1 Introduction

Radio recombination lines (RRLs) of hydrogen, helium and carbon have been unambiguously identified in the spectra obtained toward H  II regions (see review by Roelfsema & Goss 1992). The hydrogen and helium recombination lines mostly originate in hot ( $T_{\rm e} \sim$ 5000-10 000 K) regions ionized by photons of energy $\ge$13.6 eV. Since the ionization potential of carbon is 11.4 eV, low energy photons (11.4 eV $\le E <$ 13.6 eV) that escape from H  II regions can ionize gas phase carbon atoms outside the hot regions. Thus ionized carbon regions can exist in dense (hydrogen nucleus density $n_0 \sim$ 10⁵  cm^-3) photo-dissociation regions (PDRs) adjacent to H  II regions or in the neutral components (H  I or molecular) of the interstellar medium (ISM). Tielens and Hollenbach (1985) define PDRs as regions where the heating or/and chemistry of the predominantly neutral gas is governed by the FUV (6-13.6 eV) photons. Since the FUV photons are omnipresent, the PDRs, by definition encompass a substantial fraction of atomic gas in a galaxy (Hollenbach & Tielens 1997 and references therein). The dense PDRs (Tielens & Hollenbach 1985) are located at the interface of molecular clouds and H  II regions whereas the low-density ( $n_0 \sim 10^3$  cm^-3) PDRs (Hollenbach et al. 1991) are located in the diffuse interstellar gas; the ambient FUV flux sufficing to control its chemistry and heating. The ionized carbon regions in the dense PDRs are referred to as "classical'' C  II regions. These C  II regions are observationally identified by the narrow (1-10 km s^-1) emission lines of carbon at frequencies >1 GHz. Several studies have been made to understand and model the line emission from such regions (e.g. Garay et al. 1998; Wyrowski et al. 2000). These regions are not accessible to low frequency RRLs due to the increased pressure broadening ($\propto$ $\nu^{-8.2/3}$; Shaver 1975) and increased free-free continuum optical depths ( $\tau \propto \nu^{-2}$). The second class of C  II regions, referred to as "diffuse'' C  II regions, coexists with the diffuse neutral component of the ISM. The emission measures of these regions are fairly low (<0.1  cm^-6 pc; Kantharia et al. 1998) and hence these regions are observable in low-frequency RRLs of carbon as either absorption lines or emission lines due to stimulated emission from inverted populations. The diffuse C  II regions, observed in carbon lines at frequencies <1 GHz, are the focus of this paper.

The diffuse C  II region located in the Perseus arm toward the strong radio continuum source, Cas A, has been extensively studied using low frequency recombination lines of carbon. In fact, most of our knowledge on this class of C  II regions has come from these observations. Konovalenko & Sodin (1980) were the first to observe a low-frequency (26.3 MHz) absorption line toward Cas A, which was later correctly identified as the 631$\alpha$ recombination line of carbon by Blake et al. (1980). Since then, several recombination line observations spanning over 14 to 1400 MHz have been made toward this direction (Kantharia et al. 1998 and references therein). The predicted smooth transition of carbon lines in absorption at frequencies below 115 MHz to lines in emission at frequencies above 200 MHz has been demonstrated toward this direction (Payne et al. 1989). The extensive RRL data collected toward Cas A has been used in modeling the line-forming gas. The models show that the carbon RRLs originate in small, relatively cool tenuous regions ($T_{\rm e}$ = 35-75 K, $n_{\rm e}$ = 0.05-0.1 cm^-3, size $\sim$2 pc; Payne, Anantharamaiah & Erickson 1994) of the ISM. Comparison of the distribution of carbon RRLs near 327 MHz observed with the VLA ( $2\farcm7 \times 2\farcm4$) toward Cas A with H  I absorption in the same direction suggests that the carbon line-forming region coexists with the cold, diffuse H  I component of the ISM (Anantharamaiah et al. 1994).

In addition to the region toward Cas A, the distribution of the diffuse C  II regions in the Galaxy has also been studied to some extent. Surveys have been conducted near 76 MHz ( $n \sim 441$) with the Parkes 64 m telescope (Erickson et al. 1995) and near 35 MHz ( $n \sim 580$) with the Gauribidanur telescope (Kantharia & Anantharamaiah 2001) to search for carbon recombination lines, mostly in the inner part of the Galaxy. These observations have succeeded in detecting carbon RRLs in absorption from several directions in the galactic plane with longitudes ranging from l = 340$^\circ$ $\rightarrow$ 20$^\circ$. The diffuse C  II regions appear to be fairly widespread in the inner part of our Galaxy. Observations away from the Galactic plane have shown the region to be several degrees wide in galactic latitude. The positions with detections near 35 MHz were observed near 327 MHz using the Ooty Radio Telescope by Kantharia & Anantharamaiah (2001) and the emission counterparts of the carbon absorption lines were detected. Combining their observations with all other existing carbon RRL observations, they modeled the line emission at different positions in the galactic plane. While models with physical properties similar to those obtained in the direction of Cas A can fit the observed data, the possibility of carbon lines originating in regions with temperature $\le$20 K cannot be ruled out (Kantharia & Anantharamaiah 2001). If the temperature of the diffuse C  II regions is found to be low, then these regions could even be associated with the molecular component of the ISM (Konovalenko 1984; Golynkin & Konovalenko 1990; Sorochekov 1996; Kantharia & Anantharamaiah 2001). These low temperature regions may be low-density PDRs (Hollenbach et al. 1991) formed on surfaces of molecular clouds due to ionization from background FUV radiation. Although some modeling of these diffuse C  II regions using low-frequency carbon RRLs has been done, a wide range of parameter space has been found to fit the existing observations. The physical properties, distribution and association of these regions with other components of the ISM requires more investigation. In addition to carbon RRLs, ionized carbon is also traced by the [C  II] 158 ${\mu }$m line. The $158~\mu$m line emission from the Galaxy has been mapped by Bennett et al. (1994) and Nakagawa et al. (1998). They find that the [C  II] 158 ${\mu }$m emission consists of compact emission regions associated with compact H  II regions (Nakagawa et al. 1998) and a diffuse emission whose origin is not very clear. Since both the fine-structure line and the carbon RRLs require ionized carbon regions, it is possible that the two can arise from similar regions. Kantharia & Anantharamaiah (2001) tried to compare the carbon lines near 35 MHz with the [C  II] 158 ${\mu }$m emission but they did not derive any conclusive results. Hence, no detailed comparative study of the radio and FIR line emission of carbon from diffuse C  II regions exists. In this paper, we also attempt a discussion on these two tracers of ionized carbon regions.

Extensive surveys of recombination lines near 327 MHz have been made with the primary objective to study the low-density ionized gas in the Galaxy by observing low-frequency hydrogen RRLs from this gas (Roshi & Anantharamaiah 2000, hereafter Paper I; Roshi & Anantharamaiah 2001a, hereafter Paper II; Roshi & Anantharamaiah 2001b). Since the velocity coverage of these surveys was sufficient to allow detection of carbon RRLs, which are separated from the hydrogen line by $\sim$-150 km s^-1, the surveys have succeeded in detecting carbon features toward several positions in the galactic plane. The surveys have data with two different angular resolutions obtained using the Ooty Radio Telescope in two different operating modes (see Papers I and II). The carbon line data obtained from the higher angular resolution observation (2$^\circ$ $\times$ 6$^\prime$) are presented in this paper (see Paper II for spectra) and those obtained in the lower resolution (2$^\circ$ $\times$ 2$^\circ$) survey were presented in Paper I. In this paper, we present a study of the distribution and angular extent of the carbon line forming region in the galactic plane by making use of the carbon RRLs detected in the 327 MHz surveys. Interestingly, in several directions the carbon line emission observed in the surveys seems to be associated with H  I self-absorption features, which will be discussed in Roshi et al. (2002).

A summary of the observations and basic results are presented in Sect. 2. Section 3 discusses the distribution of the diffuse C  II regions in the galactic disk and compares it with the distribution of other components of the ISM. Section 4 discusses the possibility of a common origin of the carbon RRL and the diffuse [C  II] 158 ${\mu }$m line emission. The latitude extent of carbon line emission is discussed in Sect. 5. The higher resolution observations are used to study the angular extent of the carbon line emitting region, which is discussed in Sect. 6. Section 7 summarizes the paper.