SOFIA/FORCAST IMAGING OF THE CIRCUMNUCLEAR RING AT THE GALACTIC CENTER

The deconvolved images (Figure 2) display the warm dust emission from the CNR in unprecedented detail. The schematic diagram shown in Figure 4 illustrates that the CNR is observed as an ellipse due to the high inclination. Figure 4 also conveys the distinct difference between the CNR and the larger, cooler distribution of gas and dust surrounding Sgr A* observed in molecular observations (Güsten et al. 1987): the CNR is the illuminated inner edge of the cool disk of gas and dust, the CND. Assuming that the CNR is a circular ring centered on Sgr A* we extract the properties of the projected CNR ellipse: the semi-minor axis is 14'' ± 2'' (0.54 pc ± 0.08 pc), the semi-major axis is 36'' ± 2'' (1.4 pc ± 0.08 pc), and the inclination is therefore 67° ± 5°, which is consistent with the angle derived by Latvakoski et al. (1999). In addition to extracting the geometric properties of the projected CNR ellipse we determine the projected width of the ring, from which we can derive its height and opening angle (Figure 5). The projected width of the ring is ∼12'' ± 17 (0.45 pc) along the minor axis and ∼11'' ± 17 (0.4 pc) along the major axis. Since the observed ring width along the major axis is the true, unprojected width of the ring we can use that and the measured minor axis ring width, assuming they are the same, to derive the opening angle and the height. We assume the geometry shown in Figure 5 and determine an opening angle of ∼12°  ±  3° and a ring height of ∼0.29  ±  0.08 pc.

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We observe a distinct shift in the location of the peak intensities among the 19.7, 31.5, and 37.1 μm intensity maps. The 19.7 μm intensity peak is displaced radially inward from the 31.5 and 37.1 μm intensity peaks by several arcseconds, which indicates that the heating sources of the CNR are located in its interior. An intensity line cut through the southern region of the CNR is shown in Figure 6, illustrating the peak shifts. This observation strongly suggests that the CNR is identical to a classic H ii region where the 19.7 μm dust emission primarily traces the ionized gas region while the 31.5 and 37.1 μm emissions extend into the photo-dissociation region (cf. Salgado et al. 2012). Our observations are consistent with the claim that the Western Arc is the ionized inner edge of the CND excited by UV radiation from the central stellar cluster (Serabyn & Lacy 1985; Telesco et al. 1996).

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In Figures 7(a) and (b) we overlay CN 2 − 1 (Martín et al. 2012) and 6 cm radio continuum (Yusef-Zadeh & Morris 1987) contours on the 37.1 and 19.7 μm intensity maps, respectively. The CN contours trace the cooler material beyond the 37.1 μm emission region around most of the CNR while the radio contours are coincident counterparts to the 19.7 μm emission region. Figure 7(d) shows the normalized intensity line cut through the southern CNR (Figure 7(c)) across the 6 cm, 37.1 μm, and CN maps and presents the displacement of these three different emission regions, which is consistent with central heating. The region of the ionized gas emission at 6 cm lies slightly radially inward from the 37.1 μm, photo-dissociation region emission. Similarly, the 37.1 μm emission region is displaced inward relative to the molecular emission region. The morphological arrangement of these regions strongly reinforces the picture of the CNR as a centrally heated structure.

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Large column densities of dust and gas lead to extreme extinction along lines of sight toward the GC (A_V ∼ 30; Cardelli et al. 1989). The extinction toward the GC has been characterized by numerous extinction curves derived through various techniques (Cardelli et al. 1989; Rieke et al. 1989; Lutz 1999; Fritz et al. 2011). One of the primary sources of extinction is silicate dust grains, which absorb strongly at 9.7 and 19 μm. In this paper we adopt the curve of Fritz et al. (2011, hereafter referenced as F2011) derived from hydrogen emission lines of the minispiral from 1 to 19 μm observed by Short Wave Spectrometer on the Infrared Space Observatory and the Spectrograph for Integral Field Observations in the Near Infrared on the Very Large Telescope. We select the F2011 extinction curve over the others because F2011 utilize the most recent NIR (1–2.4 μm) observations of the GC. The F2011 curve is characterized by a −2.11 power-law slope at wavelengths shortward of 2.8 μm, absorption peaks in the mid-IR due to composite grains (in addition to silicates and carbonaceous grains), a 9.7 μm silicate feature optical depth of Δτ_sil = 3.86, and a K_S-band extinction of 2.62. Longward of 24 μm we extrapolate from the F2011 extinction curve by adopting the Draine (2003) interstellar extinction curve defined in Figure 10 of that paper. The extinction values at 24 μm agree between the F2011 and Draine (2003) extinction curves. From the extrapolated F2011 extinction curve, we therefore find that the ratio of the extinction at 19.7–31.5 μm, $e^{\tau _{19.7}}/e^{\tau _{31.5}}$, and at 19.7–37.1 μm, $e^{\tau _{19.7}}/e^{\tau _{37.1}}$, is 1.94 and 2.36, respectively.

After properly dereddening our images by applying the extrapolated F2011 extinction curve, we derive dust color temperature, optical depth, and total dust luminosity maps. We assume that the emission from the dust is optically thin and that the emissivity has a power-law form of ν^β and adopt an index of β = 2, which is consistent with Draine (2003). The flux from the dust at ν can be expressed as F_ν∝ν^βB_ν(T_D), where we define T_D as the color temperature of the dust.

We use the derived color temperatures to estimate the emission optical depth, and with the power-law dust emissivity, the total dust luminosity is calculated as

$$\begin{equation} L=4 \pi d^2\int _{\Omega _{\mathrm{source}}} \int _0^\infty F_{\nu _{37}}\left(\frac{\nu }{\nu _{37}}\right)^\beta \frac{B_{\nu } (T_D)}{B_{\nu _{37}} (T_D)}\,{d}\nu \,{d}\Omega , \end{equation} \tag{ 1 }$$

where $F_{\nu _{37}}$ is the observed flux at 37.1 μm, and T_D is the color temperature determined from the observed 19.7/37.1 μm emission ratio.

3.3.1. Color Temperature Map

The 19.7/37.1 μm color temperature map of the inner 6 pc of the GC is shown in Figure 8. Given an absolute photometric error of 20% the temperatures we derive are accurate within ±8 K (ignoring uncertainties in β). The highest temperature in the field peaks at 145 K at the Northern Arm ∼8'' to the east of Sgr A*. There is a decreasing radial temperature gradient going north along the Northern Arm and going west along the East–West Bar: temperatures in the Northern Arm range from 145 K to ∼90 K where it approaches the northern edge of the CNR, and the temperatures in the East–West Bar range from 140 K to ∼90 K extending ∼30'' to the east of Sgr A* and past the eastern edge of the CNR. The CNR exhibits a radially outward decreasing temperature gradient except for the eastern region, where the CNR dust emission is confused with that of the East–West Bar and Northern Arm. The temperatures range from 85 K at the inner edge of the ring to ∼65 K at the outer edge, consistent with central heating. Temperatures decrease radially due to the absorption of the dust-heating optical and UV photons. Other than the source IRS 8 (∼30'' north of Sgr A*) we do not detect any embedded sources or large fluctuations in temperature, ΔT > 15 K, along the CNR. There is therefore no evidence from our observations of star formation occurring within the CNR.

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3.3.2. Optical Depth Map at 37.1 μm

We derive the 37.1 μm optical depth map (Figure 9) from the 37.1 μm intensity map and the 19.7/37.1 color temperature map. The 37.1 μm optical depth peaks at the northern (τ_37.1 ∼ 0.4) and southern (τ_37.1 ∼ 0.3) edges of the CNR and decreases toward the eastern and western edges along the ring to ∼0.05. The increased optical depths at the north and south regions of the CNR are consistent with the enhanced column densities at those locations resulting from projection effect accompanying the high inclination of the ring, given our geometric interpretation of the ring dimensions (Figure 4). Along the Northern Arm the optical depths range from 0.04 to 0.13, peaking 28'' to the northeast of Sgr A* where the Northern Arm appears to intersect the northern CNR. The East–West Bar exhibits lower values of τ_37.1, ranging from 0.03 to 0.06, and peaks at the apparent intersection with the eastern CNR. Although the intensities are greatest at the Northern Arm and East–West Bar, the majority of the emitting dust in the field (∼75%) is located in and around the CNR. We find that the 37.1 μm optical depth traces the inner edge of the molecular CN emission (Martín et al. 2012) along the Western Arc (Figure 10). At the northern region of the CNR the 37.1 μm optical depth appears to closely trace the CN emission; we suggest this may be due to the shadowing caused by the Northern Arm and East–West Bar which permits CN production to occur closer to the inner edge of the CNR than in the southwest.

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The total gas mass of the CNR is derived and discussed in Section 4.3.

3.3.3. Luminosity Map

In Figure 11 we present the integrated luminosity contours derived from the 19.7/37.1 color temperature map and the 37.1 μm map. We find that the luminosity contours closely trace the 37.1 μm intensity map with the only difference being that the Northern Arm and East–West Bar appear much more prominent in the luminosity map relative to the CNR since the temperatures are much greater along those features. The luminosities of the Northern Arm and East–West Bar are ∼1.7 × 10⁶ L_☉ and ∼1.8 × 10⁶ L_☉, respectively. Since the Northern Arm and East–West Bar may be shadowing the eastern CNR (Latvakoski et al. 1999) we estimate the expected, total luminosity of the CNR by multiplying the Western Arc luminosity by a factor of two. We derive an expected, total CNR luminosity of ∼2.5 × 10⁶ L_☉.

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There is a "diffuse" component of the luminosity map not associated with the CNR, Northern Arm, and East–West Bar that has a luminosity of ∼2.0 × 10⁶ L_☉ integrated over the entire field of view. The total luminosity integrated over the inner 6 pc region is ∼9.7 × 10⁶ L_☉. Luminosities of the various features are summarized in Table 1.

Table 1. Sgr A West Luminosities and CNR Opening Angle

Lbkgd	LTot	LTot − Lbkgd	LNA	LBar	LCNRa	ϕ0b
(L☉ pixel−1)						(°)
70 ± 15	9.8	7.0	1.7	1.8	2.5	14 ± 3

Notes. Units given in 10⁶ L_☉. ^aExpected, total CNR luminosity derived by multiplying Western Arc luminosity by a factor of two. ^bDerived from Equation (2); total measured luminosity of observed stars in central cluster is L_Cent ∼ 2 × 10⁷ L_☉ (Krabbe et al. 1995).

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The stellar cluster near Sgr A* contains hot O and B stars as well as evolved Wolf–Rayet stars (Krabbe et al. 1995). The combined luminosity of the central cluster is estimated by Krabbe et al. (1995) to be ∼2 × 10⁷ L_☉. Since the outer boundary of the CNR is determined by the extinction of optical and UV photons as opposed to being limited by the amount of dust present to be illuminated, we can assume that the dust in the CNR absorbs all of the optical and UV photons emitted by the central cluster over the solid angle subtended by the inner wall of the CNR (see Figure 5). This allows us to perform a consistency check on the morphology derived by the observed intensity maps. The fraction of the CNR luminosity over the luminosity of the hot central cluster stars provides an estimate of the inner wall height, h, and the opening angle of the CNR, ϕ₀;

$$\begin{equation} \frac{L_\mathrm{CNR}}{L_\mathrm{Cent}}=\frac{2 \pi \,R\,h}{4\pi \,R^2},\,\, \phi _0=2\,\mathrm{{\rm arctan}}\left(\frac{L_\mathrm{CNR}}{L_\mathrm{Cent}}\right). \end{equation} \tag{ 2 }$$

From the luminosity fraction we derive an inner wall height of ∼0.35 pc and an opening angle of ∼14°, which are similar to the values derived from the observed width of the CNR in the intensity map.

Inversely, the total central cluster luminosity can be derived from the observed CNR dust luminosity and opening angle. Given an opening angle of 14° and a CNR luminosity of ∼2.5 × 10⁶ L_☉ we determine the central luminosity to be approximately 1.6 × 10⁷ L_☉, which is consistent with other luminosities also derived by the dust emission and geometric analysis (2 × 10⁷ L_☉ (Davidson et al. 1992); 2.3 × 10⁷ L_☉ (Latvakoski et al. 1999)).

In order to check the consistency of the central heating argument we calculate the theoretical equilibrium temperature of the dust in the CNR heated by the O and B stars in the central cluster. We treat the cluster as a point source at the location of Sgr A* since the size of the cluster is small compared to the radius of the CNR. The dust temperature, T_d, can then be derived from the expression shown in Equation (3),

$$\begin{equation} \pi a^2Q_*(a)\, F_*=4 \pi a^2\,Q_{\mathrm{dust}}(T_d,a)\,\sigma _{\mathrm{SB}}\,T_d{}^4, \end{equation} \tag{ 3 }$$

where Q_dust is the dust emission efficiency averaged over the Planck function of dust of size a and temperature T_d, Q_* is the dust absorption efficiency averaged over the incident radiation field, and F_* is the incident flux at the location of the dust grains. For silicate-type grains and a heating source with average temperature 35,000 K (Lacy et al. 1980) we have $Q_\mathrm{dust}(T_d, a)= 1.3 \times 10^{-6} ({a}/({0.1\,\mu \mathrm{m}}))\,T_d^2$ and Q_* ≈ 1 (Draine 2011). Assuming a distance of 1.4 pc, a total source luminosity of ∼2 × 10⁷ L_☉ (Krabbe et al. 1995), and a uniform size distribution of silicate-type dust grains with a standard interstellar medium grain size of ∼0.2 μm we derive a theoretical equilibrium temperature of 90 K which is consistent with the color temperatures we observe at the inner edge of the CNR (∼85 K).

Using the DUSTY radiative transfer code (Ivezic & Elitzur 1997) to perform an additional check on the temperature calculation, we are able to find consistent grain size parameters, that give the observed color temperatures at the inner radius of the CNR. The DUSTY model parameters are summarized in Table 2.

We consider the possibility of shock-driven heating by the high-velocity winds from the central cluster. The total estimated power contributed by the kinetic energy of the winds with a velocity of 700 km s⁻¹ and a mass-loss rate of 10⁻² M_☉ yr⁻¹ (Geballe et al. 1984) is 4 × 10⁵ L_☉, which is ∼2% of the stellar luminosity from the central cluster. We therefore conclude that the heating due to shocks is not significant compared to the radiative heating.

4.2.1. Defining the Outer Edge of the CNR

Our picture of the CNR as the illuminated inner edge of a larger, cooler distribution of gas and dust (Figure 4) allows us to calculate how deeply UV and optical photons penetrate into the ring—the point where the optical depth is ∼1. We assume the dust properties determined by the DUSTY model shown in Table 2 and an inner edge gas density of $n_{{\rm H_2}}=1.0\,\times 10^4\,\mathrm{cm}^{-3}$ (Davidson et al. 1992; Latvakoski et al. 1999). The distance to the τ_V = 1 point can be derived as

$$\begin{equation} \tau _V=1=\int _{R_\mathrm{in}}^{R_{\tau _V=1}}n(r) \, \bar{\sigma }\,{d}r, \end{equation} \tag{ 4 }$$

where n(r) is the radial density power-law with an index of −1 (Davidson et al. 1992), $\bar{\sigma }$ is the total cross section integrated over the dust size distribution, and r is the radial distance from Sgr A*. We calculate a value of $R_{\tau _V=1}=0.46$ pc which is similar to the observed width of the CNR along the major axis (∼0.42 pc) in the 37.1 μm intensity map. We note that changes in the radial density power-law index do not significantly alter the value of $R_{\tau _V=1}$; for an index of 1 we have $R_{\tau _V=1}=0.35$ pc.

4.2.2. 37.1 μm Intensity Model of the CNR

We generate a 37.1 μm intensity model of the CNR assuming its morphology to be that of an inclined, circular ring (see Figure 5). Instead of performing the full radiative transfer computations to determine the dust emission, we adopt a radial temperature power-law index of −2/3, which fits the observed temperature gradient along the major axis of the CNR in the 19/37 color temperature map. We note that a centrally heated, optically thin dust distribution would exhibit a radial temperature index of −1/3, assuming an emissivity power-law index of −2. The input parameters for the radius, R (1.4 pc), inner edge temperature, T_d (82 K), and inclination angle, θ_i (67°), are taken from observations, and we are free to manipulate the inner edge density, $n_{{\rm H_2}}$, and height (opening angle), h (ϕ₀), to fit the observed intensity map. The fitted model parameters are summarized in Table 3. Although the emitting region of the CNR is small compared to its radius, we must treat the geometry of the emitting region in careful detail since the opening angle, ϕ₀, and the illumination depth, $R_{\tau _V=1}$, will largely determine the shape of the emission peak.

Table 3. Observed and Model-derived CNR Properties

R	h	θi	Td	q	$n_{{\rm H_2}}$	Mass from τ37a
(pc)	(pc)		(K)		(× 104 cm−3)	(M☉)
1.4	0.34	67°	82	−2/3	1.0	∼610

Notes. The radius, R, temperature, T_d, radial temperature index, q, inclination angle, θ_i, and the mass are taken from observations. The CNR inner radius density, $n_{{\rm H_2}}$, and height, h, are derived from the model. ^aAssuming a gas-to-dust mass ratio of 100.

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The intensity model is shown in Figure 12(a) on the same size scale as the intensity map in Figure 12(b) and has been convolved with a 25 FWHM Gaussian to simulate the beamsize of the deconvolved images. Contours of the 37.1 μm intensity map are overlaid on the model in Figure 12(c). Intensities in our model range from 5 Jy pixel⁻¹ along the minor axis to 10 Jy pixel⁻¹ along the major axis, which is consistent with the average intensities along the minor and major axes in the observed 37.1 μm intensity map. The observed intensity contours closely trace the model; however, the southern emission peak in the Western Arc is shifted several arcseconds to the north-west of the corresponding model peak.

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A series of intensity line cuts across the model and observed CNR is shown in Figure 13. The line cuts were positioned to avoid intersecting the "clumps" at the inner edge of the CNR which is discussed in the following section. The location and amplitude of the model peaks at the Western Arc agree with the peaks from the observed intensity map. In the central (Figure 13(d)) and southern (Figure 13(e)) intensity line cuts even the widths of the model peaks closely agree with the observed intensity peak widths. The southern intensity line cut is the only cut that intersects with the observed eastern CNR; the emission at the eastern peak is ∼60% of the western peak hypothetically because the Northern Arm and East–West Bar absorb some of the UV and optical photons from the central cluster (Latvakoski et al. 1999). We do not observe the eastern CNR peak in the north and central line cuts due to confusion with the emission from the Northern Arm and East–West Bar.

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We derive the total dust mass of the CNR using the 37.1 μm optical depth map and the grain parameters from our 37.1 μm intensity model (Table 2) and assuming a gas-to-dust mass ratio of 100. Integrating over the ring in the 37.1 μm optical depth map we find a total CNR mass of ∼610 M_☉, which is roughly ∼1/2 of the mass derived by Latvakoski et al. (1999) who observed the CNR at 31 and 37 μm. The discrepancy with Latvakoski et al. (1999) is due to assuming different grain parameters. Our derived mass is two orders of magnitude less than the mass derived by Etxaluze et al. (2011) and Requena-Torres et al. (2012), and roughly four orders of magnitude less than the mass derived by Christopher et al. (2005). This inconsistency can be attributed to the difference in the tracers that we used to study the CNR and, in the case of Christopher et al. (2005), the assumption of virialized clumps. Our observed dust emission does not trace the distribution of cooler material outside the CNR (deeper into the CND).

The CNR gas density derived by our model ($n_{{\rm H_2}}=10^4\,\mathrm{cm}^{-3}$) is consistent with the density derived observationally from our 37.1 μm optical depth map. Assuming the morphological parameters of our model the apparent thickness along the line of sight through the major axis of the CNR is ∼1 pc with a corresponding 37.1 μm optical depth of ∼0.3, which implies a density of ∼1.4 × 10⁴. The gas densities we find are similar to those of other works studying the CNR dust emission (Davidson et al. 1992; Latvakoski et al. 1999).

In our analysis we assumed that the total extinction toward the CNR is constant around the ring; however, there is local extinction from the molecular component of the CND whose effect along the line of sight varies around the ring due to its inclined geometry. Christopher et al. (2005) suggest that the dust emission from the CNR does not trace all of the dust in the region due to extinction from high-density material in the molecular region. In this section, we therefore check for significant variations in our results when addressing the local, differential extinction.

The effect of local, differential extinction can be seen by comparing the emission from the southern region of the Western Arc between the 6 cm and Paschen-α (Wang et al. 2010; Dong et al. 2011) intensity maps (Figures 14(a) and (b)). The emission at the southern Western Arc drops significantly between the 6 cm and the Paschen-α maps. Using the ratio of observed Paschen-α line flux to 6 cm radio free–free emission, we derive an absolute extinction map that agrees with that of Scoville et al. (2003). We find that the absolute extinction is greater along the Western Arc than toward the inner cavity and peaks at the southern portion of the CNR. After subtracting the interstellar extinction (A_V = 30) we produce a map that represents only the local extinction (Figure 14(d)) toward the CNR. The local extinction along the Western Arc ranges from A_Pα ∼ 1 to 2 after correcting for interstellar extinction; this translates into a 19.7 μm (and 37.1 μm) extinction of less than one at the regions of peak extinction. Therefore, as a first approximation, the local, differential extinction derived by the Paschen-α and 6 cm maps is not significant at our wavelengths.

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As mentioned in Section 3.2, the 19.7 μm emission primarily traces the ionized gas region of the CNR, which is where the Paschen-α and radio free–free emission originate. Unlike for Paschen-α, we do not have a relation that provides us with the intrinsic 19.7 μm emission given the 6 cm emission. We therefore produce an extinction map relative to the extinction toward a fiducial region in the 19.7 μm and 6 cm maps (the red circle in Figures 14(c) and (d)). We assume that the intrinsic, unextinguished emission at 19.7 μm and 6 cm are directly proportional at all locations around the ring: $I_{19\,\mu \mathrm{m}}^{\mathrm{Int}}\propto I_{6\,\mathrm{cm}}^{\mathrm{Int}}$. The relative extinction at 19.7 μm is $\tau _{19\,\mu \mathrm{m}}^{{(x, y)}}-\tau _{19\,\mu \mathrm{m}}^{\mathrm{(ref)}}$, where $\tau _{19\,\mu \mathrm{m}}^{\mathrm{ref}}$ and $\tau _{19\,\mu \mathrm{m}}^{{(x, y)}}$ are the extinction values toward the reference region and toward an arbitrary position on the map, respectively. Assuming the extinction at 6 cm is negligible, the relative extinction can be derived from the relation shown in Equation (5) provides the relative extinction, where we have taken the extinction at 6 cm to be negligible.

$$\begin{equation} \left(\frac{I_{19\,\mu \mathrm{m}}^{\mathrm{Obs}}}{I_{6\,\mathrm{cm}}^{\mathrm{Obs}}}\right)_{\mathrm{ref}}=\left(\frac{I_{19\,\mu \mathrm{m}}^{\mathrm{Int}}}{I_{6\,\mathrm{cm}}^{\mathrm{Int}}}\right)_{{(x, y)}}e^{{\tau _{19\,\mu \mathrm{m}}^{(x, y)}}-\tau _{19\,\mu \mathrm{m}}^{\mathrm{ref}}}. \end{equation} \tag{ 5 }$$

We produce a map of the local extinction (Figure 14(c)) by referring to the local extinction map derived from the Paschen-α/6 cm ratio (Figure 14(d)) to determine the value of $\tau _{19\,\mu \mathrm{m}}^{\mathrm{ref}}$. The local extinction derived from the 19.7 μm/6 cm ratio ranges from A_Pα ∼ 2.5 to ∼4 (or A₁₉ ∼ 1 to ∼1.7) along the Western Arc, which is somewhat larger than obtained using Paschen-α and 6 cm maps (see below). We apply this local extinction correction to the dereddened 19.7 and 37.1 μm images and find that the total flux along the Western Arc increases by ∼60% and ∼15%, respectively. The corrected 19.7/37.1 color temperature map does not exhibit deviations greater than ±10 K (∼15%) from the uncorrected color temperature map, which is on the order of our estimated error. Since the 37.1 μm flux and the color temperature do not change significantly we choose to ignore the effect of differential extinction and stand by our original analysis. Of course the assumptions of a constant 19.7 μm–6 cm ratio likely introduces additional uncertainty to the intensity maps corrected this way.

As noted above, the local extinction derived from the 19.7 μm and 6 cm maps deviates from the extinction derived using the Paschen-α and 6 cm maps (Figure 14(d)) by a factor of ∼2. This suggests that the extinguishing material in the molecular region of the CND is very porous and "clumpy" since the Paschen-α map will reveal only the emission unabsorbed by the intervening clumps, whereas the emission at 19.7 μm can penetrate through these same clumps and appear in the 19.7 μm map. The evidence of clumpiness is consistent with the analysis of the CND performed by Genzel (1989) and Davidson et al. (1992).

At the inner edge of the Western Arc of the CNR (Figure 15) we observe several small "clumps" that have an FWHM of ∼4''–5'' (∼0.15 pc). The clumps are regions of enhanced density relative to the CNR as opposed to being temperature peaks heated by an embedded source. The clumps are displaced radially inward from the CNR; however, radial velocity observations indicate that the clumps are indeed part of the CNR (Irons et al. 2012). We identify three clumps along the central, inner edge of other CNR labeled "A," "B," and "C" from north to south. Clump B has a strong radio counterpart (Yusef-Zadeh & Morris 1987) while clump A has a prominent molecular counterpart observed in HCN emission (Christopher et al. 2005). We derive the masses and densities of the clumps from the 37.1 μm optical depth map and assume their volume can be estimated by ∼4/3 π (FWHM/2)³. The clump properties are summarized in Table 4. We find that the clumps exhibit densities ranging from 5 to 9 × 10⁴ cm⁻³, which are consistent with the low-excitation clump densities derived by Requena-Torres et al. (2012) in their large velocity gradient analysis of CO observations at the northern and southern regions of the CND. Requena-Torres et al. (2012) derive slightly larger clump sizes (r ∼ 0.3 pc) than we do, but their estimate is not well constrained since it is partly degenerate with the kinetic temperature. Under the assumption that the clumps are virialized, Christopher et al. (2005) determine a mass and density for clump A (core V in Christopher et al. 2005) of ∼2400 M_☉ and n ∼ 10⁷ cm⁻³ from the HCN emission. The virial density estimate would imply that the clumps are stable against tidal disruptions; however, our density estimates, as well as those of Requena-Torres et al. (2012), suggest the clump densities are a factor of ∼10³ too low to meet the stability requirement.

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Table 4. Observed Clump Properties

Clump	d	FWHM	Td	$n_{{\rm H_2}}$	Mass from τ37a
	(pc)	(pc)	(K)	(× 104 cm−3)	(M☉)
A	1.14	0.13	90	5	∼1.5
B	1.25	0.15	86	9	∼2.0
C	1.13	0.13	80	5	∼2.5

Note. ^aAssuming a gas-to-dust mass ratio of 100.

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We perform a simple calculation to estimate the lifetime of the clumps assuming that they are not virialized, so that their lifetime is limited by the rate at which they are azimuthally sheared as the CNR undergoes differential, Keplerian rotation around Sgr A*. Given the approximate extent of the clumps in the radial direction from Sgr A* (∼0.15 pc), we identify the recognizable lifetime of a clump with the time required for its opposite sides to separate azimuthally by a distance equal to the azimuthal separation of the clumps, ∼0.3 pc. This yields a clump lifetime of ∼40, 000 yr, or about half of the orbital period of the CNR.

Figure 16 shows the observed 37.1 μm intensity residuals after subtracting the 37.1 μm intensity model (Figure 12). The clumps appear prominently at the inner edge of the Western Arc where the emission is greater than that predicted by the model, while in between the clumps along the ring the residuals are near zero. Interestingly, we find that the intensity model over-predicts the emission "behind" the clumps, implying that they are likely shadowing the material further within the CNR. Given our derived dust grain parameters and assuming a clump density of 5 × 10⁴ cm⁻³ we calculate that the distance to the point at which τ_V = 1 within the clump is ∼0.08 pc, which is on the order of the projected clump width; therefore, the clumps may indeed be shadowing the CNR material.

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While the CND is not a fully relaxed system, its relatively high degree of order and symmetry (e.g., Jackson et al. 1993) suggest that it has undergone at least a few rotations since its formation. Consequently, the very existence of such clumps is difficult to understand if they are not self-gravitating. We will turn to this key question in a subsequent paper.