Interstellar grains: Effect of inclusions on extinction
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2011
Received: 31 August 2010
Accepted: 17 June 2011
Published: 2 February 2012
A composite dust grain model which simultaneously explains the observed interstellar extinction, polarization, IR emission and the abundance constraints, is required. We present a composite grain model, which is made up of a host silicate oblate spheroid and graphite inclusions. The interstellar extinction curve is evaluated in the spectral region 3.4–0.1 µm using the extinction efficiencies of composite spheroidal grains for three axial ratios. Extinction curves are computed using the discrete dipole approximation (DDA). The model curves are subsequently compared with the average observed interstellar extinction curve and with an extinction curve derived from the IUE catalogue data.
It is highly unlikely that interstellar grains are spherical in shape or that they are homogeneous in composition and structure. Collected interplanetary particles are nonspher-ical and highly porous and composites of very small sub-grains glued together (Brownlee, 1987). The existence of interstellar polarization requires that interstellar grains must be nonspherical. The elemental abundances derived from observed interstellar extinction also do not favour a homogeneous composition of interstellar grains. There is no exact theory to study light scattering by inhomogeneous grains (viz. porous, fluffy and composite). We have used Discrete Dipole Approximation (DDA) to study the extinction properties of the composite grains. For a description of DDA, see Draine (1988). In the present study, we calculate the extinction efficiencies for composite oblate spheroidal grains, made up of the host silicate spheroid with embedded inclusions of graphite, in the wavelength region 3.4–0.10 µm. Using these extinction efficiencies of the composite grains with a power-law grain size distribution, we evaluate the interstellar extinction curve. We also estimate the cosmic abundances, viz. silicon and carbon, for the grain models which fit the observed interstellar extinction curve. It must be mentioned here that the composite oblate grain model presented in this study has also been used to interpret the observed IR emission from circumstellar dust (Vaidya and Gupta, 2011).
In Section 2, we give the validity criteria for the DDA and the composite oblate grain models. In Section 3, we present the results of our computations and discuss them. The main conclusions of our study are given in Section 4.
1.1 Composite grains and DDA
In the Discrete Dipole Approximation (DDA), a solid particle is replaced (approximated) by an array of N dipoles. When a grain is exposed to an electromagnetic wave, each dipole responds to the radiation field of the incident wave as well as to the fields of the other N — 1 dipoles that comprise the grain (Draine, 1988).
2.1 Extinction efficiency of composite grains
In the present paper, we study the extinction properties of spheroidal grains with three axial ratios (AR), viz. 1.33, 1.5 and 2.0, corresponding to grain models with N = 9640, 25896 and 14440 respectively, for three volume fractions of inclusions; viz. 10%, 20% and 30%, in the wavelength region 3.4–0.10 µm. Figures 1(a), (c) and (d) show the extinction efficiencies (Qext) for the composite grains with the host silicate spheroids containing N = 9640, 25896 and 14440 dipoles, corresponding to an axial ratio 1.33, 1.5 and 2.0, respectively, with a host composite grain size set to a = 0.01 µ. The three volume fractions, viz. 10%, 20% and 30%, of graphite inclusions are also listed in the top (a) panel and an additional volume fraction of 40% is also displayed. The extinction in the spectral region 0.28–0.20 µm is highlighted in panel (b) of this figure for composite grains having N = 9640.
2.2 Interstellar extinction curve
The interstellar extinction curve (i.e. the variation of extinction with wavelength) is usually expressed by the ratio E(λ — V)/E(B — V) versus 1/λ. We use the extinction efficiencies of the composite grains, with a power-law size distribution (i.e. n(a) ~ a−3.5) (Mathis et al., 1977), to evaluate the interstellar extinction curve in the wavelength region of 3.4–0.10 µm. In addition to the composite grains, a separate component of small graphite grains is required to produce the observed peak at 2175 Å in the interstellar extinction curve (Mathis, 1996). The stability of the bump at 2175 Å along all the lines of sight rules out the possibility of using just composite grains, made up of silicate with graphite as inclusions, to produce the bump (Iati et al., 2001).
The average observed interstellar extinction curve (Whittet, 2003) is then compared with the model curves formed from a χ2 minimized and best-fit linear combination of the composite and graphite grains (for details, see Vaidya and Gupta, 1999).
In Fig. 3(b), we have displayed the observed extinction curve in the direction of the star HD46202 (data taken from IUE database) and its best fitting with the model AR = 1.50 (N = 25896) and grain-size distribution of a = 0.001– 0.100 µ. We have selected this particular star with R v = 3.1, from our recent analysis of extinction curves towards the directions of 27 IUE stars (Katyal et al., 2011)
Recently, Iati et al. (2004), Zubko et al. (2004), Voshchinnikov et al. (2005) and Maron and Maron (2005) have also proposed composite grain models. Very recently, Voshchinnikov et al. (2006) have proposed composite porous grain models with three or more grain populations and have used both EMT-Mie type and layered sphere calculations.
2.3 Cosmic abundances
In addition to reproducing the interstellar extinction curve, any grain model must also be consistent with the abundance constraints. Snow and Witt (1995, 1996) have reviewed several models for the interstellar dust, which provide the data on the quantities of some elements that are required to reproduce the interstellar extinction. The number of atoms (in ppm) of the particular material tied up in grains can be estimated if the atomic mass of the element in the grain material and the density of the material are known (see, e.g., Cecchi-Pestellini et al. (1995) and Iati et al. (2001)). From the composite grain models we have proposed, we estimate C abundance i.e. C/H between ~165– 200 (including those atoms that produce the 2175 Å feature), which is considerably lower than what is predicted by bare silicate/graphite grain models (e.g. C/H ~ 254 ppm, Li and Draine, 2001) but it is still significantly above the ISM value of ~110 (Mathis, 2000); ~140 (Sofia and Meyer, 2001) and ~100 (Sofia and Parvathy, 2009). The estimated Si abundance from the composite grain model presented here is between 25 and 30, which is lower than the other grain models, 32 ppm (Li and Draine, 2001) and is consistent with the recent ISM value of 25 ppm derived by Voshchinnikov and Henning (2010). For appropriate references on abundance standards and related topics, see Snow (2000) and Draine (2003).
3. Summary and Conclusions
The extinction curves for the composite spheroidal grains show a shift in the central wavelength of the extinction peak as well as a variation in the width of the peak with a variation in the volume fraction of the graphite inclusions. These results clearly indicate that the shape, structure and inhomogeneity in the grains play an important role in producing the extinction. It must be noted here that large PAH molecules are also candidates for the carrier of the interstellar 2175 Å feature—a natural extension of the graphite hypothesis (Draine, 2003).
The extinction curves for composite spheroidal grains having an axial ratio not very large (AR ~ 1.33, N = 9640) and 10% volume fractions of graphite inclusions are found to fit the average observed interstellar extinction satisfactorily. Extinction curves with other composite grain models with N = 25896 and 14440 (i.e. with axial ratios of 1.50 and 2.00) deviate from the observed curves in the UV region, i.e. beyond about the wavelength 1500 Å . These results indicate that a third component of very small particles in the composite grains may help improve the fit in the UV region (see, e.g., Weingartner and Draine, 2001). It must be mentioned here that the composite spheroidal grain model with silicate and graphite as constituent materials proposed by us is not unique (see e.g. Zubko et al., 2004). We have also attempted to fit models to the specific direction of the star HD46202 in our galaxy and show that AR = 1.50 (N = 25896) fits better in this case. Analysis is in progress for many more such directions in the galaxy.
These results clearly show that the composite grain model is more efficient, compared to bare silicate/graphite grain models, in producing the extinction and it would perhaps help to reduce the cosmic abundance constraints. Composite grain models with silicate, graphite and an additional component (e.g. PAH’s) may further reduce the abundance constraints.
We have used the composite spheroidal grain model to fit the observed interstellar extinction and have derived the abundance of carbon (C/H) and silicon (Si/H). The IRAS observations have indicated the importance of IR emission as a constraint on interstellar dust models (Zubko et al., 2004). Recently, we have used the composite spheroidal grain model to fit the IR emission curves obtained from IRAS observations (Vaidya and Gupta, 2011).
The authors thank the anonymous referee and N. V. Voshchinikkov for their useful comments in improving the manuscript. DBV thanks the organizing committee of the AOGS-2010, for providing the opportunity to present this paper at a meeting at Hyderabad, India, in July 2010. The authors acknowledge the financial support from the ISRO-Respond project (NO. ISRO/RES/2/2007-08).
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