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Modeling the infrared extinction toward the galactic center
Earth, Planets and Space volume 65, Article number: 8 (2013)
We model the ~ 1–19 μ m infrared (IR) extinction curve toward the Galactic Center (GC) in terms of the standard silicate-graphite interstellar dust model. The grains are taken to have a power law size distribution with an exponential decay above some size. The best-fit model for the GC IR extinction constrains the visual extinction to be AV ~ 38–42 mag. The limitation of the model, i.e., its difficulty in simultaneously reproducing both the steep ~ 1–3 μ m near-IR extinction and the flat ~ 3–8 μ m mid-IR extinction is discussed. We argue that this difficulty could be alleviated by attributing the extinction toward the GC to a combination of dust in different environments: dust in diffuse regions (characterized by small RV and steep near-IR extinction), and dust in dense regions (characterized by large RV and flat UV extinction).
The wavelength dependence of the interstellar extinction–known as the “interstellar extinction law (or curve)”—is one of the primary sources of information about the interstellar grain population (Draine, 2003). The Galactic interstellar extinction curves in the ultraviolet (UV) and visual wavelengths vary from one sightline to another, and can be parameterized in terms of the single parameter RV = AV/E(B − V), the total-to-selective extinction ratio (Cardelli et al., 1989). 1 Footnote 1 Larger values of RV correspond to size distributions skewed toward larger grains (e.g., dense clouds tend to have large values of RV > 4). On average, the dust in the diffuse interstellar medium (ISM) corresponds to RV ≈ 3.1.
However, the infrared (IR) interstellar extinction law, which also varies from sightline to sightline, cannot be simply represented by RV. Various recent studies have shown that there does not exist a “universal” near-IR (NIR) extinction law (Fitzpatrick and Massa, 2009; Gao et al., 2009; Zasowski et al., 2009) and the mid-IR (MIR) extinction law shows a flat curve and lacks the model-predicted pronounced minimum extinction around 7 μ m (Draine, 1989). 2 Footnote 2 It is worth noting that the flat MIR extinction curves determined for various sightlines all appear to agree with the extinction predicted by the standard silicate-graphite interstellar grain model for RV = 5.5 (Weingartner and Draine, 2001) (hereafter WD01), which indicates a dust size distribution favoring larger sizes compared to that for RV = 3.1.
Recently, using the hydrogen emission lines of the min-ispiral observed by ISO-SWS and SINFONI, Fritz et al. (2011) derived the IR extinction curve toward the inner GC from 1 to 19 μ m. The extinction curve shows a steep NIR extinction consistent with that of Nishiyama et al. (2006), (2009) and a flat MIR extinction consistent with other sight-lines (see Fig. 1). It differs from the IR extinction law toward the GC derived by Rieke and Lebofsky (1985) (hereafter RL85) and Rieke et al. (1989). Based on their observations, Fritz et al. (2011) argued that the extinction at the visual band (AV) toward the GC may be as high as AV ~ 59 mag (with the exact AV depending on the chosen gas-to-dust ratio NH/AV), much larger than AV ~ 31 estimated by Rieke et al. (1989) which is commonly adopted in the astronomical literature.
In this work, we try to use the standard interstellar grain model which consists of graphite and silicate grains (Draine and Lee, 1984) to fit the observed IR extinction curve toward the GC of Fritz et al. (2011) and constrain the total optical extinction (AV) toward the GC. Section 2 briefly describes the grain model. Our model results are presented in Section 3 and discussed in Section 4. In Section 5 we summarize the major conclusion of this work.
2. Dust Model
We take the dust to be a mixture of separate amorphous silicate and graphite grains, with the optical properties taken from Draine and Lee (1984). For the dust size distribution, we adopt a power law with an expoential cutoff at some large size: dn/da = AnHa−αexp(−a/ab) with 50 Å < a > 1 μ m, where a is the grain radius, 3 Footnote 3dn is the number density of dust with radii in the interval [a, a + da] per H nuclei, nH is the number density of H nuclei, A is the normalization constant, α is the power index, and ab is the cutoff size. In our modeling, we will have six parameters: Asi, αsi, ab,si for the silicate component, and Ac, αc, ab,c for the graphite component. The total extinction at wavelength λ is given by
where the summation is made over the two grain types (i.e., silicate and graphite), is the H column density which is the H number density integrated over the line of sight l, and Cext,i (a, λ) is the extinction cross section of grain type i of size a at wavelength λ. The goodness of fitting is evaluated by
where A obsλ is the IR extinction toward the GC derived by Fritz et al. (2011) (see their table 2), Nobs is the number of observational data points, Npara is the number of adjustable parameters (Npara = 6 if we assume different size distributions for silicate and graphite; Npara = 4 if we assume that both dust components have the same size distribution), A modλ is the model extinction computed from Eq. (1), and φ j is the weight of the observed extinction.
Assuming that ≈30% of the cosmic C is in the gas phase, WD01 adopt the solar C abundance of Grevesse and Sauval (1998) to constrain their models. For Si, they also adopt the solar abundance of Si/H = 3.63 × 10−5, but assuming a complete depletion in dust. Their CASE A models tried to seek the best fit by varying the total volume per H in both the carbonaceous and silicate distributions, while their CASE B models fixed at approximately the values found for RV = 3.1. Following WD01, we fix the total dust quantity (per H nuclei) to be consistent with the cosmic abundance constraints. Let Vtot,si be the total volume of the silicate dust, and Vtot,c be the total volume of the graphitic dust. We take Vtot,c = 2.98 × 10−cm3H−1 and Vtot,c = 2.07 × 10−27 cm3 H−1 (i.e., values for constraining all “CASE A” models of WD01) 4 Footnote 4. We will also consider Vtot,c = 3.9 × 10−27 cm3 H−1 and Vtot,c = 2.3 × 10−27 cm3 H−1 (i.e., fixed values for all “CASE B” models of WD01). 5 Footnote 5 The mass densities of amorphous silicate and graphite are taken to be ρsil ≈ 3.5gcm−3 and ρcarb ≈ 2.24gcm−3.
3. Model Extinction
To testify the dust model, we first fit the standard extinction curve of RV = 3.1. With dn/da ∝ a−3.5e−a/0.14 for amorphous silicates and dn/da ∝ a −3.1e−a/0.11 for graphite, the model closely reproduces the RV = 3.1 Galactic extinction curve. To fit the observed IR extinction curve from 1 μ m to 19 μ m toward the GC (Fritz et al., 2011), for simplicity we first assume that both graphite and silicate have the same size distribution (i.e. αsi = αc, ab,si = ab,c). We then consider models with different power indices and cutoff sizes for the two dust components to search for better fits. The best-fit results are summarized in Table 1. We note that it makes little difference either taking the same size distribution or assuming different size distributions for silicate and graphite. None of these attempts could fit the flat MIR extinction well, although “CASE B” works relatively better.
In Fig. 2 we show the “CASE B” best-fit model extinction assuming different size distributions for silicate and graphite. Compared with the observed IR extinction curve toward the GC (Fritz et al., 2011), the model extinction is a little too high at the 2.166 μ m (Brackett-γ) band and too low at ~ 7 μ m: mag while Fritz et al. (2011) obtained A2.166 ≈ 2.49 ±0.11 mag. The size distribution of αc ≈ −2.5and ab,c ≈ 0.04 μ m for graphite reproduces well the steep NIR extinction but causes the minimum extinction near 7 μ m. The small cutoff ab,c ≈ 0.04 μ m implies that the model is rich in small graphite grains so that the model extinction curve is similar to that of RV = 2.1 in the UV. The size distribution of αsi ≈ −2.9 and ab,si ≈ 0.08 μ m for silicate causes the strong silicate feature at 9.7 μ m. Our results show that it may require some dust grains with a size distribution peaking around 0.5 μ m or even larger to produce the flat MIR extinction. To avoid the complication of the silicate features we have also modeled the observed extinction but limiting ourselves to the extinction from 1 μ m to 7 μ m. To fit the MIR extinction, we have also tried models confining us to the observed extinction from 3 μ m to 19 μ m (i.e., ignoring the 1–3 μ m NIR extinction). These approaches seem to work well for the chosen wavelength range, but unfortunately, none of these attempts results in satisfactory fits for the whole range of 1–19 μ m. 6 Footnote 6 Finally, we replace graphite by amorphous carbon (AMC). But we are still not able to simultaneously fit both the NIR and MIR extinction.
The NIR extinction law toward the GC derived by Fritz et al. (2011) and Nishiyama et al. (2009) is much steeper than that derived by Rieke and Lebofsky (1985) and Rieke et al. (1989), with β ≈ −2.0 compared to the common value of α ≈ −1.6 to −1.8. For comparison, we also fit the extinction curve of Rieke et al. (1989), which is actually the RV = 3.1-type extinction, and the model also works very well with dn/da ℝ a−2.1e−a/0.08 for amorphous silicates and dn/da ℝ a−3.0e−a/0.28 for graphite. For the sake of clear comparison, we replot in Fig. 3 the results shown in Fig. 2 but in terms of A λ /AV. We see that the IR extinction toward the GC derived by Fritz et al. (2011) seems to be a combination of the steep UV-to-NIR extinction of RV = 2.1, the flat MIR extinction of RV = 5.5, and the strong silicate feature of RV = 3.1. It seems that a trimodal size distribution is required in order to achieve a close fit to the observed extinction from the UV through NIR, MIR to the silicate absorption band.
4.1 The extinction features in the 3–7 μm wavelength range
The extinction curve toward the GC obtained by Fritz et al. (2011) shows the strong 3.1 μ m H2O feature and the 3.4 μ m aliphatic hydrocarbon feature. Fritz et al. (2011) found that the COMP-AC-S model of Zubko et al. (2004) seems to best fit their observations as judged by η2/d.o.f. and the presence of the H2O ice features. The porosity of ice dust grains also makes Zubko et al. (2004) ’s extinction model to fit the GC observed extinction well. However, the ice features only appear in dense regions, while the flat extinction in the 3–7 μm range is observed towards many different sightlines, including both diffuse clouds and dense clouds. It is highly possible that some dust materials other than ices are responsible for the flat MIR extinction towards the GC and elsewhere. 7 Footnote 7 The silicate-graphite dust model considered here is suitable for the diffuse ISM and does not include ice and aliphatic hydrocarbon material. Therefore we do not expect to reproduce the 3.1 μm H2O ice feature and the 3.4μm aliphatic C–H feature.
However, these extinction features could be properly reproduced if the appropriate candidate materials are added in the dust model. For the 3.4 μm aliphatic C–H feature, Draine (2003) argued that if the graphite component is replaced with a mixture of graphite and aliphatic hydrocarbons, it seems likely that the extinction curve, including the 3.4 μm feature, could be reproduced with only slight adjustments to the grain size distribution. The 3.1 μm H2O feature may be more complicated because the H2O feature usually appears in sightlines passing through dense molecular clouds. In cold, dense molecular clouds, interstellar dust is expected to grow through coagulation (as well as accreting an ice mantle) and the dust is likely to be porous (Jura, 1980). Therefore, introducing a porous structure with ices coated on silicate, graphite and aliphatic hydrocarbon dust, both the H2O absorption feature and the 3.4 μm aliphatic C–H feature could be reproduced in the model extinction curves (Zubko et al., 2004;Gao et al., 2010).
4.2 Av: The extinction at the visual band
Rieke et al. (1989) estimated the visual extinction toward the GC to be AV ≈ 31 mag based on the extinction law of Rieke and Lebofsky (1985) (RV = 3.1). Our best-fit model for the Rieke et al. (1989) extinction law also gives AV ≈ 31.4 mag. However, with β ≈ −2.11 ± 0.06, Fritz et al. (2011) obtained RV ≈ 2.48 ± 0.06 for the extinction toward the GC based on the correlation between RV and the IR power-law index β of Fitzpatrick and Massa (2009). Fritz et al. (2011) obtained AV ≈ 44 mag by extrapolating this curve. They also argued that the X-rays can shed lights on AV, and AVtoward the GC may be higher, up to ~ 59 mag (assuming different NH/AV ratios).
Our model extinction curves suggest that models for small REV ratios work better for the steep NIR extinction obtained by Fritz et al. (2011). Since a smaller RV ratio implies a higher AV (on a per unit NIR extinction basis), this again suggests that AV toward the GC is probably larger than previous estimated. Our best-fit models suggst that AV toward the GC is ~ 42 mag (see Table 1). If we do not fix the total silicate (Vtot,si) and graphite volume (Vtot,c), instead, we allow the quantity of the silicate component to vary with respect to that of graphite: by taking the silicate-to-graphite mass ratio to be mgra/msil = 0.4, 0.5, and 0.6, our model results show that AVtoward the GC is in the range of ~ 35–45 mag. In the diffuse ISM, AV/NH ≈ 5.3 × 10−22magcm2 (WD01), which leads to NH ≈ 7.7 × 1022 cm−2 for our best “CASE B” model extinction curve. However, towards the GC, the interstellar environments should be much denser than that of the diffuse ISM. Although AV/NH is less clear for dense clouds, Cardelli et al. (1989) and Draine (1989) argued that AI/NH ≈ 2.6 × 10−22magcm2 typical of the diffuse ISM may also hold for dense clouds. If this is indeed the case, we estimate the column density NH for the sightline toward the GC to be NH ≈ 6.42 × 1022 cm−2 for our best “CASE B” model extinction curve (AI ≈ 16.69 mag). It is smaller than NH ≈ (10.5 ± 1.4) × 1022 cm−2 obtained by Fritz et al. (2011) which implies AV/NH ≈ 6.6 × 10−22magcm2. It is also much smaller than that of Nowak et al. (2012), who derived the X-ray absorbing column density to be NH ≈ 15 × 1022 cm−2.
4.3 A simple model based on combinations of multi-extinction curves
When the starlight from the GC reaches us, it may have passed through the spiral arms where star formation is actively occurring, diffuse regions, and dense regions of molecular clouds. McFadzean et al. (1989) argued that the molecular clouds along the line of sight toward the GC may contribute as much as ~ 1/3 (~ 10 mag) of the total visual extinction AV. Therefore, the extinction curve toward the GC may be a combination of different extinction curves produced by dust grains in different environments of different size distributions. The best fits of this trimodal model are shown in the last two rows of Table 1. The first row shows the best fit derived by varying the contribution of different extinction curves (i.e. RV), while the 2nd row is for fixing the RV = 5.5-type extinction to account for 1/3 of the total extinction if we assume the molecular cloud contributes as much as ~ 1 /3 (~ 10 mag) of AV towards the GC. As shown in Fig. 4, the observed IR extinction of the GC is fitted well in terms of three different extinction curves, characterized by RV = 2.1, 3.1, and 5.5, respectively, each contributing 30%, 49%, and 21% of the total AV, with the RV = 2.1 extinction representing that of the region where the dust subjects to heavy processing such as in HD 210121, a high Galactic latitude cloud (Larson et al., 1996; Li and Greenberg, 1998). 8 Footnote 8 Although the η22 is not lower than that of single RV models (see Table 1), we think that the trimodal model is an useful description because it seems reasonable that the dust in the lines of sight towards the GC is characteristics of different environments.
The ~ 1–19 μ m IR extinction curve of the GC recently derived by Fritz et al. (2011) is fitted with a mixture of graphite and amorphous silicate dust. The model has difficulty in simultaneously reproducing the steep NIR extinction and the flat MIR extinction. The best-fit model estimates the total visual extinction toward the GC to be AV ~ 38–42 mag. In view that the starlight from the GC passes through different interstellar environments, the observed extinction curve toward the GC could be a combination of different extinction curves produced by grains with different size distributions characteristic of different environments: dust in diffuse regions (characterized by small RV and steep near-IR extinction), and dust in dense regions (characterized by large RVand flat UV extinction).
E(B − V) = AB − AV is the interstellar reddening, AB is the extinction at the “B” (blue; λ ≈ 4400 Å ) band, and AV is the extinction at the “V” (visual; λV ≈ 5500Å) band.
In this work by “NIR” we mean 1 μ m < λ < 3 μ m and by “MIR” we mean 3 μ m < λ < 8 μ m.
We assume the dust to be spherical.
The abundances of C and Si given by Asplund et al. (2009) are 2.95 × 10−4 and 3.55 × 10−5, respectively. If considering the solar abundances of Asplund et al. (2009), one would get Vtot,si = 2.91 × 10−27 cm3 H−1 and Vtot,si = 1.85 × 10−27 cm3 H−1, i.e. Vtot,si/Vtot,c = 0.61/0.39, which is close to the ratio of the WD01 “CASE B” models. We also fitted the extinction curve by varying the ratio of Vtot,si/Vtot,c: by taking the silicate-to-graphite mass ratio to mgra/msil = 0.4, 0.5, and 0.6, our model results show that AV toward the GC is in the range of ~ 35–45 mag.
Fritz et al. (2011) obtained an optical depth of τ9.7 μ m ≈ 3.84 ± 0.52 relative to the continuum at 7 μ m from their interpolated extinction curve. However, in the wavelength range of the silicate features, there are too few points to extract the optical depth accurately, also because of the large errors. Considering the possible large uncertainty, we did not use τ 9.7 μ m to constraint our fitting.
Fritz et al. (2011) (see their section 5.6) argued the flat MIR extinction is not caused by the molecular clouds in front of the GC, which produce the ice features on the extinction curves. They also argued (see their section 5.8) that something else aside from ices produces the flat MIR extinction towards the GC and elsewhere, and additional pure ice grains produce the extinction features towards the GC.
In Fig. 4, although it appears to fit the extinction well in the range of 1.2−8.0μ m, the RV = 2.1 (HD210121) extinction curve actually is not the suitable extinction curve for the interstellar environment towards the GC because it predicts a very strong silicate absorption feature at 9.7 μ m.
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We thank the anonymous referees for their comments that helped improve the presentation of the paper. This work is supported by NSFC grant No. 11173007, NSF AST 1109039, and the University of Missouri Research Board, and the John Templeton Foundation in conjunction with National Astronomical Observatories, Chinese Academy of Sciences.
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Gao, J., Li, A. & Jiang, B.W. Modeling the infrared extinction toward the galactic center. Earth Planet Sp 65, 8 (2013). https://doi.org/10.5047/eps.2013.05.016
- ISM: dust
- extinction—infrared: ISM—Galaxy: center