Hydrogenated fulleranes and the anomalous microwave emission of the dark cloud LDN 1622

Abstract

We study the rotation rates and electric dipole emission of hydrogenated icosahedral fullerenes under the physical conditions of the dark cloud (DC) LDN 1622. The abundance of fullerenes is estimated by fitting theoretical photoabsorption spectra to the characteristics of the ultraviolet (UV) bump extinction in DCs. The UV bump appears to be well reproduced by a mixture of fullerenes following a size-distribution power law, which gives progressively lower abundances as the radius of the fullerene increases. We infer abundances of the order of 0.2 × 10⁻⁶n(H ₂) for C₆₀. A significant fraction of these molecules are expected to be hydrogenated. We compute the electric dipole rotational emission from these fullerene hydrides, taking into account rotational excitation and damping processes. The recent detection of anomalous microwave emission (5–60 GHz) in LDN 1622 by Casassus et al. can be explained as the result of electric dipole radiation from hydrogenated fullerenes. The bulk of the emission (10–30 GHz) appears to be associated with 60–80 carbon atom fulleranes with a degree of hydrogenation of C:H ≈ 3:1. A small contribution (∼10 per cent) of these molecules residing in the surrounding cold neutral medium and/or photodissociation region of the cloud is required to fit the high-frequency tail (40–60 GHz) of the emission.

astrochemistry, ISM: clouds, dust, extinction, ISM: molecules

1 INTRODUCTION

Statistical evidence for dust-correlated microwave emission at high galactic latitudes supports the existence of a new continuum emission mechanism in the diffuse interstellar medium (ISM) at 10–60 GHz (Kogut et al. 1996; Leitch et al. 1997; de Oliveira-Costa et al. 1999, 2002, 2004; Finkbeiner et al. 2002; Fernández-Cerezo et al. 2006). This foreground would add to the classical components of free–free emission (thermal bremsstrahlung) and synchrotron emission. Tentative evidence for ‘anomalous’ microwave emission in astronomical objects has been found by Finkbeiner et al. (2002) and Casassus et al. (2004). Unambiguous evidence for this new emission mechanism is provided by recent observations in the Perseus molecular complex (Watson et al. 2005) and in the dark cloud (DC) LDN 1622 (Casassus et al. 2006). Electric dipole radiation from small, rapidly spinning carbon-based particles (Draine & Lazarian 1998a,b) and magnetic dipole emission due to thermal fluctuations in the magnetization of magnetic grains (Draine & Lazarian 1999) have been suggested as possible mechanisms for this new continuum emission. The characteristics of the emitting particles in the Draine & Lazarian models are very general, so it is important to investigate whether the anomalous microwave emission can be explained by a minimum number of hypotheses concerning the nature of these particles. Iglesias-Groth (2005) has shown that electric dipole rotational emission of hydrogenated icosahedral fullerenes can explain the anomalous microwave emission in the Perseus molecular complex. The new detection in the DC LDN 1622 opens up the possibility of gaining further insight into the nature of the emitting particles.

The molecular cloud LDN 1622 is an example of a bright-rimmed star-forming cloud at a distance of ∼120 pc (Wilson et al. 2005) in the line of sight of the Orion B cloud. Its apparent linear size is slightly less than 1 pc. The density of molecular hydrogen is estimated in the range 10³–10⁴ cm⁻³ (Lee, Myers & Tafalla 2001). The contribution of the free–free emission or dust thermal emission is less than a few per cent of the observed emission at microwave frequencies (Casassus et al. 2006), making the cloud a specially favourable laboratory to study the characteristics of the carrier for the anomalous emission.

The presence of fullerenes in the ISM has been a subject of debate since their discovery (Kroto et al. 1985). Because fullerenes are very stable against intense radiation and can form spontaneously together with carbon dust, it is expected that they (and their complex analogues) may exist in significant amounts in the ISM, in carbon-rich objects and in the circumstellar envelopes of certain cool giants (Kroto & Jura 1992). While the existence of fullerenes in these environments has not been proved yet (e.g. Herbig 2000), detection of C₆₀₋₄₀₀ in meteorites provides a strong argument in favour of their presence in the ISM (Becker, McDonald & Bada 1993; Becker et al. 1994; Becker & Bunch 1997; Pizzarello et al. 2001). More recently, Iglesias-Groth (2004) has shown the potential of fullerenes as carriers of the 2175-Å bump and diffuse interstellar bands (DIBs). If these particles are a major contributor to the ultraviolet (UV) bump absorption, they would be ubiquitous in the various phases of the ISM, locking a significant amount of interstellar carbon. In particular, fullerenes could be present in molecular clouds such as LDN 1622 where the high densities would naturally lead to the formation of hydrogenated fullerenes (Petrie & Bohme 1994; Bettens & Herbst 1997), hereafter fulleranes. These hydrogenated forms of fullerenes are also potential carriers of DIBs (Webster 1991, 1992, 1993a). The slight polar nature of the C–H bond (0.3 D) may be sufficient for fullerenes with a modest level of hydrogenation to be effective electric dipole emitters (Iglesias-Groth 2005). In this paper, we investigate whether fulleranes could explain the anomalous microwave emission detected in the DC LDN 1622 and which among these molecules may cause the bulk of the emission.

1.1 Microwave observations of LDN 1622

The DC LDN 1622 is listed by Lee et al. (2001) and Park, Lee & Myers (2004) as a starless core. It probably acts as a foreground object absorbing diffuse emission from the most distant Orion–Eridanus complex. There is no H ii region associated with this cloud. Casassus et al. (2006) estimated that the contribution of free–free processes to the continuum emission at 30 GHz observed by the Cosmic Background Imager (CBI) is less than a few per cent. The contribution expected from thermal dust emission is also very low. This is calculated assuming a modified blackbody at 15 K with a 1.7 emissivity index, which agrees well with the Wilkinson Microwave Anisotropy Probe (WMAP) measurements at 90 GHz. The bulk of the emission measured by the CBI and WMAP in the range 20–50 GHz cannot therefore be explained by these traditional emission processes. Examination of radio-source catalogues also rules out significant contamination by any extragalactic radio source. The microwave emission of LDN 1622 is highly correlated with far-infrared (far-IR) emission in IRAS maps; thus, it is related in some way to dust. Casassus et al. noted that the 31-GHz morphology is much more similar to that in the 12-μm IRAS band than to other longer-wavelength IRAS bands, claiming that the microwave emission could possibly be related to very small grains (the most likely carrier of the mid-IR emission).

2 BASIC PROPERTIES OF fulleranes

Icosahedral fullerenes with N= 60, 80, 140, 180, 240, 320, 500, 540, 960, 1500 and 2160 carbon atoms are very stable particles that could survive for a long time in the conditions of dense clouds (Petrie, Javahery & Bohme 1993). Given their masses, relatively small radii (in the range 3.55–21.3 Å) and the physical conditions of dense clouds (T∼ 10 K), these particles are likely to spin with rates similar to those required to explain the anomalous emission via electric dipole radiation. The large symmetry of the fullerene molecules makes any significant permanent dipole unlikely, but a relatively low level of hydrogenation could lead to a weak permanent dipole moment. At most, one hydrogen atom may be bound to each of the carbon atoms of a fullerene; thus, the number, P, of hydrogen atoms of any fullerene considered here will lie in the range P= 1 to N. The hydrogen atoms of the fulleranes are expected to be located radially outward from the carbon atoms. The length of the C–H bond will be taken as in benzene, 1.07 Å (see, e.g. Braga et al. 1991). The radius of a fullerene with P hydrogen atoms will be adopted as the radius of a sphere with volume equal to the sum of the volumes of the corresponding fullerenes and P times half the volume of a sphere with diameter the length of the C–H bond. As an example, the effective radius adopted for the C₆₀H₂₀ molecule is 3.8 Å, while the radius of the C₆₀ molecule is 3.55 Å.

Given the absence of laboratory measurements of the dipole moment of hydrogenated fullerenes, we will assume here (as in Iglesias-Groth 2005) that the dipole moment is proportional to the dipole moment of the C–H bond (κ0.3D), and that the hydrogen atoms are randomly distributed on the surface of the cage in such a way that the intrinsic dipole moment of the fullerene with P hydrogen atoms can be approximated by μ∼κ 0.3P^1/2. We adopt a value κ= 1 in the calculations. Typical hydrogenation ratios s=P/N will be in the range 1/10–1/3. In the case of C₆₀, these hydrogenation ratios correspond to modest dipole moments of 0.73 and 1.34D, respectively, and for C₂₁₆₀, the largest fullerene considered in this study, 4.4 and 8D, respectively.

2.1 Moments of inertia

For fulleranes with P hydrogen atoms, we adopt as moment of inertia the sum of the moment of inertia of the relevant fullerene considered as a spherical cage of radius R, I_C= 2/3M R² (where M=N m_C and m_C is the mass of the carbon atom), and the moment of inertia of a hypothetical spherical cage of mass P times the mass of the hydrogen atom, and radius R=R${}_{\text{C}{}_{\text{N}}}$+ 1.07Å.

3 CHEMICAL EQUILIBRIUM AND FULLERENE ABUNDANCES

The chemical equilibrium of the archetypical fullerene, C₆₀, has been extensively studied in dense clouds (Millar 1992; Petrie et al. 1993; Petrie & Bohme 1994, 2000). There is general agreement that positive ions of this fullerene are at least three orders of magnitude less abundant than the neutral species, while the abundance of negative ions (C⁻₆₀) appears to be more significant (5 per cent of the abundance of the neutral species according to Millar). fullerenes become negatively charged because of the dominance of electron collisions, but the efficient attachment of a free electron at the cloud temperature is a major source of uncertainty (Petrie & Bohme 2000). Recent studies of the temperature dependence of the reaction appear to indicate an activation energy (Jaffke et al. 1994) that would effectively inhibit the formation of C⁻₆₀ and lead to even lower values of the negative ion in dense clouds. We note, however, that there is a lack of information on the activation energies for this reaction in larger fullerenes, and that the values could vary significantly from one fullerene to another. For instance Spanel & Smith (1994) observed a very small barrier for electron capture of the C₇₀. In our study, we will consider the abundances of the negative ions of fulleranes to be in the range 1–5 per cent of the neutral species independent of the size of the molecule.

The ions of hydrogenated fullerenes C⁺_NH_P, C⁻_NH_P, and the C_NH⁺_P molecule, where a proton has been adsorbed instead of a neutal hydrogen atom, will have negligible abundances in dense clouds. Thus, even if they could have higher dipole moment (particularly C_NH⁺_P) than the corresponding neutral C_NH_P molecule, their low abundance makes a significant contribution to the total electric dipole emission unlikely.

The abundance of fullerenes in DCs is unknown but could be estimated on the assumption that these molecules were responsible for the UV bump in the extinction curve. For DCs, extinction curves have been reported with values of the ratio of total to selective extinction R_V=A_V/E(B−V) in the range 4–6 (e.g. Vrba, Coyne & Tapia 1993; Strafella et al. 2001), significantly higher than the well-established value of 3.1 for the diffuse ISM. Typical extinction curves for various values of the R_V parameter can be found in Fitzpatrick (1999). For LDN 1622, we adopt the extinction curve corresponding to R_V= 5.5 (plotted in Fig. 1) and investigate which mixture of fullerenes (single and multishell) better reproduces the shape, position, and width of the UV bump in a similar manner to Iglesias-Groth (2004). We have considered different power-law size distributions and found N(R) ∝ (R/R₀)^−1.5 (where R₀ is the radius of the C₆₀) suitably describes the UV bump. It is interesting to compare the value of the index with that inferred by Iglesias-Groth (2004) for diffuse interstellar clouds. The smaller absolute value of the index in DCs implies a major role for large fullerenes with respect to the diffuse ISM, consistent with the general view that the higher R_V values observed in dense molecular clouds are most likely to represent the growth of dust grains (e.g. Mathis 1990). From the fit to the UV bump we obtain a fractional abundance with respect to H₂ of 0.18 × 10⁻⁶ for C₆₀, which is in our scheme the most abundant fullerene.We have taken into account the possible contribution of silicates to the fit. According to the above size-distribution power law, progressively lower values are derived for larger fullerenes. For instance, the fractional abundance estimated for C₁₈₀ is 0.08 × 10⁻⁶.

Figure 1

UV bump extinction of a DC with R_V= 5.5 (solid line) according to Fitzpatrick (1999). Predicted photoabsorption spectra of mixtures of fullerenes and buckyonions for a size-distribution power law of indices m=−1.5 (dashed line) and m=−2.5 (dotted line).

Comprehensive models of the formation of large hydrocarbons and carbon clusters in dense interstellar clouds, considering networks with hundreds of chemical reactions and species lead to abundance values of C₆₀ similar to what we infer from the UV bump (Bettens & Herbst 1997). These models, however, do not incorporate molecules as large as those considered here and therefore cannot verify the adequacy of the abundances derived above for larger fullerenes. As noted by these authors, it is very likely that some hydrogenation of fullerenes occurs in dense clouds. We will assume in what follows that a significant fraction of fullerenes in the DC LDN 1622 are partially hydrogenated. Hydrogenation ratios as high as s= 1/3 (where s is the ratio of the number of hydrogen to carbon atoms in the molecule) are not rare among other carbon-based molecules, for example, polycyclic aromatic hydrocarbons (PAHs), and, as discussed by Webster (1992, 1993a, b), may be rather common in fulleranes. In the following sections, we calculate the rotation rates and electric dipole emissivity of fulleranes, C_NH_P, for the physical conditions of LDN 1622, considering this as a typical DC. We assume the gas kinetic temperature and the dust temperature of the cloud to be T= 15 K. We adopt a central column density N_H= 2.4 × 10²² cm⁻² (Finkbeiner et al. 2002) and a hydrogen density n(H) = 10⁴ cm⁻³ which would be mostly (99.9 per cent) in molecular form. The abundance of metal species and free protons will be taken n(M⁺)/n(H) = 10⁻⁶ and n(H⁺)/n(H) = 0, respectively.

4 ROTATION RATES

In thermal equilibrium, fulleranes share the same temperature as the gas and would have an rms rotation frequency,

1

Assuming a cloud temperature of 15 K, we obtain the effective rotation rates ω_rad= (5/3)^0.25〈ω²〉^0.5 plotted in Fig. 2 for fulleranes with a degree of hydrogenation s= 1/3 and s= 1/N. Interactions with gas and associated plasma and IR and radio-emission processes will affect the rotation rate of fulleranes. Some processes will produce rotational damping and others will lead to rotational excitation. To study these effects we follow the formalism developed by Draine & Lazarian (1998a,b). These authors comprehensively discuss the various types of processes that produce rotational damping and/or rotational excitation of molecules in different environments of the ISM. Following their treatment, we compute the rotational damping produced by collisional drag, associated with H, H₂, and He species (neutral and ions) temporarily stuck and subsequently desorbed from the surface of the fulleranes; plasma drag caused by the interaction of the electric dipole moment of the fullerane and the electric dipole of the passing ions; and the IR emission due to the thermal emission of photons that previously heated the molecule. We also compute rotational excitation rates associated with the impact of neutral particles and ions, plasma drag, and IR emission. Increasing the degree of hydrogenation for molecules of a given radius implies an increase of the dipole moment, but we find that in the conditions of the DCs this does not cause a significant change in effective rotation rate (see the top and bottom panels of Fig. 2). We note that for the smallest fulleranes (C₆₀H₂₀) considered here, the net effect of the processes listed above is to increase the rotation rate with respect to the thermal equilibrium rotation rate, while for larger fulleranes (R≥ 4 Å) it is the opposite. However, as it is clear from the figure, the rotational damping and excitation processes do not imply a drastic change over the rotation rates computed in the simple thermal equilibrium case. The dominant rotational excitation mechanism for fulleranes of any size is the collision with neutrals. In particular, it is responsible for the slightly suprathermal rotation rates of the smallest fulleranes (60 atoms). As the size increases the influence of this process diminishes and the rotational rates become subthermal due to a major role of collisional drag. For fulleranes with radius larger than 10 Å the rotation rates converge towards the thermal equilibrium values.

Figure 2

Effective rotation rates as a function of radius for neutral fulleranes in DCs with a degree of hydrogenation s= 1/3 (top panel) and s= 1/N (bottom panel). Thermal equilibrium rotation rates (asterisks) and rates obtained considering rotational excitation and damping processes (filled diamonds) are plotted in both panels.

5 ELECTRIC DIPOLE EMISSIVITY FROM fulleranes

Emissivity curves for individual fulleranes of various sizes (including buckyonions with hydrogen atoms in the most external shell) have been computed for the conditions of the DC LDN 1622 taking into account rotational damping and excitation processes. Molecules of size R and dipole moment μ rotate with a mean square angular velocity 〈ω²〉 and, if, ω follows a Boltzmann distribution, then the emissivity per H is given by expression (63) of Draine & Lazarian (1998b).

It is assumed that the degree of hydrogenation, s, of the ensemble of molecules of radius R and N carbon atoms follows a Gaussian distribution such that the associated dipole moment distribution is Gaussian with mean μ₀= 0.3(sN)^1/2 and width parameter σ=μ₀. Fig. 3 shows the total flux emission from the cloud for fullerenes of various sizes and mean degree of hydrogenation s= 1/3, assuming that all these molecules have the same abundance 0.1 × 10⁻⁶n(H ₂). For the conversion of emissivities per H to fluxes we adopted as proton column density N_H= 2.4 × 10²² cm⁻². In order to compare with the data reported by Casassus et al. (2006), we consider the same area for the emission region, that is, a 45-arcmin-diameter circle. In the case of C₆₀, we also plot for comparison the curve for s= 1/2, s= 1/10 and for the C₆₀H molecule. The higher the degree of hy drogenation, the lower the frequency of the peak emission. It is also obvious from the figure that the most relevant emitters are the hydrides of C₆₀, the smallest molecule considered in this study and probably the most abundant fullerene based on laboratory synthesis experiments. As expected, the peak emission frequency and the strength of the emissivity decrease as the radius of the fulleranes increases. The emissivity of fulleranes with more than 240 atoms is already two orders of magnitude smaller than that of the C₆₀ hydride and peaks at a frequency of ∼3 GHz, far below the frequencies relevant to the anomalous emission detected in the cloud. Also plotted is the predicted emission flux due to the hydrogenated byckyonion C₆₀@C₂₄₀ (the same s value, only the most external shell is hydrogenated). This already makes clear the relevant role of the smallest fullerenes with 60–140 atoms in any attempt to explain the bulk of the microwave emission in LDN 1622 and the negligible role of larger fullerenes including the hydrogenated buckyonions.

Figure 3

(a) Emission fluxes of fulleranes (thin solid lines) with hydrogenation ratio s= 1/3 predicted for the DC LDN 1622 (assuming only DC conditions). Results are plotted for C₆₀,C₈₀,C₁₄₀, C₁₈₀ and C₂₄₀, and for the buckyonion C₆₀@C₂₄₀ (thick solid line). Each curve is labelled by the number of carbon atoms of the fullerene. Emission fluxes are also plotted for C₆₀ with s= 1/2 (dashed line), with s= 1/10 (dot–dashed line) and for C₆₀H (dotted line).

In Fig. 4, we plot the total flux emission curve for a mixture of fulleranes (with the number of carbon atoms N= 60–2160), following the proposed size-distribution law n(R) ∝R^−m, with m=−1.5, and compare it with the microwave observations of LDN 1622 listed in table 3 of Casassus et al. (2006), taking into account the free–free and thermal dust component reported by these authors. We show results for the three mean values of hydrogenation s= 1/10, 1/3 and 1/2, and also explore the sensitivity of the curves to different values of the fraction of negative fullerene ions in the cloud. We find that a higher abundance of negative ions results in a higher frequency of the peak emission of the mixture. Comparing the theoretical predictions with the observations, we conclude that a significant degree of hydrogenation (s∼ 1/3) is required to explain the bulk of the emission. The emissivity curves compare well with the experimental data below 30 GHz; thus, most of the observed anomalous emission could be due to these molecules. However, in the range 30–50 GHz fulleranes under DC conditions cannot apparently be the cause of the remaining excess emission.

Figure 4

Observations of LDN 1622 anomalous microwave emission by Casassus et al. (2006; filled diamonds) and predicted electric dipole rotational emission fluxes for a mixture of fulleranes (m=−1.5) with various degrees of hydrogenation, s, and ionization fraction f: s= 1/3, f= 3 per cent (solid line); s= 1/3, f= 4 per cent (dot–dashed line); s= 1/2, f= 5 per cent (dashed line), and s= 1/10, f= 3 per cent (dotted line). Curves are plotted including and not including the indicated contributions from free–free and thermal dust emission.

We show in Fig. 5 how this excess emission can be fitted if we allow for an additional contribution of fulleranes from the cold neutral medium (CNM) that may surround the cloud and also from a possible photodissociation region (PDR). The emissivity of fulleranes in the CNM phase of the ISM has been worked out by Iglesias-Groth (2005). Here, we adopt the same physical parameters for this medium [low hydrogen density n(H) = 30 cm⁻³, gas temperature of T= 100 K, and low ionization fraction n(H⁺)/n_H= 0.0012] and assume the same abundance of fullerenes relative to hydrogen than in the DC. In CNM conditions we expect the hydrogenated fullerene mixture to produce electric dipole emission with a peak in the range 30–50 GHz, which shifts to lower frequencies as the hydrogenation level increases. We have computed the expected emission for s= 1/3 as in the case of the DC and added to the previous emissivities of fullerenes in the DC. We find that an explanation of the full set of observations of LDN 1622 requires CNM fullerene emission from the equivalent of 17 per cent of the total area subtended by the DC. The resulting emission from DC plus CNM (including free–free and thermal dust emission) is plotted in the figure (dashed curve), where we can see how this model suitably reproduces the experimental data at high frequency.

Figure 5

Flux emission curves for fullerenes for a degree of hydrogenation s= 1/3 under a combination of plausible physical conditions in LDN 1622. The dotted curves: predicted emission curves for fulleranes in the DC (assuming f= 3 per cent), CNM and PDR (see the text for details). The solid thin line: the total contribution of DC, CNM and PDR emission. The dashed line: DC and CNM including free–free and thermal dust (15-K) emission. The thick solid line: the addition of a PDR contribution to the previous curve. The diamonds: as in the previous figure.

We have also studied whether the experimental data could be explained as a result of fullerane emission in the DC plus emission from a PDR. Adopting the physical parameters in Draine & Lazarian (1998b) for such a medium [n(H) = 10⁵ cm⁻³, gas temperature of T= 300 K, dust temperature of 50 K], we obtain the fullerane emission curve. As shown in Fig. 5, the PDR peak emission is located at rather high frequencies (∼70 GHz). The plotted curve assumes PDR emission in a region equivalent to about 5 per cent the area of the cloud. This contribution added to the previous estimations for the DC and CNM media produces an even better fit to the empirical data (thick solid line). A combination of DC with a larger PDR emission (∼12 per cent of the area of the cloud) and a smaller CNM contribution (12 per cent of the area) can also produce a reasonable fit to the data.

In all these cases, the major contributors to the best-fitting model are the hydrides of C₆₀. If instead of a mixture of fullerene hydrides of various sizes, we restrict the study to only the C₆₀ fullerane, we still find that the empirical data of the cloud can be reasonably well explained assuming an abundance for these molecules of ∼1 × 10⁻⁶ relative to hydrogen and a modest amount of hydrogenation C:H ≈ 3:1. This would lock about 15 per cent of the available carbon abundance. A large fraction of the emission in the frequency range 10–30 GHz can be caused by electric dipole emission of the C₆₀ fulleranes in the DC, but a significant contribution from CNM and/or a PDR region is also required to explain the observations in the 30–50 GHz range. A better fit to the observations around 10 GHz is obtained when we allow for a contribution from slightly larger molecules up to C₈₀.

It is likely that hydrogenated fullerenes display intense electronic bands in the optical and IR. Spectra of some lightly hydrogenated fullerenes are already available (see e.g. Henderson & Cahill 1993, for C₆₀H₂) and show some bands. Recent computations of tubular PAHs derived from elongated C₆₀ also reveal intense electronic transitions in the optical and near-IR (Zhou et al. 2006) and suggest that similar transitions could also take place in fullerene hydrides. Time-dependent density functional theory calculations of oscillator strengths for these molecules would be very valuable and detailed spectroscopic laboratory measurements are certainly required to prove their existence in the ISM. A future search for DIBs towards LDN 1622 may therefore be able to prove the presence of fullerene hydrides in an independent way to rotational electric dipole emission. Laboratory measurements and detailed calculations are essential. It is also possible that hydrogenated fullerenes present vibrational transitions in the mid- and far-IR. In the near future, the instruments onboard the Herschel satellite may also provide key data to shed light on the nature of the carriers of the anomalous microwave emission.

6 CONCLUSIONS

We have investigated the electric dipole rotational emission of hydrogenated forms of icosahedral fullerenes and its relation to the anomalous microwave emission in the DC LDN 1622. Because of the slightly polar nature of the C–H bond, hydrogenated C₆₀ and other fullerene hydrides are expected to have a net electric dipole moment. Assuming that these dipole moments are proportional to the square root of the number of C–H bonds in each molecule, we estimate their effective rotational rates and electric dipole emissivity in the DC environment. Rotational damping and excitation processes are computed following the comprehensive treatment by Draine & Lazarian. The abundance of fullerenes in the DC is derived based on the assumption that they are responsible for the UV bump in the extinction curve. We predict electric dipole emissivity curves for fullerene mixtures, assuming the abundance and size distribution N(R) ∝R^−1.5. The dominant electric dipole emission is associated with spinning fulleranes of small radius R≤ 3.5–5 Å. The resulting curves reproduce the recent observations of anomalous microwave emission in LDN 1622. A large part of this emission can be explained in terms of electric dipole radiation of C₆₀ hydrides with a relatively modest degree of hydrogenation level (C:H ≈ 3:1) under DC conditions. A contribution of these molecules in a hotter environment, most probably, CNM and PDR, surrounding the cloud is also required to explain the high-frequency tail of the anomalous emission.

I thank Rafael Rebolo for valuable comments and suggestions on this work. This work has been partially supported by the project PNE Herschel/Planck ESP2002-03716.