THE SUBMILLIMETER AND MILLIMETER EXCESS OF THE SMALL MAGELLANIC CLOUD: MAGNETIC DIPOLE EMISSION FROM MAGNETIC NANOPARTICLES?

Low-metallicity dwarf galaxies often exhibit surprisingly strong emission at submillimeter (submm) and millimeter (mm) wavelengths (e.g., Galliano et al. 2003, 2005; Galametz et al. 2009; Grossi et al. 2010; O'Halloran et al. 2010; Galametz et al. 2011), substantially exceeding what is expected based on the observed emission from dust at shorter wavelengths. This "submm excess" could in principle be due to a large mass of cold dust, but in some cases the implied dust masses are too large to be consistent with the observed gas mass and metallicity.

The Small Magellanic Cloud (SMC) is a prime example of this phenomenon. The dust spectral energy distribution (SED) has been measured from near-infrared through cm wavelengths. Israel et al. (2010), Bot et al. (2010), and Planck Collaboration et al. (2011b) conclude that conventional dust models cannot account for the observed 3 mm–600 μm (100 GHz–500 GHz) emission without invoking unphysically large amounts of very cold dust. Planck Collaboration et al. (2011b) further showed that the emission shortfall could not be accounted for by spinning dust.

Large submm excesses have also been reported for other low-metallicity dwarf galaxies. NGC 1705 has received particular attention (Galametz et al. 2009; O'Halloran et al. 2010; Galametz et al. 2011) and substantial excesses have also been reported for a number of other systems, including Haro 11, II Zw 40, and NGC 7674 (Galametz et al. 2011).

This excess emission challenges our understanding of interstellar dust. If the submm excess in low-metallicity dwarfs is due to thermal emission from dust, these galaxies either contain surprisingly large masses of very cold dust, or the dust opacity at submm frequencies must substantially exceed that of the dust in normal-metallicity galaxies, such as the Milky Way.

In the Galactic interstellar medium (ISM), typically 90% or more of the Fe is missing from the gas phase (Jenkins 2009), locked up in solid grains. Thus, Fe accounts for ∼25% of the dust mass in diffuse interstellar regions, although as yet we know little about the nature of the Fe-containing material. Interstellar dust models based on amorphous silicate and carbonaceous material (e.g., Mathis et al. 1977; Draine & Lee 1984; Weingartner & Draine 2001; Zubko et al. 2004; Draine & Li 2007; Draine & Fraisse 2009) often posit that the Fe missing from the gas is incorporated in amorphous silicate material, but it is entirely possible for much or most of the solid-phase Fe to be in the form of metallic Fe or certain Fe oxides, such as magnetite, that are spontaneously magnetized.

Draine & Lazarian (1999, hereafter DL99) noted that ferromagnetic or ferrimagnetic materials can have large opacities at microwave frequencies. Draine & Hensley (2012) recently re-estimated the absorption cross sections for nanoparticles of ferromagnetic or ferrimagnetic materials. They considered three naturally occurring magnetic materials—metallic iron, magnetite, and maghemite—and found that the magnetic response implies a large opacity at submm and mm wavelengths.

Here, we propose that magnetic nanoparticles may provide the 100–500 GHz opacity needed to account for the strong submm–microwave emission from the SMC. Upper limits on dust masses in the SMC are obtained in Section 2. The observed SED of the SMC, and the emission attributed to dust, is reviewed in Section 3, and in Section 4 we show that models with Milky Way dust opacities cannot reproduce the observed SED. The contribution of spinning dust is discussed in Section 5, where we show that spinning dust cannot account for the observed emission near ∼100 GHz. In Section 6, we consider dust models for the SMC that include maghemite, magnetite, and metallic iron grains. We find that the submm and mm excess in the SMC can be accounted for by a population of magnetic nanoparticles.

In Section 7, we discuss other evidence for the formation of Fe or Fe-oxide nanoparticles, and speculate on why the dust in low-metallicity galaxies such as the SMC differs from the dust in normal-metallicity spirals, such as the Galaxy. We also discuss the predicted polarization of the emission from the SMC. Our results are summarized in Section 8.

At a distance D  =  62 kpc (Szewczyk et al. 2009), the SMC provides an opportunity to study the dust in a low-metallicity dwarf galaxy. The present study will concentrate on the 238 radius (Ω = 0.00542 sr = 17.8  deg²) region (centered on $\alpha _{2000}=00^{\rm h}53^{\rm m}59\mbox{$.\!\!^{\mathrm s}$}6$, δ₂₀₀₀ = −72°40'161) studied by Planck Collaboration et al. (2011b). The 21 cm line flux from this region at SMC radial velocities is 2100 Jy MHz (mean line intensity 1318 K km s⁻¹ over the aperture; J.-P. Bernard 2012, private communication), corresponding to optically thin emission from $M({\rm H\,\mathsc{i}})=3.99\times 10^{8}\,M_{\odot }$. Stanimirovic et al. (1999) estimated that correction for self-absorption would raise the H i mass by 0.42 × 10⁸ M_☉ (for D = 62 kpc). Thus, we estimate $M({\rm H\,\mathsc{i}})=4.41\times 10^8\,M_{\odot }$ in the 0.00542 sr region. Leroy et al. (2007) find M(H₂) ≈ 0.32 × 10⁸ M_☉. Thus, we take M_H ≈ 4.73 × 10⁸ M_☉ (not including He) within the 0.00542 sr aperture.

Elemental abundances in the SMC are uncertain. Russell & Dopita (1992) estimated (Fe/H)_SMC = 0.25(Fe/H)_☉, while Kurt & Dufour (1998) estimated (O/H)_SMC = 0.2(O/H)_☉. Rolleston et al. (2003) measured the abundances in a main-sequence B star, and found (O/H) = 0.6(O/H)_☉ and (Fe/H) = 0.3(Fe/H)_☉. Lee et al. (2005) measured abundances in three B-type supergiants in the SMC wing, finding (Mg/H)  ≈  0.1(Mg/H)_☉ and (Si/H) ≈ 0.2(Si/H)_☉. Here, we adopt an overall metallicity Z_SMC ≈ 0.25 Z_☉.

An upper limit on the dust mass in the SMC is obtained from the observed gas mass combined with the estimated abundances of elements that could form dust grains. The gas in diffuse H i and H₂ in the local ISM is routinely strongly depleted in elements such as Fe and Si, with the missing material presumed to be in the form of dust. An inventory of the well-studied sightline toward ζOph allows one to estimate the dust/gas mass ratio based on the amount of C, O, Mg, Si, Fe, and other elements that are missing from the gas (Draine 2011, Table 23.1).¹ If we assume the relative abundances of heavy elements in a galaxy to be similar to solar composition (Asplund et al. 2009), then

$$\begin{eqnarray} M_{\rm dust}/M_{\rm H}&\le & 0.0091 (Z/Z_\odot) \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} M_{\rm Fe,dust}/M_{\rm H}&\le & 0.00196 (Z/Z_\odot), \end{eqnarray} \tag{ 2 }$$

where M_{Fe, dust} is the mass of Fe contained in solid material, including ferromagnesian silicates, Fe oxides, and metallic Fe. The mass of Fe in magnetic materials obviously is limited by M_{Fe, dust}. The resulting upper limits on M_dust and Fe in magnetic form are given in the first line of Table 1.

Figure 1 shows the observed global SED of the SMC, after removal of smooth foregrounds and backgrounds, from the following compilations.

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Haynes et al. (1991) reported global flux densities measured with the Parkes 64 m telescope at 1.4, 2.45 GHz, 4.75, and 8.55 GHz; the 1.4 GHz flux density is a revision of the result of Loiseau et al. (1987). Mountfort et al. (1987) measured the 2.3 GHz flux density with the Hartebeesthoeck 26 m telescope.

The TopHat balloon experiment (Aguirre et al. 2003) measured the flux in four bands (245–630 GHz) in a 240 radius region (Ω = 0.00544 sr) centered on the SMC. Foreground removal was done by subtracting the mean brightness of adjacent off-source regions. Aguirre et al. (2003) also extracted 100, 140, and 240 μm fluxes for COBE-DIRBE (Silverberg et al. 1993).

Israel et al. (2010) extracted fluxes for a 240 radius region (Ω = 0.00544 sr) centered on the SMC. We show their extractions for the 10 COBE-DIRBE bands (1.27 μm to 248 μm).

Gordon et al. (2011) extracted fluxes for a 225 radius region (Ω = 0.00484 sr) centered on the SMC, measured using the IRAC (Fazio et al. 2004) and MIPS (Rieke et al. 2004) cameras on the Spitzer Space Telescope (Werner et al. 2004). Foreground removal consisted of subtracting the mean brightness of an annulus extending from 23 to 25.

Planck Collaboration et al. (2011b) extracted fluxes for a 238 radius region (Ω = 0.00542 sr) centered on the SMC. Foreground subtraction consisted of subtracting the mean brightness of a 1° annulus around the extraction region. We include their extractions for Planck (nine bands, 30–858 GHz; Planck Collaboration et al. 2011a), WMAP (five bands, 23–94 GHz; Bennett et al. 2003), and IRAS (four bands, 12–100 μm; Miville-Deschênes & Lagache 2005). Planck Collaboration et al. (2011b) further corrected the foreground removal by taking into consideration the difference in N(H i) at Galactic radial velocities between the background annulus and the extraction aperture.²

Figure 1(a) shows the spectrum of the 0.00542 sr region centered on the SMC. We assume that the differences in coverage (Ω ranging from 0.00484 sr to 0.00544 sr) are unimportant, as most of the flux will come from the central regions. Planck Collaboration et al. (2011b) estimate that cosmic microwave background (CMB) fluctuations add emission corresponding to a mean CMB temperature excess 〈ΔT_CMB〉 = 58 μK over the 0.00542 sr extraction region (relative to the background annulus). The spectrum of this CMB excess

$$\begin{equation} (\Delta {\rm CMB})_\nu = \Omega \langle \Delta T_{\rm CMB}\rangle \frac{\partial B_\nu }{\partial T} \bigg |_{T=2.726\,{\rm K}} \end{equation} \tag{ 3 }$$

is plotted in Figure 1(a).

To isolate the emission from the dust, it is necessary to subtract free–free and synchrotron emission. We find the observations to be consistent with synchrotron and free–free spectra

$$\begin{eqnarray} F_\nu ^{\rm synch} &\approx & 36. \left(\frac{\nu }{\,{\rm GHz}}\right)^{-1.0}\,{\rm Jy} \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} F_\nu ^{\rm ff} &\approx & 11.0 \frac{g_{\rm ff}(\nu,T)}{g_{\rm ff}(10\,{\rm GHz},T)}e^{-h(\nu -10\,{\rm GHz})/kT} \,{\rm Jy} \end{eqnarray} \tag{ 5 }$$

with T = 10⁴ K. Our estimate for F^ff_ν(10 GHz) is intermediate between the 13.4 Jy estimate of Israel et al. (2010) and the 9.05 Jy estimate of Planck Collaboration et al. (2011b). Our estimates for F^ff_ν and F^synch_ν are shown in Figure 1(a). The Gaunt factor g_ff(ν, T) is obtained from Equation (10.9) of Draine (2011). For n(He⁺)/n(H⁺) = 1.08 and T = 10⁴ K, this corresponds to ∫n_en(H⁺)dV = 1.45 × 10⁶⁴ cm⁻³ and an H photoionization rate Q₀ = 3.7 × 10⁵¹ s⁻¹.

The residual after subtraction of (ΔCMB)_ν, F^ff_ν, and F^synch_ν is shown in Figure 1(b). This residual is presumed to be emission from dust and (at short wavelengths) stars. A smooth curve has been drawn through the points to guide the eye. Subtracting an estimate for the starlight continuum as in Figure 1(b), the integrated λ > 5 μm dust luminosity of the SMC is L_d(λ > 5 μm) = 1.00 × 10⁸(D/62 kpc)² L_☉.

The observed infrared and submm emission from normal-metallicity star-forming spiral galaxies appears to be consistent with physical dust models that were developed to reproduce the observed properties of dust in the diffuse ISM of the local Milky Way, including wavelength-dependent extinction and infrared emission (e.g., Weingartner & Draine 2001; Li & Draine 2001; Zubko et al. 2004; Draine & Li 2007; Draine & Fraisse 2009; Compiegne et al. 2011). The models of Draine & Li (2007, henceforth DL07) consist of amorphous silicate grains plus carbonaceous grains; the carbonaceous grains have the physical properties of graphite when large, and the properties of polycyclic aromatic hydrocarbons (PAHs) when very small. This dust model was able to reproduce the global SEDs of the galaxies in the SINGS sample (Draine et al. 2007), including 17 galaxies with 850 μm SCUBA photometry. More recently, the same model has been found to be consistent with both global and spatially resolved SEDs of normal-metallicity (i.e., 0.5 ≲ Z/Z_☉ ≲ 2) galaxies in the KINGFISH sample (Aniano et al. 2012; G. Aniano et al. 2012, in preparation), including photometry out to 500 μm.

The DL07 dust model is able to reproduce the observed emission from dust in the diffuse ISM of the Galaxy (Finkbeiner et al. 1999) out to wavelengths as long as 2 mm (see Figure 14(a) of Draine & Li 2007). However, a significant emission excess (relative to the model) appears at λ > 3 mm (ν < 100 GHz); this "anomalous microwave emission" (AME) has been confirmed by numerous observations (Planck Collaboration et al. 2011c and references therein). The AME in the Galaxy is thought to be mainly rotational emission from the PAH population (Draine & Lazarian 1998a, 1998b).

DL07 propose that the 3 μm < λ < 3 mm SEDs of entire galaxies, or large regions within a galaxy, can be fit using a dust model consisting of amorphous silicates, graphitic grains, and PAHs, and assuming that the dust heating rate is distributed according to

$$\begin{eqnarray} \frac{dM_d}{dU} &=& (1-\gamma)M_{d,\rm tot} \delta (U-U_{\rm min})\nonumber\\ &&+ \gamma M_{d,\rm tot}\frac{(\alpha -1)U^{-\alpha }}{U_{\rm min}^{1-\alpha }-U_{\rm max}^{1-\alpha }}\; {\rm for}\; U_{\rm min}\le U\le U_{\rm max},\nonumber\\ \end{eqnarray} \tag{ 6 }$$

where U is the ratio of the local dust heating rate to the heating rate produced by the solar-neighborhood starlight radiation field, M_d(U) is the mass of amorphous silicate plus carbonaceous dust with heating rates <U, and M_{d, tot} is the total dust mass. Equation (6) is a very simple distribution function, with only five parameters (M_{d, tot}, U_min, U_max, α, γ), but studies of dust emission using this distribution function for the grain heating have been successful in reproducing the global emission from galaxies, as well as the emission from ∼500 pc regions within galaxies (e.g., Aniano et al. 2012). The DL07 models are also characterized by the PAH abundance parameter q_PAH = the fraction of the dust mass contributed by PAH particles containing <10³ C atoms.

We vary five parameters—the total dust mass M_{d, tot}, the PAH abundance parameter q_PAH, and the starlight heating parameters U_min, α, and γ; U_max = 10⁷ is kept fixed. Because we do not include a realistic model for the starlight contribution to the SED, the model is fit only to data at λ > 3 μm, where reddening by dust should be minimal. Because the emission at λ ≳ 3 mm (ν ≲ 100 GHz) may include a substantial contribution from "spinning dust," the DL07 model + starlight is fit only to λ < 2 mm data.

If we allow U_min to be as low as 0.2, we obtain Model 1, shown in Figure 2. This model has a total dust mass M_{d, tot} = 1.3 × 10⁶ M_☉, exceeding the upper limit of 1.1 × 10⁶ M_☉ (see Table 1). Despite using more dust than is allowed, Model 1 provides insufficient emission at λ > 2 mm.

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Because Model 1 violates the dust abundance limit, we try fitting the DL07 model to the same data, but now limiting U_min ⩾ 0.4. The resulting Model 2 has a total dust mass that does not violate the upper limit in Table 1, but the quality of the fit to the SED is somewhat worse than for Model 1, with an even larger deficiency at λ > 2 mm (see Figure 2(b)).

We can add a spinning dust component to raise the emission in the 20–60 GHz range. The spinning dust emission in the diffuse ISM of the Galaxy peaks near 30 GHz. What is expected for spinning dust in the SMC?

The anomalous microwave emission in the Galaxy is thought to be dominated by spinning dust, with the emission coming primarily from the smallest PAHs in the size distribution, as these are the only ones that spin as fast as ∼30 GHz in the diffuse ISM (CNM, WNM, or diffuse WIM). The small-size end of the size distribution is thought to be determined by the size below which nanoparticles (molecules) would be destroyed by the interstellar hν < 13.6 eV UV background, ∼25 C atoms (Allamandola et al. 1989; Guhathakurta & Draine 1989). The threshold for grain survival is relatively insensitive to modest variations in the UV spectrum and intensity, hence we expect the lower size cutoff in the SMC to be similar to that in the Galaxy. The 5–18 μm spectrum of PAH emission from the SMC (Sandstrom et al. 2010) is broadly similar to that in normal star-forming galaxies in the SINGS sample (Smith et al. 2007), aside from an overall weakening due to lower PAH abundance, but the band ratios suggest a shift to smaller sizes (Sandstrom et al. 2012).

Thus, we expect the spinning dust emission from the SMC to be similar to that in the Galaxy, with the strength scaled down in proportion to the inferred PAH abundance. A slight shift to higher frequencies seems possible.

Draine & Lazarian (1998a, 1998b) argued that the anomalous microwave emission in the Galaxy, with an observed emissivity per H nucleon [j^(sd)_ν(30 GHz)/n_H]_MW ≈ 1 × 10⁻¹⁷ Jy sr⁻¹ cm² H⁻¹, is primarily rotational emission from the PAH population. The PAH abundance is measured by q_PAH, the fraction of the total dust mass contributed by PAHs with <10³ C atoms. Dust in the solar neighborhood is thought to have q_PAH ≈ 4.6%. Li & Draine (2002) found that q_PAH in the SMC was spatially variable and, on average, much lower than in the Milky Way. Sandstrom et al. (2010) confirmed this, finding a mean 〈q_PAH〉 ≈ 0.6%. We expect the dust/gas ratio in the SMC to be lower by about a factor ∼Z_SMC/Z_☉ ≈ 0.25. Therefore, the PAH abundance per H is down by about a factor ∼(0.6/4.6) × 0.25 = 0.033. Thus, we estimate the spinning dust emission in the SMC to be

$$\begin{eqnarray} \nonumber \left[\frac{j_\nu ^{\rm (sd)}(30\,{\rm GHz})}{n_{\rm H}}\right]_{\rm SMC} &\approx & 0.033\times 1\times 10^{-17}\,{\rm Jy}\,{\rm sr}^{-1}\,{\rm cm}^2\,{\rm H}^{-1} \\ &\approx & 3.3\times 10^{-19}\,{\rm Jy}\,{\rm sr}^{-1}\,{\rm cm}^2\,{\rm H}^{-1} \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} \Delta F_\nu ^{\rm (sd)}(30\,{\rm GHz})&\approx & \left[\frac{j_\nu ^{\rm (sd)}(30\,{\rm GHz})}{n_{\rm H}}\right]_{\rm SMC}\times \frac{M_{\rm H}}{m_{\rm H}}D^{-2} \approx 5\,{\rm Jy}.\nonumber\\ \end{eqnarray} \tag{ 8 }$$

In Figure 2, we have added an emission component with a spectrum³

$$\begin{equation} \Delta F_\nu ^{\rm (sd)} = \Delta F_\nu ^{\rm (sd)}(\nu _0) \left(\frac{\nu }{\nu _0}\right)^2 \exp [1-(\nu /\nu _0)^2] \end{equation} \tag{ 9 }$$

representative of what is expected for spinning dust. The SMC SED suggests that the spinning dust peak may be near ∼40 GHz. If we set ν₀ = 40 GHz and ΔF^(sd)_ν(40 GHz) = 5 Jy—consistent with the estimate in Equation (8)—the 20–50 GHz observations are accounted for, as seen in Figure 2.

While spinning dust appears able to account for the observed 20–50 GHz emission, the emission between 50 and 300 GHz remains much stronger than expected. Bot et al. (2010) suggest that the 50–300 GHz excess could also be due to spinning dust emission. However, theoretical models of rotational emission from small grains (Draine & Lazarian 1998b; Ali-Haïmoud et al. 2009; Hoang et al. 2010, 2011; Silsbee et al. 2011) predict little rotational emission above ∼100 GHz unless high densities and warm gas temperatures are present in the emitting regions. For example, Draine & Lazarian (1998b, see Figure 13) calculated the spinning dust emission from a model photodissociation region (PDR) with n_H = 10⁵ cm⁻³, T = 300 K, illuminated by a radiation field U ≈ 3000. The PDR was assumed to have abundances of small grains relative to big grains reduced by a factor of five relative to diffuse clouds in the solar neighborhood, approximating the observed reduction in q_PAH in the SMC. Viewed face-on, the total IR luminosity/area L_TIR/A ≈ 3.6 × 10⁻³U erg cm⁻² s⁻¹ = 11 erg  cm⁻² s⁻¹. The spinning dust emission for this model peaked near 110 GHz, with (νL^(sd)_ν)_100 GHz/A = 7.4 × 10⁻⁷ erg cm⁻² s⁻¹. Thus, L_TIR/(νL^(sd)_ν)_100 GHz ≈ 1.5 × 10⁷.

At 100 GHz, the model in Figure 2(b) has a deficit ΔF_ν ≈ 25 Jy, corresponding to (νΔL_ν)_100 GHz = 4πD²(νΔF_ν)_100 GHz = 3000 L_☉. To account for this would require PDRs with a luminosity L_IR = 4.5 × 10¹⁰ L_☉—completely inconsistent with the observed L_TIR = 1 × 10⁸ L_☉. We therefore conclude, in agreement with Planck Collaboration et al. (2011b), that spinning dust cannot account for the observed 50–200 GHz emission in the SMC. Here, we consider magnetic dust grains as an alternative.

Because magnetic materials have enhanced absorption at microwave and submm frequencies, it is of interest to see whether the mm- and cm-excess seen in the SMC could be due in part to thermal emission from magnetic grain materials. In Figures 3 and 4, we model the observed emission from the SMC as the sum of three components: "normal" dust (the amorphous silicate, graphite, and PAH model of DL07), a population of magnetic grains, and spinning dust. In each case, the spinning dust contribution is assumed to peak at 40 GHz, with the peak flux density adjusted to fit the observations in Figure 1(a), giving a reasonably good fit in the 20–60 GHz region.

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Metallic iron nanoparticles are introduced in Figure 3. We consider Fe grain temperatures of 40 K (Figure 3(a)) and 20 K (Figure 3(b)). If the Fe nanoparticles are, for the most part, free-fliers heated by typical starlight, then T ≈ 40 K is expected (see Figure 4 of Draine & Hensley 2012). If, on the other hand, the Fe nanoparticles are inclusions in larger composite grains, then the T ≈ 20 K temperature is appropriate, consistent with the temperature of the "normal" dust. In each case, the Fe grain abundance is adjusted to reproduce most of the observed emission near 100 GHz, then a model using DL07 dust is used to provide the additional emission required to reproduce the observed SED at shorter wavelengths, and finally a spinning dust component peaking at 40 GHz is added to bring the model into agreement with the 20–50 GHz observations.

We also consider nanoparticles of maghemite (Figure 4(a)) and magnetite (Figure 4(b)). For these, we assumed temperatures T ≈ 17 K consistent with being inclusions within nonmagnetic dust grains.

The model with maghemite (Figure 4(a)) has M_Fe = 2.2 × 10⁵ M_☉ of Fe in maghemite (total maghemite mass 3.1 × 10⁵ M_☉) and the model with magnetite (Figure 4(b)) has M_Fe = 2.2 × 10⁵ M_☉ of Fe in magnetite (total magnetite mass 3.0 × 10⁵ M_☉). The Fe mass, and total dust mass, does not violate the mass budget (see Table 1). We conclude that the observed mm-wave emission from the SMC can be accounted for by models with reasonable abundances of normal dust plus metallic Fe, maghemite, magnetite, or some combination of these three materials.

If the nanoparticles are present as inclusions in larger grains, then it is clear that the size distribution of the larger particles can be adjusted to be compatible with the observed wavelength-dependent extinction in the SMC. But is it possible for the bulk of the interstellar Fe to be in free-flying nanoparticles? We have calculated the extinction contribution in the optical and UV, assuming that 100% of the Fe is in particles of a single type, and using dielectric functions for Fe, Fe₃O₄, and γ-Fe₂O₃ from Draine & Hensley (2012). Figure 5 shows the calculated extinction per H, together with the observed extinction in the SMC Bar (Gordon et al. 2003). In no case does the calculated extinction/H exceed the observed extinction. Therefore, the observed extinction is not incompatible with the possibility that much of the Fe is in free-flying nanoparticles.

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Nevertheless, we consider it most likely that the bulk of the magnetic nanoparticles would be present as inclusions in larger grains, since we know that most of the grain mass is in grains with radii a ≳ 0.1 μm

7.1. Alternative Models

7.2. Solid-phase Iron in Low-metallicity Galaxies

7.3. High-frequency Magnetism and the Gilbert Equation

7.4. Polarization

The principal conclusions of this paper are as follows:

• 1.  
  We show (see Figures 3 and 4) that the SED of the SMC can be approximately reproduced by a mixture of "normal" dust (illuminated by a plausible range of radiation intensities) plus emission from a population of small (a ≲ 0.01 μm) magnetic nanoparticles. We consider three magnetic materials: metallic Fe, magnetite Fe₃O₄, and maghemite γ-Fe₂O₃. It appears that any of these three materials, or a combination of them, can provide enough emission at λ > 1 mm so that a combination of "normal dust," spinning dust, and magnetic dust can account for the observed SED of the SMC.
• 2.  
  If conditions in the SMC are conducive to a large fraction of the interstellar Fe being in magnetic nanoparticles, other low-metallicity galaxies may also have mm-wave emission dominated by magnetic dipole emission.
• 3.  
  While it seems natural for the magnetic nanoparticles to be inclusions in larger grains, the observed extinction does not rule out the possibility that the magnetic nanoparticles might be independent free-fliers.
• 4.  
  If the magnetic nanoparticles are present as randomly oriented inclusions in larger silicate grains, then the polarization is expected to fall as the frequency decreases below ∼200 GHz. It may be possible to test this prediction with measurements by Planck of the polarized emission from the SMC.
• 5.  
  Our models are based on high-frequency magnetic properties as estimated by Draine & Hensley (2012) using the Gilbert equation. Laboratory studies of the high-frequency (ν ≳ 100 GHz) magnetic properties of metallic Fe and Fe oxides are needed to improve our understanding of magnetism at high frequencies.

We thank J.-P. Bernard, K. Gordon, F. P. Israel, S. Stanimirovic, and G.W. Wilson for helpful discussions regarding the SMC. We thank the referee, Caroline Bot, for valuable comments that led to improvements in the manuscript. This research made use of NASA's Astrophysics Data System Service, and was supported in part by the NSF grant AST 1008570. B.H. acknowledges support from an NSF Graduate Research Fellowship under grant No. DGE-0646086.