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

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2. The hot carbon stars

2.1. The sample of unreddened HC stars

First of all, we intend to identify unreddened objects among a sample of about 140 documented HC stars. They exhibit SEDs earlier than the CV1-SED (the earliest SED in Paper I), i.e. bluer colour indices. Finding simultaneous observation sets or consistent non-simultaneous data was the main difficulty we met when dealing with variable stars of Paper I. Most stars considered here are non-variable to the present accuracy of measurements or variables of very small range (e.g. the Hp-data of ESA, vols.11-12). Easier analyses are thus expected. The opposite situation was actually observed since:

  • less data was available on the average for every star,

  • most earlier stars are intrinsically fainter than the previously studied ones, resulting in larger scatter in the observations,

  • no colour index can be found as sufficiently constant on the HC-range and thus no colour-latitude diagrams could be used,

  • no colour-colour diagram documented with sufficient accuracy (like [FORMULA] = [0.78]-[1.08] vs. [1.08]-K-[FORMULA] in Fig. 2 of Paper I, as adapted from Baumert 1972) could be found with a reddening vector nearly rectangular to a narrow intrinsic locus.

Fortunately, many of those stars are nearby objects with distances less than 900 pc, and with high galactic latitudes. Thus we were able to select 51 stars presumably unreddened (see Table 1), making use of the maps of interstellar extinction as published by FitzGerald (1968), Neckel & Klare (1980), and Burstein & Heiles (1982). The approach differs here from the analysis of the CV stars in Paper I where various diagrams were first used, and then consistency with field maps checked.


[TABLE]

Table 1. A list of the fifty-one HC stars found unreddened in the present study. The stars entries in the C catalogue (Stephenson 1989) are given. By "unreddened", we mean a star with [FORMULA].


2.2. The classification scheme of HC stars

To apply our pair method we split the sample of 51 unreddened star into six boxes or groups we name HC0 to HC5. The SEDs of two stars in the same box, should not differ significantly (outside errors) in a systematic way, throughout the entire spectral range. The seventeen photometric bands used range from [FORMULA] to the second ([25]) IRAS band as adopted in Paper I. The sixteen intrinsic indices:

[EQUATION]

and dispersions were finally calculated for every HC-group. The process was achieved by trial and error. Two accumulations appear (18 stars for HC2 and 9 stars for HC4 in Table 1) which were helpful. Then, the intermediary SEDs were put into HC3 while those earlier than HC2 could be gathered in HC1. The SEDs later than HC4 could be clustered in a single (HC5) group just intermediary between HC4 and CV1. The sixth (and earliest) group (HC0) was finally added to attempt the study of 4 reddened stars (no unreddened SED available). It is poorly defined and the corresponding values of the indices are only tentative. Actually, the SEDs earlier than HC0 were classified as oxygen-rich ones (see Sect. 3) and the above four stars might be similar wrongly-classified objects. We are here at the junction between carbon-rich and oxygen-rich SEDs.

The main features of the six groups are shown in Table 2 where mean values of three colour indices ranging from blue to IR are given. They are bluer than their counterparts of the CV-groups for cool variables (see Table 1 of Paper I). The indices increase along the sequence HC0 to HC5 which is also the case along the sequence CV1 to CV6, with the exception of [FORMULA] which remains close to 1.1 for CV1 to CV6, a remarkable property turned to advantage in Paper I. This is the reason why the transition between both categories was placed here (HC5-CV1) at an effective temperature of about 3300 K. The variability criterion did not prevail since about one-fourth of the HC stars are actually variables. As opposite to the case of CV stars, a correlation is observed with the spectral classification (R0 to R3 and C0 to C2 for HC3 and earlier groups; R4 and later and C3 or C4 for HC4 and HC5) but this is not a tight one.


[TABLE]

Table 2. The six photometric groups (G) of the unreddened HC stars. The C-entry (Stephenson 1989) of a representative star is mentioned for each group (C4094 has actually [FORMULA]). Three mean colour indices are given with their standard deviations. The closer oxygen-type SEDs "Ox" for giants (g) is quoted in the last column.


2.3. The pair method applied to HC stars

The method described in Sect. 4 of Paper I was then applied to the whole sample including reddened and unreddened stars as well. It makes use of the differences

[EQUATION]

between the observed magnitudes

[EQUATION]

and, for a given group tentatively considered, the mean unreddened indices [FORMULA]. If the latter are properly selected (i.e. if the appropriate HC-group is considered), a linear relation is thus expected between [FORMULA] and the adopted reddening law [FORMULA], the extinction [FORMULA] at [FORMULA] = 1.25 [FORMULA] being the slope and [FORMULA] = [FORMULA] - [FORMULA] the intercept. If the selected group and/or the adopted extinction law are wrong, the relation is no longer a linear one. The method is illustrated in Fig. 1 with the star C378 = HD 16115. It is shown to be HC2 with no appreciable reddening, i.e.

[EQUATION]

Strong curvatures are observed when the indices of HC1 or HC3 are used instead. The reader is referred to Paper I for full details, especially concerning the statistical analysis we apply. In the case of the [FORMULA] J-type star C378, no peculiarity was found, except for a slight excess in U (the extreme point on the right), a measurement which was ignored in the final statistics.

[FIGURE] Fig. 1. The plot of y vs. r illustrating Eqs. (1) and (2) in the case of C378 = HD 16115 (HC2, E(B-V) = 0.0). The slope is [FORMULA] the extinction at [FORMULA] and the intercept is [FORMULA] the dereddened magnitude at [FORMULA]. See Sect. 2.2. for details.

We have studied the 140 stars for grouping and extinction evaluation. The results are given in Tables 3 and 4 (only available in electronic form at the CDS), for 119 classical HC-stars and 21 peculiar stars (including RCB variables, AC Her...). In Table 3, there are 17 variables from GCVS (14.3%), 12 suspected variables from NSV (10.1%) which makes 24.4% of variables and 75.6% (90 stars) of "constant" stars. The same format is used as in Table 3 of Paper I.

For oxygen-type SEDs, the indices [FORMULA] were taken with respect to V-magnitudes instead of [FORMULA]. This is the usual practice in the literature cited in Sect. 1. The intercepts of the linear fits in Figs. 6 to 9 are thus the dereddened values [FORMULA]

2.4. The obtained extinctions

The intervals between two neighbouring HC-groups are larger in effective temperature than they are between the CV-groups. The preliminary calibrations yield 6000-3300 K and 3300-2000 K for the whole HC and CV ranges respectively. This is also illustrated by the range in "closer" oxygen-types as quoted in Table 2. The analysis of HC stars extinctions could then be less accurate than its counterpart for CV stars (Paper I). Our [FORMULA] excesses are confronted in Fig. 2 to the field values extracted from the maps published in the literature. The correlation with FitzGerald (1968) is good but substantial scatter appears since the author provides only ranges. We show in Fig. 2 the comparison with the data of Neckel & Klare (1980) and Burstein & Heiles (1982). The linear fit found is:

[EQUATION]

with a correlation coefficient of only 0.902 (see Eq. 6 of Paper I for a definition). The standard deviation of the slope is 0.041 while it is 0.04 on a single ordinate estimate. The first bisector is thus at about two standard deviations from the above fit, which is not as good as the results of Paper I (which were within one standard deviation). The lower accuracy of the photometric data used here and the larger intervals in the HC-grid when compared to the CV-one, may be responsible for this situation. Finally, there is a marginal indication of an overestimate of about [FORMULA] on the excesses determined for this sample, to be compared to [FORMULA] or less in Paper I.

[FIGURE] Fig. 2. 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 HC stars. The regression line (4) is also shown.

[FIGURE] Fig. 3. Same as Fig. 1 for C 3066 = HD 100764: strong IR excesses are observed for [FORMULA] (H-filter and beyond) when compared to the extrapolated dashed line (unreddened HC1).

2.5. The case of C 3066 = HD 100764

According to Mendoza (1968), some of the early R stars appear to have near IR excesses. Dominy et al. (1986) however found no excess in their infrared photometry of 31 early (R, CH, BaII) carbon stars. Having obtained extinction corrections for a sample of 119 classical HC stars (excluding RCB stars which are separately discussed in Sect. 3.), we checked the dereddened SEDs for such excesses against the mean intrinsic SED of the relevant HC-group. We ignore here a few (say 2 or 3) possible excesses as suggested by unconfirmed old data. Finally we are left with two stars (2 out of 126) namely C 4595 = HD 189605 (HC5, E(B-V)=0.16 with some excess from L') and C 3066 = HD 100764 (HC1, E(B-V)=0.0 with strong excesses starting from H). The former star has very strong excesses in the IRAS band-passes at 12 [FORMULA] and 25 [FORMULA] and is considered by Chan (1994) as a possible carbon star with IR silicate signature on the grounds of its low resolution IRAS spectrum (IRAS Science Team 1986, henceforth called LRS). The strength of the excesses we obtain (2.9 mag and 3.9 mag at 12 [FORMULA] and 25 [FORMULA] respectively) are in favour of this interpretation. This star will be discussed with other IR silicate CV carbon stars in a forthcoming paper.

The result E(B-V)=0.0 for HD 100764 is in excellent agreement with the published maps of interstellar extinction. The observed HIPPARCOS parallax is [FORMULA] i.e. a distance of [FORMULA] to sun. For V=8.84 we adopted, one obtains [FORMULA] Statistics on inaccurate observed parallaxes are moreover affected by biases (Knapik et al. 1998). The estimate of true parallax is 1.48 mas for a pseudo-star replacing HD 100764 in a corrected (de-biased) sample. We would then obtain [FORMULA]. The true value is lying probably between 1.06 and -0.31, since a statistical study by Vandervort (1958) showed that [FORMULA] for R0-R2 stars, which is about halfway. This is also roughly consistent with 0.7 for K0 III stars. We study now in detail this latter star which is much earlier (HC1 against HC5, which corresponds to say 4700 K against 3500 K). This result is further confirmed by the (near IR) colour temperature Tc=4605 K and the CN-index of 29.8 (a measurement of the CN bands strengths in the red system) obtained by Baumert (1972), to be compared to the average values for the HC1-group, viz. [FORMULA] and [FORMULA].

This object is thus the only non-RCB HC1 star to be associated with a thick dust shell. Parthasarathy (1991) studied the spectral distribution of the IR excesses and attributed them to a spherical circumstellar dust shell. He concluded that this object might be similar to the carbon stars with IR silicate excesses (Little-Marenin 1986, Willems & de Jong 1986). There is however no silicate signature in the [FORMULA] spectrum obtained by Skinner (1994) which invalidates a possible connection. A slight emission near [FORMULA] attributable to SiC is possibly present. The faintness of this feature can be explained on the grounds of a large optical depth of the shell. Skinner's analysis was conducted in terms of either a spherical shell in which very large grains [FORMULA] of amorphous carbon are needed, or a disc (presumably pole on) with a distribution including small grains but peaked towards large grains ([FORMULA] instead of [FORMULA] for interstellar grains). The large grains were required to provide the large excesses observed in the IRAS range.

We show in Fig. 3 the result of our analysis of HD 100764. It is remarkable that [FORMULA], with practically no deviating point except for a slight excess in U (extreme right on the diagram) which is only marginally significant. The IR excesses start from the H-filter (extreme left in the diagram). The energy corresponding to this emission excess has to be compensated for by some absorption on the whole star spectrum. We emphasize here that our results rely upon the SED HC1, as deduced from 13 unreddened stars and confirmed through 19 reddened stars successfully analysed and classified HC1. We are left with two possible conclusions concerning the circumstellar extinction:

  • it is essentially independent of wavelength 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.

The former hypothesis requires the optical depth in both absorption and scattering to be a constant within a few percents according to our results. This is not very likely although not impossible in principle. Large carbonaceous grains would then be expected, and substantial scattering due to large albedos might occur. High angular resolution in the visible range may help in establishing whether blurred images are indeed present. The latter possibility seems more likely, but constraints are raised by the data at hand. Let us assume that no extinction is present on the line of sight. We subtract our HC1-model extrapolated on the whole spectral range, thus obtaining the spectrum of the dust shell (see Fig. 4). Clearly, a wide distribution in dust temperatures is observed from an inner 900-1300 K to outer values less than 200-300 K (the true values depend on the nature and size of grains). The coordinates adopted in Fig. 4 make the areas proportional to the integrated fluxes which gives [FORMULA] and [FORMULA] i.e. [FORMULA] No other source in the field seems able to contribute appreciably. The total flux is [FORMULA] which corresponds to [FORMULA] Adopting the observed parallax or the estimated true parallax, one obtains [FORMULA] or -3.0 respectively, the true value lying probably close to -2 or -2.5. This calculation confirms that HD 100764 is not a TP-AGB star.

[FIGURE] Fig. 4. The diagram of radiated powers for the HD 100764 star and shell (see Sect. 2.4.). Beyond [FORMULA] the star curve is an extrapolation of our model.

Skinner (1994) used a cylindrical disc in his model. Assuming the star is radiating isotropically and the disc as being isotropic, our result would imply that the disc extends for [FORMULA] from its equator, as seen from the star, which is a rather thick disc. This is a lower limit corresponding to a disc optically thick on [FORMULA] As a consequence, the line of sight has to be within a cone of [FORMULA] half-angle around the polar axis. This estimate could be perverted if appreciable light is scattered in the disc preferentially towards the observer. Efficient scattering in the IR would however require very large grains which brings us back to the first possibility.

The HC1 stars (i.e. basically early R carbon stars) are low luminosity objects ([FORMULA] 0.4, Vandervort 1958, Gordon 1968, Richer 1975) well below the AGB. Helium flashes in a shell (thermal pulses) thus cannot be the mechanism which generated the shell from HD 100764. If core helium flash in a RGB star could be responsible, we should observe at least a few similar objects. A special model is probably required.

The chemical peculiarities of some low luminosity giants (BaII, CH, extrinsic S stars..) are usually explained in terms of mass transfer or wind accretion in a binary system (McClure et al. 1980, McClure & Woodsworth 1990, Han et al. 1995, Jorissen et al. 1998). The formerly more massive component, now a white dwarf, polluted its companion while a mass loosing TP-AGB star. Dominy (1984) did not find any evidence that HD 100764 might be a binary star and the same situation prevails from HIPPARCOS data (HIC 56551 in ESA 1997). More generally, McClure (1997) found no evidence for binary motion in 16 years of radial-velocity observations of a sample of 22 R-type carbon stars. This is however not a definitive argument against the binary hypothesis but the exceptional nature of HD 100764 would be confirmed in case of detection.

We found large dust temperatures (at least 900 K), wide angular extension and substantial powering of the shell. As proposed by Skinner (1994), the companion wind may have been channeled into a disc (and not onto the surface of HD 100764 which would explain the absence of s-processed elements in the star spectrum). With mass shed through the external Lagrangian point, the disc might be a circumbinary one. Also photocenters deviations were not detected by HIPPARCOS when separation is low and period close to one year (ESA). A much shorter period would result in observable variable velocities. Rather stringent conditions probably restrain the life time of such a configuration which would explain why no other such object is known at present. Finally, the disc geometry might look like the one proposed by Waelkens et al. (1996, their Fig. 2) for HD 44179 (The Red Rectangle), a peculiar A-supergiant orbiting a low-mass object, except that the latter one is viewed nearly edge-on. HD 100764 seen equator-on would mimic a non-variable IRAS C star. This is the reason why we are currently searching for reddened HC stars among them. Unfortunately, short wavelengths data is usually missing.

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Online publication: February 23, 1999
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