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Astron. Astrophys. 344, 263-276 (1999)

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6. The carbon Miras

6.1. The pair method applied to carbon-rich Miras

The carbon-rich Miras were not included in Paper I due to their large amplitudes of variation. Miras (especially oxygen-rich ones) are known to exhibit light curves which do not repeat faithfully from one cycle to the other (Lockwood & Wing 1971, Lockwood 1972). Notes in the General Catalogue of Variable Stars (Kholopov et al. 1985, henceforth called GCVS, and extensions published in the Information Bulletin on Variable Stars 1985 to 1997) contain frequently mean maximum values, while the range of extreme maximum and minimum are quoted in the main table. The SEDs of Paper I were more easily defined from small amplitude variables. Semi-regulars with relatively large amplitudes (SRa) were however included and sets of nearly simultaneous multicolour photometry selected whenever possible. There was some evidence that the photometric group of those stars may change with phase. The effect is still more pronounced in the case of many Miras. The results now available from the data at hand are given for 73 carbon Miras in Table 5 (only available in electronic form at the CDS). Unfortunately, sufficient multicolour measurements at various phases are available for only a limited sample of Miras. Seventy-five entries can be found in the first part of Table 5, each of them corresponding to an analysed SED. Fifty-six carbon Miras have thus been studied with a solution found (group and E(B-V) determined at least at one phase). Uncertain and incomplete results are reported for 17 additional Miras (and 17 SEDs) in the second part of Table 5. They are considered as very provisional but may be of some help. We had frequently to collect data secured during different cycles at phases within a given range like 0.05-0.15 or 0.3-0.5 for instance, and attribute the obtained SED to phases 0.1 or 0.4 respectively. This is of course a poor substitute for simultaneous multicolour photometry, and poorer meaning and lower accuracy necessarily result. The elements were usually taken from the GCVS and its extensions. The elements from HIPPARCOS (ESA 1997, vol. 11) were also considered. They give phases consistent with those from GCVS, at least roughly, with the exception of C828 = R Ori for which we adopted the HIPPARCOS values JD 2448673.5 + 379:d0 (ESA).

As expected, the redder the SED, the later the obtained photometric group. The earliest group is thus obtained at phases close to maximum light or slightly after (typically phases 0.00-0.15) and a later one is usually observed at phases close to minimum light (0.4-0.6). Effective temperature variations and opacity effects during pulsation cycles are coupled with angular diameter variations. There is a relatively well-defined relation between the effective temperatures and our CV-classification (Bergeat & Knapik 1999). An extensive study should be based on a larger body of data and this is what we are planning to do in the near future. For the time being, we present a few cases of carbon Miras (U Cyg, R Lep, V1426 Cyg = CIT13 and CW Leo = IRC+10216) we found sufficiently documented for our purposes.

6.2. The carbon Mira U Cyg

In most cases, the colour excess found at intermediary or late phases is larger than its counterpart at early phases close to maximum. Sometimes the difference between colour excesses deduced at various phases is not significant. This is not the case of the Mira C4817 = U Cyg. The [FORMULA] vs. [FORMULA] diagram at three phases are plotted in Fig. 4 (CV3 and E(B-V)=0.54 at [FORMULA], CV5 and E(B-V)=0.85 at [FORMULA], and CV6 and E(B-V)=0.81 at [FORMULA]). Unfortunately, no IR data was available at [FORMULA] and the corresponding (CV5) solution should be attributed a lower weight. The star is seen in a strongly reddened field and E(B-V)=0.2 to 0.9 is expected from the maps in FitzGerald (1968), if its assumed distance lies between 0.5 and 1.0 kpc, a reasonable range from HIPPARCOS data (HIP 100219A, ESA). It is located just outside Zone 299 of Neckel & Klare (1980) where E(B-V) increases steeply from 0.4 at 400 pc to 0.75 at 600 pc. We found a slightly smaller colour excess (0.42) for V Cyg, a carbon Mira located in the same field (0.4-0.6 kpc). Finally, we consider the above value at maximum (i.e. 0.54) as representative of the interstellar extinction on the line of sight, and attribute the additional 0.3 excess at intermediary phases to CS grains. The star U Cyg is representative of carbon Miras with large changes in CV-group. These ranges are experienced during every cycle and we interpret them in terms of large amplitudes in effective temperature (possibly 600 K for U Cyg, e.g. 2300-2900 K).

[FIGURE] Fig. 4. Same as Fig. 2 for C4817 = U Cyg at three phases: maximum light and two intermediary phases with corresponding regression lines plotted. Infrared excesses due to thermal emission from CS grains are noted for [FORMULA] (from the H-filter and beyond). See text for details.

6.3. The cool end of the sequence

Colour excesses substantially larger than the expected interstellar value are frequently noticed for the coolest (CV5 to CV7) Miras even at phases close to maximum light (see Sect. 3 and Table 1). If CS grains are truly responsible of the additional extinction inferred, this is exactly what to expect. Concurrently, we have searched for pieces of evidence of a cooler intrinsic SED (say CV8), but we were unable to document such a group. More precisely, we failed to detect high galactic latitude stars with consistent SEDs substantially redder than the one adopted for CV7. In addition, no low galactic latitude star was found with accurate interstellar extinction from maps, whose dereddening could lead to a SED redder than CV7. If confirmed, this would imply that the coolest carbon variables have effective temperatures of nearly [FORMULA] The much lower temperatures sometimes quoted, would then be due to strong CS opacity effects, the direct stellar photons observed being too few. Consequently, the seven groups (CV1 to CV7) previously defined prove a sufficient framework for Miras analyses, at least on the basis of the presently available data.

6.4. The nearby Mira C833 = R Lep

The coolest objects with large amplitudes of variations are classified as CV6 or CV7 stars. They radiate a large part of their energy in the IR range. They often display the same CV-group upon a large phase interval or even upon several cycles, for thousands of days. Variations of effective temperature less than 300 K are thus indicated along such time intervals. Some of those stars also exhibit long term variations like R For or R Lep (e.g. Whitelock et al. 1997). We present now a study of C833 = R Lep, a nearby cool carbon Mira which was recently faint on several cycles ([FORMULA] and later). The HIPPARCOS elements ([FORMULA]) yield a good phase fit to the recent observations. Our main analysis deals with previous "bright" cycles. The group was CV6 with varied selective extinctions derived. Its HIPPARCOS observed parallax is [FORMULA] (ESA) which would make it an underluminous star.

HIPPARCOS measurements are however affected by biases (Knapik et al. 1998), especially the Lutz-Kelker bias. Knapik et al. studied the space distribution of carbon giant stars from HIPPARCOS data and calculated the true parallaxes of an unbiased sample made of the same stars. The estimate of true parallax we obtained for R Lep is 2.97 mas only, which would imply [FORMULA], in the locus of carbon variables of the PL-relation of Bergeat et al. (1998a, their Fig. 1a, slightly above its lower edge. According to this result, R Lep is not markedly underluminous, but this is of course a statistical argument, and the only way to make sure is a new and more accurate parallax measurement. According to published maps, this nearby star (300 pc) should be affected by a negligible interstellar extinction. As shown by the [FORMULA] vs. [FORMULA] diagram (Fig. 5), [FORMULA] is observed at maximum light, and [FORMULA] at [FORMULA]. The additional 0.58 mag. can be attributed to CS dust. From the near IR (JHKL) photometry of Whitelock et al. (1997) and visual magnitudes from AAVSO (Mattei 1997), we anticipate for those faint cycles of R Lep the same group CV6 with [FORMULA] near maximas and minimas respectively. The increase of the colour excesses relative to the "bright" cycles, ranges from 0.4 at maximum light to 0.7 at minimum light. An additional 0.6-1.4 mag. dimming of the dereddened [FORMULA] is observed which could be due to a contribution of large neutral carbonaceous grains. Unfortunately, this latter result is unconfirmed since we are missing simultaneous multicolour photometry in the visible. The visual light curve published by Mattei show a possibly similar event around JD 2436000. This interpretation would imply additional selective and neutral extinctions occurring on the line of sight in dense puffs, with no important change in the star properties (CV6). The star then returns to the normal "bright" level by "dust clearing", the grains leaving the line of sight and/or decreasing strongly in density by dilution during expansion and/or destructive collisions. We have already discussed the occurrence of such dense puffs in the vicinity of RCB-variables (see Paper II). Additional data is however needed before a firmer conclusion can be reached.

[FIGURE] Fig. 5. Same as Fig. 2 for C833 = R Lep (during bright cycles) at two phases close to maximum and minimum respectively. The small reddening at maximum light is attributed to interstellar extinction on the line of sight. The corresponding regression lines are plotted. Infrared excesses due to thermal emission from CS grains are noted for [FORMULA] (from the K-filter and beyond). See text for details.

6.5. The CV7 Mira C5348 = V1426 Cyg = CIT13

Other cases with appreciable contributions of the interstellar and CS reddenings on a very cool intrinsic SED (presumably CV7) are more difficult to deal with. This is the case of C5348 = V1426 Cyg = CIT13 which appears as a CV7 star irrespective of the phase of the observations used (see Fig. 6). The colour excess found close to maximum light [FORMULA] is 0.42 which is close to the 0.4 field value estimated from published maps. Two analyses with nearly simultaneous data could be made at [FORMULA] and 0.77 respectively. The slight difference between those excesses is not significant and the additional 0.7 mag. on E(B-V) can be attributed to the CS reddening. The objects like CIT13 are intermediary between the cool optical Miras, e.g. R Lep (CV6) and R For (CV7), and the extreme objects like CW Leo = IRC+10216 (also a CV7 star: see next subsection).

[FIGURE] Fig. 6. Same as Fig. 2 for C5348 = V1426 Cyg = CIT13 at three phases (maximum and intermediary phases respectively). The reddening at maximum light (during bright cycles) at two phases close to maximum and minimum respectively. The small reddening at maximum light is attributed to interstellar extinction on the line of sight. The corresponding regression lines are plotted. Infrared excesses due to thermal emission from CS grains are noted for [FORMULA] (from the K-filter and beyond). See text for details.

6.6. The extreme object C2619 = CW Leo = IRC+10216

The object CW Leo is an extreme cool dust-enshrouded carbon star whose extended shell and detailed chemistry deserved many studies (see Glasgold 1996for a review and more recently Doty & Leung 1998). Other galactic objects belong to the same category like LL Peg = AFGL3068 an even more obscured carbon Mira (Sopka et al. 1985, Le Bertre et al. 1995 and Winters et al. 1997) with a period of 700 d. CW Leo is classified as a Mira variable of period 630 d in the GCVS. It was unfortunately too faint for HIPPARCOS observation but this is a nearby object (100-250 pc from sun is usually adopted; e.g. Bergeat et al. 1978). A negligible interstellar extinction is thus expected from maps in the literature, which is a favourable circumstance.

The published photometric observations of CW Leo are less numerous that might be anticipated from the large number of references found in the SIMBAD database at CDS. In addition, we need nearly simultaneous multicolour photometry from UV to IR since the ranges of variations are large even in the IR. Here, we apply our method to the short wavelengths [FORMULA] data and IR observations of Le Bertre (1988) near JD 2446918, and another SED near JD 2446225 making use, in addition, of Alksnis (1989) and Le Bertre (1987, see also 1992). The former SED at phase 0.27 is the best defined since all the data is nearly simultaneous. The later one at a phase of roughly 0.16 is in fact a "composite" since compatible observations at the same phase from other cycles were added at some wavelengths. The level of confidence is thus lower, but we wished to explore a SED closer to maximum light. We were convinced a priori that our method which makes use of the direct (transmitted as opposite to scattered) photons would not work here, due to large CS opacities and presumably, substantial multiple scattering. The [FORMULA] vs. [FORMULA] diagram of Fig. 7 displays the satisfactory (surprisingly enough) solutions CV7 with the large extinctions [FORMULA] and 2.4 respectively, which are entirely local to the source. The colour excess of 3.7 is the largest one we derived so far for a carbon star. If this analysis is correct, the effective temperature of the central object should be in the 1900-2200 K range found from the CV7 stars with measured angular diameters (Bergeat & Knapik 1999). An IR excess increasing from r=0.62 (H-filter and beyond) is noted with little difference between our two epochs as shown also by the light curves of Le Bertre (1992). This is the thermal emission from CS dust located in a very extended region. We must emphasize that any neutral extinction on the line of sight would remain undetected here. If effectively present, it prevents us from subtracting the net flux derived from the extrapolated regression lines in order to disentangle the CS emission. Light scattered in the observing lobe may also intervene and this point is discussed hereafter in Sect. 6.7.

[FIGURE] Fig. 7. Same as Fig. 2 for C2619 = CW Leo = IRC+10216 at two phases. No appreciable contribution from interstellar extinction is expected on the line of sight. The regression lines corresponding to the two solutions CV7 with E(B-V)=3.67 and 2.34 respectively, are shown. Infrared excesses due to thermal emission of CS grains are noted for [FORMULA] (from the H-filter and beyond). See text for details.

We have also tested the influence of the adopted extinction law. To this purpose the "outer cloud" law of Mathis (1990) was used instead of the mean law for the diffuse medium he quoted (see his Table 1). The "outer cloud" law is less selective in the visible than the law for the diffuse medium we used successfully. It can be modeled by introducing larger grains in increased proportions. No reasonable fit for any CV-group could be obtained here. To illustrate the point, the diagram for the groups CV6 and CV7 and the "outer cloud" law is shown in Fig. 8. Appreciable curvatures can be seen on the entire spectral domain. It does not mean that any other combination of a CV-SED and special extinction law is ruled out, but that the agreement observed in Fig. 7 is the best obtained so far and needs to be explained. The statement that can be made is that the selective part of the large extinction found follows a law which is close to the mean law for the diffuse interstellar medium, at least at two phases and for wavelengths shorter than [FORMULA] . From this point, constraints result on the fraction of light scattered in the instrumental observing lobe. If wavelength dependent, it has to be small (negligible here means less than 10-20% of the total light). Substantial scattering is however required by transfer models to explain the extensions of CW Leo images in the visible and the CS polarization at the K-band (e.g. Groenewegen 1997). The remaining possibilities are neutral scattering by large grains or a scattered contribution proportional to the transmitted light. Concerning the latter case, scattered photons reaching the observer through such a thick "dust atmosphere", come from the external layers where the scattering cross section affects light transmitted by the deeper layers (we derived total optical depths in excess of 6 and 10 at [FORMULA]). It is however difficult to believe that the variations with wavelength of the scattering coefficient and directivity of scattering by (presumably) small grains, may combine in order to produce a substantial wavelength-independent fraction of the total transmitted light. The assumption of large scatterers not included in our calculated optical depths seems more likely. Jura (1994) proposed a distribution of amorphous carbon spheres close to the MRN one used for the interstellar extinction, in the small radii range. He also added large grains such as the graphitic component found in primitive meteorites (Bernatowicz et al. 1996and references therein). The balance between absorbed radiation and dust emission could have helped in a spherically symmetric object, which is not the case of IRC+10216 (e.g. Kastner & Weintraub 1994and references therein). Recent observations shown that, if the red [FORMULA] or near IR [FORMULA] images may keep some axial symmetry (Haniff & Buscher 1998), this is definitely not the case of the IR emission, at least during recent years, which comes from five (or possibly seven) resolved bright knots separated by opaque portions (Weigelt et al. 1998, Haniff & Buscher 1998). Skinner et al. (1998) recently obtained HST-WFPC2 images of CW Leo at [FORMULA] A bright nebula with a dark lane is seen, the authors compare to the one of AFGL2688 (Cygnus Egg Nebula, a bipolar structure). A brighter point like source is however observed in the southern lobe of the CW Leo nebula which is probably the central star. Strong scattering is thus conspicuous.

[FIGURE] Fig. 8. Same data as Fig. 7 (CW Leo = IRC+10216) for CV6 and CV7 with the "outer cloud" extinction law of Mathis (1990). No linear fits can be accepted on those curved plots for [FORMULA] which means this law is not suitable here.

Images at various short wavelengths would help in setting constraints on the properties of the scattering grains which we believe are large in size. More simultaneous multicolour photometric data has to be obtained before firmer conclusions could be drawn on this fascinating object.

6.7. Discussion of carbon Miras

Fundamentally, carbon-rich Miras and SR or Lb variables populate the same sequence of SEDs. We have found again that Miras exhibit, on the average, larger IR excesses which are interpreted in terms of dust shells with intermediary or large optical optical depths (e.g. Lorenz-Martins & Lefèvre 1993, 1994). What is new is our evaluation of the selective CS extinction. We already noted in Sect. 4.2 of Paper I that noticeable curvatures are observed in the IR in part of our dereddening diagrams, while a good linear fit is obtained at shorter wavelengths. It was interpreted as CS emission from dust shells of substantial optical depths. For Miras and IRAS C stars, those features practically become the rule. The selective CS extinctions found are indicative of small grains (radii [FORMULA]) on the line of sight. Decreasing albedo for single scattering [FORMULA] with increasing wavelength is found for distributions of grains intended to explain the mean interstellar extinction law (see Draine & Lee 1984) we used here. Thus, scattered photons should not yield the agreement observed for the extreme object CW Leo. The albedo for single scattering is not however the whole story since the scattering should be increasingly multiple at shorter wavelengths because of increasing opacity (e.g. Lefèvre et al. 1982, 1983). For a given albedo function [FORMULA] the probability for a scattered photon to finally escape absorption and thus to reach the observer, is increasingly reduced for decreasing wavelengths. This latter opacity effect attenuates the influence of the [FORMULA] (that is what we would observe in an optically thin shell where single scattering predominates at every considered wavelength). There is however no reason why the spectral energy distribution of scattered photons should follow the CV7-SED attenuated according to the interstellar law we used, i.e. the transmitted light. Thus we conclude that, in CW Leo, the contribution of photons scattered to the observer by small (selective) grains [FORMULA] is negligible. Our arguments do not apply to eventual large (non-selective) grains with transmitted and scattered contributions independent of wavelength. We emphasize again that they would escape detection in the present approach. In other words, we only observe direct photons from CW Leo at short wavelengths, unless the possible contribution of large grains [FORMULA] cannot be neglected. If the latter is negligible, the CS emission (IR excesses) can be determined from the dereddening diagram. To this purpose, a magnitude difference could be tentatively derived between [FORMULA] from the observations and [FORMULA] of Eq. (4) as extrapolated from our model (the straight lines in dereddening diagrams).

Carbon Miras are very few: we were able to find only 73 documented Miras out of nearly 585 carbon stars (687 SEDs) studied so far. Seventeen analyses could not be safely achieved, decreasing the number of well-studied Miras down to 56 stars. It can be seen in Table 1 that 12 Miras (or possibly so) are classified CV7 at least at some phase, and 7 Miras (or possibly so) can be found in Tables 2 and 3 for CS and SC stars respectively. Unfortunately, many Miras could be studied at only one phase due to missing data. The earliest group reached by some carbon Miras (R Ori and R CMi two CS stars, and Y Per) is HC5 close to their maximum light. The corresponding maximum in effective temperature lies in the 3600-3000 K range.

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© European Southern Observatory (ESO) 1999

Online publication: March 10, 1999