6 Angular extent of carbon line-forming regions

Since only coarse resolutions are available at the low frequencies that diffuse C  II regions can be studied using recombination lines and observations at different frequencies have different angular resolutions, it has been difficult to obtain definitive estimates of the angular and linear sizes of the diffuse C  II regions. The ambiguity in the distances to these regions and the uncertainty in the angular size makes it difficult to obtain strict constraints on the linear size. Kantharia & Anantharamaiah (2001) modeled the carbon line data at three frequencies (35, 76 and 327 MHz) and obtained different physical models for different angular sizes of the line-forming region. They also attempted interferometric imaging of one position in the galactic plane in carbon recombination line using the VLA to obtain the angular extent of the line forming region. They obtained a lower limit on the angular size of 10'. Clearly the angular size is an important parameter entering into the modeling of these regions and needs to be understood better. Since carbon lines are detected extensively in our low-resolution survey, it is likely that the diffuse C  II regions are either 2$^\circ$ or more in angular extent or else consist of several small $\le$2$^\circ$ clumps within the beam. In this section we try to answer the question "do the line-forming regions consist of clumps with emission confined to small angular regions or is the emission extended and uniform over a large area?'' We make use of the high-resolution data to answer this question.

   

Table 2: Summary of the study of latitude extent of carbon line emission.

Position	$T_{\rm L}/T_{{\rm sys}}$ 1	$\Delta V$	$V_{\rm {LSR}}$	$V_{{\rm res}}$ 4	rms2	$t_{{\rm int}}$
	$\times$ 103	km s-1	km s-1	km s-1	$\times$ 103	hrs
Observations towards l = 0 $.\!\!^\circ$0
G0.0-2.5avg	0.13(0.02)	39.3(6.1)	4.3(2.6)	4.8	0.03	44.6
G0.0+2.5avg	0.32(0.03)	15.6(1.8)	2.9(0.7)	3.4	0.05	49.6
G0.0-3.0avg				7.6	0.03	32.1
G0.0+3.0avg	0.27(0.04)	12.5(2.2)	3.3(0.9)	3.4	0.06	37.7
G0.0-3.5avg				4.8	0.07	19.7
G0.0+3.5avg	0.34(0.06) 3	10.3(2.0)	2.8(0.8)	3.4	0.07	26.1
G0.0+0.0avg	0.20(0.02)	23.6(2.5)	2.7(1.0)	3.4	0.03	94.2
Observations towards l = 13 $.\!\!^\circ$9
G13.9-2.0avg	0.27(0.09) 3	9.2(3.5)	19.8(1.5)	4.8	0.09	29.0
G13.9+2.0avg	0.25(0.05)	11.0(2.5)	18.5(1.1)	4.8	0.05	30.8
G13.9|b|>1	0.15(0.05) 3	10.0(3.8)	18.5(1.6)	4.8	0.05	38.6
G13.9+0.0avg	0.23(0.04)	9.5(2.0)	18.9(0.8)	3.4	0.05	59.8
	0.12(0.03)	26.6(6.9)	44.6(2.9)	3.4	0.05	59.8

¹ The line intensities are given in units of $T_{\rm L}/T_{{\rm sys}}$, where $T_{\rm L}$ is the line
   antenna temperature and $T_{{\rm sys}}$ is the system temperature.
² rms is in units of $T_{\rm L}/T_{{\rm sys}}$.
³ Tentative detection.
⁴ The resolution to which the spectra are smoothed for estimating line parameters.

Figure 8: Carbon line emission near l = 35$^\circ$. Top five panels on the left show the spectra observed with an angular resolution of 2$^\circ$ $\times$ 6$^\prime$ toward the positions marked on each frame and the lowermost panel shows the spectrum obtained by averaging the five spectra. The observed positions are marked by the slanted lines on the 11 cm continuum map from Reich et al. (1990). The slanted lines represent the 2$^\circ$$\times$ 6$^\prime$ ORT beam. The LSR velocity and the width of the lines as a function of galactic longitude are shown in the plot on the right-hand side. The vertical bar represents the 3 $\sigma$ error in the estimated parameters.

6.1 Clumps in the diffuse C II regions

Figure 9: Carbon line emission toward a 5$^\circ$ (along l) wide region centered at l = 4 $.\!\!^\circ$25 and b = 0$^\circ$. The spectra shown in the panels in the first column are obtained by averaging the high-resolution (2$^\circ$  $\times$  6$^\prime$) survey data over a 2$^\circ$  $\times$  1$^\circ$ area centered on the galactic coordinates indicated in each frame. The top three spectra in the second column are from the low-resolution (2$^\circ$  $\times$  2$^\circ$) survey, observed toward the galactic coordinates indicated in each frame. The lowermost spectrum in the second column is obtained by averaging the high-resolution survey data over the 5$^\circ$ wide region. The LSR velocity and the width of the lines from the spectra averaged over a 2$^\circ$  $\times$  1$^\circ$ region, as a function of galactic longitude are shown in the right-hand side plot. The vertical bars represent the 3 $\sigma$ error in the estimated parameters. The narrow feature near 8 km s-1 is observed in all the spectra indicating that the line-forming region is fairly extended in the sky plane. The observed positions are marked by the slanted lines on the 11 cm continuum map from Reich et al. (1990). The slanted lines represent the 2$^\circ$  $\times$  6$^\prime$ beam of the ORT.

If the line emission arises in a homogeneous region with an angular extent of several degrees, then the line parameters observed at positions within this angular span are expected to be similar. Examination of the observed spectra in the high-resolution survey shows that at several positions there is considerable change in the line parameters when the beam center is shifted by $\sim$6' in declination. For example, the width of the observed carbon line toward the position G5.19+0.02 is $\sim$8 km s^-1 is about one-third the line width observed toward G5.33-0.03 ($\sim$23 km s^-1). The beam centers of the two positions are separated by $\sim$9$^\prime$. Another example is toward the direction l = 35 $.\!\!^\circ$1 and b = 0$^\circ$ (see Fig. 8). Carbon line is clearly detected in the integrated spectrum obtained by averaging the high-resolution survey data over the longitude range l = 34 $.\!\!^\circ$85 to 35 $.\!\!^\circ$31 (0 $.\!\!^\circ$5 (along l) $\times$ 2$^\circ$ (along b) region). However on examining the five contiguous spectra (observed with a 2$^\circ$$\times$ 6$^\prime$ beam) separated by $\sim$6$^\prime$, we find that the lines at positions with l < 35$^\circ$ have different central velocities compared to those at positions with l > 35$^\circ$ (see Fig. 8). Such behavior is exhibited toward many other positions separated by $\sim$6$^\prime$. This suggests that line emission in these directions arises from distinct diffuse C  II regions or else that the diffuse C  II regions have sub-structure on scales of $\sim$6$^\prime$. The near kinematic distance corresponding to the central velocity (48.6 km s^-1) of the line in the integrated spectrum (Fig. 8) is 3.3 kpc, which is close to the line-of-sight distance to the spiral arm 3 at this longitude. If the angular extent of the clump at l < 35$^\circ$ is $\sim$6$^\prime$ then it corresponds to a linear size $\sim$6 pc at the near kinematic distance. It, therefore, is likely that the diffuse C  II regions toward G35.1+0.0 consist of such small line-forming clumps.

6.2 Extended diffuse C II regions

A subset of our data also shows a behavior different from what we discussed in the previous section. The high resolution data within the longitude range l = 1 $.\!\!^\circ$75 to 6 $.\!\!^\circ$75 (within Field 2) seems to indicate the occurrence of a single C  II region extended over a region of angular size $\sim$5$^\circ$ in longitude. A similar extended ($\sim$2$^\circ$$\times$ 6$^\circ$) C  II region is also observed toward l = 13 $.\!\!^\circ$9, b = 0$^\circ$ (Field 3). These extended C  II regions are discussed in detail below.

   
6.2.1 Carbon line emission toward field 2

Here we examine the line emission seen from part of the 6$^\circ$ wide Field 2 (l = 1 $.\!\!^\circ$75 to 6 $.\!\!^\circ$75) that we mapped using the high resolution data. Most of the high-resolution spectra from this region detected a $\sim$14 km s^-1 wide carbon line centered on $\sim$8 km s^-1. To improve the signal-to-noise ratio of the line emission from the extended C  II region, we averaged the spectra over a region 1$^\circ$ (along l) $\times$ 2$^\circ$ (along b). The averaged spectra are shown in Fig. 9. The $\sim$14 km s^-1 wide component is clearly seen in all the spectra. Table 3 gives the line parameters obtained from Gaussian fits to the spectra. The large angular extent of the $\sim$14 km s^-1 wide component is also evident from the detection of this component in the low-resolution observations toward G2.3+0.0, G4.7+0.0 and G7.0+0.0 (see Fig. 9) with almost the same line parameters. The near kinematic distance corresponding to the central velocity of 8 km s^-1 at l = 5$^\circ$ (for l < 4$^\circ$ the estimated distance increases) is $\sim$2.5 kpc. A 5$^\circ$ wide cloud at a distance of 2.5 kpc would have a physical size of $\sim$220 pc. This is a fairly large diffuse C  II region.

Figure 10: Carbon line emission toward a 2$^\circ$ (along l) wide region centered at l = 13 $.\!\!^\circ$9 and b = 0$^\circ$. The spectra on the left are obtained by averaging the high-resolution (2$^\circ$  $\times$  6$^\prime$) survey data over a 2$^\circ$  $\times$  0 $.\!\!^\circ$5 region centered at the galactic coordinates indicated in each frame. The top two spectra on the right are obtained by averaging the data over 2$^\circ$  $\times$  1$^\circ$ region and that labeled "AVG'' is obtained by averaging thedata over the 2$^\circ$ region. The spectrum marked "Module'' is from the low-resolution (2$^\circ$  $\times$  2$^\circ$) survey toward l = 13 $.\!\!^\circ$9 and b = 0$^\circ$. The LSR velocity and the line width using the spectra averaged over a 2$^\circ$  $\times$  0 $.\!\!^\circ$5 region, as a function of galactic longitude are shown in the plot on the right-hand side. The vertical bars represent the 3 $\sigma$ error in the estimated parameters. The narrow component is observed in all the spectra with the same central velocity indicating the presence of an extended diffuse C  II region. The observed positions are marked by the slanted lines on the 11 cm continuum map from Reich et al. (1990). The slanted lines represent the 2$^\circ$  $\times$  6$^\prime$ beam of the ORT.

6.2.2 Carbon line emission toward field 3

Within the 2$^\circ$ wide field centered at l = 13 $.\!\!^\circ$9, b = 0$^\circ$, 20 positions were observed with a 2$^\circ$ $\times$ 6$^\prime$ beam as shown in Fig. 10. To improve the signal-to-noise ratio on the line emission from any extended C  II region we averaged the data over a 2$^\circ$$\times$ 0 $.\!\!^\circ$5 region. The resultant spectra are shown in the left hand side panels of Fig. 10. The carbon line in the spectra is clearly composed of a narrow and a broad component. These spectra were further integrated over two sets of 10 positions giving a spectrum of a region which is 2$^\circ$$\times$ 1$^\circ$ large. These two spectra are shown in the top two right hand side panels. The observed carbon line profile is well-fitted by a narrow ( $\Delta V =$ 7 km s^-1) and a broad ( $\Delta V =$ 42 km s^-1) Gaussian. Detailed line parameters obtained from the Gaussian fits are listed in Table 4. In the lower two right hand side panels of Fig. 10, the high resolution spectra averaged over a 2$^\circ$ region and the low resolution spectrum over the same region are shown. The two spectra match well within errors and clearly show the presence of the two components. Since the wide component is likely to be a blend of many narrow components with slightly different velocities, we require more sensitive and higher angular resolution observations to resolve the broad component into the individual components. The narrow component is likely to arise in a single cloud which is at least 2$^\circ$ in extent along galactic longitude. Moreover, the gas toward this longitude has a latitude extent of $\pm 3$$^\circ$ (see Sect. 4) and the spectra toward $b \neq 0$$^\circ$ shows the presence of a narrow component (see Fig. 7) with almost similar line parameters as those obtained for the narrow component toward this direction in the Galactic plane. A slight increase in line width observed at higher latitudes might be a result of the poor signal-to-noise ratio of the spectra at higher latitudes compared to those near l = 0 $.\!\!^\circ$0, which makes the Gaussian decomposition of the broad and narrow features somewhat uncertain. Thus, it appears that the diffuse C  II region in this direction is extended over $\sim$6$^\circ$ in latitude and at least 2$^\circ$ in longitude.

   

Table 3: Summary of the study of angular extent of carbon line emission in field 2.

Position	$T_{\rm L}/T_{{\rm sys}}$ 1	$\Delta V$	$V_{\rm {LSR}}$	$V_{{\rm res}}$ 3	rms 2	$t_{{\rm int}}$
	$\times$ 103	(km s-1)	(km s-1)	(km s-1)	$\times$ 103	(hrs)
Average over 2$^\circ$$\times$ 1$^\circ$
G2.25+0.0	0.35(0.04)	14.7(1.8)	7.9(0.7)	2.1	0.07	95.9
G3.25+0.0	0.36(0.03)	17.7(2.0)	7.6(0.8)	2.1	0.07	85.4
G4.25+0.0	0.37(0.04)	14.0(1.7)	8.5(0.7)	2.1	0.07	93.7
G5.25+0.0	0.51(0.04)	12.9(1.1)	8.8(0.5)	2.1	0.07	84.8
G6.25+0.0	0.36(0.05)	11.1(1.7)	8.2(0.7)	2.1	0.08	64.2
Average over 2$^\circ$$\times$ 5$^\circ$
G4.25avg	0.39(0.02)	14.4(0.9)	8.6(0.4)	2.1	0.04	424

¹ The line intensities are given in units of $T_{\rm L}/T_{{\rm sys}}$, where $T_{\rm L}$ is the line antenna temperature and $T_{{\rm sys}}$ is the system temperature.
² rms is in units of $T_{\rm L}/T_{{\rm sys}}$.
³ The resolution to which the spectra are smoothed for estimating the line parameters.

   

Table 4: Summary of the study of angular extent of carbon line emission in field 3.

Position	$T_{\rm L}/T_{{\rm sys}}$ 1	$\Delta V$	$V_{\rm {LSR}}$	$V_{{\rm res}}$ 3	rms 2	$t_{{\rm int}}$
	$\times$ 103	(km s-1)	(km s-1)	(km s-1)	$\times$ 103	(hrs)
Average over 2$^\circ$$\times$ 0 $.\!\!^\circ$5
G13.22-0.36	0.41(0.09)	8.7(2.1)	50.9(0.9)	1.8	0.13	43.6
	0.57(0.08)	11.1(1.7)	36.5(0.7)	1.8	0.13	43.6
	0.50(0.06)	16.2(2.4)	18.6(1.0)	1.8	0.13	43.6
G13.65-0.12	0.33(0.05)	32.4(5.4)	42.4(2.3)	1.8	0.14	46.3
	0.73(0.11)	6.3(1.1)	18.6(0.5)	1.8	0.14	46.3
G14.09+0.12	0.48(0.08)	7.4(1.4)	18.9(0.6)	1.8	0.11	43.9
	0.30(0.04)	22.3(3.8)	40.9(1.6)	1.8	0.11	43.9
G14.53+0.36	0.33(0.04)	28.3(3.5)	23.3(1.5)	1.8	0.10	49.1
	0.24(0.05)	12.6(3.3)	48.5(1.4)	1.8	0.10	49.1
Average over 2$^\circ$$\times$ 1$^\circ$
G13.44-0.24	0.36(0.03)	40.6(4.4)	36.8(1.9)	1.8	0.11	89.9
	0.48(0.09)	5.9(1.3)	18.5(0.5)	1.8	0.11	89.9
G14.31+0.24	0.25(0.06)	8.5(2.3)	17.8(1.0)	1.8	0.09	93.0
	0.27(0.03)	38.5(4.5)	35.8(1.9)	1.8	0.09	93.0
Average over 2$^\circ$$\times$ 2$^\circ$
G13.88+0.00	0.32(0.02)	41.5(2.8)	36.7(1.2)	1.8	0.06	182.9
	0.35(0.04)	6.8(1.0)	18.4(0.4)	1.8	0.06	182.9

¹ The line intensities are given in units of $T_{\rm L}/T_{{\rm sys}}$, where $T_{\rm L}$ is the line antenna temperature and $T_{{\rm sys}}$ is the system temperature.
² rms is in units of $T_{\rm L}/T_{{\rm sys}}$.
³ The resolution to which the spectra are smoothed for estimating the line parameters.

The line-of-sight toward this longitude intercepts the spiral arms 3, 2 and 4 which are nominally located at radial distances of $\sim$1.9, 3.7 and 14.1 kpc respectively from the Sun (see Fig. 4). The near and far kinematic distances corresponding to the observed central velocity (18.4 km s^-1) of the narrow component are 2.3 and 14.2 kpc. If the cloud is located at the near distance and the angular extent of the narrow line emitting region is at least 2$^\circ$ $\times$ 6$^\circ$ then it corresponds to a physical size perpendicular to the line-of-sight > $80 \times 200$ pc. This, again, is a fairly large diffuse C  II  region.

In summary, our data toward Field 2 and 3 indicate the presence of extended C  II regions - extending over $\sim$200 pc or more. Line emission from many other positions suggests that structure in diffuse C  II regions on scales of $\sim$6 pc is common.