Temperature Dependence of Absorption Coefficients (2024)

THE ASTROPHYSICAL JOURNAL, 496:10581066, 1998 April 1
© 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

V. MENNELLA, 1 J. R. BRUCATO, 1 L. COLANGELI, 1 P. PALUMBO, 2 A. ROTUNDI, 2 AND E. BUSSOLETTI 2

Received 1997 July 8; accepted 1997 October 31

ABSTRACT

We have measured the absorption coefficient per unit mass of cosmic dust analog grains, crystalline fayalite and forsterite, amorphous fayalite, and two kinds of disordered carbon grains, between 20 m and 2 mm over the temperature range 29524 K. The results provide evidence of a significant dependence on temperature. The opacity systematically decreases with decreasing temperature; at 1 mm, it varies by a factor of between 1.9 and 5.8, depending on the material, from room temperature to 24 K. The variations are more marked for the amorphous grains. The wavelength dependence of the absorption coefficient is well fitted by a power law with exponent that varies with temperature. For the two amorphous carbons, (24 K) 1.2 with increases of 24% and 50% with respect to the room-temperature values. A 50% increase is found for amorphous fayalite, characterized by (24 K) = 2. A less pronounced change of with temperature, 14% and 10%, is observed for crystalline forsterite, (24 K) = 2.2, and fayalite, (24 K) = 2.3, respectively. For amorphous fayalite grains, the millimeter opacity at 24 K is larger by a factor of 4 than that of the crystalline counterpart. In addition, a temperature dependence of the infrared bands present in the spectrum of the two crystalline silicates is found. The features become more intense, sharpen, and shift to slightly higher frequencies with decreasing temperature. The results are discussed in terms of intrinsic far-infraredmillimeter absorption mechanisms. The linear dependence of the millimeter absorption on temperature suggests that two-phonon difference processes play a dominant role.

The absorption coefficients reported in this work can be useful in obtaining a more realistic simulation of a variety of astronomical data concerning dust at low temperatures and give hints to better identify its actual properties. In particular, they are used to discuss the origin of the diffuse far-infraredmillimeter interstellar dust emission spectrum. It is proposed that composite particles formed of silicate and amorphous carbon grains can reproduce the observations. The presence of these particles in the diffuse medium is consistent with the recent interstellar extinction model by Mathis.

Subject headings: dust, extinctioninfrared: ISM: continuummethods: laboratory

FOOTNOTES

1 Osservatorio Astronomico di Capodimonte, via Moiariello 16, I-80131 Napoli, Italy.

2 Istituto di Fisica Sperimentale, Istituto Universitario Navale, via A. De Gasperi 5, I-80133 Napoli, Italy.

§1. INTRODUCTION

Most of the current information on solid particles in interstellar and/or circ*mstellar environments has been deduced from the analysis of their typical UV, visual, and IR spectral features. In this respect, IR spectroscopy has provided useful clues for the identification of the dust properties. In fact, the fundamental interatomic vibrations of the most abundant cosmic elements fall in the spectral region 230 m. The identification of materials in space cannot be based on the observation of only a few typical IR bands, since functional groups present in different compounds may give rise to similar spectral features. Therefore, in order to assess the nature and the composition of cosmic dust, a complete spectral coverage of the IR region is necessary. The Infrared Space Observatory (ISO) satellite is providing a wealth of data that will allow a quantum leap in this direction (e.g., A&A, Vol. 315).

Further constraints on the grain properties, such as structure (crystalline, amorphous), nature (dielectric, metallic), and morphology (shape, dimension, clustering), can come from the far-infraredmillimeter (FIR-mm) spectral range. At present, the knowledge of the cosmic dust opacity at these wavelengths is less accurate than at shorter wavelengths. The study of cosmic dust in the FIR-mm range merits attention because it can also give crucial information on astrophysical parameters involved in Galactic, extragalactic, and cosmological studies. For instance, the FIR-mm grain opacity represents a key parameter to infer (1) the contribution of various phases of the interstellar medium to the total emission from galaxies, (2) the dust mass-loss rate from evolved stars surrounded by dusty envelopes, (3) the dust mass and temperature in circ*mstellar and interstellar regions, and (4) the contribution of the diffuse dust emission to the observed cosmic microwave background.

Various authors have considered, both from theoretical and experimental points of view, the effect of grain size, shape, chemical composition, and physical structure on the dust opacity at long wavelengths (e.g., ; Wright 1987; ; ). Besides these factors, the temperature can significantly affect the optical properties of grains in space. Despite this, very few laboratory measurements of opacity at low temperature are available for cosmic dust analog grains.

Day (1976) studied the FIR (50300 m) extinction of two amorphous magnesium silicates and found no variation from 77 to 373 K. However, the peak extinction ratio of 1020 m bands tended to increase by a factor of approximately 1.5. More recently, Agladze et al. (1994, 1996) measured the temperature dependence of the absorption coefficient per unit mass for amorphous and crystalline enstatite and forsterite powders and for amorphous MgO · 2SiO₂ between 3.5 and 15 cm^-1 at low temperatures (1.230 K). These authors found that the low-temperature absorption coefficient is about 4 times smaller for crystalline forsterite than for the amorphous grains. More interesting, an unusual behavior was observed for the amorphous silicates namely, the millimeter absorption coefficient decreases with temperature down to about 20 K and then increases again at very low temperatures. A weaker temperature dependence of the absorption was found for crystalline enstatite and forsterite powders. In this framework, it appears relevant to extend the study of the temperature dependence of the FIR-mm optical properties, in terms of both power indices and absolute absorption efficiencies, to other cosmic dust analog silicates and carbon grains.

In this paper we present the temperature dependence (from room temperature down to 24 K) of the absorption coefficient per unit mass in a wide spectral range (20 m2 mm) for two different kinds of amorphous carbon grains and three silicates, characterized by different composition (Fe-rich and Mg-rich olivines) and structural order degree (crystalline and amorphous). These materials can be important constituents of interstellar dust and have been invoked to explain typical spectral features observed in astronomical environments in different spectral ranges (e.g., ; ; Mathis 1996). The data set we have obtained represents a further step toward a more accurate evaluation of cosmic dust properties and of other related physical quantities in different astrophysical environments. The opacities at the lowest temperatures considered are useful to infer the properties of the particles responsible for the observed interstellar thermal emission and to discriminate among different contributions. Measurements performed over wide spectral and temperature ranges are appropriate for applications to environments where grain thermal gradients are expected, such as circ*mstellar and star-forming regions. Moreover, laboratory absorption coefficients are useful to check the validity of extrapolations used in the past to infer the properties of cosmic dust at low temperature.

In § 2 we describe the sample production methods and the setup used for low-temperature measurements. The results are presented in § 3 and discussed in § 4. The implications for the current interpretations of the diffuse FIR-mm dust emission are reported in § 5.

§2. LOW-TEMPERATURE EXTINCTION MEASUREMENTS

The silicate and carbonaceous grains studied in this work can be considered representative of the two main cosmic dust populations. Different experimental techniques were used to produce small particles. Amorphous carbon grains (ACAR) were synthesized by hom*ogeneous condensation of carbon vapors obtained by striking an arc discharge between two carbon electrodes in an Ar quenching atmosphere (10 mbar). Scanning and transmission electron microscopy (SEM and TEM) show that the ACAR sample morphology is dominated by chainlike aggregates of spheroidal grains with an average diameter of about 10 nm (Rotundi et al. 1998). Similar morphological properties characterize the other soot (BE), produced by burning benzene in the air, although the average grain diameter is 30 nm. The two kinds of amorphous carbon differ in their UV-visual and IR spectral behaviors on account of their different electronic, microstructural, and vibrational properties (e.g., Colangeli et al. 1995b; Mennella et al. 1995b, 1995c).

As far as the silicates are concerned, the two extreme forms of natural olivine [Mg, Fe]₂ SiO₄, fayalite (Fe-rich), and forsterite (Mg-rich) minerals, were considered. They were provided by Ward's Natural Establishment Inc. and come, respectively, from the iron mine of Forsythe, Quebec (Canada), and Jackson County, North Carolina (USA). Calibrated mass amounts of bulk material were ground for 1 hour in an agate mill to prepare fine crystalline powders. Amorphous fayalite grains were produced by vaporizing, in an oxygen atmosphere at 10 mbar pressure, the natural target material with an Nd:YAG laser operating at 1064 nm (Continuum model Surlite II). The peak energy was 600 mJ per laser pulse with a repetition rate of 10 Hz. The elemental composition of the three silicates was determined by means of an energy-dispersive X-ray (EDX) system, linked to a SEM microscope (Cambridge model FE360). The EDX results on several areas of the samples showed that, in the formula [Mg_x, Fe_1-x]₂ · SiO₄, x is 0.9, 0.06, and 0.09, for forsterite, fayalite, and amorphous fayalite, respectively. In the following, these materials will be indicated as FOR, FAY, and FAYA, respectively. It is interesting to note that the elemental composition of condensed FAYA grains is only slightly different from that of the starting material, due to the rapid laser evaporation and condensation in the oxygen atmosphere (; Stephens et al. 1995). SEM microscopy of the crystalline grains shows a power-law distribution of dimensions with an average diameter of 0.2 and 0.6 m for FAY and FOR, respectively. The morphology of FAYA is determined by the thermodynamic conditions during the laser-induced evaporation (e.g., ; ). Aggregates of spherical particles with an average diameter of 13 nm, organized in chainlike structures, and isolated spheres, with an average diameter of 35 nm, characterize the FAYA (Ferrini et al. 1998).

The density of silicate grains was measured with a stereopycnometer (Quantachrome model SPY-2) by using helium gas for volume determination. The results are reported in Table 2. They are consistent with EDX results and with the trend observed for olivine, whose density varies from 3.2 (FOR) to 4.2 g cm^-3 (FAY).

The samples for transmission measurements were prepared by embedding the materials in low-density polyethylene matrices by the standard hot-pellet technique (e.g., Mennella et al. 1995a). For the present low-temperature experiment we prepared pellets with a diameter of 13 mm and a thickness greater than 2 mm. With this small pellet size the dust mass amount needed to obtain a good absorbance level (see eq. [1]) was smaller than in previous measurements (Mennella et al. 1995a). However, the required amount of grains is still too large to prevent the use of deposition on polyethylene substrates. Since the low-temperature experimental setup does not allow us to orient samples at the Brewster angle or to use a beam polarized parallel to the plane of incidence, we took advantage of the sample thickness to eliminate interference effects on the spectra. Finally, the pellet size allows us to efficiently dissipate the power incident on the sample and, consequently, to reach a low-temperature limit.

Low-temperature measurements were carried out with a closed-cycle helium cryostat (Galileo vacuum). The sample is tightly fixed with two indium gaskets in a copper holder, which, in turn, is mounted on the cold finger. This resides at the center of the cryostat head, which is equipped with two polyethylene windows. The cooling of the sample is started when the system pressure is less than 1 × 10^-6 mbar. The pressure decreases below 1 × 10^-7 mbar when the sample finger and its cold shield reach 10 K. A small resistive heater, operated by a programmable controller, allows the cold-finger temperature, measured with a Si thermometer, to be stabilized within 0.1 K or changed from the low-temperature limit to room temperature. A second Si thermometer (1.5 × 3 mm²) was mounted on the sample to evaluate the temperature difference between the holder and the sample itself. Several calibration runs, performed under the same experimental conditions as those used for transmission measurements (i.e., with samples exposed to the spectrometer beam) allowed us to obtain a temperature calibration curve for the samples embedded in the polyethylene pellets. The minimum attainable temperature was 24 K. The uncertainty on the sample temperature is within ±1 K over the considered temperature range. Calibration runs showed that 10 minutes are sufficient to reach the thermal equilibrium between the cold finger and the sample.

For transmission measurements the cryostat head was set in the sample compartment of a Fourier transform-IR spectrometer (Bruker model IFS 66V), operating at a pressure of 10^-1 mbar to reduce air absorption. Several optical setups of the spectrophotometer were used to cover the whole spectral range 20 m2 mm. A mercury lamp, four mylar beamsplitters, with thicknesses ranging from 6 to 125 m, a deuterated triglycine sulfate thermal element with a polyethylene window, and a Si bolometer were used for the FIR-mm spectral region (see also Mennella et al. 1995a). The bolometer, equipped with a cold low-pass filter (cutoff = 200 m), was operated at 1.4 K by pumping a liquid helium bath in a Dewar mounted on an external port of the spectrometer with a polyethylene window. In each spectral range, the spectra were derived by the standard fast Fourier transform technique from interferograms obtained by co-adding several scans. The overlap between the spectral ranges resulting from each optical configuration allowed the corresponding spectra to be reliably knitted together into a single spectrum. The spectral resolution was 2 cm^-1 over the considered spectral range.

§3. RESULTS

Here T is the absolute temperature, S is the pellet cross section, while t(, T) and t_p(, T) represent the transmission of a pellet containing a sample mass M and of a blank polyethylene pellet, respectively. Since the extinction of the analyzed materials decreases as the wavelength increases, we used samples with higher masses in the millimeter spectral region in order to have a signal at the middle of the detector dynamic range. The corresponding grain volume filling fraction f is reported in Table 2 for the analyzed samples. Note that all the samples are in the form of submicron grains. Therefore, K_ext(, T) coincides with the absorption coefficient K(, T) in the examined spectral range. In the following we will refer to the latter quantity.

It is useful to mention that spectral variations are observed for blank polyethylene pellets. The absorption continuum slightly decreases as the temperature decreases; the variations are less than 10% in the millimeter region at 24 K. More evident changes take place in the band spectrum. The B_1u mode becomes more intense and shifts from 72.3 cm^-1 at 293 K to 78.5 cm^-1 at 24 K. A band at 433 cm^-1, not evident at room temperature, appears in the spectra recorded at 200 K and becomes more intense as the temperature decreases. The bands at 474 and 387 cm^-1 do not vary appreciably with the temperature. Similar spectral changes were reported for both low- and high-density polyethylene by other authors ( and references therein).

The absorption coefficient for the examined materials over the whole analyzed spectral range is reported in Figures 15. The error on the curves is within 2% in the spectral range up to 500 m, while it rises up to 10% for longer wavelengths. However, a larger systematic error, due to the slight change in the detector sensitivity for different samples, is present at long wavelengths. K() is featureless for ACAR, BE, and FAYA samples at room temperature. For the latter material, the tail of the 20 m band is evident. On the contrary, the two crystalline materials, FAY and FOR, show several IR features. The IR band positions for these two materials are reported in Table 1 (see also Fig. 6). The dependence of the mass absorption coefficient on the wavelength can be well approximated by a power law, K() ^-. The spectral indices have been estimated by a least-squares fit to the experimental data; the results are reported in Figure 7. A single power index is required to fit K() over the examined spectral range for ACAR and BE in agreement with previous data (Mennella et al. 1995a). For the silicate grains, was estimated in the range 100 m 2 mm; for the FAYA sample the spectral index is 1.4, lower than the value, 2, found for FAY and FOR crystalline silicates.

Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7

The spectra of FAY and FAYA are quite different and are compared in Figure 8. While the crystalline sample is characterized by several sharp bands, a single band, which consists of the contributions of the smeared bands present in the crystalline counterpart, is present in the amorphous material. Moreover, an enhancement in the absorption at long wavelengths is evident; at 1 mm the absorption of FAYA is enhanced by a factor of 6.5.

Fig. 8

Important spectral variations take place in all samples at low temperature. The opacity systematically decreases with decreasing temperature (see Figs. 15). At 1 mm, the absorption coefficient for crystalline FAY and FOR samples at 24 K is, respectively, a factor of 1.9 and 2.6 lower than the value at room temperature. The decrease is more marked for the amorphous grains; for the same temperature range, the factors at 1 mm are 2.6, 3.4, and 5.8 for ACAR, BE, and FAYA, respectively. The variations produce a change in the spectral index . Its temperature dependence is reported in Figure 7. For the FAYA sample, varies from 1.35 at 295 K to 2.04 at 24 K. Similar variations, by factors of 1.24 and 1.51, are found for ACAR and BE materials, respectively, although the carbonaceous grains have lower -values at room temperature. Less marked changes occur for the two crystalline samples; the spectral index varies by a factor of 1.14 and 1.10 for FOR and FAY, respectively.

Finally, a temperature dependence of the IR absorption bands is observed for the two crystalline silicates. The difference between K(, 295) and K(, 24) is shown in the linear plot of Figure 6. The absorption features become more intense, sharpen, and shift to slightly smaller wavenumbers (see also Table 1) with decreasing temperature. Except for the bandshift, these variations resemble those produced by an improvement of the spectral resolution. Actually, as we will see in § 4, they are due to a real sharpening of the IR modes, which occurs at low temperature.

§4. DISCUSSION

The results obtained on submicronic silicate and carbonaceous grains show a significant temperature dependence of the FIR-mm absorption coefficient per unit mass in terms of absolute values and spectral index. There are several factors that can contribute to determining the spectral behavior of the dust opacity at long wavelengths. The origin of the variations we found must be identified in the structure of the materials rather than in morphological parameters. In general, when a crystalline solid becomes disordered, a relaxation of the selection rules that govern the excitation of vibrational modes occurs. In contrast to crystalline solids, where only a small number of lattice vibrations are optically active, in disordered materials the breakdown of the selection rules can induce coupling of photons to phonons, which are inactive in crystals. Therefore, the absorption spectrum represents a convolution of the phonon density of states (DOS) with a matrix element. Assuming that this last quantity varies smoothly with the wavelength, the spectral behavior should reflect that of the DOS. Trends of the DOS proportional to ^-2 and ^-1 are expected for three- and two-dimensional structures, like amorphous carbon and layered silicates, respectively, at low energies (Kittel 1976; ; Mennella et al. 1995a). The comparison of FAYA and FAY spectra (see Fig. 8) presents a good example in which the weakening and broadening of allowed one-phonon features, present in the crystalline grains, give rise to a single band in the amorphous sample. This behavior is interpreted in terms of an activation of modes and of an increased dispersion in bond lengths and angles and, thus, in bond strength. A further consequence of the disorder is the decrease of the integrated band intensity.

On the basis of the previous considerations, the effects of temperature on the IR modes in silicates are mainly due to the contraction of the material structure at low temperature. The reduced interatomic distance induces a stronger coupling constant and thus, a progressive shift to higher frequencies of vibrations (). Moreover, the reduction of active phonons at low temperature determines a lower damping coefficient and thus the observed band width decreases and intensity increases (see Fig. 6). The temperature effects on the FAYA are less evident because the disorder effects prevail.

As far as the FIR-mm range is concerned, the main sources of absorption are two-phonon difference processes, although a contribution is expected from three-phonon processes, the one-phonon red wing, and disorder-induced one-phonon processes in the case of structurally disordered solids (e.g., Mitra 1985; Thomas 1991). Some amorphous materials show anomalous behavior at long wavelengths and very low temperature, which has been interpreted in terms of a two-level tunneling model (Bösch 1978; Agladze et al. 1996). Detailed models for all the mentioned processes are extremely difficult to obtain (Thomas 1991). However, the temperature dependence of K can be a useful diagnostic for discriminating among the various absorption processes. When the condition h kT holds (where is the frequency, T is the temperature, h and k are the Planck and Boltzmann constants, respectively) K varies as T^n-1, where n is the order of the difference process (Mitra 1985; Thomas 1991 and references therein). For our samples, in the millimeter region, where the previous relation is valid for all temperatures considered, the absorption coefficient has a linear temperature dependence, as shown in Figure 9. This result suggests that two-phonon difference processes play an important role. Moreover, K tends to a value different from zero as T tends to zero, indicating the existence of the one-phonon red wing in crystalline materials (Thomas 1991). For the amorphous materials this behavior can be interpreted by a disorder-induced one-phonon contribution.

Fig. 9

At very low temperatures, the millimeter absorption in glasses is governed by two-level tunneling systems that determine a decrease of K down to 10 K and then an increase of K at lower temperatures (; Bösch 1978). Recently, Agladze et al. (1996) have studied the millimeter (0.72.9 mm) temperature dependence over the range 1.230 K for crystalline enstatite and forsterite grains, their amorphous precursors, and the amorphous silicate MgO · 2SiO₂. They have found that small amorphous silicate grains show the characteristic temperature trend associated with the two-level systems in bulk glasses. The power indices for amorphous forsterite and enstatite studied by Agladze et al. (1996) are respectively, about 1.5 and 1.7 at very low temperatures. They increase up to 2.5 at 10 K and then decrease to 2 for temperatures slightly above 20 K. The -value for MgO · 2SiO₂ is 1.2 and shows a weak temperature dependence.

Since there is an overlapping of both temperature and wavelength ranges, a comparison with our results is possible. To this end, the local field correction factor on measured k_a(), due to the polyethylene matrix used to disperse grains, has been considered. For crystalline particles, which are not agglomerate, the absorption efficiencies for a sphere both in vacuum and in polyethylene have been computed by Mie theory, while the "continuous distribution of ellipsoids" (CDE) model (e.g., Huffman 1989) was adopted to account for the grain agglomeration of the other three samples (). For ACAR and BE the optical constants derived by Zubko et al. (1996) up to 2 mm were used, while for the silicates we considered the optical constants of olivine [(Mg_x, Fe_1-x)₂ · SiO₄ with x = 0.5] reported by Dorschner et al. (1995) up to 0.5 mm. The resulting factor in the FIR-mm region is 1.4, 1.35, and 1.3, for BE, ACAR, and FAYA, respectively, and 2.3 for FAY and FOR. The values of the grain absorption coefficient at 1 mm, extrapolated to vacuum, are reported in Table 2. Embedding in the matrix also affects the spectral profile of IR bands. In particular, bands typically shift on a few cm^-1 to higher wavenumbers going from KBr to vacuum (Colangeli et al. 1995a). A similar shift is expected for polyethylene to vacuum, since the two matrices have similar indices of refraction in IR.

After the correction for the matrix effect, the millimeter grain absorption coefficient at 24 K for FAYA is 4 times larger than that of crystalline grains. The same factor is reported by Agladze et al. (1996) at 20 K in the case of amorphous and crystalline forsterite, even if a dependence of the result on sample preparation exists. For crystalline forsterite, K(1 mm, 24 K) = 0.16 cm² g^-1, lower than the values of 0.22 and 0.25 cm² g^-1 at 20 K reported by Agladze et al. (1996) for the two forsterite samples. On the other hand, for FAYA K(1 mm, 24 K) = 0.86 cm² g^-1, a factor of 1.8 larger than the average value (0.48 cm² g^-1) of their three amorphous forsterite samples. This discrepancy can be due to the activation of two tunnel systems, which occurs in this temperature range, or to a compositional difference. However, since the value (24 K) = 2 that we find for FAYA fits well to the (T) trend reported by Agladze et al. (1996) for amorphous enstatite and forsterite, we have extrapolated the absorption coefficient for FAYA at 20 K and obtained K(1 mm, 20 K) = 0.47 cm² g^-1 with = 2.3. These values are in good agreement with those of 0.48 cm² g^-1 and = 2.2 for amorphous forsterite. Since FOR and FAY are the two extreme forms of natural olivine, we can assume that K(1 mm, 20 K) is 0.5 cm² g^-1 with = 2.25 for amorphous materials of this class of silicates. The derived low-temperature mass opacity for olivine is 1.7 times the value usually adopted for interstellar silicates.

As far as the two carbonaceous grain materials are concerned, at 24 K they have a similar spectral index and opacity. To the best of our knowledge, performed the only measurement of the absorption coefficient per volume unit, , for carbon particles of 9 nm in diameter at 1.2, 2, and 4.2 K in the range 503 cm^-1. They found (1 mm, 2 K) = 0.35 cm^-1 and 1.5, stable with temperature. By considering the filling factor reported by and a density 1.85 g cm^-3, typical for carbon grains, we obtain K(1 mm, 2 K) = 4.4 cm² g^-1. This information, together with our measurements, is insufficient to search for a similar temperature behavior to that observed in silicates, and further measurements are needed. However, since find no absorption variation with temperature in a range where the two-level tunneling effect should be relevant, it looks probable that the absorption decreases and the spectral index increases with decreasing temperature. Thus, by linearly interpolating K and we derive for amorphous carbon grains K (1 mm, 20 K) = 20 cm² g^-1 with = 1.23. The result is 40 times larger than the grain opacity estimated for amorphous olivine.

§5. IMPLICATIONS FOR INTERSTELLAR DUST EMISSION

The results presented in the previous sections allow a better identification of the cosmic dust properties and a more reliable estimation of dust-related quantities in a variety of astronomical environments. Here we briefly discuss the implications of the FIR-mm opacity behavior at low temperatures for the current interpretations of the interstellar dust emission. Various balloon-borne experiments and the COBE satellite have measured the Galactic emission and found a high degree of correlation with IRAS maps and 100 m emission (see Smoot 1995 for a review of recent results). The observations of the diffuse emission are consistent with a range of dust temperatures 425 K (Wright et al. 1991; Sodroski et al. 1994; Reach et al. 1995; Fischer et al. 1995). To get insight into the nature of the emitting dust, fits to the emission are usually performed with a modified blackbody function expressed as K₀(/₀) B(, T_d) where B(, T_d) is the Planck function and K₀(/₀) is the emissivity of the dust at the temperature T_d, with K₀ the emissivity at the frequency ₀. This analysis gives an emissivity law for the interstellar dust with a spectral index 1.5 (e.g., Fischer et al. 1995; Masi et al. 1995). Such a value of the spectral index indicates an excess emission with respect to the ² emissivity expected in the low-frequency limit. However, in the case of the Galactic spectrum measured with COBE FIRAS, heavily weighted toward the Galactic plane, Wright et al. (1991) found that the spectrum is equally well fitted by a single-component temperature ( = 1.65, T_d = 23.3) or by a warm (T₁ = 20.4 K) and a cold (T₂ = 4.77 K) dust component with = 2. According to these authors, the cold dust can be considered a convenient way to express the observed excess emission. Its presence is confirmed by a more detailed analysis of the COBE FIRAS data by Reach et al. (1995), which found the cold component also at high Galactic latitude and evidenced a correlation in terms of optical depths with the warm dust. The same authors considered several hypotheses about the origin of the excess emission: cold dust formed of very small grains, large grains, or fractal particles, or an enhanced submillimeter emissivity of the dust that produces the warm component. At present, no definitive attribution is possible.

The interpretation in terms of a cold dust component is strongly dependent on the assumption that = 2 is the true spectral index value for the emissivity at low frequencies according to the principle of causality. The value of 1.5, obtained with one-component fits, is interpreted as due to a distribution of temperatures along the line of sight, which broadens the spectrum and lowers the observed value of the spectral index.

We want to recall here that the Kramers-Kronig theorem gives 2 as 0. The crucial point is, of course, to know below which frequency is 2. Laboratory measurements show that the previous condition does not hold for analog grains in the millimeter range. In addition, a significant temperature dependence of the spectral index is observed in the range 425 K. Thus, the attribution of the excess emission to a cold component appears questionable. On the other hand, on the basis of laboratory results, the hypothesis that the low-frequency excess emission may be due to enhanced submillimeter emissivity of the warm dust remains to be considered and is discussed below.

From the derived low-temperature emissivities, it is evident that neither carbon nor silicate grains alone can reproduce the observed trend with 1.5. Only a combination of these two components can fit the interstellar emission. We note that, in principle, this approach is in agreement with extinction models that indicate silicates and carbon grains as the major constituents of interstellar dust. To check this possibility, we considered the emission spectrum of the Galactic plane in Aquila reported by Masi et al. (1995). The data set consists of their ARGO balloon-borne measurements at 0.5, 0.8, 1.2 and 2 mm and of the 140 and 240 m COBE DIRBE and IRAS 100 m observations of the same region. All the data are normalized to the 100 m value detected by IRAS (see Masi et al. 1995 for further details). As a fitting function we adopted the sum of two modified blackbodies that is normalized to the same wavelength. We used T_carb = T_sil = 20 K and the emissivity of amorphous olivine and carbon grains at 20 K reported in § 4. This choice is justified by the values of T_d = 20.3 ± 0.8 K and = 1.54 ± 0.11 found by Masi et al. (1995) with a single-component fit. The free parameter of the fit is R, the ratio of silicate to carbon mass. The best fit, reported in Figure 10, was obtained with R = 4.47 ± 0.36 with ²/dof = 2.6.

Fig. 10

Note that the temperature we assumed for the fit does not agree with the values expected for silicate and carbon particles at the thermal equilibrium in the diffuse interstellar medium. In fact, by using the optical constants for "astronomical silicates" and the interstellar radiation field adopted by for a solar neighborhood, estimated the temperature of silicate grains T_sil 17.5 K for a size 0.010.04 m. With the same radiation field and the optical constants reported by Zubko et al. (1996), we found T_carb 22 K for amorphous carbon grains of 0.010.03 m. On the other hand, the narrow temperature range along the lines of sight deduced by COBE FIRAS data analysis suggests that two-composition models with grains having widely different temperatures and comparable abundance cannot produce the observed emission (Reach et al. 1995).

On the basis of the above reported discussion, the result of our fit can be interpreted by attributing the emission to composite grains formed of silicates and amorphous carbon grains. In this case, a temperature between the equilibrium values of the two separate components is expected, the exact value depending on the relative abundance of the constituents. This hypothesis is fully consistent with the recent interstellar dust model presented by Mathis (1996), which takes into consideration the updated constraints. Interestingly enough, the ratio of silicate to carbon mass resulting from our fit is in agreement with the mass ratios (46) reported by Mathis for silicate and carbon grains that form composite particles. Of course, low-temperature extinction measurements of composite grains and/or their modeling with low-temperature optical constants would be advisable to further support our conclusion.

An interesting aspect of describing interstellar emission in terms of composite particles is the possibility of unifying extinction and emission models for interstellar dust and of having stronger constraints to define the properties of grains in space. Another followup is the possibility of exploiting the IRAS 100 m maps to infer information about fluctuations in the microwave background radiation. In fact, since only one temperature component is responsible for both FIR and millimeter emission, the spatial fluctuations observed in IRAS maps will be comparable to those expected at longer wavelengths.

ACKNOWLEDGMENTS

We would like to thank S. Masi and P. Salatino for density measurements and S. Inarta, N. Staiano, and E. Zona for their technical assistance during laboratory measurements. This work has been supported by ASI, CNR, and MURST research contracts.

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FIGURES

Full image (50kb) | Discussion in text
FIG. 1.Absorption coefficient per unit mass vs. wavelength for BE. Curves from top to bottom refer to 295, 200, 160, 100, and 24 K.
Full image (50kb) | Discussion in text
FIG. 2.Absorption coefficient per unit mass vs. wavelength for ACAR. Curves from top to bottom refer to 295, 200, 160, 100, and 24 K.
Full image (54kb) | Discussion in text
FIG. 3.Absorption coefficient per unit mass vs. wavelength for FOR. Curves from top to bottom refer to 295, 200, 160, 100 and 24 K.
Full image (49kb) | Discussion in text
FIG. 4.Absorption coefficient per unit mass vs. wavelength for FAY. Curves from top to bottom refer to 295, 200, 160, 100, and 24 K.
Full image (57kb) | Discussion in text
FIG. 5.Absorption coefficient per unit mass vs. wavelength for FAYA. Curves from top to bottom refer to 295, 200, 160, 100, and 24 K.
Full image (70kb) | Discussion in text
FIG. 6.Absorption coefficient per unit mass vs. wavelength for FOR (a) and FAY (b) at room temperature (dotted lines) and 24 K (continuous lines).
Full image (33kb) | Discussion in text
FIG. 7.Temperature dependence of the spectral index determined with least-squares fit to the absorption coefficient per unit mass in the range 0.12 mm for ACAR (open triangles), BE (filled squares), FAYA (open squares), FOR (filled circles), and FAY (open circles) grains. The typical error on reported points is 0.04.
Full image (39kb) | Discussion in text
FIG. 8.Absorption coefficient per unit mass at room temperature for FAY (continuous curve) and FAYA (dotted curve).
Full image (69kb) | Discussion in text
FIG. 9.Temperature dependence of the absorption coefficient per unit mass at 2 mm for (a) ACAR (filled squares) and BE (filled triangles); (b) FAYA (filled circles); (c) FOR (open triangles) and FAY (open squares).
Full image (45kb) | Discussion in text
FIG. 10.Fit of the interstellar dust emission in Aquila (l = 35°). The data set, from Masi et al. (1995), consists of their ARGO balloon-borne measurements at 0.5, 0.8, 1.2, and 2 mm and of the 140 and 240 m COBE DIRBE and IRAS 100 m observations. All the data are normalized to the 100 m brightness detected by IRAS. The line is the best fit obtained by using the laboratory emissivity for silicate and carbon grains at 20 K and T_carb = T_sil = 20 K. The best-fit silicate-to-carbon mass ratio is 4.47 ± 0.36 with ²/dof = 2.6.

TABLES

TABLE1
TEMPERATURE DEPENDENCE OF IR BAND POSITIONS IN
CRYSTALLINE FAYALITE (FAY) AND FORSTERITE (FOR)

MATERIAL	PEAK POSITIONS (cm-1)
	T = 295 K	T = 160 K	T = 24 K
FAY...	480	481	481
	451	451	450
	406	410	411
		384	384
	364	367	368
	322	324	326
			313
	254	257	259
	201	202	203
	184	187	189
FOR...	471	472	474
	416	419	420
	400	402	403
	379	382	384
	359	363	364
	293	295	297
	138	139	140

Image of typeset table | Discussion in text

TABLE2
MILLIMETER PROPERTIES OF SILICATE AND AMORPHOUS CARBON GRAINS IN VACUUM

Sample	(g cm-3)	f	g	ka(10 cm-1, 295 K) (cm2 g-1)	(295 K)	ka(10 cm-1, 24 K) (cm2 g-1)	(24 K)
FOR...	3.31 ± 0.03	0.11	0.84	0.43	2.04	0.16	2.32
FAY...	3.89 ± 0.01	0.10	0.85	0.41	1.98	0.21	2.18
FAYA...	3.94 ± 0.03	0.06	0.90	5.0	1.35	0.86	2.04
ACAR...	1.87 a	0.01	0.95	69	0.94	26.00	1.17
BE...	1.81 a	0.01	0.93	72	0.76	21.00	1.15

a From Colangeli et al. 1995b.

Image of typeset table | Discussion in text