Modeling the infrared extinction toward the galactic center

Abstract

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 A_V ~ 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 R_V and steep near-IR extinction), and dust in dense regions (characterized by large R_V and flat UV extinction).

1. Introduction

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 R_V = A_V/E(B − V), the total-to-selective extinction ratio (Cardelli et al., 1989). ^{1 1} Larger values of R_V correspond to size distributions skewed toward larger grains (e.g., dense clouds tend to have large values of R_V > 4). On average, the dust in the diffuse interstellar medium (ISM) corresponds to R_V ≈ 3.1.

However, the infrared (IR) interstellar extinction law, which also varies from sightline to sightline, cannot be simply represented by R_V. 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 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 R_V = 5.5 (Weingartner and Draine, 2001) (hereafter WD01), which indicates a dust size distribution favoring larger sizes compared to that for R_V = 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 A_V ~ 59 mag (with the exact A_V depending on the chosen gas-to-dust ratio N_H/A_V), much larger than A_V ~ 31 estimated by Rieke et al. (1989) which is commonly adopted in the astronomical literature.

Fig. 1.

IR extinction laws compiled from the literature. Red stars plot A _λ /A_Ks toward the GC based on H lines (Fritz et al., 2011). Blue triangles are derived from stars toward the GC (RL85). Green squares are derived from the red clump giants toward the GC (Nishiyama et al., 2009). Cyan diamonds are the Galactic plane average extinction at ǀlǀ < 5° and ǀbǀ < 2° (Gao et al., 2009). The other three kinds of symbols plot the extinction laws obtained from sightlines away from the GC. For comparison, the extinction curves calculated from the interstellar grain model (WD01) for R_V = 3.1 (black solid line) and R_V = 5.5 (black dot-dashed line) are also shown.

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 (A_V) 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 = An_Ha^−αexp(−a/a_b) with 50 Å < a > 1 μ m, where a is the grain radius, ^{3 3}dn is the number density of dust with radii in the interval [a, a + da] per H nuclei, n_H is the number density of H nuclei, A is the normalization constant, α is the power index, and a_b is the cutoff size. In our modeling, we will have six parameters: A_si, α_si, a_b,si for the silicate component, and A_c, α_c, a_b,c for the graphite component. The total extinction at wavelength λ is given by

((1))

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 C_ext,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

((2))

where A ^obs_λ is the IR extinction toward the GC derived by Fritz et al. (2011) (see their table 2), N_obs is the number of observational data points, N_para is the number of adjustable parameters (N_para = 6 if we assume different size distributions for silicate and graphite; N_para = 4 if we assume that both dust components have the same size distribution), A ^mod_λ 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 R_V = 3.1. Following WD01, we fix the total dust quantity (per H nuclei) to be consistent with the cosmic abundance constraints. Let V_tot,si be the total volume of the silicate dust, and V_tot,c be the total volume of the graphitic dust. We take V_tot,c = 2.98 × 10⁻cm³H⁻¹ and V_tot,c = 2.07 × 10⁻²⁷ cm³ H⁻¹ (i.e., values for constraining all “CASE A” models of WD01) ^{4 4}. We will also consider V_tot,c = 3.9 × 10⁻²⁷ cm³ H⁻¹ and V_tot,c = 2.3 × 10⁻²⁷ cm³ H⁻¹ (i.e., fixed values for all “CASE B” models of WD01). ^{5 5} The mass densities of amorphous silicate and graphite are taken to be ρ^sil ≈ 3.5gcm⁻³ and ρ_carb ≈ 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 R_V = 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. α_si = α_c, a_b,si = a_b,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.

Table 1.

Model parameters for fitting the GC IR extinction curve.

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 α_c ≈ −2.5and a_b,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 a_b,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 R_V = 2.1 in the UV. The size distribution of α_si ≈ −2.9 and a_b,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 6} Finally, we replace graphite by amorphous carbon (AMC). But we are still not able to simultaneously fit both the NIR and MIR extinction.

Fig. 2.

Comparison of the model extinction curve (red solid line) with the ~1–19μm IR extinction of the GC (blue squares) observed by Fritz et al. (2011). Also shown are the extinction curves of R_V = 2.1 (dotted line, see Cardelli et al. (1989)), R_V = 3.1 (dashed line, WD01) and R_V = 5.5 (dot-dashed line, WD01) with the silicate absorption features added (Draine, 2003).

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 R_V = 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 /A_V. 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 R_V = 2.1, the flat MIR extinction of R_V = 5.5, and the strong silicate feature of R_V = 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.

Fig. 3.

Same as Fig. 2 but with the y-axis plotted as A _λ /A_V. The GC IR extinction curve of Fritz et al. (2011) is normalized to A_V = 42 mag (blue squares). Also shown is the GC extinction of Rieke et al. (1989) (cyan triangles), taking A_V = 31 mag.

4. Discussion

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 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 A_v: The extinction at the visual band

Rieke et al. (1989) estimated the visual extinction toward the GC to be A_V ≈ 31 mag based on the extinction law of Rieke and Lebofsky (1985) (R_V = 3.1). Our best-fit model for the Rieke et al. (1989) extinction law also gives A_V ≈ 31.4 mag. However, with β ≈ −2.11 ± 0.06, Fritz et al. (2011) obtained R_V ≈ 2.48 ± 0.06 for the extinction toward the GC based on the correlation between R_V and the IR power-law index β of Fitzpatrick and Massa (2009). Fritz et al. (2011) obtained A_V ≈ 44 mag by extrapolating this curve. They also argued that the X-rays can shed lights on A_V, and A_Vtoward the GC may be higher, up to ~ 59 mag (assuming different N_H/A_V ratios).

Our model extinction curves suggest that models for small RE_V ratios work better for the steep NIR extinction obtained by Fritz et al. (2011). Since a smaller R_V ratio implies a higher A_V (on a per unit NIR extinction basis), this again suggests that A_V toward the GC is probably larger than previous estimated. Our best-fit models suggst that A_V toward the GC is ~ 42 mag (see Table 1). If we do not fix the total silicate (V_tot,si) and graphite volume (V_tot,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 m_gra/m_sil = 0.4, 0.5, and 0.6, our model results show that A_Vtoward the GC is in the range of ~ 35–45 mag. In the diffuse ISM, A_V/N_H ≈ 5.3 × 10⁻²²magcm² (WD01), which leads to N_H ≈ 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 A_V/N_H is less clear for dense clouds, Cardelli et al. (1989) and Draine (1989) argued that A_I/N_H ≈ 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 N^H for the sightline toward the GC to be N_H ≈ 6.42 × 10²² cm⁻² for our best “CASE B” model extinction curve (A_I ≈ 16.69 mag). It is smaller than N_H ≈ (10.5 ± 1.4) × 10²² cm⁻² obtained by Fritz et al. (2011) which implies A_V/N_H ≈ 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 N_H ≈ 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 A_V. 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 R_V = 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 A_V 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 R_V = 2.1, 3.1, and 5.5, respectively, each contributing 30%, 49%, and 21% of the total A_V, with the R_V = 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 8} Although the η2² is not lower than that of single R_V 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.

Fig. 4.

Comparison of the GC IR extinction of Fritz et al. (2011); blue squares) with the best fit model extinction (red solid line) obtained from the combination of three extinction curves of R_V = 2.1 (28%, dotted line), R_V = 3.1 (39%, dashed line), and R_V= 5.5 (33%, dot-dashed line). Also shown are the observed extinction toward the GC by Nishiyama et al. (2009); green triangles) and the best fit with our dust model (see Section 3; red dotted line).

5. Summary

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 A_V ~ 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 R_Vand flat UV extinction).