The Astrophysical Journal, 633:272–281, 2005 November 1 # 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.
TEMPERATURE DEPENDENCE OF THE SUBMILLIMETER ABSORPTION COEFFICIENT OF AMORPHOUS SILICATE GRAINS N. Boudet Centre d’Etudes Spatiales des Rayonnements, 9 Avenue du Colonel Roche, BP 4346, Toulouse Cedex 4, France;
[email protected]
H. Mutschke Astrophysikalisches Institut und Universita¨ts-Sternwarte, Schillerga¨chen 3, D-07745 Jena, Germany
C. Nayral Centre d’Etudes Spatiales des Rayonnements, 9 Avenue du Colonel Roche, BP 4346, Toulouse Cedex 4, France
C. Ja¨ger Astrophysikalisches Institut und Universita¨ts-Sternwarte, Schillerga¨chen 3, D-07745 Jena, Germany
J.-P. Bernard Centre d’Etudes Spatiales des Rayonnements, 9 Avenue du Colonel Roche, BP 4346, Toulouse Cedex 4, France
T. Henning Max-Planck-Institut fu¨r Astronomie, Ko¨nigstuhl 17, D-69117 Heidelberg, Germany
and C. Meny Centre d’Etudes Spatiales des Rayonnements, 9 Avenue du Colonel Roche, BP 4346, Toulouse Cedex 4, France Receivved 2004 July 19; accepted 2005 June 23
ABSTRACT We have measured mass absorption coefficients of amorphous silicate materials for wavelengths between 100 m and 2 mm (5–100 cm1) and at temperatures between 300 and 10 K. For both interstellar analog MgSiO3 and simple silica SiO2, we find evidence for a strong temperature and frequency dependence. We define two distinct wavelength regimes, 500 m–1 mm and 100–250 m, for which the absorption coefficient presents different trends with frequency. To evaluate this frequency dependence, we fit our absorption coefficient using two power laws with spectral index that varies with temperature. We do not find a significant variation of with temperature between 100 and 250 m, whereas between 500 m and 1 mm a pronounced anticorrelation between T and exists. Globally, -values decrease from 2.5 to 1.5 between 10 and 300 K. This anticorrelation for interstellar analog grains has the same trend as the one observed using the balloon-borne experiment PRONAOS. We show that physisorbed water is not responsible for the observed temperature and frequency dependence and that OH groups could be at the origin of the submillimeter properties of the materials. As discussed in the literature, OH groups are often related to tunneling processes in two-level systems (TLS). In the case of the more complex MgSiO3 silicates, TLS could also be produced by the Mg+2 ions, which act as network modifiers, similar to how they act with OH groups. Subject headinggs: dust, extinction — infrared: ISM — ISM: molecules — methods: laboratory — molecular processes
1. INTRODUCTION
wavelength range) and a single grain temperature T along the line of sight, the emission spectrum for a population of spherical grains of radius a in the Rayleigh approximation is given by
The interstellar medium (ISM) represents 4% of the mass of the Galaxy, and its dust component (composed of submicronsized solid grains) accounts for roughly 1% of the ISM. Despite such a relatively small contribution to the total mass, the efficiency with which the dust scatters, absorbs, and reradiates starlight ensures that it plays a key role in the Galactic energy balance. Dust controls the star formation process and is an important player in the dynamics of protostellar disks (Yorke & Henning 1994). The far-infrared/submillimeter emission from the ISM is dominated by a dust component composed of grains large enough to be at thermal equilibrium with the incoming radiation field, at temperatures of a few tens of K (Mathis et al. 1977; Draine & Lee 1984; Desert et al. 1990). An important component of these grains is silicates. They explain in particular the absorption bands at 9.7 and 18 m and are predominantly in the amorphous state. Assuming an optically thin interstellar medium (which is valid in the submillimeter
I ¼ a 2 Qabs Ngrain B (T );
ð1Þ
where I is the spectral intensity (in MJy sr1), B (T ) is the Planck function, Qabs is the absorption efficiency, and Ngrain is the column density of grains. Absorption efficiency at long wavelengths depends on various parameters: size, shape, chemical composition, agglomeration state, and temperature (for a review, see Yorke & Henning 1994). The knowledge of the absorption efficiency and its variation with temperature is of great importance to infer key information from astronomical observations, such as dust mass and temperature, in various sites of the ISM and to estimate reliably the contribution of the dust emission to the observed cosmic microwave background. Such information 272
SUBMILLIMETER ABSORPTION IN SILICATE GRAINS is crucial for the scientific exploitation of data from the Atacama Large Millimeter Array (ALMA) and the Planck and Herschel missions. For spherical grains, the absorption efficiency Qabs can itself be related to the mass absorption coefficient (, a) (in cm2 g1) through (; a) ¼
3 Qabs : 4 a
ð2Þ
Thus, laboratory measurements of the mass absorption coefficient can be used to characterize the absorption efficiency. However, such data for astrophysically relevant materials at farinfrared and millimeter wavelengths and at low temperatures are hardly available. Moreover, direct spectroscopic astronomical observations of such extended thermal dust emission have always been limited by the strong atmospheric absorption, requiring balloon-borne or satellite experiments, or measurements of the brightest emission through a few atmospheric windows. In this context of a relative lack of reliable and accurate laboratory and astrophysical data, our view of submillimeter dust emission is still mainly based on theoretical assumptions. It is known that at low temperatures the submillimeter absorption in crystalline dielectric materials results from the longwavelength wing of some fundamental vibrational bands, leading to a temperature-independent quadratic dependence on frequency. Such a temperature-independent quadratic dependence is also expected in this wavelength range for the free-carrier absorption of light in metallic materials, and for the Debye phonon absorption in three-dimensional amorphous solids. It is thus widely accepted that the thermal dust submillimeter emission spectrum could be expressed as a blackbody emission modified by a powerlaw dependence of the wavelength, assuming a constant and temperature-independent exponent of the order of 2 (also called the emissivity spectral index), following the expression k B ðk; T Þ: ð3Þ I ¼ 0 k0 Recently the French balloon-borne experiment PRONAOS (Programme National d’Observations Submillime´triques) measured the low extended surface brightness of the ISM in four broadband filters covering the wavelength range from 200 to 1100 m (Lamarre et al. 1994; Serra et al. 2001). This enabled simultaneous measurements of both the temperature and the emissivity spectral index. Over various sites of the ISM, a synthesis of PRONAOS observations revealed an anticorrelation between the dust grain mean temperature T and the emissivity spectral index , with -values down to 1 at 80 K and up to 2– 2.5 at 10 K (Dupac et al. 2003). It has been argued that if the origin of such anticorrelation remains unclear, it should not be attributed to distribution of grains with different temperatures along the line of sight; it is more likely due to a temperature dependence of the intrinsic optical properties of the materials that constitute the grains. In addition, the all-sky data of the FIRAS (Far Infrared Absolute Spectrophotometer) instrument on board the COBE (Cosmic Background Explorer) satellite have revealed the existence of a significant millimeter excess of the dust emission with respect to a single graybody law. This has been interpreted by several authors as due to the presence of very cold dust (5–7 K) in the ISM (Reach et al. 1995; Finkbeiner et al. 1999) in addition to the warmer component responsible for the emission maximum near 100 m. However, the millimeter excess appears to be extremely well correlated with the FIR dust emission, even in view of more recent observations with angular resolution better
273
than FIRAS. This is indicative of a situation in which the excess could also be produced by unidentified processes intrinsic to the grain component radiating at thermal equilibrium, without requiring an additional colder component. The optical properties could strongly change between room temperature and a few tens of K, especially at far-infrared and submillimeter wavelengths (for a review, see Henning & Mutschke 1997). The experimental temperature dependence of the mass absorption coefficient is an important diagnostic of the physics governing absorption and emission processes. However, very few submillimeter spectroscopic studies at variable temperature in the range 10–100 K are available on materials of astrophysical interest. Agladze et al. (1996), for example, measured the temperature dependence of the absorption but in a restricted temperature and wavelength range (1.2–30 K and 0.7–2.9 mm) for crystalline enstatite (MgSiO3), forsterite (Mg2SiO4), and their amorphous submicron-sized grain precursors. They could observe, in some samples, an anticorrelation between spectral index and temperature in this millimeter and very low temperature range. They identified the physics underlying this behavior as resonant light absorption in a distribution of two-level systems. Mennella et al. (1998) measured the temperature dependence of the absorption coefficient between 295 and 24 K and for wavelengths between 20 m and 2 mm on different cosmic analog grains (amorphous carbon grains, crystalline silicates, and amorphous fayalite FeSiO4). They deduced over the whole 100 m– 2 mm range a wavelength-independent spectral index for the absorption coefficient and found a significant temperature dependence of the spectral index, more or less pronounced, depending on material composition. For example, amorphous fayalite shows an increase of its spectral index from 1.35 up to 2.04 as the temperature goes down. They attribute this behavior to two-phonon difference processes. Previously, in highly absorbing silica-based glasses, Bo¨sch (1978) observed a strong temperature dependence of the absorption coefficient near the millimeter wavelength range (above 500 m), characterized by a spectral index of the order of 1.6 at 300 K, which drops down to around 3 at 10 K. Bo¨sch interpreted such temperature-dependent behavior in terms of the TLS ‘‘tunnelling model,’’ first formulated by Phillips (1972) and, independently, by Anderson et al. (1972). The TLS model predicts three different processes: at low temperatures, a resonant absorption between the millimeter wave and a distribution of asymmetric two-level systems (as observed by Agladze); and at higher temperatures, two associated thermally activated relaxation processes (hopping and phonon-assisted tunneling). To get high spectral index values up to 3, Bo¨sch superposed such thermally activated processes to vibrational absorption in the charge-disordered distribution of the amorphous structure, as modeled by Schlo¨mann (1964). In this framework, it appears crucial to perform measurements on more amorphous materials than did Mennella et al. (1998), who studied only an amorphous iron-based silicate, and in a more extended temperature and wavelength range than did Agladze et al. (1996). This is also of prime interest for the data analysis of the PRONAOS experiment and the future Herschel and Planck missions. Furthermore, even if the variations of absorption with temperature have been discussed, the phenomenological origin remains unclear. More experimental studies are required in order to progress in the understanding of the physical and chemical grain properties responsible for the temperature-dependent optical behavior observed in the ISM. Our approach is to try to identify properties of the solid state (especially lattice disorder or discrete defects) and the underlying physical mechanisms that could be involved in these phenomena.
274
BOUDET ET AL.
In this paper, we present the temperature dependence (from 300 to 10 K) of the mass absorption coefficient between 100 m and 2 mm (5–100 cm1) for different amorphous silicate materials. We studied three types of amorphous silica materials (SiO2) and two kinds of amorphous enstatite (MgSiO3) with different structure, morphology and chemical characteristics. In x 2, the sample choice is explained, and a description of the material structures is given. Section 3 is devoted to a description of sample preparation for spectroscopy and setup used for low-temperature measurements. In x 4, we detail our data analysis of transmission spectra, and the experimental results are presented and discussed in x 5. Conclusions and perspectives of this work are given in x 6. 2. SAMPLE STRATEGY It is clear that interstellar dust along a line of sight consists of a wide range of complex aggregates, silicates, and carbonaceous grains. Thus, the observed submillimeter behavior should result from common properties of amorphous grains, mostly dominated by silicate species. A better understanding of optical properties does not necessarily require working on realistic interstellar analogs; one way is to work first on simple solids showing these properties. That is why we have chosen to combine a study of the more simple amorphous silicate, which is silica, SiO2, and an amorphous MgSiO3, which is a classical astronomical silicate analog. These two families of amorphous silicate samples have been selected because of their differences in terms of chemical composition and grain morphology. Thus, we compare silica spherical grains (diameters 1.5 and 0.5 m), silica-fumed agglomerates (7 nm spherical particles linked together to form micrometersized chains), and MgSiO3 grains ground in a mill (micrometersized grains of undefined shape). The size of all the grains studied is much smaller than the wavelengths; no size effect is expected (Rayleigh limit). Bulk silica consists of SiO4 tetrahedra sharing their oxygen atoms. Each of the four oxygen atoms is covalently bonded to at least one silicon atom to form either a siloxane (SiOSi) or a silanol (SiOH) functionality. Amorphous silica is closely related to the cristobalite structure, but the local order is believed to be limited to crystalline domains of up to 2 nm in diameter, which have completely random orientations. Depending on the synthesis processes, silanols are obviously present as the main surface defects, but silanols can also be internal defects, such as SiOH groups trapped into the structure (Serp et al. 2002; Iler 1979; Waddell & Evans 1997). We have to make clear the distinction between water content and silanol content; both of them vary quite a lot from sample to sample, depending on the synthesis procedure (dry or wet processes). It is well known (Serp et al. 2002) that several layers of physisorbed water (molecular water weakly bonded to the surface) can cover the hydrophilic monolayer formed by hydroxyl groups (SiOH), terminating the bulk at the silica surface. According to the literature (Serp et al. 2002; Ek et al. 2001), heating at 200 C can easily remove physisorbed water (a small difference in the desorption temperature values can be found because of different heating rates, gas flows, or pressures, but a general behavior is yet to be described). A thermal treatment above this temperature leads to the condensation of silanol groups (formation of siloxane functionality and loss of molecular water). Different kinds of surface silanol have to be distinguished: geminal hydroxyl groups (two OH groups bonded to one silicon atom) and isolated hydroxyl groups (only one OH group bonded to one silicon atom). When the hydroxyl groups are close enough at the surface they can interact weakly (vicinal interaction) by the hydrogen bonding. Dehydroxylation processes occur slowly from 200 C
Vol. 633
up to 1200 C; the first step is the condensation of these close OH groups to leave at the surface only geminal and isolated groups. Above 800 C, the surface consists of hydrophobic siloxane groups (preventing rehydration) and isolated hydroxyl groups, which can be fully removed at temperatures of about1200 C (by calcination). Thus, the disorder in amorphous SiO2 is related to a lack of periodicity in the (SiO2) network and, of course, to the nature and content of SiOH defects. It is important to note that in contrast to crystallized samples, we cannot expect exactly the same bulk properties for different amorphous silica samples just because their disorders are not the same (especially the SiOH content). We have complemented the selection of samples by two different amorphous magnesium silicates with pyroxene stoichiometry (MgSiO3). The MgSiO3 glass was produced by melting the appropriate precursors at 1913 K and subsequent fast quenching of the hot liquid to room temperature (Ja¨ger et al. 1994; Dorschner et al. 1995). The second amorphous magnesium silicate of the same composition was synthesized by the sol-gel method, which is based on the chemical polymerization of silicates in a liquid phase at low temperatures. Metal organic compounds such as tetraethoxysiloxane and magnesium methylate served as precursors. After the evaporation of the solvents methanol and water from the produced gels, the remaining magnesium silicate powder was heated to 870 K in order to achieve a densification of the silicate framework and a removal of porosity accompanied by a condensation of OH groups. The complete synthesis is described in a previous paper (Ja¨ger et al. 2003). Crystalline pyroxenes are inosilicates containing chains of silicon oxygen tetrahedra (SOT) that share two oxygens. The (Mg) cations are located between the adjoining chains and possess well-defined coordination spheres. In contrast to the crystalline structure, the amorphous material is composed of a disordered network of SOTs connected by bridging oxygens. The incorporation of metal oxides destroys part of the oxygen bridges and forms nonbridging oxygen accompanied by a widening of the structure. In the case of pyroxene glass it is assumed that, in addition to the disordered network of SOTs, further structureforming arrangements such as chains, rings, sheets, and isolated tetrahedra occur (Mysen et al. 1982). Consequently, as for the silica, the amorphous structure of the magnesium silicates is not a well-defined state. The relative proportions and the distribution of the isolated SOTs, chains, rings, and sheets can differ in networks of the same average stoichiometry. In the sol-gel–produced magnesium silicates, the Mg+2 ions can also act as a network former (Ja¨ger et al. 2003). In addition, OH groups remaining from the sol-gel synthesis act as network modifiers (Iler 1979) and can strongly influence the silicate’s properties. For instance, it has been found that crystallization of the silicates occurs at considerably lower temperatures when the network contains isolated OH groups. This is due to the reduced viscosity, which strongly lowers the activation energy for crystallization, e.g., for the sol-gel silicates (Scholze 1988; Ja¨ger et al. 2003). The formation of SiOH bonds in cosmic magnesium silicate particles has to be taken into account, since H2O, as the most abundant oxygen-bearing molecule, plays a very important role in the condensation of circumstellar silicates (Gail & Sedlmayr 1998). 3. EXPERIMENTAL METHODS 3.1. Materials To perform transmission measurement on samples, we worked with two kinds of matrices: KBr for spectroscopy (Merck) in the
No. 1, 2005
275
SUBMILLIMETER ABSORPTION IN SILICATE GRAINS TABLE 1 Sample Characteristics
Sample
Densitya (g cm3)
rb
Mass of Material (mg)
Mass of PE (mg)
fc
gd
tref (5–40 cm1)
All silica samples................... MgSiO3 glass (A)e ................. MgSiO3 glass ( B) .................. MgSiO3 sol-gel (A)e .............. MgSiO3 sol-gel (B) ...............
2 2.71 ... 2.7 ...
3.8 6.66 ... 6.6 ...
100 10 400 10 400
150 160 50 160 50
0.23 0.021 0.593 0.021 0.496
0.93 ... 0.323 ... 0.342
0.92 ... 0.783 ... 0.834
a
Density of compact material measured by a He pycnometer. Real part of the dielectric constant for wavenumbers lower than 100 cm1 (in this wavenumber range, r is assumed to be independent of the temperature and the wavenumber). c Filling factor of silicate in the PE pellet. d Correction factor for spherical particles. e Two different concentrations, A and B, in order to have good signal-to-noise ratio at short and long wavenumbers. b
mid-infrared wavelength range, and polyethylene for spectroscopy (Merck) in the far-infrared to submillimeter wavelength range. We used commercially available amorphous silica powder consisting of monosized spherical particles with 1.5 m diameter (Monospheres 1500, Merck), silica spheres with 0.5 m diameter from Lancaster, and fumed silica from Aldrich. Fumed silica is composed of 0.007 m spheres, which are fused into short chains, very highly branched, 0.1–0.2 microns long, with a high surface area. We carried out measurements on two different enstatite samples of MgSiO3: MgSiO3 sol-gel prepared by a sol-gel process (details of the synthesis are given in Ja¨ger et al. 2003) and MgSiO3 glass prepared by high-temperature melting (Dorschner et al. 1995). The density and dielectric constants of these materials are given in Table 1. 3.2. Sample Preparation We carefully mixed our material powder with matrix powder, using ethanol and ground for several minutes in order to obtain a homogenous mixture. We put this mixture in an oven at 70 C for 30 minutes to evaporate the ethanol solvent. After drying, we pressed our mixture, applying 10 tons of pressure for 3 minutes to make the pellet. The final material mass embedded in the sample is determined by weighting the pellet and taking into account the dust-to-matrix mass ratio (weighting is performed by means of a microbalance with a sensitivity of 1 g of the starting mixture). This method ensures a good material homogeneity in the pellet, even if we cannot exactly control the degree of aggregation. The diameter of pellets is 13 mm with a variable thickness, depending on the total amount of material in the pellet. At the longest wavelengths, the absorption coefficient of silicates is very weak, and its reliable determination requires a sufficient amount of material embedded in the polyethylene (PE) matrix. All SiO2 samples were prepared by embedding 100 mg of material in 150 mg of polyethylene. For the MgSiO3 samples, we used samples with 400 mg of material embedded in 50 mg of PE for the 5–40 cm1 wavenumber range and 10 mg of material embedded in 160 mg of matrix for the 40–100 cm 1 wavenumber range (Table 1). We also prepared a blank PE pellet of 170 mg used for reference measurements in order to determine the absorption and reflection losses related to the PE matrix (see x 3.4). 3.3. Experimental Setup Low-temperature measurements were carried out with a continuous flow helium cryostat (CryoVac KONTI Spektro B) adapted to the sample spectrometer compartment. In the cryostat, samples were cooled via helium exchange gas, which enables a uniform sample temperature. The sample mount of the cryostat
provides two sample positions, which can be alternatingly placed in the beam. The temperature of liquid helium–cooled walls of the sample chamber and of the sample are controlled by two silicon diode temperature detectors. The minimum attainable temperature was 6 K, and the sample temperature uncertainty is 1 K. Spectra were recorded at 300, 200, 100, 30, and 10 K. The FIR transmission spectra were recorded using a Bruker 113v Fourier transform infrared spectrometer. The instrument covers the spectral range from 5 to 200 cm1, using three different mylar beam splitters with thicknesses of 12, 23, and 125 m. Transmittance spectra were determined by dividing spectra obtained with a sample in the optical path by spectra obtained without a sample. The overlap between spectral ranges coming from the beam splitter choice allowed the different spectra to be merged into a single spectrum. Spectral resolution of the 113v instrument was set to 0.5 cm1 for the 125 m beam splitter (5–40 cm1 region) and 1 cm1 for the 12 and 23 m beam splitter (40–100 cm1 region). For the spectral range 5–40 cm1, we used a Si bolometer operated at 1.5 K, and for the larger wavenumbers we used a deuterated triglycine sulfate (DTGS) detector with a polyethylene window. 3.4. Measurement Procedure The transmission measurements are performed during a cooling cycle of the sample from room temperature (300 K) to 10 K. At each temperature (200, 100, 30, and 10 K) chosen for a measurement, the temperature is stabilized by electrical heating against the cooling by LHe flow. Then, at each temperature, spectra are taken for the sample and the empty reference position in the sample mount. Transmission spectra, t, are calculated as the ratio of both. After warming up, another measurement at room temperature is done to check for possible irreversible changes during the cooling cycle. Because of the substantial amount of time and effort required for the LHe consumption, only one cycle has been performed for each of the samples. The measurements were done in two runs from 2003 November to 2004 February. From transmission spectra, we determined the temperature and frequency dependence of the mass absorption coefficient, using the following formula derived from the Lambert-Beer law: (; T ) ¼
S t ð; T Þ ln ; M tref ð; T Þ
ð4Þ
where ¼ 1/k is the wavenumber in cm1, S ¼ 1:3 cm2 is the pellet cross section area, M is the mass of embedded material, t is the transmission spectrum of the material embedded in the
276
BOUDET ET AL.
Vol. 633 4. DATA ANALYSIS
Fig. 1.—Transmission spectra between wavenumbers of 5 and 40 cm1 for fumed silica: 300 K (solid line), 200 K (dot-dashed line), 100 K (short-dashed line), 30 K (dotted line), and 10 K (long-dashed line).
matrix, and tref is a reference transmission spectrum that takes into account the absorption produced by the matrix plus the incoherent (wavelength-averaged) reflection losses at the pellet surfaces. For tref at shorter wavelengths, where PE absorbs itself, the transmission spectrum of a blank PE pellet is used. This is possible because the sample concentration of sample pellets measured in this wavelength range is low, so reflection losses are the same as those of blank PE pellets. At larger wavelengths (5–40 cm1), absorption losses in PE are negligible (below 1%), but reflection losses are enhanced by the high sample concentration of sample pellets measured in this wavelength range. Here the reference transmission can be reduced to a wavelength-independent value tref ¼ (1 R)2 , R being the reflectance [R ¼ (1 neA )2 /(1 þ neA )2 ] of an effective material composed of sample and matrix = 2 ¼ Re("eA )1 2 can material. The effective refractive index neA easily be calculated using the Bruggeman rule (given as eq. [2] in Mennella et al. 1998), neglecting the comparably small imaginary parts in all the dielectric functions. For MgSiO3 glass, with Re("eA ) ¼ 4:06 (see x 4) one finds a reflectivity of the surface of about 0.11 and therefore a transmission reference factor of tref ¼ 0:783 (for MgSiO3 sol-gel, tref ¼ 0:834), whereas for a pure PE pellet ("eA ¼ 2:3), the transmission reference factor would amount to about tref ¼ 0:92 (see Table 1). We used this last value for the silica samples that have a high concentration of PE. We have to correct transmission spectra for multiple reflections on the polyethylene matrix faces, which give periodical fringes related to the matrix thickness (Fig. 1). These pelletinduced fringes are particularly important at long wavelengths, where the material absorptivity is poor. In order to remove these fringes, we performed a least-squares fit on the transmission spectrum in the wavenumber range 5–40 cm1 using a secondorder polynomial. We optimized the choice of the two extreme wavenumber values in order to reach the best fit using 2 criteria. The uncertainties on the corrected transmission value (t/tref ) are evaluated to 2%, taking into account errors from transmission fringe removal and uncertainties on tref values. It leads to a kappa uncertainty: () ¼ ð1:3/M Þ0:02. For silica samples, with a mass of embedding materials equal to 100 mg, the absolute uncertainty is 0.26 cm2 g1. For magnesium silicate samples, depending on the material mass embedded in the PE, the uncertainties are equal to 0.065 cm2 g1 between 5 and 40 cm1, and to 2.6 cm2 g1 at higher wavenumbers.
If the grains are sufficiently dispersed in the PE matrix, the mass absorption coefficient derived from formula (4) is a good approximation for the single-grain mass absorption coefficient. However, at the concentrations used for our measurements, the interaction between the grains and with the PE host medium has to be taken into account, which is done by using the Bruggeman effective medium rule. At sample volume filling factors f of up to 0.3, the approximation given by Mennella et al. (1998; see their eq. [5]) can be used to compute a correction factor g for the single-grain mass absorption coefficient relative to the mass absorption coefficient of an effective medium with filling factor f. This approximation is only valid for spherical particles; we apply it to calculate the correction factor of SiO2 samples that contain spherical grains ( f ¼ 0:21, g ¼ 0:93; see Table 1). To calculate g-factors for high-concentration pellets ( f > 1/3; 400 mg sample plus 50 mg PE), the exact Bruggeman model (Henning et al. 1995) has to be applied. For these high concentrations, the influence of the particle shape on the resulting theoretical mass absorption coefficient of such a pellet is very weak. Therefore, the exact Bruggeman model (for which the theoretical mass absorption values for a continuous medium and a single sphere can be compared) can be used to calculate g-factors. For example, for a pellet with f ¼ 0:593, derived from the above mass ratio plus a pellet porosity of 20% (computed from the thickness of the pellet and the volumes of sample and PE), and with a sample dielectric constant of " ¼ 6:66 þ i"i (MgSiO3 glass) and a matrix (PE plus air) dielectric constant of "h ¼ 1:58, we find an effective dielectric constant of "eA ¼ 4:06 þ i0:443"i . This results in a mass absorption coefficient ¼ ð4/kf Þ0:110"i or ¼ ð2/kÞ0:371"i, whereas for a single spherical MgSiO3 glass particle one would find ¼ ð2/kÞ9/(6:66 þ 2)2 "i or ¼ ð2/kÞ0:120"i . This gives a correction factor of g ¼ 0:12/0:371 ¼ 0:323. In the same way, we determine a correction factor of 0.342 for the MgSiO3 sol-gel product (Table 1). We correct our MgSiO3 mass absorption coefficients with these correcting factors. For the irregular MgSiO3 grains, at low concentrations, there is no good way to calculate a correction factor g; depending on the particle shape, the Bruggeman rule can give very small values for elongated grains but also values close to unity for spheres (Henning et al. 1995). Therefore, we choose to fit the MgSiO3 spectra obtained with low-concentration pellets to those obtained with high-concentration pellets. Because of the uncertainty related to the particle shape even for the highconcentration pellets and because of the fact that the Bruggeman model is only a model, which in some respects may not exactly describe the real behavior of our samples, we estimate the maximum error caused by this single-particle correction to be about 30%. 5. RESULTS AND DISCUSSION 5.1. Temperature Dependence of the Absorption The mass absorption coefficients between 100 and 5 cm1 (i.e., in the wavelength range 100 m–2 mm) are plotted for temperatures 300, 200, 100, 30, and 10 K for MgSiO3 glass, the MgSiO3 sol-gel product, amorphous silica 1.5 m monospheres, and fumed silica in Figures 2–5, respectively. The apparent feature occurring sporadically around 45 cm1 and followed by a lower signal-to-noise ratio at higher wavenumber is due to a lower efficiency of the beam splitter used. All samples show a strong frequency and temperature dependence of the mass absorption coefficient. It is remarkable that all measured samples present a similar frequency and temperature dependence. This global behavior is
No. 1, 2005
SUBMILLIMETER ABSORPTION IN SILICATE GRAINS
Fig. 2.—Mass absorption coefficient for MgSiO3 glass synthetized by melting at high temperatures: 300 K (solid line), 200 K (dot-dashed line), 100 K (shortdashed line), 30 K (dotted line), and 10 K (long-dashed line).
independent of morphology and composition and is characterized by a systematic decrease of the absorption when the temperature is lowered. This decrease is greatly enhanced as the wavenumber falls from 100 to 10 cm1. The values of the mass absorption coefficients measured at 10 cm1 are given in Table 2 for each temperature. It appears that the mass absorption coefficient is typically lowered by a factor of 10 between 300 and 10 K. The absolute values of the mass absorption coefficient for SiO2 at 10 cm1 and at low temperatures are close to the standard opacity value of 0.3 cm2 g1 adopted for the diffuse interstellar medium (Draine & Lee 1984). The absorption decline is all the more important for lower wavenumbers. In our log-log plots, the slope value is equal to the spectral index. Thus, the regular decrease of the slope translates directly into an increase of the mean spectral index . At room temperature the absorption increases quite linearly with wavenumber, resulting in a quite constant spectral index value over the whole submillimeter range ( between 1 and 1.6, depending on the samples). As the temperature goes down, the absorption spectra are characterized by a break in the absorption curves around 30 cm1 for all samples, but it is especially obvious for fumed silica and SiO2 1.5 m monospheres. On both sides of this break a quite linear behavior is observed. For this reason we choose to quantify the spectral index in two wavenumber ranges away from the break, 10–20 and 50–100 cm1. The spectral index values over a range are obtained from a linear
Fig. 3.—Mass absorption coefficient for MgSiO3, synthetized by sol-gel reaction.
277
Fig. 4.—Mass absorption coefficient for 1.5 m–sized silica monospheres.
least-squares fit to the data. The results are presented in Tables 3 and 4 and in Figures 6 and 7. It can be seen that between 50 and 100 cm1 the spectral index has values between 0.9 and 1.7 at 300 K, quite stable or very slightly increasing when the temperature is lowered to 10 K. Between 10 and 20 cm1, the increase of the spectral index is much stronger, as shown in Figure 8. In this wavenumber range, the spectral index increases from values in the range 1.1–1.6 at room temperature, to 2.1–2.8 at 10 K, according to the samples. It should be noted that our spectral index values at low temperatures are different from the usual value of 2 adopted for interstellar dust. Our results show that we observe a general T-dependent optical behavior in the submillimeter domain both for MgSiO3 samples, which are considered astronomical silicates, and for simple silica samples. The coverage of our measurements enables us to compare our results with those of Mennella et al. (1998) and Agladze et al. (1996) on amorphous grains. Unlike the results obtained by Mennella et al. for amorphous FeSiO4, we clearly distinguish two different absorption behaviors with wavelength. We fit the FIR absorption with two different spectral index power laws depending on the wavelength range, whereas Mennella et al. use a single power-law index. Generally speaking, our samples present a more pronounced spectral index variation with temperature, between 10 and 20 cm1. Our -values decrease by a factor of 2.5 between 30 and 300 K against a maximum factor of 1.5 in Mennella et al. In agreement with the results obtained by Agladze et al. for amorphous silicates, we find a decrease of the -value between 10 and 30 K for the wavenumber range
Fig. 5.—Mass absorption coefficient for fumed silica.
278
BOUDET ET AL.
Vol. 633
TABLE 2 Mass Absorption Coefficient at 10 cm 1 Sample
(at 10 K )
(at 30 K )
(at 100 K )
(at 200 K)
(at 300 K )
Silica monospheres (1.5 m)............. Fumed silica....................................... MgSiO3 glass ..................................... MgSiO3 sol-gel ..................................
0.33 0.45 0.22 0.12
0.36 0.51 0.25 0.15
0.73 1.26 0.37 0.32
1.79 2.18 0.53 0.59
5.66 3.75 0.75 0.98
10–20 cm1, but we do not see a drastic change in the absorption coefficient between these two temperatures. 5.2. Comparison with PRONAOS Data As we saw, we certainly cannot assume a constant spectral index over the whole submillimeter spectral range. For silica monospheres—for example, 1.5 m—at a temperature of 10 K, the value of the spectral index drops from 2.77 in the wavelength range 10–20 cm1 to 1.27 in the wavelength range 50–100 cm1 (see Tables 3 and 4). The PRONAOS determination of both the temperature and the spectral index is based on the measurements of the low brightness emission in four broad spectral bands [(k)/k ¼ 0:3] at effective submillimeter wavelengths of 200, 260, 360, and 580 m (assuming I to be of the form given in eq. [3]). As discussed in x 1, such temperature and spectral index determination implies the assumption of an optically thin medium, a unique temperature, and a spectral index over that wavelength range. Therefore, if the spectral index of the interstellar dust varies slightly over the submillimeter range, as it does in our samples, the determination of its value should depend on the number, positions, and widths of the optical filters through which the dust emission is measured. In that sense, a valid comparison between our laboratory data and the PRONAOS results requires us first to simulate emission spectra and then to use the full PRONAOS data analysis processing to get a spectral index value. Thus, to perform this comparison we multiplied each absorption spectrum by a blackbody emission at the corresponding temperature to simulate the emission spectra, following expressions (1) and (2). Figure 8 shows the temperature dependence of an effective spectral index as determined from our silica monosphere, 1.5 m, while Figure 9 shows, for comparison, the temperature dependence of the spectral index deduced from the synthesis of the PRONAOS observations. It appears that, first, the resulting temperature dependence of the spectral index remains quite similar to the one presented in Figure 6. Second, such temperature-dependent spectral index behavior has the same temperature trend as the one observed by PRONAOS. In particular, there is a comparable anticorrelation between temperature and spectral index characterized by the same variation range of the spectral index (between 1 and 2.7). The main difference is that, in the PRONAOS data, the decrease of the spectral index values happens at a lower temperature than that for laboratory measurements. Such a difference suggests that the properties of the interstellar grains probably differ slightly from our
laboratory samples. It is clear that further laboratory studies on various amorphous silicate-based grains are necessary to confirm if the temperature dependence of the spectral index is a general behavior. In particular, it is important to determine what the material parameters (morphology, structure, chemical composition, and defects) that first induce and then enhance the spectral index variation are, especially in the low temperature range. 5.3. Influence of Physisorbed H20 Depending on the state of the surface, the hydrophilic character varies quite a lot from sample to sample (this is related to the synthesis processes). Molecular physisorbed water contents measured by thermogravimetric analysis (TGA) are 3.2% for 1.5 m SiO2 monospheres, 3% fumed silica, 4.7% MgSiO3 sol-gel product, 1.8% for 0.5 m SiO2 monospheres, and 0.3% for MgSiO3 glass. As shown in Figure 10, when 1.5 m monospheres are heated up to 200 C, 3.2% of molecular water is desorbed. The weight loss, between 200 C and 1000 C, is attributed to the slow desorption of the different silanols (surface or internal). A complementary study has shown that we observe the same submillimeter behavior at room temperature both for the 1.5 m SiO2 monosphere sample and for the same sample heated up to 200 C (i.e., after molecular water removal). Besides, the water contents of the two kinds of MgSiO3 samples are very different because of their different synthesis processes. The solgel procedure is a wet process, whereas glass production requires a very high temperature and prevents hydration. Indeed, in the MgSiO3 sol-gel MIR spectrum (Fig. 11), we clearly observe the features characteristic of molecular water, a very broad band around 3440 cm1 (attributed to H2O stretching), and the 1640 cm1 band due to H2O bending (Davis & Tomozawa 1996). Their total absence in the MgSiO3 glass MIR spectrum is obvious. Yet, MgSiO3 sol-gel and MgSiO3 glass samples show a very similar spectroscopic behavior in the submillimeter range at variable temperature (Figs. 2 and 3). Thus, comparison between these samples leads us to conclude that the physisorbed molecular water content is not responsible for the temperature-dependent submillimeter optical phenomenon observed here. 5.4. Influence of SiOH Bonding and Metal Cations Assuming that the optical behavior observed is closely related to the intrinsic properties of the materials, a deeper chemical characterization is of course required and is currently underway. Concerning our samples, Figure 12 shows the 450–2000 cm1
TABLE 3 Spectral Index Values between 10 and 20 cm1 Sample
(at 10 K)
(at 30 K)
(at 100 K )
(at 200 K )
(at 300 K )
Silica monospheres (1.5 m)............. Fumed silica....................................... MgSiO3 glass ..................................... MgSiO3 sol-gel ..................................
2.77 2.44 2.14 2.74
2.66 2.16 2.05 2.46
2.01 1.44 1.79 1.89
1.57 1.31 1.72 1.67
1.1 1.12 1.58 1.44
No. 1, 2005
279
SUBMILLIMETER ABSORPTION IN SILICATE GRAINS TABLE 4 Spectral Index Values between 50 and 100 cm1 Sample
(at 10 K)
(at 30 K )
(at 100 K )
(at 200 K )
(at 300 K)
Monospheres (1.5 m) ............................ Fumed silica............................................. MgSiO3 glass ........................................... MgSiO3 sol-gel ........................................ SiO2 Lancaster ......................................... SiO2 Lancaster annealed at 900 C ..........
1.27 1.28 1.58 1.92 1.34 1.41
1.28 1.33 1.62 1.93 1.38 1.51
1.24 1.31 1.51 1.72 1.33 1.39
1.13 1.26 1.52 1.73 1.37 1.63
0.94 1.12 1.52 1.68 1.21 1.66
range of the MIR spectrum for 1.5 m SiO2 monospheres, fumed silica, and MgSiO3 samples, which all show a strong T-dependence in the submillimeter range. Vibrational modes of SiO2 lead to the following three main bands: 1. 470 cm1: rocking SiOSi. 2. 800 cm1: bending SiOSi. 3. 1100 cm1: stretching SiO. For 1.5 m monospheres and fumed silica samples, we notice the presence of a 970 cm1 band, which is characteristic of SiOH stretching (Zarubin 2001; Fidalgo & Ilharco 2001). In the MgSiO3 samples (Figs. 11 and 12) this band cannot be identified. It is fully hidden in the very broad band connecting bending SiOSi and stretching SiO in one broad feature. The presence of SiOH groups could be a common characteristic of the samples showing a strong T-dependent optical behavior. Comforting this assumption, the temperature dependence observed for 0.5 m silica monospheres (Fig. 13) disappears totally when these monospheres receive a thermal treatment at 900 C for 24 hr, leading to the full elimination of molecular water but also to the elimination of most of the SiOH surface groups. The role of SiOH groups has been previously mentioned in the literature and may be regarded as a reasonable hypothesis. In particular, the effect of OH content on FIR absorption measurements on silica glass has been investigated (Ohsaka & Oshikawa 1998; von Schickfus & Hunklinger 1976; Stolen & Walrafen 1976). Hutt et al. (1989), for example, studied the OH influence on the far-infrared properties of two types of synthetic silica containing different concentrations of residual water (so that the OH contribution can be assessed), and at three temperatures, 300, 200, and 80 K. They showed
Fig. 6.—Temperature dependence of the spectral index determined between 10 and 20 cm1 by least-squares fits for MgSiO3 sol-gel ( plus signs), MgSiO3 glass (asterisks), 1.5 m monospheres (triangles), and fumed silica (squares).
that the presence of OH in silica increased the FIR absorption and induced a temperature-dependent absorption centered near 30 cm1 but covering the range 20–100 cm1. For silica with very small OH content, they did not find signs of temperaturedependent absorption. What could be the phenomenology underlying such behavior? Following Hutt et al. (1989), we believe that OH simply cannot increase the coupling between radiation and the bulk phonon, thus enhancing the one-phonon absorption, which is a temperature-independent process. On the other hand, in such SiOH bonding, OH groups cannot be considered entirely free to rotate. Thus, in the three-dimensional energy potential of the amorphous structure, it seems reasonable to assume that the disorder induces closely spaced local energy minima, in which an OH group can switch. This corresponds to the dynamics of a ‘‘particle’’ in an asymmetric double-well potential. At sufficiently low temperatures, the dynamics involves only the two lowest energy levels. The corresponding quantum mechanical description of this dynamics is the TLS tunneling model. Thus, it is reasonable to consider SiOH a cause of the local disorder that could be involved in these processes. In the case of the more complex MgSiO3 silicates, the defects involved could also be created by the Mg+2 ions, which act as network modifiers, similar to OH groups. In a disordered network, their positions should not be very well defined, allowing for closely spaced local energy minima as well. This is supported by the spectroscopic behavior of the MgSiO3 glass, for which the temperature dependence of the submillimeter spectrum is not very different from that of the sol-gel MgSiO3, although the content of SiOH bonds is at least 1 or 2 orders of magnitude less, due to the production
Fig. 7.—Temperature dependence of the spectral index determined between 50 and 100 cm1 by least-squares fits for MgSiO3 sol-gel product ( plus signs), MgSiO3 glass (asterisks), SiO2 monospheres (triangles), fumed silica (squares), Lancaster monospheres (diamonds), and Lancaster monospheres annealed at 900 C (crosses).
Fig. 8.—Spectral index variations for 1.5 m–sized silica monospheres calculated with PRONOAS data processing.
Fig. 9.—Anticorrelation between temperature and spectral index, observed by PRONAOS.
Fig. 10.—Thermogravimetric analysis of 1.5 m–sized silica monospheres.
Fig. 11.—IR spectra of MgSiO3 glass and sol-gel. MgSiO3 glass transmission has been translated by a factor of 1.3.
Fig. 12.—IR spectra of MgSiO3 glass, fumed silica, and 1.5 m–sized silica monospheres.
Fig. 13.—Mass absorption coefficient for Lancaster monospheres, with and without annealing treatment.
SUBMILLIMETER ABSORPTION IN SILICATE GRAINS at high temperature. If this is true, then the temperature dependence for the sol-gel silicate could also be determined by the Mg+2 ions because of their much higher concentration in the network compared to OH groups. The influence of the metal cation concentration on the temperature dependence will be studied in a subsequent paper. 6. CONCLUSIONS Our far-infrared measurements on different amorphous silicates show a strong temperature and frequency dependence for both interstellar analog grains and simple silica. The global behavior is independent of morphology (bulk, chainlike aggregates), synthesis process (sol-gel or glassy products), and composition (MgSiO3 and SiO2). It is remarkable that the spectral index value at low temperature is different from the standard value of 2 generally adopted by astronomers. As far as the mass absorption is concerned, we obtain a value close to 0.3 cm2 g1 at 10 cm1 and at low temperature. This is in agreement with the standard value generally adopted by astronomers. Contrary to previous studies describing the submillimeter optical behavior, we define two spectral indices, depending on the wavenumber range. Between 10 and 20 cm1, our data show an anticorrelation between temperature and spectral index, whereas between 50 and 100 cm1, the spectral index is quite constant with temperature. Furthermore, using our SiO2 laboratory spectra, we determined the spectral index variations with temperature as it would have been measured by the balloon-borne experiment PRONAOS. This simulation reveals that our laboratory results present a trend similar to that
281
indicated by the PRONAOS temperature-spectral index anticorrelation. Nevertheless, the decrease of spectral index in the PRONAOS observations occurs at a temperature lower than that for the laboratory measurements. More systematic studies are required to confirm, on different kinds of materials, the presence of this anticorrelation and to determine its characteristics according to morphology, structure, and defects. Concerning the chemical and physical causes of the temperature and frequency dependence of the mass absorption coefficient, we can exclude the physisorbed water contribution. We consider defects (silanol or the Mg+2 network modifier) as possible factors influencing the FIR absorption, which could be associated with resonant and relaxation processes in two-level systems (TLS). Interpretations in terms of TLS models will be developed in forthcoming papers (C. Meny et al. 2005, in preparation; J. P. Bernard et al. 2005, in preparation). It will be necessary to better characterize the defects’ influence and to link laboratory results with a theoretical model. These studies aim at the elaboration of a new dust model, taking into account temperature effects of intrinsic properties of interstellar grains.
We are grateful to Walter Teuschel and Gabriele Born for their help with sample preparation and spectroscopic measurements. This work is part of a laboratory astrophysics joint effort between the University of Jena and the MPI for Astronomy, Heidelberg, and has been supported by the French program PCMI (Physique et Chimie du Milieu Interstellaire).
REFERENCES Agladze, N. I., Sievers, A. J., Jones, S. A., Burlitch, J. M., & Beckwith, S. V. W. Ja¨ger, C., Mutschke, H., Begemann, B., Dorschner, J., & Henning, T. 1994, 1996, ApJ, 462, 1026 A&A, 292, 641 Anderson, P. W., Halperin, B. I., & Varma, C. M. 1972, Philos. Mag., 25, 1 Lamarre, J. M., et al. 1994, Infrared Phys., 35, 277 Bo¨sch, M. A. 1978, Phys. Rev. Lett., 40, 879 Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425 Davis, K. M., & Tomozawa, M. 1996, J. Non-Cryst. Solids, 201, 177 Mennella, V., Brucato, J. R., Colangeli, L., Palumbo, P., Rotundi, A., & Desert, F.-X., Boulanger, F., & Puget, J. L. 1990, A&A, 237, 215 Bussoletti, E. 1998, ApJ, 496, 1058 Dorschner, J., Begemann, B., Henning, T., Ja¨ger, C., & Mutschke, H. 1995, Mysen, B., Virgo, D., & Seifert, F. 1982, Rev. Geophys. Space Phys., 20, 353 A&A, 300, 503 Ohsaka, T., & Oshikawa, S. 1998, Phys. Rev. B, 57, 4995 Draine, B. T., & Lee, H. M. 1984, ApJ, 285, 89 Phillips, W. A. 1972, J. Low Temp. Phys., 7, 351 Dupac, X., et al. 2003, A&A, 404, L11 Reach, W. T., et al. 1995, ApJ, 451, 188 Ek, S., Root, A., Peussa, M., & Niinisto¨, L. 2001, Therm. Acta, 379, 201 Schlo¨mann, E. 1964, Phys. Rev., 135, A413 Fidalgo, A., & Ilharco, L. M. 2001, J. Non-Cryst. Solids, 283, 144 Scholze, H. 1988, in Glas ( Berlin: Springer), 136 Finkbeiner, D. P., Davis M., & Schlegel, J. D. 1999, ApJ, 524, 867 Serp, P., Kalck, P., & Feurer, R. 2002, Chem. Rev., 102, 3085 Gail, H. P., & Sedlmayr, E. 1998, in The Molecular Astrophysics of Stars and Serra, G., Giard, M., Bernard, J.-P., Stepnik, B., & Ristorcelli, I. 2001, CR Galaxies, ed. T. W. Hartquist & D. A. Williams (Oxford: Clarendon Press), 285 Acad. Sci. Paris, 1, 1215 Henning, T., Michel, B., & Stognienko, R. 1995, Planet. Space Sci., 43, 1333 Stolen, R. H., & Walrafen, G. E. 1976, J. Chem. Phys., 64, 2623 Henning, T., & Mutschke, H. 1997, A&A, 327, 743 von Schickfus, M., & Hunklinger, S. 1976, J. Phys. C, 9, L439 Hutt, K. W., Phillips, W. A., & Butcher, R. J. 1989, J. Phys. Condensed Matter, Waddell, W. H., & Evans, L. R. 1997, Kirk-Othmer Encyclopedia of Chemical 1, 4767 Technology ( New York: Wiley) Iler, R. K. 1979, in The Chemistry of Silica ( New York: Wiley), 546 Yorke, H. W., & Henning, T. 1994, in IAU Colloq. 146, Molecules in the Ja¨ger, C., Dorschner, J., Mutschke, H., Posch, T., & Henning, T. 2003, A&A, Stellar Environment, ed. U. G. Jorgensen ( Berlin: Springer), 186 408, 193 Zarubin, D. P. J. 2001, J. Non-Cryst. Solids, 286, 80
