3 Distribution of the carbon line forming gas in the Galactic disk

   
3.1 Observed longitudinal variation of integrated line Intensity

The variation of velocity-integrated line-to-continuum temperature ratio, velocity-integrated line strength of carbon RRLs and continuum temperature with galactic longitude observed in the low-resolution survey is shown in Fig. 2. The line-to-continuum ratio for optically thin case is approximately given by (Shaver 1975),

$$% \frac{T_{\rm L}}{T_{\rm C}} \sim -\tau_{\rm L} + \frac{T_{\rm e} \tau_{\rm L}}{T_{\rm C} \beta_n},$$ (1)

where $T_{\rm L}$, $T_{\rm C}$ and $T_{\rm e}$ are the line brightness temperature, continuum brightness temperature and electron temperature respectively and $\tau_{\rm L}$ is the non-LTE line optical depth. $\beta_n \sim 1 - \frac{kT_{\rm e}}{h\nu} \frac{{\rm d}~\ln(b_n)}{{\rm d}n}$ for $\Delta n$ = 1 transition. Here k is the Boltzmann's constant, h is the Planck's constant, $\nu$ is the frequency of the line emission and b_nis the departure coefficient. $\beta_n$ is a measure of the non-LTE effects on the level populations. For getting Eq. (1), it is also assumed that the beam dilution is negligible and the measured continuum temperature is approximately the background temperature at the location of the line-forming region. Since $-\beta_n \sim$ 50-100 at levels near $n \sim 272$ for typical physical conditions of the line-forming region, the line-to-continuum ratio is approximately the line optical depth even for the case where $T_{\rm e} \sim T_{\rm C}$. If we assume that beam dilution is negligible and the background temperature is the measured continuum temperature, both of which might not be true for all longitudes, then we can conclude that the top panel of Fig. 2 shows the variation of velocity-integrated line optical depth with longitude. If the assumptions are not valid, then the plotted values will be the apparent integrated optical depth which would be a lower limit on the actual integrated optical depth. The integrated optical depth (top panel in Fig. 2) is constant ($\sim$0.01 km s^-1) within $3\sigma$ measurement errors for most of our detections. From the top and middle panels, it is evident that line emission is concentrated in the longitude range 358$^\circ$ $\rightarrow$20$^\circ$ with a few detections at longitudes between 20$^\circ$ and 89$^\circ$. The strongest integrated line strength and continuum are observed toward the Galactic center. This is a good case of stimulated emission; the optical depth toward this region is not enhanced as compared to the neighboring longitudes. The bump near l = 80$^\circ$ (see Fig. 2) seen in all three distributions is from the gas associated with the well-known Cygnus complex located in the nearby Orion spiral arm. There are only a couple of detections in the fourth quadrant.

After examining the observed distribution of the line emission with longitude (Fig. 2) and various factors at play, we conclude that the paucity of detections at longitudes outside the range 358$^\circ$< l < 20$^\circ$ may not be real but a result of one or more of the following selection effects: 1) reduced background radiation field leading to reduced stimulated emission and hence weaker lines. This, we believe is the reason for fewer detections at longitudes >20$^\circ$. Since the intensity of carbon RRLs is amplified by the non-thermal background continuum due to stimulated emission (Paper I), the gradual drop in the non-thermal continuum with increasing longitudes might be partially responsible for the drop in the line strengths and subsequently lesser number of detections between longitudes 20$^\circ$ and 80$^\circ$. 2) Beam dilution within the large low resolution survey beam leading to reduced line strengths and our sensitivity-limited sample failing to detect these lines. This is likely the dominant cause of non-detection of lines in the fourth quadrant. The ORT has an equatorial mount and electrical phasing is used to point the telescope along the declination axis. At longitudes l < 355$^\circ$ due to a variety of reasons (e.g. improper phasing) the telescope sensitivity drops and also the beam size increases (Roshi 1999). The drop in the continuum temperature at these longitudes (Fig. 2) is a result of this effect. On the other hand, negligible beam dilution effects could be one of the reasons we detect the carbon lines from the Cygnus region ($l \sim 80$$^\circ$) located in the nearby Orion arm despite the background radiation field being weaker than the regions between l=20$^\circ$ to 80$^\circ$ and the presence of increased beam size as in negative longitudes.

Figure 2: Velocity integrated carbon line-to-continuum temperature ratio (top panel), velocity-integrated carbon line temperature (middle panel) and the continuum emission (bottom panel) near 327 MHz, observed in the low-resolution (2$^\circ$ $\times$ 2$^\circ$) survey, plotted as a function of galactic longitude. The horizontal lines in the top and middle panels indicate the observed positions where carbon lines are detected. The vertical bar represents the 3 $\sigma$ uncertainty in the plotted parameters. The dashed lines in these plots indicate observed positions with no detections and give the upper limit on the quantities plotted. These limits were estimated from the rms noise ($\sigma$) on the spectra and assuming a typical width for the carbon line as 17 km s-1. The continuum temperature plotted in the bottom panel is the measured antenna temperature corrected for the beam efficiency factor (0.65) and is same as $T_{\rm C}$ discussed in Sect. 3.1 under the assumptions stated in that section.

Figure 3: Longitude-velocity (l-v ) diagrams constructed from carbon RRL emission at 327 MHz data: a) using data from low-resolution (2$^\circ$ $\times$ 2$^\circ$; Paper I) survey; b) using data from high-resolution (2$^\circ$ $\times$ 6$^\prime$) survey. The marker indicates the central velocity whereas the length of the segment indicates the line width of the detected carbon lines. The four spiral arms (1 to 4 as designated by Taylor & Cordes 1993) are shown as solid lines in each of the l-v diagrams. The dashed and dotted lines in each frame correspond to gas at galactocentric distances of 3.7 kpc and 7 kpc respectively. The dash-dot-dot-dot-dash line indicates the locus of tangent points.

The few positions where carbon lines were detected in the longitude range 20$^\circ$ to 80$^\circ$ show the presence of either H  II regions or supernova remnants within the 2$^\circ$ $\times$ 2$^\circ$ region centered at these positions, which suggests that the carbon line emission might be associated with star forming regions. Moreover, these detections appear at velocities close to the tangent point velocities at those longitudes. The long path lengths near the tangent points might have favored the detection of carbon lines in these directions. Higher sensitivity observations of these regions should show more detections in this longitude range if this is the case. Indeed, our high-resolution survey data has detected carbon lines at several positions between l = 20$^\circ$ to 38$^\circ$ as listed in Table 1. This clearly indicates that diffuse C  II regions exist in this longitude range and the selection effects noted above are likely responsible for their non-detections in the low-resolution survey.

   
3.2 $\mathsfsl{l}$- $\mathsfsl{v}$ diagram

The longitude-velocity diagram constructed from RRL observations of the galactic plane can be used to understand the distribution of the carbon line-forming gas in the galactic disk if we make the standard assumption that the observed central velocity of the line is due to differential galactic rotation. The l-v diagrams plotted for the low-resolution and high-resolution survey data (Figs. 3a and b) show that the carbon line emission arises from gas located at galactocentric distances beyond 3.7 kpc. The line-forming gas at longitudes $\le$50$^\circ$ is confined between galactocentric distances of 3.7 kpc and 7.0 kpc. Moreover, line emission in the low-resolution survey for longitudes $\le$50$^\circ$ shows, in general, some confinement to the spiral arms. The galactic rotation model used here has been taken from Burton & Gordon (1978) after scaling it to $R_\odot$ = 8.5 kpc and $\theta_0$ = 220 km s^-1. Figure 4 shows the location of the line-forming regions obtained from the low-resolution survey in the plane of our Galaxy between l = 4$^\circ$ to 20$^\circ$. These regions have been placed at the near kinematic distance. This is a reasonable assumption since the large beam width (2$^\circ$ $\times$ 2$^\circ$) of the low-resolution survey is likely to make the observations more sensitive to nearby regions. From the figure, it appears that most of the carbon line-forming gas in this longitude range is associated with spiral arm 3. Only toward l = 9 $.\!\!^\circ$3, the near kinematic distance places the line emitting region near spiral arm 2. No line emission is detected from spiral arm 1 in this longitude range. In the high-resolution survey, line emission is detected over a wider velocity range between l = 0$^\circ$ and 40$^\circ$ compared to that in the low-resolution survey (Fig. 3). In general, the velocity range over which carbon lines near 327 MHz are detected in the surveys is similar to the velocity spread of spiral arm tracers, for example, hydrogen RRLs near 3 cm from H  II regions (Lockman 1989). No line emission is detected from spiral arm 4 in the longitude range 20$^\circ$ to 89$^\circ$ in both surveys. A few line detections in this longitude range have velocity close to the tangent points. This is also a feature seen in the l-v diagram of spiral arm components in this longitude range (see, for example, 3 cm RRL emission from H  II regions; Lockman 1989). In summary, the l-v diagram of carbon line emission displays several similarities with those of spiral arm tracers.

Figure 4: Locations of the carbon line emitting regions (filled circles) between l = 4$^\circ$ to 20$^\circ$ are shown in galactocentric coordinates. The regions are placed at the near kinematic distances estimated using the observed central velocity of carbon line emission. Most of the detected carbon line forming regions in this longitude range lie in spiral arm 3. The region of the galactic disk covered by the 2$^\circ$ wide field centered at G13.9+0.0 is also shown. This region intercepts spiral arms 3, 2 and 4 at a distance $\sim$1.9, 3.7 and 14.1 kpc from the Sun.

We compared the l-v diagrams obtained from the 327 MHz survey with those obtained from the carbon absorption line data near 76 MHz (Erickson et al. 1995) and 35 MHz (Kantharia & Anantharamaiah 2001) since the observations at these three frequencies overlap in the longitude range l = 332$^\circ$ $\rightarrow$ 20$^\circ$. The l-v diagrams show similar features. At all the three frequencies, most of the detections are at longitudes <20$^\circ$. The l-v diagrams obtained from the three observations indicate that the detected carbon line forming regions are confined between galactocentric distances of 3.7 to 8 kpc suggesting that they arise in the same diffuse C  II regions. However, the width of lines detected in absorption in many cases are larger (up to a factor of 2) than that of emission lines observed in the low-resolution survey. The different line widths can be due to (a) different beam widths of the surveys and (b) effect of pressure and radiation broadening which have a strong dependence on the principal quantum number ($\alpha$ n^8.2 and n^8.8 respectively for widths in km s^-1; Shaver 1975). Interestingly, the width of the absorption line seems to extend over the velocity range over which emission lines are observed in the high-resolution survey at the corresponding longitudes. Absorption lines near 76 MHz have been detected extensively at longitudes 340$^\circ$ < l < 360$^\circ$ for which we have few detections near 327 MHz. This is likely a case of lack of sensitivity (see Sect. 3.1 for more details) than any intrinsic property of the line-forming regions. The general similarity of the l-v diagrams obtained from the three observations indicates that the carbon lines observed near 76 MHz and 35 MHz are the absorption counterparts of the carbon lines detected in emission near 327 MHz.

3.3 Radial distribution

An l-v diagram gives a qualitative understanding of the distribution of ionized gas in the galactic disk. However, a more quantitative study can be made by computing the average emission as a function of the galactocentric radius. Since the ionized gas at "near'' and "far'' kinematic distances will be at the same galactocentric distance, the radial distribution is not affected by the two-fold ambiguity in estimating the line-of-sight distance. However the distribution will depend on several other factors: (a) the sensitivity of the observations to line-forming regions at different distances along the line-of-sight; (b) amplification of line intensity due to stimulated emission by galactic non-thermal background; (c) choice of the rotation model used for the computation.

The radial distribution of the different traces of the interstellar medium (Fig. 5) are computed using the method described in Paper I. In the computation for the carbon lines near 327 MHz, the Gaussian fits to the observed profiles were used instead of the actual spectra. This was necessary since the typical peak line intensity to rms noise for a carbon line detection is only $\sim$3 to 4. Using the Gaussian fit profile also eliminates any contamination from the hydrogen line emission, particularly for $R_{{\rm GC}}$ < 2 kpc. We have used the carbon line data from the low-resolution survey between l = 4$^\circ$ to 84$^\circ$ in the computation since in this longitude range other components of the ISM (H  II regions and ¹²CO emission) are well sampled and hence a direct comparison of their distribution with the carbon line data is possible.

Figure 5: The radial distributions (average emission $\Gamma$ vs. galactocentric radius $R_{{\rm GC}}$) of different components of the ISM are shown in the figures. The radial distribution of a) carbon RRL emission from the galactic plane near 327 MHz, b) carbon RRL emission from the galactic plane near 327 MHz in the longitude range l = 4$^\circ$ to 20$^\circ$, c) hydrogen RRL emission from H  II regions near 3 cm and d) "intense'' ( $T_{\rm A} >$ 0.5 K) 12CO emission from the galactic plane. The radial distributions in a), c) and d) were computed using the data in the longitude range 4$^\circ$ < l < 84$^\circ$ where all the components of the ISM are well sampled. The data are taken from Paper I (327 MHz carbon RRL), Lockman (1989) (RRLs from H  II regions) and Dame et al. (1987) (12CO).

The radial distribution obtained from the low-resolution survey carbon line data (see Fig. 5a) shows that the average emission extends from $R_{{\rm GC}}$ = 2.5 kpc to 9 kpc with a prominent peak near 6 kpc. About 90% of the total observed carbon line emission originates between galactocentric distance 3.7 kpc and 8 kpc. The distribution falls off steeply on either side of the 6 kpc peak, the half width being 3.0 kpc. However, the true distribution is likely to be narrower than this because the broadening of the distribution due to intrinsic velocity dispersion has not been taken into account. An increase in line emission near 8.5 kpc is also seen which is due to the Cygnus loop region in the nearby Orion arm.

The spiral arm structure in the galactic disk should be evident in the radial distribution if the line emission shows some confinement to the spiral arms. In Fig. 5b, the carbon line distribution computed using data in the longitude range, l = 4$^\circ$ to 20$^\circ$ is shown. Since most of the carbon line emission we detect is from this longitude range, it resembles the distribution in Fig. 5a with the prominent peak near 6 kpc clearly seen and the small peak near 8.5 kpc missing. As discussed in Sect. 3.2, the line emission in this longitude range is likely to be confined to spiral arm 3, which naturally explains the peak at 6 kpc since the average distance to the spiral arm is $\sim$6 kpc. Comparing Figs. 5a and b, it is seen that (a) shows slight excess emission near 4 kpc. Although there is no prominent peak in our low resolution data (Fig. 5a) there is some carbon RRL emission at 4 kpc distance associated with spiral arm 2. Moreover, we do detect emission from spiral arm 2 from several positions within this longitude range in our high resolution survey data (see Fig. 3b). Future higher resolution, sensitive observations are required to check the widespread presence of carbon line emission in spiral arm 2 in the inner Galaxy.

We compared the radial distribution of the carbon line emission with other components of the ISM to check for any similarities that may exist. We find that the radial distribution of carbon lines is distinct from that of H  I. The latter is observed up to the outer reaches of the Galaxy (Burton 1988) whereas the carbon line emission is confined to galactocentric distances between 2.5 kpc to 9 kpc with well-defined peaks in its radial distribution. Comparing the radial distribution of carbon line emission with the distribution of the 3 cm hydrogen RRL emission from compact H  II regions and "intense'' ¹²CO emission (Figs. 5c and d), both spiral arm tracers (Solomon et al. 1985), we find a number of similarities. Both, the 3 cm hydrogen RRL emission and ¹²CO emission are confined (see Figs. 5c and d; for details see Paper I) in the range $R_{{\rm GC}}$ = 2.5 kpc to 9 kpc which is similar to the carbon line emission. A peak near 6 kpc is seen in the distribution of 3 cm hydrogen RRL emission and considerable ¹²CO emission is present at the radial distance of 6 kpc, which is similar to that seen in the distribution of carbon line emission. We conclude that the carbon line emission near 327 MHz has similar galactic disk distribution as that of the star-forming regions. This result may appear somewhat different from what we know about the gas toward Cas A - where the morphology of the carbon line forming gas resembles the distribution of H  I observed in absorption across Cas A (Anantharamaiah et al. 1994) and no hydrogen RRL has been detected (Sorochenko & Smirnov 1993). However, it is not contradictory since in the inner Galaxy, the distribution of H  I observed in absorption resembles that of ¹²CO. H  I with $\tau_{{\rm HI}} >$ 0.1 shows an 85% probability of being associated with ¹²CO emission (Garwood & Dickey 1989).