M-BAND SPECTRA OF DUST-EMBEDDED SOURCES AT THE GALACTIC CENTER

In order to calibrate the CO ice, we selected IRS 2L as a calibration source. Indeed, IRS 2L has been identified as a B-type star (Clénet et al. 2001), it is thus free of CO bandhead absorption and has a relatively flat spectrum in the M band. Its spectrum shows a high signal to noise and well pronounced ice absorption with only weak traces of CO gas absorption. Moreover, we have assumed that the overall absorption toward IRS 2L is dominated by line-of-sight ice-absorption since this source is located close but not inside the mini-spiral area and is clearly not behind the CND material. For all these reasons, the line shape of the IRS 2L spectrum can be used as a template for the foreground ice absorption toward all other sources in the field and to correct for the contribution of this ice feature (see Figures 3 and 6(a)). In the following, we assume that the foreground CO ice absorption has the shape of the template spectrum but we allow for a small variation in the amount of this absorption from source to source.

On the other hand, the absorption trough toward short wavelengths in the IRS 2L spectrum is indicative of a possible contribution of XCN absorption (see Section 3.3, and references therein). Therefore, this spectrum is also well suited to calibrate a possible XCN line-of-sight absorption.

To derive the CO ice absorption spectrum shown in Figure 6(a), we smoothed the IRS 2L spectrum and got rid, in this way, of the features not belonging to the CO ice feature, which are the Pf_β and the prominent feature between the P and R branches (at about 4.67 μ) of the CO gas feature; we then normalized the continuum to one.

The individual source spectra were divided by the resulting ice foreground absorption spectrum diluted by an additional adjustable continuum contribution (which accounts for a possible variation in the amount of absorption), with the condition that the spectral region between the P and R branches of the remaining gaseous absorption should be at the same flux density level as the continuum around 4.73 μm and 4.80 μm wavelength.

In this process, we assumed that the spectral region centered at a wavelength of 4.73 μm and 4.80 μm (i.e., between the ¹²CO and ¹³CO and longward of the ¹³CO absorption features) is a continuum and therefore, must be at the same level as the continuum region longward of the ¹³CO absorption feature in the final corrected spectra, as it is the case in the theoretical CO spectrum (see Figures 8 and 6(b)). This procedure is feasible since both the CO ice absorption and the center of the CO gas absorption are well separated from each other (by about a FWHM of the CO ice absorption feature).

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The resulting spectra are shown in Figure 9.

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Under these conditions, we find a mean value of the diluting continuum of about 4 Jy for all the sources in the field, including the calibrator source IRS 2L (the values of the diluting continuum toward individual sources are shown in Table 1). This means that the mean foreground solid CO extinction spectrum is obtained by shifting the template spectrum shown in Figure 6(a) by 4 Jy. Then, the continuum is at 5 Jy (4+1 Jy) and the minimum of the absorption is at about 4.25 Jy (4+0.25 Jy). Defining the "absorption strength" as being the ratio between the continuum intensity and the minimum absorption intensity (i.e; I_c/I_a), the solid CO absorption strength is about 1.2 (i.e., 5/4.26 ∼ 1.2), while the one of the template is of 3.8 (1/0.26 ∼ 3.8). This means that about 1/3 of the ice template absorption strength is due to foreground material along the line of sight which corresponds to an optical depth of τ∼ 0.1–0.2 (τ = −ln(I_a/I_c)). For residual ice absorption, see comments in Section 3.2. Allowing for larger amounts of foreground absorption leads to an over-correction of the spectral region between the CO P and R branches.

Please notice that a dilution was also needed in the case of the IRS 2L spectrum (which was used to derive the template spectrum) because gaseous CO and Pf_β features are also present in this spectrum even though they are not very prominent. Thus, correcting this spectrum for the foreground solid CO extinction should also take into account that the region between the P and R branches of the gaseous CO feature and the regions between the ¹²CO and ¹³CO and longward of the ¹³CO absorption features are part of the continuum.

The column density of solid-state CO can be derived via N(CO)_s ∼ τW_S/A with the FWHM of the line W_S in cm⁻¹ and with the absorption strength A = 1.7 × 10⁻¹⁷ cm molecule⁻¹ (Sandford et al. 1988). From the fact that on average about one third of the ice-template depth (Figure 6(a)) absorption is due to foreground material in order to reproduce the line shape of the CO gaseous absorption shown in Figure 8, we derive an optical depth of the foreground solid CO absorption of τ∼ 0.1–0.2. With W_S∼ 6–7 cm⁻¹∼ 0.016 μm (see Figure 6), we obtain N(CO) ∼ 7 × 10¹⁶ cm⁻² (see Table 2).

Using a CO versus H₂ abundance ratio for typical diffuse Galactic molecular clouds ([¹²CO]/[H₂] = 3 × 10⁻⁶), we then estimate the molecular gas column density associated to the foreground solid CO as N(H₂) ∼ 2.3 × 10²² cm⁻² (see Table 2 for more details). If the absorption takes place in the diffuse ISM, we find values for the visible extinction of A_V = 14–28 (for τ = 0.1) or 27–53 (for τ = 0.2) using the value of A_V/N(H₂) of about (1–2) × 10⁻²¹ mag cm⁻² (Bohlin et al. 1978; Moneti et al. 2001; see Table 2). An A_V/N(H₂) of 1 × 10⁻²¹ mag cm⁻² would be consistent with the case where a dominant fraction of neutral hydrogen is molecular (Bohlin et al. 1978).

In several nearby galaxies (e.g., M33, NGC4565, M101), far-infrared continuum measurements have revealed the presence of an extended T = 16–18 K cold dust component that is smoothly distributed over the disk and is likely heated by the diffuse interstellar radiation (Neininger et al. 1996; Hippelein et al. 2003; Suzuki et al. 2009). Warmer dust components are more concentrated toward the spiral arms of these systems and associated with star-forming regions. The temperature range is right at or just below the temperatures at which CO desorbs from ice mantels, such that one can expect an appreciable amount of CO ice being associated with this component (Collings et al. 2003; Bisschop et al. 2006; Acharyya et al. 2007). This ISM phase can obviously not exclusively be associated with the dense star-forming molecular cloud complexes in the spiral arms but covers an extended cold dust distribution, also strongly associated with the inter-arm region. It is quite likely that a similarly extended component is existent within the Milky Way, such that the line of sight toward the GC samples this cold ISM phase extensively.

Low temperatures (Burgh et al. 2007) and the relevance of hydrogenation processes on grain surfaces (O'Neill et al. 2002; Viti et al. 2000) indicate that in fact a very large portion of CO may be frozen out in diffuse and translucent clouds. This indicates that a substantial fraction of the extinction is caused by the dust associated with the corresponding more volatile H₂ gas that remains in the gas phase (see e.g., Duley 1974; Lee 1972, 1975). Alternatively, mixed models in which a significant portion of the extinction takes place in a diffuse ISM, with little CO and no CO ice, and in dense clouds with higher abundances of CO and CO ice are plausible as well.

This indicates that the hydrogen column (along with the dust) associated with the frozen out CO can fully account for the extinction of 25–30 mag toward the GC, which is consistent with the findings by Schödel et al. (2007), Scoville et al. (2003). In case that the absorption takes place predominantly in dense molecular clouds, we find values of A_V = 1–2 which do not account for the observed values of 25–30 mag. (see Table 2).

Since only less than one third of the interstellar extinction can be attributed to the dense ISM (Whittet et al. 1997), more than two thirds have to be attributed to the diffuse Galactic ISM. If this latter is in a cold neutral phase (CNM; Jones 2002; Wolfire et al. 1995; Field et al. 1969; Ferriere et al. 1988), it would support our finding and our use of the molecular abundance value of the diffuse ISM.

The R = 800 (Δv = 375 km s⁻¹) spectra corrected for CO ice absorption show a gaseous ¹²CO rotation-vibration absorption around 4.666 μm and an indication for a gaseous ¹³CO rotation-vibration absorption around 4.77 μm. These absorption features are weak in the IRS 2L spectrum, therefore the latter was not used to calibrate the foreground gaseous ¹³CO absorption. We show in Figure 8, the theoretical spectrum of these absorptions as calculated by Moneti et al. (2001) smoothed to our spectral resolution. Compared to this model, our observed relative strengths of the two isotopic line absorptions (see Figure 9) indicate temperatures higher than T = 10 K or the presence of a mixture of warm (T ≫ 10 K) and cold (T ⩽ 10 K) gas absorption.

As stated by Moneti et al. (2001), the ¹²CO lines are highly saturated (also, Geballe et al. (1989) quote optical depths of τ∼ 2 in the J = 1 − 0 R(2) line of IRS 1 and IRS 3 with overall lower absorption depths in the J = 1 − 0 R(5) line). On the other hand, due to the low abundance of the ¹³CO, its lines are not expected to be saturated. Therefore, in what follows, we will use the prominent ¹³CO R(0) line to estimate the foreground CO gaseous absorption and its corresponding optical extinction.

For the hot and non-embedded IRS 16 sources, the estimate of the ¹³CO absorption strength corresponds to that expected for cold (T ⩽ 10 K) molecular gas (see Figure 9). This is also true for IRS 16C that is located off the mini spiral and therefore also most likely free of local GC absorption. Since the gas and dust temperatures at the GC are much higher than that, we identify this ¹³CO line absorption as being due to foreground extinction due to gaseous and determine an optical depth at our spectral resolution of $\tau _{^{13}{\rm CO}} \sim 0.11\pm 0.02$.

Assuming a fractional abundance in dense molecular clouds of [¹³CO]/[H₂] ∼ 5 × 10⁻⁶ (Rodriguez-Fernandez et al. 2001) and a temperature in the foreground material of the order of ∼10 K, we get a ¹²CO column density based on the ¹³CO absorption of about N(¹²CO) ∼ 3.2 × 10¹⁸, using the following equation (Geballe et al. 1972; Tielens et al. 1991; Moneti et al. 2001; Eyres et al. 2004),

$$\begin{equation} N(^{13}{\rm CO})_g \sim 3\times 10^{14} \tau T \Delta v/(J+1) \times {\rm exp}(E/kT), \end{equation} \tag{ 1 }$$

where J and E are the rotational quantum number and the energy above the ground of the absorbing level, respectively. Our result is consistent with the ¹²CO column density found by Moneti of N(¹²CO)_g∼ 6.6 × 10¹⁸.

Given the uncertainties in the temperature, the isotopic CO abundance ratio, the A_V/N(H₂) ratio, optical depth measurement, and the spectral resolution, the corresponding visual extinction A_V covers a large range of values with a minimum of the order of 25 mag which is consistent with previously published results. This indicates that the gaseous CO absorption in dense molecular clouds can also account for the foreground extinction to the GC and that it can be comparable to the amount of extinction traced by the deep CO ice absorption features in diffuse clouds. In Section 3.4, we investigate how much of the extinction may be associated with the dust and gas envelopes around the embedded stars at the GC.

Based on 63 μm [O i] ³P₁ → ³P₂ emission line measurements, Jackson et al. (1993) find a total of 300 M_☉ of neutral atomic hydrogen within the 1.5 pc radius CMD. The dominating amount of that emission is located along the northern spiral arm. With an overall extend of the northern arm of about 40'' × 5'' this results in mean mass surface density of ∼1.5 M_☉ arcsec⁻². From the 22'' resolution map of the [O i] line emission shown in their Figure 5, we conclude that no more than about 1/5 of the material traced by the 63 μm [O i] line is located along the inner 20'' section of the northern arm. From the analysis of the [O i] line emission the authors deduce a mean combined H i and H₂ particle density of (1–3) × 10⁵ cm⁻³.

Bradford et al. (2005) mapped the ¹²CO(7–6) line emission within the CND. A part of the molecular line emission that can be attributed to the northern arm covers mostly the inner 20'' portion of it. For the northern arm Stacey et al. (2004) derive a gas mass of 5–50 M_☉. From the analysis of the CO(7–6) line emission the authors deduce a mean combined H i and H₂ particle density of 3 × 10⁴ cm⁻³. This value is consistent with the one used for bow shock modeling of these sources by Tanner et al. (2002, 2005).

From the mean particle density $n_{\rm HI,H_2}$ (per cm³) and the mean diameter of the sources of 01 follows a mean gas mass of the gas and dust shell of about $M_{\rm gas}[M_{\odot }]=1.7 \times 10^{-9} n_{\rm H \,{\mathsc i},H_2} \eta \zeta$. Here, η is an area filling factor (in projection on the sky) of the mini spiral that we assume to be of the order of 10%. The pileup of mini-spiral material due to the interaction with the bow shock is described by the factor ζ. A bow shock source has typically moved half way through an approximately 4'' long stretch of the mini spiral. The bow shock typically extends over about half a 01 diameter sphere. In this scenario, the bow shock may contain about ζ = 4''/01 = 10 times more gas and dust than the surrounding mini-spiral ISM. The actual enhancement of the flux density in the bow shock is probably much larger due to scattering of light from the central illuminating star. The amount of scattered light depends on the grain size spectrum (see comments on IRS 21 in Tanner et al. 2002). For densities in the range of 3 × 10⁴ cm$^{-3} \le n_{\rm H\,{\mathsc i},H_2} \le$ 3 × 10⁵ cm⁻³ we obtain total gas masses of a few 10⁻³ M_☉ up to 10⁻² M_☉. These masses could be larger by about an order of magnitude if the fractional abundances of CO versus H₂ for the diffuse ISM of 3 × 10⁻⁶ is used. Since the mini-spiral gas densities derived from sub-millimeter CO(7–6) and FIR [O i] line data are typical for the dense ISM, this would not be appropriate.

For the dust-embedded hot stars like IRS 1W, IRS 10W, and IRS 21 we find that due to their expected fast stellar winds (mass losses of 10⁻⁴ M_☉ yr⁻¹ at a velocity of typically 1000 km s⁻¹; Najarro et al. 1997; Tanner et al. 2002, 2005) the kinetic luminosity of that wind is comparable to that of the bow shock mass load due to the motion of the star through the mini spiral (i.e., 10⁻³ to 10⁻² M_☉ at a velocity of 200–300 km s⁻¹ over 10 to 20 years travel time through the northern arm). This leads to the fact that a bow shock is formed. If either of the two kinetic luminosities is much more dominant than the other then either a large cavity would be blown into the mini spiral or the motion of the star through the mini spiral would not lead to a recognizable interaction.

In this section, we calculate the typical source intrinsic 4.666 μm CO gas line absorption depths expected for the stellar dust envelopes assuming total gas masses of a few 10⁻³ M_☉ up to 10⁻² M_☉. We derive optical depths of the ¹³CO R(0) lines for the different observed sources from Equation (1). For our calculations, we derived the H₂ column density by dividing the gas mass estimates by the sky-projected area of the individual sources. Motivated by the brightness profiles for individual sources as given by Tanner et al. (2005) and taking into account the irregular horseshoe-like shape of the bow shocks we doubled the stand-off radius estimates in order to include all of the material. Then, given the densities suggested by the CO(7–6) and [O i] lines we have used fractional abundances of ¹³CO versus H₂ of 5 × 10⁻⁶ in order to derive gaseous ¹³CO column densities.

On the other hand, we consider that the gas and dust in the shells and bow shocks are likely to be warm. Measurements and model calculations of the circumstellar shells in IRS 21, IRS 1W, IRS 5, IRS 10W by Tanner et al. (2002, 2005) and IRS 3 by Pott et al. (2008) indicated dust temperatures between 400 K and 1000 K. Moreover, the 10 μm dust temperature map by Cotera et al. (1999) yield averaged dust temperatures of 200 K toward the mini spiral and most of the compact dust-embedded sources.

Besides, we assume that the random motions δv within the stellar winds and bow shock regions are of the order of 15 to 25 km s⁻¹ (Bradford et al. 2005; Eyres et al. 2004) possibly up to ∼100 km s⁻¹ (see spectra in Figure 5 of Jackson et al. 1993). The FWHM of ∼100 km s⁻¹ toward the individual sources obtained by Geballe et al. (1989) is most likely due to the velocity difference of the individual line-of-sight clouds.

We find that if the gas masses of the stellar shells or bow shocks are of the order of a few times 10⁻³–10⁻² M_☉ and if we use doppler line widths of 25 km s⁻¹ <δv< 100 km s⁻¹, then we obtain ¹³CO optical depths of the local gas of τ_c ∼ 0.07–0.26. At our spectral resolution of 375 km s⁻¹, we get optical depths of the order of τ_c ∼ 0.02 which is in the range of the corrected optical depths for foreground extinction listed in Table 1. In that table, we give the observed optical depths τ₀ of the ¹³CO R(0) derived from the spectra shown in Figure 9 of all observed sources at a resolution of 375 km s⁻¹. The actual optical depth at the line center at higher spectral resolutions may be higher. The τ_c values are the optical depths corrected for the mean foreground ¹³CO gas absorption as determined from the spectrum of the non-embedded hot IRS16C star (τ_IRS16C∼ 0.11 ± 0.02; see Section 3.1.3). The absorption depths toward all other sources are higher and can be determined with a correspondingly smaller uncertainty. Except for IRS 3, 9, 5 13, 21, and 29 the optical depths are 2σ to 3σ higher than that obtained toward IRS 16C.

This indicates that even though the 4.666 μm CO gas line absorption contains contributions from the intervening spiral arms, local molecular gas, and clouds close to the GC, a substantial amount of absorption observed at high-spectral resolution can be expected to be due to the circumstellar shells of the dust-embedded sources (see the case of IRS 3 below).

This finding can be discussed in the context of the Fabry–Pérot spectroscopic measurements by Geballe et al. (1989). These spectra were obtained through 5'' diameter apertures; 35 in the case of IRS 7. In all cases, these large apertures contain flux density contributions from several of the bright M-band sources that we study here. These apertures are also ideally matched to the extended mini spiral which is also bright in this wavelength domain. Furthermore, the pointing toward individual sources discussed by Geballe et al. (1989) was carried out by offsetting from a visible star and "in most of the cases by peaking up on the infrared signal." No accuracy is given for this process. In summary, these individual measurements are sensitive to absorption covering about 20 square arcseconds each. Compared to the 06 diameter slit in seeing as good as 07 this represents a dilution of the absorption from the individual stars by up to a factor of 40. The large area and the numerous possible absorbers may also be responsible for the width of the absorptions of 75–100 km s⁻¹.

For several sources observed by Geballe et al. (1989), radial velocities are known: IRS 1W: 20 ± 50 (Genzel et al. 2000), IRS 5: 110 ± 60 (Tanner et al. 2002, 2005), IRS 7: −103 ± 15 (Genzel et al. 2000), and IRS 8: +15 ± 30 (Geballe et al. 2006). For IRS 3, the findings by Geballe et al. (1989), Viehmann et al. (2005, 2006), and Pott et al. (2008) indicate that it is not located within the central half parsec—implying low radial velocities. In fact, IRS 3 could be an example of a source for which the absorption due to the circumstellar shell may be of importance. The prominent J = 1 − 0 R(2) absorption at 0 km s⁻¹ is significantly weaker in the J = 1 − 0 R(5) line indicating a colder or possibly lower column density component (Geballe et al. 1989). Since IRS 3 is a warm dusty source with a possibly low radial velocity, therefore, the absorption line at 0 km s⁻¹ could potentially be attributed to the gas and dust shell it is embedded in.

For IRS 1, the strong absorption at about 20 km s⁻¹ reported by Geballe et al. (1989) falls close to the radial velocity of the source and could be an intrinsic absorption feature. Similarly, the radial velocities of IRS 5, IRS 8, and possibly IRS 3 fall into or very close to the 0–75 km s⁻¹ range where all of the sources show absorption. Therefore, the foreground and intrinsic source absorptions could blend with each other. For IRS 7, Geballe et al. (1989) report intrinsic photospheric absorption with a prominent feature at −130 km s⁻¹ close to the radial velocity of the star. However, if a substantial amount of absorbing material is associated with the IRS 7 bow shock that highlights the interaction of the stellar atmosphere with a wind from the central region, then the source intrinsic absorption could also be closer to the 0–75 km s⁻¹ interval and blend with the foreground absorption. This may explain the slightly larger total line width seen toward that source.

With the exception of the early-type stars IRS 13 and IRS 16NE the known radial velocities (e.g., Genzel et al. 2000; Blum et al. 1996, 2003) of all other stars listed in Table 3 should show intrinsic absorption features outside the 0–75 km s⁻¹ interval.