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	$\lambda _{\rm c,30}$	fwhm	flux	P/C	$T_{\rm MgS}$		Object	$T_{\rm cont}$	p	$\lambda _{\rm c,30}$	fwhm	flux	P/C	$T_{\rm MgS}$
	[K]		[$\mu$m]	[$\mu$m]	[W/m2]		[K]			[K]		[$\mu$m]	[$\mu$m]	[W/m2]		[K]
NGC 40	150	0	33.6	10.1	5.9e-13	0.7	110		T Dra	1210	0	30.2	10.1	4.8e-13	0.4	200
IRAS 00210	285	0.5	28.4	10.7	6.4e-13	0.8	300		RAFGL 2155	460	0	28.8	8.2	5.7e-12	0.6	400
IRAS 01005	130	1	30.0	11.1	6.6e-13	1.5	220		IRAS 18240	160	1	32.8	13.1	1.0e-12	1.0	130
HV Cas	1040	0.2	33.5	10.6	1.5e-13	0.3	100:		IRC+00 365	910	-0.3	28.6	11.7	1.9e-12	0.4	500
RAFGL 190	275	0	30.9	13.0	1.6e-12	0.3	180		RAFGL 2256	390	0	29.5	12.0	1.9e-12	1.0	350
R Scl	2605	-0.2	33.2	13.9	1.1e-12	1.1	90		K3-17	100	1	34.1	11.5	1.0e-12	0.9	90
IRAS Z02229	235	0	29.1	10.1	8.3e-12	1.7	300		IRC+10 401	765	0	30.0	10.0	2.0e-12	0.3	300
RAFGL 341	380	0	29.8	9.4	9.4e-13	0.4	250		IRAS 19068	1165	-0.7	28.5	10.1	2.0e-13	0.4	500:
IRC+50 096	855	-0.2	28.8	9.2	1.9e-12	0.3	500		NGC 6790	290	0	29.8	15.6	9.8e-13	1.4	300
IRAS 03313	325	0	28.6	7.8	5.4e-13	0.4	300		RAFGL 2392	890	0	27.7	8.6	3.4e-13	0.5	500
U Cam	1775	0	31.9	11.8	3.9e-13	0.6	150		NGC 6826	150	0	32.7	10.5	1.1e-12	2.0	120
RAFGL 618	235	-1	38.0	10.9	5.4e-12	0.2	40a		IRAS 19454	140	1	36.3	13.1	6.4e-13	0.3	50
W Ori	2450	0	31.3	8.4	3.1e-13	0.4	150		HD 187885	175	0	29.6	10.8	5.2e-12	1.0	200
IC 418	120	1	30.8	11.3	5.5e-12	0.9	180		RAFGL 2477	290	0	30.7	12.5	2.3e-12	0.6	170
V636 Mon	1215	0	29.8	10.1	1.7e-13	0.2	250:		IRAS 19584	580	0	28.1	7.5	8.5e-13	1.5	400
RAFGL 940	810	0	28.2	10.2	3.5e-13	0.5	500		IRAS 20000	210	0	29.4	12.1	2.5e-12	1.5	300
IRAS 06582	315	0	29.5	10.3	1.1e-12	0.4	300		V Cyg	1110	0	30.5	11.5	1.3e-12	0.3	200
HD 56126	170	0	30.0	12.0	2.9e-12	0.8	150		NGC 7027	125	1	32.8	11.0	1.7e-11	0.4	110
CW Leo	535	0	28.6	8.8	2.7e-10	0.6	400		S Cep	1340	0.1	31.2	9.4	4.4e-13	0.2	130
NGC 3918	90	1	33.3	8.5	7.1e-13	1.0	120		RAFGL 2688	200	-1	31.1	10.4	5.9e-11	0.3	70a
RU Vir	1045	0	30.4	10.1	5.3e-13	0.6	180		RAFGL 2699	540	0	29.0	11.4	5.9e-13	0.7	300
IRAS 13416	115	1	31.6	15.8	2.8e-12	0.4	200a		IC 5117	130	1	31.2	9.7	7.3e-13	0.6	150
II Lup	625	0	29.5	10.1	3.9e-12	0.3	400		RAFGL 5625	300	0	30.3	11.8	4.4e-12	0.4	200
V Crb	1430	0	30.4	10.1	1.8e-13	0.3	150:		IRAS 21489	415	0	29.3	9.7	1.1e-12	0.6	350
K2-16	155	0.5	34.4	12.0	3.4e-13	0.3	80		SAO 34504	210	0	29.1	10.3	1.3e-11	2.0	250
IRAS 16594	140	1	29.8	12.1	9.9e-12	0.9	250		IRAS 22303	345	0	30.3	10.5	1.0e-12	0.7	300
NGC 6369	100	1	34.6	10.1	9.5e-13	1.1	90		IRAS 22574	160	0	31.2	13.6	5.9e-13	0.4	150
IRC+20 326	770	-0.7	29.1	10.2	7.4e-12	0.5	300		RAFGL 3068	290	0	32.4	14.7	8.4e-12	0.4	120
CD-49 11554	140	1	30.2	14.0	4.7e-12	0.7	200a		RAFGL 3099	470	0	29.5	10.9	2.6e-12	0.7	400
HB 5	120	0	35.5	11.5	1.0e-12	0.4	70		IRAS 23304	115	1	30.1	13.4	2.3e-12	1.1	250
RAFGL 5416	290	0	30.4	12.5	2.2e-12	0.5	220		IRAS 23321	175	0	34.5	13.3	6.6e-13	0.3	70
IRC+40 540	485	0	28.6	9.1	8.9e-12	0.6	400
non detections
R For	1215	0	-	-	<1e-14	<0.1	-		T Lyr	3305	0	-	-	<1e-14	<0.1	-
SS Vir	2040	0	-	-	<1e-14	<0.1	-		S Sct	2105	0	-	-	<4e-14	<0.3	-
Y CVn	2200	0	-	-	<2e-13	<0.2	-		V Aql	3665	-0.3	-	-	<1e-14	<0.1	-
RY Dra	2525	0	-	-	<1e-13	<0.2	-		V460 Cyg	2875	0	-	-	<5e-14	<0.5	-
C* 2178	1110	0	-	-	<1e-13	<0.5	-		PQ Cep	1625	0	-	-	<1e-14	<0.1	-
V1079 Sco	3085	-0.5	-	-	<5e-14	<0.2	-		TX Psc	3105	0	-	-	<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,

$$F(\lambda)=A \times B(\lambda,T) \times {\lambda}^{-p},$$ (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.

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.

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.