excesses are found for [FORMULA] (H-filter and beyond) when compared to the extrapolated dashed lines. See text for details.

The situation appears as different in deep minimas where a contribution of neutral extinction by large grains seems required. For C 3982 = RS Tel, we have obtained G0sg and E(B-V)=0.07 (interstellar value) at JD 2445217 where V=9.91 was adopted (close to maximum), and G0sg and E(B-V)=0.71 at JD 2445544 deep in a minimum where V=15.05 was adopted (see Fig. 9). The extra [FORMULA] obtained is CS in origin. The dereddened magnitudes are [FORMULA] and [FORMULA] respectively which could imply more than 3 mags of neutral extinction in addition to the selective component (both contributions would equalize in the UV-blue part of the spectrum). The intrinsic star variations probably amount to a few tenths of a magnitude. This result is suggestive of rapid grain growth in forming dense puffs, followed by destructive collisions then leading to much smaller (selective) grains during clearing. Our results in Table 5 are thus consistent with the analysis of Hecht et al. (1984) and Zubko (1997), with the following conclusions:

  • the bright RCB stars studied here at the observed maximas (either oxygen or carbon-type SEDs) have no appreciable CS dust extinction on the line of sight, the observed extinction being interstellar in origin when present,

  • relatively small grains are observed which generate a selective circumstellar law not too far from the adopted law for interstellar extinction, except at deep minima where large grains and additional neutral extinction are required for dense puffs,

  • the same photometric group is deduced for a given star at various phases consistent with the idea that the variations are essentially non-stellar (see however Rao & Lambert 1997 who find from spectral analysis a difference of 500 K between the maximas and minimas of R CrB); additional data on more stars is needed.

[FIGURE] Fig. 9. Same as Fig. 6 for RS Tel: strong IR excesses are found from the K or J-filter when compared to the extrapolated dashed lines. See text for details.

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999
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