A&A 390, 533-553 (2002)
DOI: 10.1051/0004-6361:20020603

The carrier of the "30'' $\mu $m emission feature in evolved stars[*],[*]

A simple model using magnesium sulfide

S. Hony1 - L. B. F. M. Waters1,2 - A. G. G. M. Tielens3,4

1 - Astronomical Institute ``Anton Pannekoek'', Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
2 - Instituut voor Sterrenkunde, K.U. Leuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium
3 - SRON Laboratory for Space Research Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
4 - Kapteyn Astronomical Institute PO Box 800, 9700 AV Groningen, The Netherlands

Received 4 March 2002 / Accepted 16 April 2002

We present 2-45 $\mu $m spectra of a large sample of carbon-rich evolved stars in order to study the "30'' $\mu $m feature. We find the "30'' $\mu $m feature in a wide range of sources: low mass loss carbon stars, extreme carbon-stars, post-AGB objects and planetary nebulae. We extract the profiles from the sources by using a simple systematic approach to model the continuum. We find large variations in the wavelength and width of the extracted profiles of the "30'' $\mu $m feature. We modelled the whole range of profiles in a simple way by using magnesium sulfide (MgS) dust grains with a MgS grain temperature different from the continuum temperature. The systematic change in peak positions can be explained by cooling of MgS grains as the star evolves off the AGB. In several sources we find that a residual emission excess at $\sim$26 $\mu $m can also be fitted using MgS grains but with a different grains shape distribution. The profiles of the "30'' $\mu $m feature in planetary nebulae are narrower than our simple MgS model predicts. We discuss the possible reasons for this difference. We find a sample of warm carbon-stars with very cold MgS grains. We discuss possible causes for this phenomenon. We find no evidence for rapid destruction of MgS during the planetary nebula phase and conclude that the MgS may survive to be incorporated in the ISM.

Key words: stars: AGB and post-AGB - stars: carbon - circumstellar matter - stars: mass-loss - planetary nebulae: general - infrared: stars

1 Introduction

The far infrared (IR) spectra of carbon-rich evolved objects; i.e., carbon-rich AGB stars (C-stars), post asymptotic giant branch objects (post-AGBs) and planetary nebulae (PNe) are typified by a broad emission feature around 30 $\mu $m. This "30'' $\mu $m feature was first discovered in the far-IR spectra of CW Leo, IC 418 and NGC 6572 by Forrest et al. (1981). Since then this feature has been detected in a wide range of carbon-rich evolved objects from intermediate mass loss C-stars (Yamamura et al. 1998) to post-AGBs and PNe (Omont 1993; Cox 1993; Omont et al. 1995; Jiang et al. 1999; Szczerba et al. 1999; Hony et al. 2001). The feature is commonly found in C-rich post-AGBs and PNe however with varying band shapes and varying feature to continuum ratios (Goebel & Moseley 1985; Waters et al. 2000; Hrivnak et al. 2000; Volk et al. 2002)

Goebel & Moseley (1985) proposed solid magnesium sulfide (MgS) as the possible carrier of the "30'' $\mu $m feature. Their suggestion is based on the coincidence of the emission feature with the sole IR-resonance of MgS (Nuth et al. 1985; Begemann et al. 1994) and the fact that MgS is one of the expected condensates around these objects (Lattimer et al. 1978; Lodders & Fegley 1999). Several authors have taken up on this suggestion and compared observations with laboratory measurements of MgS. These comparisons were further facilitated by the publication of the optical constants of MgS in the IR range by Begemann et al. (1994). These authors found that the far IR excess of CW Leo can be successfully modelled using MgS grains with a broad shape distribution.

More recently, Jiang et al. (1999) and Szczerba et al. (1999) have modelled the spectra taken with the Short Wavelength Spectrometer (SWS) (de Graauw et al. 1996) on-board the Infrared Space Observatory (ISO) (Kessler et al. 1996) of the C-star IRAS 03313+6058 and the post-AGB object IRAS 04296+3429 respectively. They find that for these sources which show a strong "30'' $\mu $m feature, the elemental abundances of Mg and S are consistent with MgS as the carrier of the feature.

Hrivnak et al. (2000) and Volk et al. (2002) have analysed ISO spectra of a sample of post-AGBs. They find that the profile of the "30'' $\mu $m feature varies between sources. Although these authors state that this decomposition is not unique, they find that their "30'' $\mu $m feature is composed of two sub features: one feature peaking near 26 $\mu $m and an other near 30 $\mu $m. Using these two components in varying relative amounts they are able to explain the range of features found in their sample. Based on the discovery of these sub features they consider the carrier(s) of the "30'' $\mu $m feature to be unidentified.

Other materials have also been proposed as carriers of the "30'' $\mu $m feature. Duley (2000) suggests that the "30'' $\mu $m feature may be indicative of carbon-based linear molecules with specific side groups. Such molecules have strong absorption bands throughout the 15-30 $\mu $m range. Papoular (2000) discusses the possible contribution of carbonaceous dust grains with oxygen in the structure. Some of these materials may show IR emission in the 20-30 $\mu $m range. Since the optical properties of such grains are sensitive to the exact composition they might be able to explain the range of features found in the C-rich evolved stars. Recently, Grishko et al. (2001) have proposed hydrogenated amorphous carbon (HAC) as a possible carrier of the "30'' $\mu $m feature.

The ISO mission has provided an excellent database of observations to study the properties of the "30'' $\mu $m feature in detail and test the suggested identifications systematically. The wavelength coverage of the SWS instrument (2-45 $\mu $m) is sufficient to determine a reliable continuum. The sensitivity of the ISO spectrograph allows detection of relatively weak features. The resolving power of the instrument ($\lambda$/ $\Delta\lambda = 500$-1500) makes it feasible to study possible substructure in the "30'' $\mu $m feature. Thus these observations allow a study of the "30'' $\mu $m feature in unprecedented detail in a large sample of sources.

In this paper, we investigate the shape and strength of the "30 $\mu $m'' in a wide range of objects from visual visible C-stars, extreme C-stars, post-AGBs to PNe in order to further test the MgS or other identifications and map systematic differences between the feature in different classes of sources.

Our paper is organised as follows. In Sect. 2, we describe the sample and the data reduction. In Sect. 3, we present the way in which we modelled the continuum in order to extract the feature properties. In Sect. 4, we present the full range of extracted profile shapes and peak positions of the "30'' $\mu $m feature and we discuss the possible ways of interpreting the observed profiles. In Sect. 5, we develop a simple model using MgS for the "30'' $\mu $m feature. In Sect. 6, we present the model results and compare them to the astronomical spectra. In Sect. 7, we present a correlation study between several feature properties and stellar parameters. Finally, in Sect. 8, we discuss the implications of our model results and the consequences for the MgS identification. In particular, we discuss possible causes for the deviating profiles and the possibility that MgS produced in carbon-rich evolved stars will be incorporated in the interstellar medium (ISM).

2 Observations


Table 1: Source list. Observational details of the sources in this study.
Object IRAS name Obs.a $\alpha$ $\delta$ TDTb Sp./T Obj. Type
    Mode (J2000) (J2000)   kK  
NGC 40 00102+7214 01(3) 00 13 01.10 +72 31 19.09 30003803 WC PN
IRAS 00210+6221 00210+6213 01(1) 00 23 51.20 +62 38 07.01 40401901   C-star
IRAS 01005+7910 01005+7910 01(2) 01 04 45.70 +79 26 47.00 68600302 OBe post-AGB
HV Cas 01080+5327 01(1) 01 11 03.50 +53 43 40.30 62902503   C-star
RAFGL 190 01144+6658 01(2) 01 17 51.60 +67 13 53.90 68800128   C-star
R Scl $^{\dagger}$ 01246-3248           C-star
-   01(2) 01 26 58.10 -32 32 34.91 37801213    
-   01(2) 01 26 58.05 -32 32 34.19 37801443    
IRAS Z02229+6208 Z02229+6208 01(1) 02 26 41.80 +62 21 22.00 44804704 G0 post-AGB
RAFGL 341 02293+5748 01(1) 02 33 00.16 +58 02 04.99 80002450   C-star
IRC+50 096 03229+4721 01(2) 03 26 29.80 +47 31 47.10 81002351   C-star
IRAS 03313+6058 03313+6058 01(1) 03 35 31.50 +61 08 51.00 62301907   C-star
U Cam 03374+6229 01(2) 03 41 48.16 +62 38 55.21 64001445   C-star
RAFGL 618 04395+3601 01(3) 04 42 53.30 +36 06 52.99 68800561 B0 PN
W Ori 05028+0106 01(3) 05 05 23.70 +01 10 39.22 85801604   C-star
IC 418 05251-1244 01(2) 05 27 28.31 -12 41 48.19 82901301 361 PN
V636 Mon 06226-0905 01(1) 06 25 01.60 -09 07 16.00 86706617   C-star
RAFGL 940 06238+0904 01(2) 06 26 37.30 +09 02 16.01 87102602   C-star
IRAS 06582+1507 06582+1507 01(2) 07 01 08.40 +15 03 40.00 71002102   C-star
HD 56126 $^{\dagger}$ 07134+1005         F5 post-AGB
-   06 07 16 10.20 +09 59 48.01 71802201    
-   06 07 16 10.30 +09 59 48.01 72201702    
-   01(3) 07 16 10.20 +09 59 48.01 72201901    
CW Leo 09451+1330 06 09 47 57.27 +13 16 42.82 19900101   C-star
NGC 3918 11478-5654 01(1) 11 50 18.91 -57 10 51.10 29900201   PN
RU Vir 12447+0425 01(2) 12 47 18.43 +04 08 41.89 24601053   C-star
IRAS 13416-6243 13416-6243 01(3) 13 45 07.61 -62 58 18.98 62803904   post-AGB
II Lup 15194-5115 06 15 23 04.91 -51 25 59.02 29700401   C-star
V Crb 15477+3943 06 15 49 31.21 +39 34 17.80 25502252   C-star
PN K 2-16 $^{\dagger}$ 16416-2758         WC PN
-   01(1) 16 44 49.10 -28 04 05.02 29302010    
-   01(2) 16 44 49.10 -28 04 05.02 67501241    
IRAS 16594-4656 16594-4656 01(1) 17 03 09.67 -47 00 27.90 45800441   post-AGB
NGC 6369 17262-2343 01(1) 17 29 20.80 -23 45 32.00 45601901 WC82 PN
IRC+20 326 17297+1747 01(1) 17 31 54.90 +17 45 20.02 81601210   C-star
CD-49 11554 17311-4924 01(2) 17 35 02.41 -49 26 22.31 10300636 BIIIe post-AGB
PN HB 5 17447-2958 01(3) 17 47 56.11 -29 59 39.70 49400104   PN
RAFGL 5416 17534-3030 01(1) 17 56 36.90 -30 30 47.02 12102004   C-star
T Dra 17556+5813 01(2) 17 56 23.30 +58 13 06.38 34601702   C-star
RAFGL 2155 18240+2326 01(1) 18 26 05.69 +23 28 46.31 47100261   C-star
IRAS 18240-0244 18240-0244 01(1) 18 26 40.00 -02 42 56.99 14900804 WC PN
IRC+00 365 18398-0220 01(2) 18 42 24.68 -02 17 25.19 49901342   C-star
RAFGL 2256 18464-0656 01(1) 18 49 10.35 -06 53 03.41 48300563   C-star
PN K 3-17 18538+0703 01(2) 18 56 18.05 +07 07 25.61 49900640   PN
IRC+10 401 19008+0726 01(1) 19 03 18.10 +07 30 43.99 87201221   C-star
IRAS 19068+0544 19068+0544 01(1) 19 09 15.40 +05 49 05.99 47901374   C-star
NGC 6790 19204+0124 01(1) 19 22 57.00 +01 30 46.51 13401107 703 PN
RAFGL 2392 19248+0658 01(1) 19 27 14.40 +07 04 09.98 85800120   C-star
NGC 6826 19434+5024 01(4) 19 44 48.20 +50 31 30.00 27200786 504 PN
IRAS 19454+2920 19454+2920 01(1) 19 47 24.25 +29 28 11.78 52601347   post-AGB
HD 187885 19500-1709 01(2) 19 52 52.59 -17 01 49.58 14400346 F2 post-AGB
RAFGL 2477 19548+3035 01(1) 19 56 48.26 +30 43 59.20 56100849   C-star
IRAS 19584+2652 19584+2652 01(1) 20 00 31.00 +27 00 37.01 52600868   C-star
IRAS 20000+3239 20000+3239 01(1) 20 01 59.50 +32 47 33.00 18500531 G8 post-AGB
V Cyg $^{\dagger}$ 20396+4757           C-star
-   01(2) 20 41 18.20 +48 08 29.00 42100111    
-   01(2) 20 41 18.20 +48 08 29.00 42300307    

Table 1: continued.
Object IRAS name Obs.a $\alpha$ $\delta$ TDTb Sp./T Obj. Type
    Mode (J2000) (J2000)   kK  
NGC 7027 $^{\dagger}$           2005 PN
-   01(4) 21 07 01.71 +42 14 09.10 02401183    
-   01(1) 21 07 01.70 +42 14 09.10 23001356    
-   01(2) 21 07 01.70 +42 14 09.10 23001357    
-   01(3) 21 07 01.70 +42 14 09.10 23001358    
-   01(4) 21 07 01.63 +42 14 10.28 55800537    
S Cep 21358+7823 01(1) 21 35 12.80 +78 37 28.20 56200926   C-star
RAFGL 2688   01(3) 21 02 18.80 +36 41 37.79 35102563 F5 post-AGB
RAFGL 2699 21027+5309 01(1) 21 04 14.70 +53 21 02.99 77800722   C-star
IC 5117 21306+4422 01(1) 21 32 30.83 +44 35 47.29 36701824 773 PN
RAFGL 5625 21318+5631 01(1) 21 33 22.30 +56 44 39.80 11101103   C-star
IRAS 21489+5301 21489+5301 01(1) 21 50 45.00 +53 15 28.01 15901205   C-star
SAO 34504 22272+5435 01(2) 22 29 10.31 +54 51 07.20 26302115 G5 post-AGB
IRAS 22303+5950 22303+5950 01(1) 22 32 12.80 +60 06 04.00 77900836   C-star
IRAS 22574+6609 22574+6609 01(2) 22 59 18.30 +66 25 49.01 39601910   post-AGB
RAFGL 3068 23166+1655 01(2) 23 19 12.48 +17 11 33.40 37900867   C-star
RAFGL 3099 23257+1038 01(1) 23 28 16.90 +10 54 40.00 78200523   C-star
IRAS 23304+6147 23304+6147 01(3) 23 32 44.94 +62 03 49.61 39601867 G2 post-AGB
IRAS 23321+6545 23321+6545 01(1) 23 34 22.53 +66 01 50.41 25500248   post-AGB
IRC+40 540 23320+4316 01(2) 23 34 27.86 +43 33 00.40 38201557   C-star
non detections
R For 02270-2619 01(1) 02 29 15.30 -26 05 56.18 82001817   C-star
SS Vir 12226+0102 01(1) 12 25 14.40 +00 46 10.20 21100138   C-star
Y CVn 12427+4542 01(2) 12 45 07.80 +45 26 24.90 16000926   C-star
RY Dra 12544+6615 01(3) 12 56 25.70 +65 59 39.01 54300203   C-star
C* 2178 14371-6233 01(1) 14 41 02.50 -62 45 54.00 43600471   C-star
V1079 Sco 17172-4020 01(1) 17 20 46.20 -40 23 18.10 46200776   C-star
T Lyr 18306+3657 06 18 32 19.99 +36 59 55.50 36100832   C-star
S Sct 18476-0758 01(2) 18 50 19.93 -07 54 26.39 16401849   C-star
V Aql 19017-0545 01(2) 19 04 24.07 -05 41 05.71 16402151   C-star
V460 Cyg 21399+3516 01(1) 21 42 01.10 +35 30 36.00 74500512   C-star
PQ Cep 21440+7324 01(1) 21 44 28.80 +73 38 03.01 42602373   C-star
TX Psc 23438+0312 06 23 46 23.57 +03 29 13.70 37501937   C-star

a SWS observing mode used (see de Graauw et al. 1996). Numbers in brackets correspond to the scanning speed.
b TDT number which uniquely identifies each ISO observation.
$^{\dagger}$ These spectra have been obtained by co-adding the separate SWS spectra also listed in the table, see text.
Effective temperatures from 1Mendez et al. (1992), 2Perinotto (1991), 3Kaler & Jacoby (1991), 4Quigley & Bruhweiler (1995) and 5Latter et al. (2000).

\par\includegraphics[width=8.8cm,clip]{h3527f01.eps} \end{figure} Figure 1: The IRAS two-colour diagram for the sources studied in this sample. The triangles represent the C-stars, the squares are the post-AGB objects, the stars are the PNe and the diamonds are the C-stars without a "30'' $\mu $m feature detected. The dashed line represents the position of blackbodies of different temperatures. The dotted line sketches the evolution of a C-star with a detached, expanding and cooling circumstellar shell.

We present observations obtained with ISO of a sample of bright IR sources at different stages along the evolutionary track from C-star via post-AGB object to PN. The observations presented here consist of data obtained with the ISO/SWS using astronomical observing template 06 and 01 at various speeds. These observing modes produces observations from 2.3 to 45 $\mu $m with a resolving power ( $\lambda/\Delta\lambda$) ranging from 500 to 1500. The sample consists of all carbon-rich evolved objects in the ISO archive which exhibit a "30'' $\mu $m feature stronger than 8 Jy peak intensity and have been observed over the full 2.3-45.2 $\mu $m wavelength range of the ISO/SWS. This peak intensity and the typical noise level of SWS band 4 (29-45.2 $\mu $m) allows to extract a reasonably reliable feature strength and profile. The complete wavelength coverage is needed in order to provide a sufficient baseline to estimate the continuum. We have further completed the sample with all observed C-stars with an IRAS 25 $\mu $m flux over 13 Jy. These sources serve as a control group since we would expect to detect the "30'' $\mu $m feature based on this brightness, the typical noise levels and the typical feature over continuum level. These sources without the "30'' $\mu $m feature detected are listed separately in Table 1. It should be emphasised that the ISO archive does not contain a statistically representative sample of objects. The database of observations for the carbon stars provides a reasonable sampling over stellar properties (e.g. mass-loss rates or colour temperatures). However the post-AGB sample is heavily biased towards the "21'' $\mu $m objects; a peculiar type of C-rich post-AGB object. The sample of PNe contains a collection of either bright, well-known or well-studied objects without a proper statistical selection. It also contains a relatively large proportion of PNe with hydrogen-poor central stars. The total sample of 75 sources contains 48 C-stars, 14 post-AGB objects and 13 PNe. We have detected the "30'' $\mu $m feature in 36 out of 48 C-stars.

We present in Fig. 1 the IRAS two-colour diagram for the sources in our sample following van der Veen & Habing (1988). There are four sources in our sample without an entry in the IRAS point source catalogue. For these sources we have used ISO/SWS and LWS observations at 12, 25, 60 and 100 $\mu $m to calculate the IRAS colours. For IRAS Z02229, no measurements at 60 and 100 $\mu $m are available. In Fig. 1, the warmest sources are located in the lower left corner. These are the optically visible carbon stars with a low present-day mass-loss rate ( $\dot{M}\simeq10^{-8}{-}10^{-7}~M_{\odot}$). With increasing mass loss the stars become redder and move up and to the right. After the AGB, when the mass loss has terminated, the dust moves away from the star and cools; i.e., these sources move further to the top-right corner of the diagram. The C-stars located above the main group of C-stars have a clear 60 $\mu $m excess. This is evidence for an additional cool dust component. Some of these sources are known to have an extended or detached dust shell around them (Young et al. 1993). The empty region between the C-stars and the post-AGBs is physical. When the mass loss stops the star quickly loses its warmest dust and within a short time span (<1000 yr) the star moves to the right in the two-colour diagram. Notice how the sources without a detected "30'' $\mu $m feature cluster on the left of the diagram, i.e., among the warmest C-stars.

2.1 Data reduction

The SWS data were processed using SWS interactive analysis product; IA3 (see de Graauw et al. 1996) using calibration files and procedures equivalent with pipeline version 10.1. Further data processing consisted of extensive bad data removal primarily to remove the effects of cosmic ray hits and rebinning on a fixed resolution wavelength grid. If a source has been observed multiple times and these observations are of similar quality and of comparable flux-level these data are co-added after the pipeline reduction. These sources are indicated in Table 1 with a dagger ($^{\dagger}$). Since the features we discuss here are fully resolved in all observing modes, we combine the data obtained in all different modes to maximise the S/N. Although the wavelength coverage of the SWS instrument is well suited to study the profile of the "30'' $\mu $m feature, there are some important instrumental effects which hamper the unbiased extraction of the emission profiles. We discuss these below.

2.1.1 Splicing

\par\includegraphics[width=8.8cm,clip]{h3527f02.eps} \end{figure} Figure 2: Examples of the splicing of the SWS band 3D (19.5-27.5 $\mu $m) and 4 (28.9-45.2 $\mu $m) data. We show the data before (grey line) and after splicing (black line). All data have been scaled to form a continuous spectrum. As can be seen; after splicing, the slope of band 3D and band 4 match. We do not show the band 3E data. The sharp rise at 27 $\mu $m in R Scl and IRC+40 450 is an instrumental artifact (see text for details).

One complete SWS AOT01 spectrum is obtained in 12 different subbands. These subbands are observed through 3 different rectangular apertures which range in size from $14\arcsec\times20\arcsec$ at the shortest wavelengths to $20\arcsec\times33\arcsec$ at the longest wavelengths. All these data are independently flux calibrated and need to be combined to form one continuous spectrum for one source. We apply scaling factors to combine the different subbands to obtain the continuous spectra. The C-stars and post-AGB objects we present in this study all have a small angular extent even compared to the smallest aperture used. Therefore we don't expect large jumps to be present due to the differences between the apertures used. The angular extent of some PNe can be large compared to the sizes of the apertures. If there is a clear indication of flux jumps due to aperture changes we have not included the source in our sample.

2.1.2 Leakage
At wavelengths longer than between 26 and 27.5 $\mu $m the data of SWS subband 3D are affected by leakage adding flux from the 13 $\mu $m region. The sources used to derive the instrumental response function are all stellar sources without circumstellar material. These calibration sources are all very blue and emit much more flux at 13 $\mu $m relative to 26 $\mu $m than the cool, red sources we present in this study. Therefore these calibrators are more affected by the leakage than our sources. The instrumental response function derived in this way has been implicitly corrected for leakage for the blue sources. This resulted in fluxes in red sources to be systematically underestimated. More recent calibrations ($\ge$OLP 10.0), have been corrected for this effect. With the improved calibrations, the resulting slopes of the spectra beyond 26 $\mu $m have been checked and are in general agreement with the slope of subband 4.

2.1.3 The 27.0-27.5 and 27.5-29.0 $\mu $m region
At wavelengths longer than 27.0 $\mu $m the data of subband 3D show a sharp increase which is found throughout the complete database of ISO/SWS observations independent of source type. The data of subband 3E (27.5-29.0 $\mu $m) are generally unreliable both in shape and absolute flux level. These combined instrumental effects make it inherently difficult to interpret the 27-29 $\mu $m spectra. Any substructure detected solely in this region alone should be distrusted.

The instrumental effects between 27 and 29 $\mu $m and the fact that each of the subbands is independently flux calibrated make it necessary to devise a strategy for splicing the band 3D, 3E and 4 data. There is unfortunately no objective way to choose this strategy. We choose to assume minimal spectral structure between the end of subband 3D and the beginning of band 4, i.e. to splice the subband 3D-4 data in such a way that the matching slopes of 3D and 4 also match in flux level. Some examples are shown in Fig. 2. The observed discontinuities between subbands are relatively small (<20 per cent) and can be understood as the result of absolute flux calibration uncertainties alone.

2.2 Full spectra

\par\includegraphics[width=17.1cm,clip]{h3527f03.eps} \end{figure} Figure 3: Overview of the spectra of carbon stars exhibiting the "30'' $\mu $m feature. The spectra are ordered according to continuum temperature from high to low temperature, bottom to top, left to right. The dashed line marks $\lambda=26~ \mu$m.

\par\includegraphics[width=17cm,clip]{h3527f04.eps} \end{figure} Figure 4: Overview of the spectra of post-AGB objects (left panel) and PNe (right panel) exhibiting the "30'' $\mu $m feature. The spectra are ordered according to continuum temperature from high to low temperature, bottom to top. The dashed line marks $\lambda=26~ \mu$m. The spectrum of RAFGL 618 although warmer than NGC 3918 is shown at the top of the PNe for clarity.

The resultant spectra for the sources that exhibit a "30'' $\mu $m feature are shown in Figs. 3, 4. The SWS spectra of this large group of objects show a spectacular range in colour temperature, molecular absorption bands and solid state features. The C-stars have molecular absorption bands of C2H2 at 3.05, 7-8 and 14 $\mu $m, of HCN at 7 and 14 $\mu $m, CO at 4.7 $\mu $m and C3 at 4.8-6 $\mu $m. The sharp absorption band at 14 $\mu $m is due to C2H2and HCN. There is an emission feature due to solid SiC at 11.4 $\mu $m. In the reddest C-stars, we find the SiC in absorption. We also find evidence for a weak depression in the 14-22 $\mu $m range in the reddest objects. This depression could be due to aliphatic chain molecules like those found in RAFGL 618 (Cernicharo et al. 2001).

The post-AGBs and PNe exhibit many, sometimes broad solid state emission features. In many sources we find emission due to polycyclic aromatic hydrocarbons in the 3-15 $\mu $m range. There is a broad plateau feature from 10-15 $\mu $m which may be due to hydrogenated amorphous carbon (Guillois et al. 1996; Kwok et al. 2001). Many post-AGBs and two PNe in the sample have a feature peaking at 20.1 $\mu $m, called the "21'' $\mu $m feature in the literature. Recently the carrier of this feature has been identified with TiC (von Helden et al. 2000). The feature at 23 $\mu $m found in IRAS 18240 and PN K3-17 is likely due to FeS (Hony et al. 2002). These absorption and emission features have to be taken into account when determining the profile of the "30'' $\mu $m feature or the shape of the underlying continuum.

Focusing on the "30'' $\mu $m feature we can see variations in the strength and shape of the band. The most marked difference is however a shift in the peak position going from 26 $\mu $m in some of the AGB stars to 38 $\mu $m in the PNe. The dashed line in Figs. 3 and 4 indicates $\lambda=26$$\mu $m. There are systematic changes in the appearance of the "30'' $\mu $m feature from the C-stars to the PNe. The feature in the C-stars almost exclusively peaks at 26 $\mu $m. There are some exceptions like R Scl. In the post-AGB sample, the feature is broader and in some sources the feature peaks long ward of 26 $\mu $m. In the PNe sample, there are no sources that peak at 26 $\mu $m. However, the appearance of a broad feature like the "30'' $\mu $m feature is sensitive to the shape of the underlying dust continuum, especially since we have a sample with such a wide range of continuum colour temperatures.

3 Continuum


Table 2: Measured properties. $T_{\rm cont}$, p are the parameters of the modified blackbody function fitted to the continuum. $\lambda _{\rm c,30}$ and P/C are the feature centroid position and peak over continuum ratio. $T_{\rm MgS}$ is the derived temperature of the MgS grains.
 cont. "30'' $\mu $m feature   cont. "30'' $\mu $m feature  
Object $T_{\rm cont}$p $\lambda _{\rm c,30}$ fwhmfluxP/C $T_{\rm MgS}$  Object $T_{\rm cont}$p $\lambda _{\rm c,30}$ fwhmfluxP/C $T_{\rm MgS}$
 [K] [$\mu $m][$\mu $m][W/m2] [K]   [K] [$\mu $m][$\mu $m][W/m2] [K]
NGC 40150033.610.15.9e-130.7110  T Dra1210030.210.14.8e-130.4200
IRAS 002102850.528.410.76.4e-130.8300  RAFGL 2155460028.88.25.7e-120.6400
IRAS 01005130130.011.16.6e-131.5220  IRAS 18240160132.813.11.0e-121.0130
HV Cas10400.233.510.61.5e-130.3100:  IRC+00 365910-0.328.611.71.9e-120.4500
RAFGL 190275030.913.01.6e-120.3180  RAFGL 2256390029.512.01.9e-121.0350
R Scl2605-  K3-17100134.111.51.0e-120.990
IRAS Z02229235029.110.18.3e-121.7300  IRC+10 401765030.010.02.0e-120.3300
RAFGL 341380029.89.49.4e-130.4250  IRAS 190681165-0.728.510.12.0e-130.4500:
IRC+50 096855-  NGC 6790290029.815.69.8e-131.4300
IRAS 03313325028.67.85.4e-130.4300  RAFGL 2392890027.78.63.4e-130.5500
U Cam1775031.911.83.9e-130.6150  NGC 6826150032.710.51.1e-122.0120
RAFGL 618235-  IRAS 19454140136.313.16.4e-130.350
W Ori2450031.38.43.1e-130.4150  HD 187885175029.610.85.2e-121.0200
IC 418120130.811.35.5e-120.9180  RAFGL 2477290030.712.52.3e-120.6170
V636 Mon1215029.810.11.7e-130.2250:  IRAS 19584580028.17.58.5e-131.5400
RAFGL 940810028.210.23.5e-130.5500  IRAS 20000210029.412.12.5e-121.5300
IRAS 06582315029.510.31.1e-120.4300  V Cyg1110030.511.51.3e-120.3200
HD 56126170030.012.02.9e-120.8150  NGC 7027125132.811.01.7e-110.4110
CW Leo535028.68.82.7e-100.6400  S Cep13400.
NGC 391890133.38.57.1e-131.0120  RAFGL 2688200-
RU Vir1045030.410.15.3e-130.6180  RAFGL 2699540029.011.45.9e-130.7300
IRAS 13416115131.615.82.8e-120.4200a  IC 5117130131.29.77.3e-130.6150
II Lup625029.510.13.9e-120.3400  RAFGL 5625300030.311.84.4e-120.4200
V Crb1430030.410.11.8e-130.3150:  IRAS 21489415029.39.71.1e-120.6350
K2-161550.534.412.03.4e-130.380  SAO 34504210029.110.31.3e-112.0250
IRAS 16594140129.812.19.9e-120.9250  IRAS 22303345030.310.51.0e-120.7300
NGC 6369100134.610.19.5e-131.190  IRAS 22574160031.213.65.9e-130.4150
IRC+20 326770-0.729.110.27.4e-120.5300  RAFGL 3068290032.414.78.4e-120.4120
CD-49 11554140130.214.04.7e-120.7200a  RAFGL 3099470029.510.92.6e-120.7400
HB 5120035.511.51.0e-120.470  IRAS 23304115130.113.42.3e-121.1250
RAFGL 5416290030.412.52.2e-120.5220  IRAS 23321175034.513.36.6e-130.370
IRC+40 540485028.69.18.9e-120.6400          
non detections 
R For12150--<1e-14<0.1-  T Lyr33050--<1e-14<0.1-
SS Vir20400--<1e-14<0.1-  S Sct21050--<4e-14<0.3-
Y CVn22000--<2e-13<0.2-  V Aql3665-0.3--<1e-14<0.1-
RY Dra25250--<1e-13<0.2-  V460 Cyg28750--<5e-14<0.5-
C* 217811100--<1e-13<0.5-  PQ Cep16250--<1e-14<0.1-
V1079 Sco3085-0.5--<5e-14<0.2-  TX Psc31050--<3e-14<0.1-

a Temperature determination uncertain due to optically thick MgS emission.

In order to extract the profiles of the "30'' $\mu $m features and compare them from source to source, we model the underlying continuum due to the emission of other circumstellar (CS) dust components. First, we present the way we construct these continua and in Sect. 4, we discuss the resulting profiles.

To model the underlying continuum we use a simplified approach. We represent the continuum with a single temperature modified blackbody,

 \begin{displaymath}F(\lambda)=A \times B(\lambda,T) \times {\lambda}^{-p},
\end{displaymath} (1)

where $\lambda$ is the wavelength, $F(\lambda)$ is the flux density of the continuum, $B(\lambda,T)$ is the Planck function of temperature T, p is the dust emissivity index and A is a scaling factor.

\par\includegraphics[width=8.8cm,clip]{h3527f05.eps} \end{figure} Figure 5: Examples of the fitted continuum. We show the spectra (black line), the selected continuum points (diamonds) and the fitted modified blackbody (grey line).

We have chosen this approach to estimate the continuum over doing a radiative transfer calculation for reasons of simplicity. The bulk of the CS dust around these sources consists of some form of amorphous carbon grains that do not exhibit sharp emission features in the wavelength range of interest. Therefore, a radiative transfer calculation will not yield extra insight into the shape or strength of the continuum while introducing many more modelling parameters. This method has the advantage that we can compare the feature in such a diverse group of sources in a consistent way. Of course Eq. (1) does not directly allow us to incorporate important effects such as optical depth or temperature gradients. However varying the p-parameter can mimic these effects to some extent.

The p-parameter reflects the efficiency with which the dust grains can emit at wavelengths larger than the grain size. Reasonable values of p in the region of interest are between 1 and 2. Crystalline materials have this value close to 2 and amorphous materials have a p-value between 1 and 2, while layered materials have an emissivity index close to 1. A temperature gradient in the dust shell will result in a broader spectral energy distribution (SED). This is mimicked by a lower value of p. Likewise an optically thick dust shell will result in a broader SED, which again can be reproduced by reducing the value of p.

We use a ${\chi}^{2}$ fitting procedure to determine the values of Tand p fitted to selected continuum points in the ranges 2-22 $\mu $m. If available we also use the LWS spectra to verify the continuum at the long wavelength end of the "30'' $\mu $m feature. The 50-100 $\mu $m continuum gives an even stronger constraint on the value of p. For most cases the resultant continuum runs through the 45 $\mu $m region of the SWS spectrum. A remarkable exception to this is the spectrum of RAFGL 3068. The 2-24 $\mu $m spectrum is well fitted with a single 290 K Planck function. However we find a large excess of this continuum at 45 $\mu $m and the available LWS spectrum is not well represented in level or slope. Possibly this is due to the optically thick dust shell or a biaxial dust/temperature distribution.

\par\includegraphics[width=8.8cm,clip]{h3527f06.eps} \end{figure} Figure 6: Centroid of the "30'' $\mu $m feature with respect to the [25]-[60] colour. The symbols are like in Fig. 1. There is a clear trend for the centroid position of the "30'' $\mu $m feature to move to longer wavelengths the redder the object is.

The values for T and p are listed in Table 2. One remarkable fact is that the C-stars are well fitted by a single temperature Planck function over the complete wavelength range of SWS. The IR SEDs of the post-AGBs and PNe are in general less broad and many sources are better fitted with a p-value of 1. We stress however that the derived p values cannot be used to constrain the crystal structure or the average size of the dust grains in view of the aforementioned effects of temperature gradients and optical depth.

4 Profiles

\par\includegraphics[width=8.8cm]{h3527f07.eps} \end{figure} Figure 7: Emissivities for different sources as deduced from the ISO spectra. There are large differences in the profile of the excess emission. Notice the shift in peak position and change in width of the circumstellar "30'' $\mu $m feature going from the C-stars to post-AGBs to PNe (top to bottom).

Using the continua defined in this way, we measure the following properties of the "30'' $\mu $m feature: the centroid wavelength ( $\lambda _{\rm c,30}$), i.e., the wavelength where the integrated flux in the feature at either side is equal; the full width at half maximum (fwhm); the flux in the "30'' $\mu $m feature and the height of the peak of the "30'' $\mu $m feature after continuum subtraction over the continuum ratio, i.e., the peak to continuum ratio (P/C). The measured values are listed in Table 2. We list upper limits for P/C and the flux for the sources without detection. In Fig. 6, we show the relation between the [25]-[60] colour and $\lambda _{\rm c,30}$. There is a clear reasonably smooth trend for the feature to move to longer wavelengths with redder IRAS colours. This indicates that the temperature of the dust is an important parameter in determining the profile of the "30'' $\mu $m feature since [25]-[60] is a direct measure of the dust temperature provided that the dust composition in the different sources is similar.

We first try to remove the effect of temperature by dividing by the continuum; a method that is commonly applied. Using the modelled continua as described in Sect. 3, we convert the observed features to relative excess emission by dividing by the continuum and subtracting 1.

If the feature emission is optically thin and the temperature of the carriers of the feature is equal to the continuum temperature the derived excess emissions are proportional to the absorptivity ( $\kappa _{\rm abs}$) of the carrier and if the carrier is the same in these sources then the derived band shape should be the same for all sources. However, we find large variations in the derived profiles. In Fig. 7, we show some examples of the derived profiles. Most notable are variations in peak position and the appearance around 26 $\mu $m. Such changes, albeit within a smaller range of feature peak positions have led other authors (Volk et al. 2000,2002) to conclude that the "30'' $\mu $m feature is composed of two features and the observed variations are due to varying relative contributions of these two components. One key question is: "What possible causes could there be for the observed large variations in band shape?''. We discuss three possibilities below. First, optical depth effects. Second, temperature effects. Finally, we discuss multiple band carriers.

The optically thin assumption most likely holds because the optical depth in the circumstellar shell strongly decreases towards longer wavelengths. Note, in this respect that the "30'' $\mu $m feature is never found in absorption (however, see also Sect. 6.2). Hence, optical depth effects are not responsible for the observed profile variations.

Whether the temperature of the amorphous carbon grains (defining the shape of the continuum) and the temperature of the "30'' $\mu $m carrier are equal is very uncertain. The temperature of a dust grain in a circumstellar envelope is determined by the distance to the star, the absorption properties in the wavelength range where the star or the dust shell emits light and the grain size. In case the temperature of the grains species responsible for the continuum and the "30'' $\mu $m emission feature are not the same, the resulting excess profiles will also not be the same from source to source even if the carrier of the band is the same. The differences will be very pronounced when the emission feature is broad. In this case systematic difference between sources are bound to occur in league with the strongly changing continuum temperature. Thus, the temperature of the carrier of the "30'' $\mu $m feature is an important parameter that determines the profile of the emission.

There may be multiple carriers involved as discussed before. In this case the feature near 26 $\mu $m dominates in the warmest objects while the cooler objects are more and more dominated by emission towards 35 $\mu $m. However, this scenario has its difficulties since it would require changes in the composition of the dust in the relatively dispersed and cold nebular surroundings of a post-AGB object or even during the PN phase. Such chemical changes can only occur extremely slowly, if at all.

Lastly, variations in grain shape or variations in shape distribution can influence the emission profiles. The optical properties of materials with a high value of the refractive index are sensitive to the grain shape. Variations in the shape distribution will lead to variations in the profiles.

In our analysis, we will focus on explaining the profile variations with temperature variations and the effects of variations in the shape distribution of the emitting dust grains.

5 MgS

\par\includegraphics[width=8.8cm]{h3527f08.eps} \end{figure} Figure 8: The effect of grain shape. We show the absorptivity of MgS as a function of grain shape. The numbers between brackets refer to the axis ratios of the elliptical grains. For comparison we show the derived emissivities of RAFGL 190 and NGC 7027.

Since, it has been demonstrated for a few sources that MgS is a viable candidate (Begemann et al. 1994; Jiang et al. 1999; Szczerba et al. 1999), we first test MgS as a possible candidate for the carrier of the feature. With the large sample of good quality spectra in this study we are able to test this possible identification systematically in a large population of evolved objects.

As explained above we cannot derive a priori information on the temperature of the "30'' $\mu $m carrier from the observations. Our knowledge is further limited by the fact that even for some of the candidate materials like MgS or FeS the optical properties are measured only in a limited wavelength range. We lack measurements in the UV, optical and near-IR range, which may well dominate the dust heating. We have decided to test the MgS identification, leaving the grain temperature as a free parameter. We adopt the method we describe below.

5.1 Material

We use the optical constants as published by Begemann et al. (1994). Of the materials they measured, Mg0.9Fe0.1S is closest to pure MgS. The real and imaginary part of the refractive index (n and k values) are given from 10-500 $\mu $m.

5.2 Shapes

From the n and k values we can calculate the absorption cross-sections for various grain shapes and shape distributions in the Rayleigh limit following Bohren & Huffman (1983, Chapters 5, 9 and 12). The absorption cross-section of MgS around 30 $\mu $m is very sensitive to the grain shape. In Fig. 8, we show the results of using different grain shapes on the absorption properties of MgS. We use a continuous distribution of ellipsoids (CDE) for the grain shapes. This shape distribution was used by Begemann et al. (1994) and gave a good fit to the "30'' $\mu $m feature observed in CW Leo. The same shape distribution was further used by Jiang et al. (1999) and Szczerba et al. (1999). They found reasonable fits for the two sources they study. As can be clearly seen in Fig. 8 when comparing the spheres with the CDE calculations, the feature broadens and the peak position shifts to longer wavelengths using the CDE shape distribution. The width of the feature calculated using CDE matches that of the observed "30'' $\mu $m feature well (e.g. RAFGL 190 in Fig. 8, see also Fig. .1).

5.3 Temperature

\par\includegraphics[width=8.8cm]{h3527f09.eps} \end{figure} Figure 9: The effect of grain temperature on the MgS emission feature. We fold the $\kappa _{\rm abs}$ of MgS in a continuous distribution of ellipsoids (CDE) shape distribution with a Planck function of different temperatures. The shape and position of the feature are modified substantially.

To estimate the MgS temperature ( $T_{\rm MgS}$) we use the continuum subtracted spectra with the continuum as derived in Sect. 3. The emission from MgS grains is calculated using the $\kappa _{\rm abs}$ folded with a Planck function with the temperature of the grain. Due to the smooth and broad shape of the resonance the profile of the emission is very sensitive to $T_{\rm MgS}$. In particular the peak position changes strongly with $T_{\rm MgS}$. This allows us to estimate $T_{\rm MgS}$from the continuum subtracted profiles. This method is most sensitive for $T_{\rm MgS}$ < 300 K. Above 300 K, further changes in the profile are more subtle since the major part of the feature falls in the Rayleigh-Jeans domain of the Planck function.

We use this temperature estimate and the observed band strength in the continuum subtracted spectra to synthesise a MgS feature in order to compare with the astronomical spectra. In conclusion, we adopt MgS with a CDE shape distribution and allow both the strength and the temperature of the MgS grains to vary with respect to the underlying continuum.

6 Model results

\par\includegraphics[width=18cm,clip]{h3527f10.eps} \end{figure} Figure 10: Examples of the modelling results using measure MgS optical constants in a CDE shape distribution. We show the observed spectra (black), the modelled continua (dashed), the spectra with the MgS contribution subtracted (gray) and the composite of the continuum and the MgS contributions (thin black line).

In Fig. 10 we show a few typical examples of how our model results compare to the observed spectra. In Fig. .1 we show the observed spectra, the composite of the continuum and the synthetic MgS feature and the residuals after subtracting the MgS feature for the complete sample. The fits are very satisfactory in 50 out of 63 cases. In $\sim$25 sources the synthetic spectra obtained with this very simple model are able to explain the detailed profile of the "30'' $\mu $m feature very well. The onset and range of the feature and even the slight depression between 26-30 $\mu $m are reproduced by the model. We show a zoomed view of the 30 $\mu $m region of a few sources that are very well fitted by this simple model in Fig. 11. Notice the different apparent shapes of the feature that the model is able to explain. Volk et al. (2002) discuss the "30'' $\mu $m feature in IRAS 23304 and find that they need 2 separate unidentified components in order to understand the shape of the feature. Figure 11 illustrates that this is not necessarily required.

Examining the complete sample of observed "30'' $\mu $m features and the synthetic spectra, we find there are some systematic deviations. In the sample of C-stars and post-AGB objects there are numerous examples where the major part of the "30'' $\mu $m feature is explained well by our model, but the observed spectra show excess emission in the 26 $\mu $m region. The excess is not accounted for using our CDE fits. The most extreme case is IRAS 19584 but several sources exhibit the same behaviour. In Sect. 6.1, we discuss the origin of this discrepancy.

In some cases the synthetic spectra over-predict the flux at the longest wavelengths. This can be due to the very simplistic method we have used to estimate the continuum level. As the dust optical depth decreases with increasing wavelengths, the continuum level estimated from shorter wavelengths might over-predict the true continuum level. Note, however, that the discrepancies between the modelled and the observed spectra in the 26 $\mu $m region and the 40 $\mu $m region cannot be considered completely independently. If we were to weaken the strength of the MgS feature this would yield a better fit around 45 $\mu $m but would increase the discrepancy around 26 $\mu $m. We also note that MgS produces a weak continuum contribution at 45 $\mu $m (see for example Fig. 9). This continuum contribution is already taken into account when fitting the overall continuum, but it is still present in the calculated MgS contribution. Therefore, our model may slightly over-predict the fluxes near 45 $\mu $m.

As a class, the spectra of most PNe show another systematic difference. The peak position of the "30'' $\mu $m feature lies in general at longer wavelengths than in the post-AGB sources. This is in accordance with the picture of a slowly expanding and cooling dusty envelope. We can simulate the same shift in peak position using MgS grains. However the fits we obtain fail to reproduce the relatively narrow width of the observed profile. We discuss this deviation of the profiles in Sect. 6.3.

There are 4 sources in the sample that have a broader "30'' $\mu $m feature than can be fit by our simple model. Of these sources, IRAS 13416 and CD-49 11554 show a slightly flattened and broadened feature while in the cases of RAFGL 618 and RAFGL 2688 the feature is very broad with a depression around 30 $\mu $m. The latter sources are known to have a very large dust column along the line of sight. Most likely the feature shape is due to optical depth effects. We discuss these sources further in Sect. 6.2.

Despite these systematic deviations it is clear that our simple model is able to explain the profile of the "30'' $\mu $m feature in good detail in a very wide range of objects. We conclude that the carrier of the "30'' $\mu $m feature in the C-stars and post-AGB objects is solidly identified with MgS and that the variations in peak position reflect differences in grain temperature.

\par\includegraphics[width=8.8cm,clip]{h3527f11.eps} \end{figure} Figure 11: Examples of spectra that are very well fitted with MgS in a single temperature, CDE shape distribution. The black lines represent the data and the grey line the model. The different sources have been offset for clarity. The excess around 23 $\mu $m in IRAS 18240 is due to FeS (Keller et al. 2002; Hony et al. 2002). Notice how the model is able to explain the profile of the "30'' $\mu $m feature found in the full range of objects in our sample.

6.1 26 $\mu $m excess

\par\includegraphics[width=8.8cm,clip]{h3527f12.eps} \end{figure} Figure 12: Some examples of sources with a 26 $\mu $m excess compared to the model spectra. We show the data (full black line) the model using the CDE calculation (full grey line) and the composite model using both spherical MgS grains and the CDE calculation (dashed line). We show below the emission of spherical MgS grains at a temperature of 250 K. The continuum in RAFGL 2155 runs above the observed spectrum at the shortest wavelengths, this may be due to molecular absorptions (see Sect. 2.2)

As discussed above we find about 25 sources that are very well fitted by our simple model. Using similar parameters we also find about 25 sources which show an excess near 26 $\mu $m. Evidently, there is a contribution from an additional dust component in the latter sources. In considering this additional dust component we find that MgS itself is the best candidate. The wavelength region where this excess occurs (26 $\mu $m) is also the wavelength where the generic main resonance of MgS occurs. Spherical MgS grains exhibit a resonance at 26 $\mu $m. In our model, the MgS profile is broader and peaks at a longer wavelength because we use the calculated absorption cross-sections in a CDE shape distribution. There is no a priori reason why the shape distribution should be close to this distribution. In this respect, it is rather surprising that our simple model works so well for so many sources. We can simulate a different shape distribution by adding the contributions of spherical grains to the CDE profile. This approach is permitted since we assume optically thin emission and thus the contribution of different components add linearly. In Fig. 12, we show the result of such a composite model for one C-star and for one post-AGB object. The relative amounts of spherical grains added to the model is $\sim$35 per cent. We keep the temperature of the spherical and the CDE grains the same as in the initial model. As can be seen the spherical grains contribute at the position where our initial model fails. We conclude that variations in the distribution over grain shapes can explain the variations we observe in the profile of the "30'' $\mu $m feature.

6.2 Optically thick shells

The feature found in CD-49 11554, IRAS 13416, RAFGL 618 and RAFGL 2688 is different from the others in the sense that it is broader and flatter. This is especially true for RAFGL 618 and RAFGL 2688 where the profile even shows a central depression. We investigate the effect of optical depth on the emission profile. We model the effect of optical depth with two simple limiting cases.
$\displaystyle I_{1}(\lambda)$=$\displaystyle B(\lambda,T_{\rm MgS}) \times (1-{\rm e}^{-\rho\kappa_{\lambda}l}) ~{\rm and}$ (2)
$\displaystyle I_{2}(\lambda)$=$\displaystyle I_{0}(\lambda,T_{\rm MgS}) \times {\rm e}^{-\rho\kappa_{\lambda}l},$ (3)

where $T_{\rm MgS}$ is the temperature of the MgS, $B(\lambda,T)$is the Planck function of temperature T, $\rho$ is the mass density of MgS, l is the column length and $I_{0}(\lambda,T)$ is MgS emission of temperature T. $I_{1}(\lambda)$ is the limiting case of a column of MgS with a single temperature of $T_{\rm MgS}$. $I_{2}(\lambda)$ represents the case of foreground absorption only; i.e., MgS emission of temperature $T_{\rm MgS}$ obscured by a column of MgS with negligible emission. In both cases the resulting profile will be broader than the optically thin case. For a long column $I_{1}(\lambda)$ approaches $B(\lambda,T_{\rm MgS})$ while $I_{2}(\lambda)$ becomes double peaked with a depression where $\kappa_{\lambda}$ peaks. The resulting $I_{1}(\lambda)$ profile will never show a central depression. We show the effects of incorporating the optical depth in Fig. 13. Indeed, these methods yield a broadened profile closer to what is observed. The second method reproduces the central depression found in RAFGL 2688. It is important to stress that the curves shown in Fig. 13 are not the result of a proper radiative transfer modelling of the CS shell or an attempt to fit the observed spectrum of the source. Nevertheless, they are able to explain the general characteristics of the "30'' $\mu $m profile in the deviant sources well.
\par\includegraphics[width=8.8cm,clip]{h3527f13.eps} \par\end{figure} Figure 13: The effects of optical depth of the profile of the MgS emission. We show the absorbed MgS emission following Eqs. (2) and (3) (grey dashed and solid lines), the profile of the "30'' $\mu $m feature of RAFGL 2688 (solid black line) and the optically thin MgS emission (dashed black line).

6.3 PNe profiles

\par\includegraphics[width=8.8cm,clip]{h3527f14.eps} \end{figure} Figure 14: The absorptivity of MgS grains coated with various types of materials. The modelled grains are composed of 80 per cent MgS and 20 per cent coating by volume. The models have been obtained by adding 5 ellipsoidal core-mantle grain of axes ratios (10:1:1), (3:1:1), (1:1:1), (3:3:1) and (10:10:1) of equal volume. For comparison we show the absorptivity of MgS in a CDE distribution (7) and the excess in NGC 7027 (8). We show the absorptivity of FeS (1) and amorphous carbon (5) grains with a MgS coating, both with core volume of 20 per cent of the grain. None of the modelled composite grains is able to explain the profile of the emission found in many PNe.

For 9 out of 13 PNe the observed "30'' $\mu $m feature is much narrower than in our model. Of the other four cases we discussed the profile of RAFGL 618 in Sect. 6.2. It is important to note that the remaining three cases (NGC 6790, IRAS 18240 and K 2-16) are the PNe with the highest continuum temperature among the PNe in our sample.

In Fig. 8, we compare the shape of the "30'' $\mu $m profile of NGC 7027 with the profiles due to differently shaped MgS grains. As can be seen an oblate MgS grain with an axes ratio of 10:10:1 exhibits a "30'' $\mu $m feature which peaks at the right position. At present we don't know of a physical reason for a preferred oblate grain shape in PNe, and a broader CDE shape distribution in the C-stars and post-AGB objects (see also Sect. 8.4).

The shape of a resonance is also influenced by the presence of a coating. MgS is very hygroscopic. Under conditions where oxygen is available in the gas phase MgS can be oxidised and transformed into MgO (Nuth et al. 1985; Begemann et al. 1994). It is possible that the MgS is transformed as the central star of the PN heats up and the UV radiation progressively dissociates the CO molecules yielding gas phase oxygen. This could lead to MgS grains which are coated by a thin layer of MgO. We have modelled such grains using the electrostatic approximation following Bohren & Huffman (1983, Chap. 5). The result is shown in Fig. 14, curve 6. As can be seen the "30'' $\mu $m resonance is split into two features due to the MgO coating. The feature at the red wavelength is shifted to longer wavelengths compared to the pure MgS resonance. However the main feature is on the blue side of 25 $\mu $m towards the strong resonance at 18 $\mu $m in the pure MgO material, in clear contrast with the observations.

We explore other possible coatings on MgS grains to test their ability to explain the narrow feature observed in the PNe and the lack of emission at 26 $\mu $m. We find that of the composite grains we tested none give a satisfactory explanation. Mixtures of MgS and FeS have been discussed in the literature to investigate the nature of the "30'' $\mu $m feature (Begemann et al. 1994; Men'shchikov et al. 2001; Henning 2000). Curves 1 and 2 in Fig. 14 show the result of embedding an FeS core in a mantle of MgS and embedding a MgS core in a mantle of FeS, respectively. The latter compares most favourably with the position of the feature in the PNe. However, the substructure found in the spectrum of the composite grain around 33-37 $\mu $m is not found in the PNe spectra.

Szczerba et al. (1999) examine grains of amorphous carbon with a mantle of MgS to compare with the 30 $\mu $m feature in two post-AGB objects. We show simulated spectra of such grains and MgS grains coated with amorphous carbon in Fig. 14, curves 3 and 4 respectively. Curve 3 clearly does not match the observed feature in the PNe. As can been seen in curve 4 the MgS grains coated with amorphous carbon absorb less at 26 $\mu $m than pure MgS and are therefore a better spectral match to the "30'' $\mu $m feature of the PNe. However, the feature to continuum ratio in these grains is about a factor 2.5 lower than in the pure MgS grains requiring a factor 2.5 more mass in the MgS component in order to explain the observed band strength. Note also that such grains will still produce a weak feature at 26 while in some PNe spectra we find no excess at that wavelength at all.

Lastly, in curve 5 (Fig. 14) we show the effect of water ice on the MgS grains. The effects on the optical properties of a water ice coating are marginal and the profile cannot explain the PNe observations. We conclude that of the composite materials we have experimented with MgS grains coated with amorphous carbon give the best spectral match. However we find no composite grains that match satisfactorily.

We stress that although our model does not reproduce the "30'' $\mu $m profile in the PNe in its width it is safe to assume that its carrier is MgS based. These PNe are believed to be the evolutionary descendants of the sources which exhibit the MgS feature. The shift in peak position compared to the post-AGB objects follows naturally from an expanding and cooling shell. Also, the feature strength for the PNe is similar to these found in the post-AGBs further strengthening the physical link between the MgS in the C-stars and the post-AGBs on one hand and the "30'' $\mu $m feature in the PNe on the other (see also Sect. 7).

7 Correlations

\par\includegraphics[width=8.5cm,clip]{h3527f15.eps} \end{figure} Figure 15: "30'' $\mu $m feature properties versus the peak wavelength of the continuum. The symbols are the same as in Fig. 1. We show in panel  a) the ratio of the integrated flux in the "30'' $\mu $m feature to the integrated flux in the SWS spectrum. In panel b), we show the peak over continuum values. We also show the average values for the C-stars, the post-AGBs and the PNe. The non-detections are not taken into account in determining the mean values. The centroid wavelength of the "30'' $\mu $m feature is shown in panel c).

\par\includegraphics[width=8.8cm,clip]{h3527f16.eps} \end{figure} Figure 16: The centroid position of the "30'' $\mu $m feature versus the MgS temperature in the model. The symbols are the same as in Fig. 1. We show a power-law function fitted to the data with the dashed line.

Using the large database of sources available we can study some of the properties of the "30'' $\mu $m feature statistically. We have found it most convenient to characterise the sources by the temperature of the fitted continuum. We use the wavelength where the derived continuum peaks ( $\lambda_{\rm max,cont}$) as an indicator of the continuum temperature. The derived continuum temperature itself is less well suited because of the systematic difference in the power law index we find between classes of sources. The sources are rather uniformly distributed over $\lambda_{\rm max,cont}$ as well.

First, we show in Fig. 15a the relation between the $\lambda_{\rm max,cont}$ and the ratio of the integrated flux in the "30'' $\mu $m feature to the total flux in the SWS spectrum (I30/ $I_{\rm SWS}$). The C-stars demonstrate a clear increase of I30/ $I_{\rm SWS}$ with decreasing continuum temperature. The post-AGB objects emit systematically a larger fraction, of up to 25 per cent, in their "30'' $\mu $m feature. The PNe emit a similar fraction in the "30'' $\mu $m feature as the post-AGB objects although with a larger scatter. Notice that the sample contains a number of PNe with warm dust indicative of young PNe. There are a few sources which do not follow the general trend. The C-stars, R Scl, IRAS 19584 and RAFGL 2256, exhibit an atypically strong "30'' $\mu $m feature. These latter two sources are further typified by very weak molecular absorptions near 14 $\mu $m (see also Fig. 3). These observed anomalies are indicative of deviating conditions in the outflows of these sources, possibly a recently halted period of efficient dust formation. The post-AGB object IRAS 19454 has a very weak and cold "30'' $\mu $m feature. RAFGL 618 has a weak feature due to self-absorption (see Sect. 6.2).

The increasing strength of the "30'' $\mu $m feature in the AGB stars in not surprising. Since the emission is optically thin I30 is proportional to the amount of MgS. The low values of $I_{30}/I_{\rm SWS}$ for the warmest C-stars reflects the fact that there is little dust around these sources and most of the IR radiation comes from the stellar photosphere. Cooler C-stars have more dust and thus more MgS. The difference between the coolest C-stars and the post-AGBs is more surprising. The fact that post-AGBs emit a larger fraction in the "30'' $\mu $m feature is due to two effects. First since the dust shell becomes optically thin in the visible some fraction of the light is emitted at shorter wavelengths. Second, the temperature of the MgS decreases less rapidly than the temperature of the other dust components (see below).

It is clear that any dust component which produces 30 per cent of the IR light has to be abundant. In order to quantify the (relative) amounts of MgS present in the CS shells of these objects will require radiative transfer modelling which is beyond the scope of this paper. We can however in first approximation study the relative amounts of MgS compared to the other cold dust components by studying the peak to continuum ratio (P/C). In Fig. 15b, we show the P/C versus the $\lambda_{\rm max,cont}$. The majority of the sources lies within the 0.3-1.0 range in P/C. We indicate a few clear outliers. R Scl, IRAS 19584 and RAFGL 2256 have a very strong "30'' $\mu $m feature indicating again that these sources have "too much'' MgS for a normal C-star. The PNe NGC 6790 and NGC 6826 have an exceptionally strong MgS feature. Note that NGC 6790 also has a very warm continuum, much like a post-AGB source or a very young PN. The strong SiC band at 11 $\mu $m is consistent with this. We also show the averages for each of the classes of sources. The average P/C for C-stars is 0.5, for post-AGB objects 1.0 and for the PNe it is 0.9. The similar ratios for the post-AGB objects and the PNe suggests that the carrier of the "30'' $\mu $m feature in the PNe is indeed directly related to the MgS feature in the post-AGBs. Furthermore, the similar ranges found for the post-AGB objects and the PNe argues against any process which results in a destruction of the MgS grains during the PN phase.

In Fig. 16, we show the derived MgS temperature versus the centroid position of the "30'' $\mu $m feature. The two are well correlated. For convenience, we have fitted a power-law function (without physical meaning) to the relation.

T_{\rm MgS} = 5.1\times 10^{14}~\left(\lambda_{\rm c,30}\right)^{-8.34}.
\end{displaymath} (4)

It is not surprising that $T_{\rm MgS}$ and $\lambda _{\rm c,30}$are correlated since we have used the feature profile to estimate the $T_{\rm MgS}$. However, using Fig. 16 or Eq. (4) one can easily derive the MgS temperature from a given observation. Also indicated in the figure are IRAS 13416 and RAFGL 2688; as can be seen they fall outside the correlation. This is due to the optical depth effects discussed above.

\par\includegraphics[width=8.8cm,clip]{h3527f17.eps} \end{figure} Figure 17: The derived MgS temperature versus the continuum temperature. The symbols are the same as in Fig. 1. We show in the box in the lower right the continuum temperature of the sources without a "30'' $\mu $m feature detected. The inset shows a blow up on a logarithmic scale up of the sources with a continuum temperature below 1000 K.

Lastly, we show in Fig. 17 the relation we find between the temperature of the continuum ( $T_{\rm cont}$) and the temperature of the MgS ( $T_{\rm MgS}$). We find, tracing the evolution from hot dust sources (C-stars) to the PNe, that the MgS temperature decreases correspondingly. Surprisingly, we find for warmest sources in the sample, with $T_{\rm cont}$ > 1000 K, very cold MgS. We propose two explanations for this phenomenon. First, it may be due to the absorption properties of MgS. If MgS cannot efficiently absorb the stellar light in the optical or near-IR part of the spectrum the grains remain cold. Alternatively, the MgS grains may be located further away from the star (see below). In the inset, we show a blow-up of the left side of the figure. There is a clear correlation between $T_{\rm cont}$ and $T_{\rm MgS}$. The MgS in the post-AGB sources is systematically warmer than expected on the basis of the C-stars. Apparently, in the process of becoming a post-AGB object, when the dust shell becomes detached and moves away from the star, the general dust cools down more rapidly than does the MgS. Note that the difference in dust temperature between the coldest C-stars and the warmest post-AGBs is seen most clearly in the [12]-[25] colour or $\lambda_{\rm max,cont}$ but is also found in the [25]-[60] colour (e.g. Fig. 1). The different behaviour of the continuum and the MgS is nicely illustrated in Fig. 15c where we show that while the continuum becomes redder the position of the "30'' $\mu $m feature does not change. This effect is the cause for the discontinuity between the C-stars and the post-AGB object seen in Figs. 15a and b. The physical cause for this must be due to the fact that MgS is actually (partially) heated by mid-IR radiation. The mid-IR radiation is much slower to respond to the termination of the AGB. Conversely, this implies that mid-IR radiation is a less important heating agent for the other dust components present.

8 Discussion

8.1 Carrier

The models using MgS we present do very well in explaining the profile of the feature found in the C-stars and post-AGB objects. The model does not do as well in explaining the profile of the feature found in the PNe. However, the smooth relation found between the [25]-[60] colour and the $\lambda _{\rm c,30}$ shows a gradually changing profile with dust temperature. This suggests one carrier or closely related carriers. Also the similar P/C values for the different classes of objects is indicative of one carrier.

Recently Grishko et al. (2001) proposed HAC as the carrier of the mid-IR emission features in C-stars, post-AGBs and PNe. HAC is a very plausible dust component in those environments (e.g. Duley & Williams 1981; Goebel 1987; Borghesi et al. 1987; Henning & Schnaiter 1999). However, the mid and far-IR optical properties of HAC are dominated by a $\lambda^{-1}$continuum (Bussoletti et al. 1987). Grishko et al. (2001) identified some 13 weak spectral features in the range from 19-120 $\mu $m. The strongest of which occur at 21, 27 and 57 $\mu $m. We consider HAC a unlikely candidate for the circumstellar "30'' $\mu $m emission feature because the laboratory features are weak in contrast to the astronomical data and because the far-IR features of HAC are not observed in the astronomical spectra.

8.2 The effect of model simplifications

It is remarkable that our simple model works so well. We have applied various simplifications in order to be able to study the whole sample in a unified way. These simplifications necessarily lead to differences between the models and the observations. Instead of assuming a single temperature modified blackbody for the shape of the continuum one can certainly obtain a more detailed fit by taking into account the structure of the CS envelope and the opacities of the different molecular and dust constituents. Our method works well because the contributions of the other known other dust components around 30 $\mu $m are well behaved, smooth and thus indeed form a continuum. Moreover, the shape of our modelled continuum between 20-50 $\mu $m is not a strong function of the emissivity index (p) and varying the p-parameter or the temperature doesn't yield qualitatively different continuum shapes or levels. We already pointed out that in some cases our model fails at the longest wavelengths of the SWS observations, which may be related to our method to estimate the continuum.

We use a single temperature for the MgS to model its contribution. In the very extended envelope of a C-star or in the nebulous environments in the post-AGBs and PNe, the temperature of any dust component will not be constant but decreases as a function of the distance to the star. The fact that we still get good results using a single temperature is a clear indication that the emission is optically thin and that the density of the MgS falls off sharply with distance. In an optically thin environment we know that $T_{\rm dust}\propto\sqrt{R}$, where R is the distance to the star. If the density distribution drops with distance as R-2 or steeper, the contributions are weighted to the highest temperature part of the envelope where $T_{\rm dust}$ and thus the source function is highest. If the density distribution is flatter there is relatively more dust far away than close by. In this case we will observe MgS with a range of temperatures. Also sources that are not optically thin will emit a feature broader than our single temperature MgS model (see also Sect. 6.2). We conclude that in the majority of the sources the "30'' $\mu $m emission is due to optically thin emission which is dominated by the highest temperature MgS closest to the star.

8.3 Shape

We find that a CDE shape distribution fits many observations well. A CDE shape distribution is used to model a collection of irregularly shaped grains. Irregularly shaped grains can for example result from grain growth by agglomeration (Blum et al. 2000).

We find evidence for differences in the shape distributions between sources. We have tested for correlations between the strength of the 26 $\mu $m excess (due to spherical MgS grain) and the CDE component and other parameters like the mass-loss rate, the P/C, the continuum temperature or the feature temperature. We find no clear correlations. We do however note that we find little evidence for the 26 $\mu $m excess in the hottest C-stars. Stars in our sample with a continuum temperature above 1000 K do not exhibit the excess. Below 1000 K we find both sources with and without the 26 $\mu $m excess. Note also that the occurrence rate of the 26 $\mu $m excess in the sample of post-AGB objects is high. Because the emission in the post-AGB phase may be dominated by the dust closest to the star and hence lost at the tip of the AGB during a phase of heavy mass loss (at a rate much higher than during the general AGB phase), this might suggest that the shape distribution of the grains changes to become more spherical towards the end of the AGB, possibly as a function of mass-loss rate.

8.4 Planetary nebulae

The profile of the "30'' $\mu $m feature we find in most PNe is narrower than in our model. The largest discrepancy occurs around 26 $\mu $m. Our model fits are able to explain the shift in centroid position observed in the PNe; however, the models that explain the band-shift best, over-predict the flux at 26 and 40 $\mu $m.

There are several observational properties that are important when considering explanations for the observed discrepancies. First, there is the similar values of P/C in the sample of post-AGBs and PNe (Fig. 15b). This indicates that the carriers are related and similar in abundance. Second, the smooth trend we find in the centroid position of the "30'' $\mu $m feature with the [25]-[60] colour (Fig. 6). The PNe profiles follow the general trend. This indicates that the main effect for the peak shift also in the PNe is due to temperature. We also note that there are three non-PNe sources in our sample with cold MgS (R Scl, IRAS 19454 and IRAS 23321). These sources are well fitted by our model. This indicates that the narrow profiles are particular to the PN environment.

We have explored possible MgS based heterogeneous grains and variations in MgS grain shape. The heterogeneous grains we have explored do not compare satisfactorily with the observed profile in the PNe. MgS grains coated with a layer of amorphous carbon provide a somewhat better match in terms of the band shape however the contrast of the feature with respect to the continuum is strongly reduced. The reduced band strength is in contradiction with the observed peak over continuum ratios.

We find that the emission from plate-like MgS grains appears similar to the feature found in the PNe. In Sect. 6.1 we consider an extra contribution of spherical MgS grain to the "30'' $\mu $m feature at 26 $\mu $m. The varying strength of this contribution demonstrates that there are variations in the grains shape distribution between sources. The question is: "Is it possible that the narrow "30'' $\mu $m feature in the PNe is carried by flattened MgS grains?'' This would either imply that the MgS grain shape distribution in the PNe is heavily skewed to the plate-like grains or that the oblate grains emit more efficiently.

The origin of these variations in the shape distribution are unclear. They may reflect variations in the formation and destruction of grains. We do not know of a mechanism that drives towards oblate grains shapes during the PN-phase or a mechanism that selectively destroys spherical and prolate grains. Note, that the peak over continuum value in the PNe is similar to those found in the post-AGB objects arguing against a destruction of a part of the MgS grains. It is important to remark that in the CDE distribution only $\sim$20 per cent of the grains is oblate with an axis ratio of 1: ${1}\over{5}$ or more extreme, i.e. with axes ratios of 1:X:Y, where Y is smaller than ${1}\over{5}$ and X can vary between $\sqrt{X}$ and 1. Such axes ratios are required in order to shift the peak position to the wavelength where the "30'' $\mu $m feature in the PNe peaks and to suppress the emission at 26 $\mu $m.

Alternatively, these inferred shape variations may result from a shape dependent heating of grains. In the C-stars, likely, heating and cooling occurs at IR wavelengths. Because the grains are small compared to these wavelengths the temperature will be shape independent. However, in the PNe heating occurs through absorption of visible and UV radiation, which scales with the cross-section. Hence in that case dust temperatures will be shape dependent. Indeed flattened grains have on average a larger geometric cross-section compared to their volume that spherical or prolate grains.

As noted before, the PNe in the sample with the warmest dust continuum are well fitted by our model. The model fails in the PNe sample at MgS temperatures below $\sim$90 K. Perhaps, the observed discrepancies are due to changes in the optical properties of pure MgS at low temperatures. No laboratory measurements of MgS at these temperatures are published. FeO has the same lattice structure as MgS and measurements of FeO at different temperatures (10 K, 100 K, 200 K and 300 K) are available (Henning & Mutschke 1997). We have used FeO as an analogue to examine the effect of temperature. The trend with lower temperature is for the FeO resonance at 20 $\mu $m to become narrower and stronger with respect to the continuum. There is a small shift in the peak position. Comparing the 300 K measurement to 10 K the latter resonance peaks $\sim$0.1 $\mu $m more to the blue for spherical grains. Like MgS, FeO is also very sensitive to the shape of the grains. Using a CDE shape distribution the resonance of the 10 K sample lies $\sim$$\mu $m on the blue side of the 300 K resonance. If we translate this behaviour to the MgS data and the "30'' $\mu $m feature in the PNe it worsens the situation since we would expect a stronger contribution at shorter wavelengths exactly where our model already over-predicts. As an alternative, one might speculate that a change in lattice structure at low temperatures may occur resulting in different optical properties. It is interesting to note that Berthold (1964) reports that MgS can condense in two lattice structures: cubic and hexagonal. This author finds that hexagonal MgS exhibits a narrower mid-IR resonance than cubic and amorphous MgS.

We conclude that, although it is possible to find MgS based candidate materials that provide a better spectral match to the observed "30'' $\mu $m feature in the PNe no explanation for the "30'' $\mu $m profiles in the PNe is completely satisfactory at this time.

8.5 MgS temperature

We have found that the "30'' $\mu $m feature is very well explained with MgS provided that the continuum temperature and the MgS can be substantially different from each other (see also Fig. 17). Moreover, the temperature difference changes between classes of sources. In the C-stars we find that MgS is colder than the continuum while in the post-AGB sample the MgS grains are warmer. The temperature difference and the fact that the continuum temperature varies relative to the MgS temperature implies that the MgS grain are not in thermal contact with the amorphous carbons grains that carry the continuum. Thus, MgS is condensed in these environments into separate grains.

The relatively warm hot MgS that we observe in the post-AGB sample is certainly a phenomenon that deserves further study. As pointed out above, this must be due to a difference in the heating properties of MgS relative to the other dust constituents. We suggest that due to the strong resonance in the mid-IR MgS is (partially) heated by IR radiation. This may cause a temperature difference as observed. It requires measured optical constants for MgS over a much wider wavelength range than now available and radiative transfer modelling to understand the detailed temperature behaviour of the MgS grains.

We have shown in Fig. 17 that the warmest C-stars that exhibit the "30'' $\mu $m feature have cold MgS. We consider two possible explanations for this behaviour. First, MgS can be cold because it is unable to absorb the radiation from the central source efficiently. This would require that the MgS grains are very transparent in the visible and near-IR where these warm C-stars emit most of their radiation. In this case a cooler star will emit more radiation at wavelengths where MgS can absorb and as a result the MgS grains will be warmer. This explanation is consistent with our notion that MgS is (partially) heated by IR radiation.

A second intriguing possibility is that the MgS around these sources is located far away from the star. R Scl, U Cam and W Ori are known to have a detached dust shell (Zuckerman 1993). These shells are formed during an earlier phase when the mass-loss rate was higher than the current mass-loss rate (Willems & de Jong 1988). If during this phase the AGB star was already a C-star, MgS could have condensed in the outflow and be present in the detached shell. We have sketched in Fig. 1 the evolution of a star which suffers a brief period of enhanced mass loss. First, the star becomes redder during the phase of high mass loss. When the shell becomes detached the 12 $\mu $m flux quickly drops while the inner edge of the dust shell moves away from the star and the warmest dust is rapidly lost. The star moves back to the locus of the warmest C-stars but with an excess of cold dust. The excess of cold dust is observable as a 60 $\mu $m excess. The sources mentioned above indeed show the 60 $\mu $m excess. We note that some stars with 60 $\mu $m excess do not show the "30'' $\mu $m feature.

To distinguish between these two possibilities requires radiative transfer modelling and a more detailed investigation of these particular sources which is beyond the scope of this paper. The location and temperature of the MgS in the warmest C-stars will be further discussed in a forthcoming paper (Hony et al., in prep.).

8.6 MgS in the ISM

The behaviour of the MgS we find in this study has implications for our understanding of the fate of MgS that is produced during the C-star phase. Previously, the existence of MgS in the ISM has been excluded because of the lack of spectral signature at 26 $\mu $m. We have shown that at low dust temperatures no emission signature is expected at 26 $\mu $m. For the dust temperatures in the ISM we would expect a smooth feature at wavelengths longer than 35 $\mu $m. In this respect it is interesting to note that the peak to continuum (P/C) values in the post-AGB and PNe sample are similar. We find no evidence for a rapid destruction by the UV radiation field in the PN. This shows that the MgS will indeed be injected into the ISM. Of course, in the ISM the contrast will be much less because the injected material will be diluted with other star-dust and general ISM material. Nevertheless a search for the "30'' $\mu $m feature in the ISM may be very worthwhile. In this respect it is important to note that Chan et al. (1997) have discussed a broad emission feature they observed along several lines of sight towards the galactic centre. The feature they observed is similar to the "30'' $\mu $m feature observed in the C-rich post-AGB objects.

9 Summary and concluding remarks

We present a large sample of 63 ISO/SWS spectra of carbon-rich evolved objects that exhibit a "30'' $\mu $m feature. The feature is detected along the complete evolutionary track from low mass loss C-stars and extreme C-stars via post AGB objects to PNe.

We present a simple approach to determine the continuum. We study the profile of the "30'' $\mu $m feature after continuum subtraction. We find large systematic variations in the appearance of the "30'' $\mu $m feature. We firmly identify the carrier of the feature with MgS in a CDE shape distribution. The profile of the observed feature is consistent with MgS provided that the temperature of the MgS can be different from the bulk of the dust. This approach allows us to model, in a unified way, the profiles of the "30'' $\mu $m feature in a wide range of objects even when the feature can appear extremely different.

We find an additional component at 26 $\mu $m in $\sim$25 sources. We argue that this component is due to differences in the distribution over shapes of the MgS grains; specifically, it requires a distribution more weighted to spherical MgS grains. We find no clear correlations of this excess with other properties of the sources. The self-absorbed "30'' $\mu $m features of RAFGL 618 and RAFGL 2688 reflect the high optical depth in the "30'' $\mu $m feature in these sources.

We find that the typical profile of the "30'' $\mu $m feature in the PNe is narrower than predicted by our model. We consider several possible explanations. We find that flattened MgS grains provide a better spectral match to the "30'' $\mu $m feature in the PNe. However it is presently unclear why in the PNe environment the "30'' $\mu $m feature is dominated by flattened grains.

We find that the temperature of the MgS grains is different from the bulk of the dust. Therefore, they cannot be in thermal contact with the other dust species but must exist as separate grains. In the C-stars MgS is colder than the other dust while in the post-AGB objects MgS is warmer. Likely, this is because the MgS is efficiently heated by mid-IR radiation which is less important in the C-stars.

The behaviour of the temperature of the MgS for the hottest C-stars is enigmatic. The hottest sources have very cold MgS grains. We propose two explanations for this phenomenon. First, the "30'' $\mu $m feature in these sources may be due to a previous mass-loss phase and the MgS is thus located far from the source and cold. Second, the MgS grains absorb very inefficiently in the optical and near-IR and therefore the hottest C-stars do not heat the MgS grains well.

We examine the feature over continuum ratio to study the relative proportion of MgS to the other dust components. We find no evidence for rapid destruction of MgS grains during the PNe phase and possibly MgS grains may survive to be incorporated into the ISM.

We would like to emphasise the need for further measurements of the optical properties of astrophysically relevant materials at all relevant wavelengths. This study has put forwards some very interesting questions in relation to the absorption properties of MgS in the optical and near-IR and also concerning low temperature effects. Unfortunately, no published laboratory measurements are available to test some of our scenarios and conclusions.

SH and LBFMW acknowledge financial support from NWO Pionier grant 616-78-333. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of NASA's Astrophysics Data System Bibliographic Services. IA3 is a joint development of the SWS consortium. Contributing institutes are SRON, MPE, KUL and the ESA Astrophysics Division.



Online Material

Appendix A: Model Fits

\par\includegraphics[width=17.5cm,clip]{h3527f18.eps} \end{figure} Figure A.1: "30'' $\mu $m feature modelled using MgS optical properties. We show the observed spectra (black), the modelled continua (dashed), the spectra with the MgS contribution subtracted (gray) and the composite of the continuum and the MgS contributions (thin black line).

\end{figure} Figure A.1: continued.

\end{figure} Figure A.1: continued.

\end{figure} Figure A.1: continued.

\end{figure} Figure A.1: continued.

\end{figure} Figure A.1: continued.

\end{figure} Figure A.1: continued.

\end{figure} Figure A.1: continued.

\par\includegraphics[width=18cm,clip]{h3527f26.eps} \end{figure} Figure A.2: C-stars with a weak or without a ``30'' $\mu $m feature. We aslo show the fitted continuum (dashed line). The sources are sorted according to decreasing continuum temperature. We refrain from showing a MgS model. In those cases where the strength of the "30'' $\mu $m feature allowed to extract a temperature of the MgS the value is listed in Table 2.

\end{figure} Figure A.2: continued.

Copyright ESO 2002