# Arecibo-Green Bank-LOFAR Carbon Radio Recombination Line observations toward
cold H i Clouds

D. Anish Roshi  Arecibo Observatory/University of Central Florida  W. M.
Peters Naval Research Laboratory, Washington, DC  K. L. Emig  Jansky Fellow of
the National Radio Astronomy Observatory  National Radio Astronomy
Observatory, 520 Edgemont Rd, Charlottesville, VA 22903, USA  P. Salas  Green
Bank Observatory, 155 Observatory Road, Green Bank, WV 24915, USA  J. B. R.
Oonk  Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden,
The Netherlands  Netherlands Institute for Radio Astronomy (ASTRON), Postbus
2, 7990 AA Dwingeloo, The Netherlands  SURF/SURFsara, Science Park 140, 1098
XG Amsterdam, The Netherlands  M. E. Lebrón  Department of Physical Sciences,
University of Puerto Rico, Río Piedras Campus, San Juan, PR 00931, USA  J. M.
Dickey  School of Natural Sciences, University of Tasmania, Hobart, TAS 7001,
Australia

###### Abstract

We present results from a search for radio recombination lines in three H i
self-absorbing (HISA) clouds at 750 MHz and 321 MHz with the Robert C. Byrd
Green Bank Telescope (GBT), and in three Galactic Plane positions at 327 MHz
with the Arecibo Telescope. We detect Carbon Recombination Lines (CRRLs) in
the direction of DR4 and DR21, as well as in the galactic plane position
G34.94+0.0. We additionally detect Hydrogen Recombination Lines (HRRLs) in
emission in five of the six sightlines, and a Helium line at 750 MHz towards
DR21. Combining our new data with 150 MHz LOFAR detections of CRRL absorption
towards DR4 and DR21, we estimate the electron densities of the line forming
regions by modeling the line width as a function of frequency. The estimated
densities are in the range 1.4 $\rightarrow$ 6.5 cm-3 towards DR4, for
electron temperatures 200 $\rightarrow$ 20 K. A dual line forming region with
densities between 3.5 $\rightarrow$ 24 cm-3 and 0.008 $\rightarrow$ 0.3 cm-3
could plausibly explain the observed line width as a function of frequency on
the DR21 sightline. The central velocities of the CRRLs compare well with CO
emission and HISA lines in these directions. The cloud densities estimated
from the CO lines are smaller (at least a factor of 5) than those of the CRRL
forming regions. It is likely that the CRRL forming and H i self-absorbing gas
is located in a denser, shocked region either at the boundary of or within the
CO emitting cloud.

##  1 Introduction

Stars form from the collapse of molecular clouds, which must, in turn, be
formed continuously in order to sustain star formation in the Galaxy. It has
been suggested that a fraction of the interstellar regions exhibiting H i
self-absorption (HISA) are sites of molecular cloud formation (Gibson et al.,
2000; Klaassen et al., 2005). HISA occurs when foreground cold atomic gas
absorbs the 21cm emission line from warm H i gas behind it. Many HISA regions
have a low atomic fraction but little or no 12CO emission, implying that a
significant amount of “CO dark” molecular gas is present (Klaassen et al.,
2005). In other cases the HISA is well mixed with CO emitting molecular gas
(Li & Goldsmith, 2003).

While spectral line studies have inferred molecular gas content in HISA
regions, observational constraints on the molecular formation process are
still lacking. There are a few possible molecule formation processes that have
been discussed in the literature (see review by Dobbs et al., 2014). These
include a converging flow, such as a gas flow caused by the expansion of an H
ii region or supernova remnant, which could enhance the local gas density
resulting in the formation of molecules. Another possibility is a quasi-static
cloud contraction process where a slight increase in ambient pressure
accelerates the phase transition from atomic to molecular gas.

Observations of radio recombination lines (RRLs) of ionized carbon, H i 21cm
absorption, and CO emission may be used to put constraints on the molecular
formation processes in HISA regions. RRL optical depth has a strong inverse
dependence on the electron temperature ($\propto T_{e}^{-2.5}$, where $T_{e}$
is the electron temperature). Thus RRLs from ionized carbon (CRRLs) are
preferentially detected toward cold regions. The inferred neutral gas
densities toward HISA regions are a few times 103 cm-3 (Li & Goldsmith, 2003;
Klaassen et al., 2005). CRRLs from neutral regions with such densities are
expected to be brighter at lower frequencies (${\mathrel{\mathchoice{\lower
2.9pt\vbox{\halign{$\m@th\displaystyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\textstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\scriptstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\scriptscriptstyle\hfil#\hfil$\cr<\crcr\sim\crcr}}}}}$1
GHz; Roshi & Kantharia, 2011; Kantharia & Anantharamaiah, 2001; Salgado et
al., 2017a).

The detection of low-frequency CRRLs from a well known HISA region – the
Heeschen-Riegel-Crutcher region (HRC, Heeschen, 1955; Riegel & Crutcher, 1972)
– was reported by Roshi & Kantharia (2011); Oonk et al. (2019). By combining
multi-frequency CRRL and H i data, Roshi & Kantharia (2011) were able to
constrain the physical properties and processes in the HRC cloud. These
include electron temperature, electron density, line of sight (LOS) path
length, hydrogen nuclear density, hydrogen atomic density, and hydrogen
molecular density. The derived physical properties along with constraints on
the background ultraviolet (UV) radiation field were then used to estimate the
H2 formation and dissociation rates in the cloud. They show that the H2
formation rate exceeds the H2 dissociation rate, suggesting that the cloud is
in the process of converting H i to H2 and will convert all of its atomic
hydrogen into the molecular form over a time scale
${\mathrel{\mathchoice{\lower
2.9pt\vbox{\halign{$\m@th\displaystyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\textstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\scriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\scriptscriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}}}$$10^{5}$
years.

In this paper, we expand our observational study toward the HISA regions
detected along the sightlines toward the H ii region DR21, and the supernovae
remnants (SNRs) DR4 & HB21. These were selected based on HISA detection in the
Leiden/Argentine/Bonn 21cm line survey data (Kalberla et al., 2005). Unlike
the HRC cloud, the selected directions have intense background Far-UV
radiation fields due to the presence of star forming regions. These
observations therefore will allow us to probe molecule formation in very
different environments compared to the HRC cloud. Radio recombination line
observations were made with the GBT at 321 and 750 MHz. We also present
results from blind recombination line observations made toward three positions
(G34.20+0.0, G34.94+0.0, G35.17+0.0) in the Galactic plane with the Arecibo
telescope. These observations were made at 327 MHz. The positions were
selected because an earlier CRRL survey has detected lines in this part of the
galactic plane with an angular resolution of 2o$\times$ 0.5o(Roshi et al.,
2002). The observations and data analysis procedure are described in Section 2
and 3 respectively. The results of recombination line observations and the
estimation of physical properties by combining our data with LOw Frequency
ARray (LOFAR; van Haarlem et al., 2013) and other previous CRRL observations
(Oonk et al. in preparation) and existing H i and CO line data are presented
in Section 4. A summary of the results and future work are given in Section 5.

##  2 Observations

The source name, coordinates, date of observations, center frequency of
observations, full-width at half maximum (FWHM) beamwidth and the telescope
used for the observations are given in Table 1.

The 321 and 750 MHz observations with the GBT (Project code GBT12A-352) used
the Green Bank Spectrometer for measuring the power spectrum. For the 750 MHz
observations, the spectrometer was configured to have eight 12.5 MHz sub-
bands, with each sub-band divided into 4096 spectral channels. The sub-bands
were tuned to observe eight $\alpha$ RRL transitions (n=201, 203, 205 to 210,
$\Delta n=1$) within the PF1_800 receiver bandwidth. We use the quantum number
n=206 when referring to the final spectrum at this frequency obtained by
averaging all the transitions (see Section 3; also Table 2). The RRL
transitions were selected such that they are located at frequency ranges
relatively free of strong radio frequency interference (RFI). We observed in
‘standard frequency switch’ mode, with a switching period of 1 sec and
frequency offset of 2.0 MHz ($\sim$ 815 km s-1 at the observing frequency).

For the 321 MHz observations, we used three 12.5 MHz sub-bands with 8192
spectral channels each to observe RRLs with the PF1_342 receiver. The 3 sub-
bands were centered at the observing frequencies 325.15, 309.62 and 341.87
MHz. The separation between RRL transitions near 340 MHz is $\sim$ 3.7 MHz.
Thus multiple RRL transitions were observed in each sub-band. The RRLs
observed are the $\alpha$ transitions corresponding to n = 268, 271, 273, 275,
276 and 277. We use the quantum number n=273 when referring to the final
spectrum at this frequency obtained by averaging all the transitions (see
Section 3; also Table 2). We observed in ‘standard frequency switch’ mode,
with a switching period of 1 sec and frequency offset of 1.0 MHz ($\sim$ 910
km s-1). We used 9-level sampling mode since observations were to be made in
the presence of RFI, although these transitions were relatively free of strong
RFI. We observed 3C 295 to determine the telescope pointing correction and for
flux density calibration.

We used the Mock spectrometer for the 327 MHz Arecibo observations (Project
code A3333). The 327 MHz receiver has a 3dB bandwidth of $\sim$ 30 MHz, and
there are eight $\alpha$ RRL transitions (principal quantum number n=268 to
275, $\Delta n=1$) within this frequency range. We configured the Mock
spectrometer with a 160 MHz clock frequency and set the bandwidth divisor to 4
to observe all eight RRL transitions simultaneously. This configuration
provided 40 MHz observing bandwidth with 8192 spectral channels, for a
spectral resolution of 4.9 kHz. The observations were made in a ‘pseudo’
frequency switching mode based on the standing waves in the blocked aperture
of the telescope, which have a separation in frequency of $\sim 1.1$ MHz. Each
one minute scan in ’standard on’ mode was followed by scans offset by $-500$
and $+500$ km s-1from the source velocity. At the central rest frequency of
326.5 MHz, this corresponds to switching the first local oscillator frequency
by $\sim 545$ kHz. The $\pm 500$ km s-1 shift allowed us to observe all eight
hydrogen and carbon RRLs simultaneously, because they are separated by only
149.6 km s-1. The power spectrum was integrated for 1 sec, and 60 of them were
written to a fits file every minute at the end of each scan. We observed a
‘standard ON/OFF’ scan with calibrated noise switching at the beginning of
each observation to measure the on-source continuum antenna temperature. We
also observed a flux density calibrator, 3C 394, in ‘standard ON/OFF’ mode
with noise switching to calibrate the noise cal value in Jy.

The power spectrum was integrated for 1 sec, and 60 of them were written to a
fits file every minute at the end of each scan. We observed a ‘standard
ON/OFF’ scan with calibrated noise switching at the beginning of each
observation to measure the on-source continuum antenna temperature. We also
observed a flux density calibrator, 3C 394, in ‘standard ON/OFF’ mode with
noise switching to calibrate the noise cal value in Jy.

##  3 Data reduction

We used
GBTIDL111https://gbtidl.nrao.edu/222https://www.l3harrisgeospatial.com/Software-
Technology/IDL to create 1 second integration bandpass corrected spectra for
the GBT observations. GBTIDL routines were also used to correct the bandpass
for each sub-band from the frequency switched data set. The GBTIDL routine
vshift was used to apply LSR velocity correction for each CRRL transition. The
bandpass and velocity corrected spectra were written to a text file for each
CRRL transition. These spectra were then edited for RFI.

The RFI affected data may be sorted into three types: (a) A majority (90%) of
the RFI were narrow band, confined to one or two spectral channels. The
amplitude of each varies slowly over several tens of minutes. (b) In a few
cases (40% of the observing time) the frequency and strength of the RFI were
time dependent, but could be easily identified in 1 sec integrated spectra.
(c) Rarely (10% of the observing time), the frequency of RFI sweeps across a
large fraction of the sub-bands in a few seconds. Excising the RFI thus
requires careful editing of the data both in time and frequency domains, for
which we developed an RFI editing program in
MATLAB333https://www.mathworks.com/products/matlab.html.

The RFI editing program uses a channel weighting scheme to edit out the RFI.
Each channel is assigned unity weight at the start. If a channel is identified
as affected by RFI or corrupted by instrumental problems, then the weight of
that channel is set to zero. The weighted spectra are then averaged across
time. Identification of RFI is currently done manually by examining each 1 sec
spectrum. For the GBT data sets, the weighted average spectrum forms the final
spectrum for each RRL transition and sight line.

We followed similar steps to analyze the Arecibo data set. Phil Perillat’s IDL
routines444http://www.naic.edu/~phil/software/software.html were used to
generate a spectrum covering the full 40 MHz bandwidth. A spectrum covering a
1000 km s-1 range centered on each of the 8 RRL transitions was extracted.
These spectra were then edited for RFI using the MATLAB RFI-editing routine
described above, and the weighted average was taken to get the spectrum
corresponding to each RRL transition. Because the observations were made with
in-band frequency switching, each RRL spectrum was ‘folded’ to improve the
integration time. The spectra were re-sampled using a Fourier transform method
(Roshi et al., 2005) and aligned in velocity range. The ‘folded’ spectra for
the different transitions were then re-sampled to a common velocity resolution
and averaged to get the final integrated spectrum. This analysis method was
tested by observing an off-source position for 2 hours with the Arecibo
telescope at 327 MHz. No spurious line like feature was detected in this data
set up to a 50 mK level. The weights were processed in the same way as the
spectrum during the resampling process, so the final spectrum has associated
channel weights. These indicate the number of 1 second data points included in
each spectral channel. Fig. 1 shows an example RRL spectrum toward G34.94+0.0
obtained with the Arecibo telescope along with the weights. The typical
variation in weights across the final averaged spectrum is $\sim$10%.

##  4 Results

The observed positions are shown in Fig. 2 (see Table 1). The RRL spectra
obtained toward these positions are shown in Figs. 3 & 4. The frequency of
observation, atom producing the RRL, line antenna temperature, LSR (Local
Standard of Rest) velocity and FWHM line width obtained from the spectra are
given in Table 2. CRRLs were detected toward DR4, DR21, G34.94+0.0 and
G34.2+0.0 (tentative detection) at all of the observed frequencies. Hydrogen
lines were detected toward positions DR4, DR21, G34.90+0.0, G34.2+0.0
(tentative detection) and G35.17+0.0 (tentative detection) at all of the
observed frequencies. Helium and heavy element recombination lines were
detected towards DR21 at 750 MHz. No lines were detected towards HB21, with a
limiting sensitivity of 5 mK. The listed line widths are corrected for
broadening due to spectral resolution using the equation $\sqrt{\Delta
V_{obs}^{2}-\Delta V_{res}^{2}}$, where $\Delta V_{obs}$ is the observed line
width and $\Delta V_{res}$ is the spectral resolution.

In the following subsections we combine our. new RRL observations with LOFAR
and other existing CRRL, H i and CO data sets to constrain the physical
properties of the line forming regions. The implicit simplifying assumptions
made in the modeling presented below to estimate the physical properties are
that the line forming region is homogeneous gas with uniform temperature and
density. A brief discussion of the observed hydrogen and helium line formation
is also presented. We note here that the LOFAR detections of CRRLs in
absorption near 150 MHz towards DR4 (see Section 4.1.2) and DR21 (see Section
4.2.1) are the highest frequency carbon recombination line absorption reported
to date.

###  4.1 DR4

DR4 is a shell-type SNR located in the Cygnus-X region. A detailed study of
the H i 21cm line associated with the SNR was done by Landecker et al. (1980)
and Ladouceur & Pineault (2008). They used data from the DRAO synthesis
telescope; the latter authors also used the CGPS data set (Taylor et al.,
2003). The angular resolution of the 21 cm observations was better than
2$\farcm$5\. The H i line emission and absorption in this direction are quite
complex. The 21 cm line analysis indicates that the SNR blast wave is
compressing the H i gas into a shell. The velocity structure of the H i line
could be explained as an expanding shell (either due to the SNR blast or the
stellar wind of the progenitor) with speed $\sim$ 25 km s-1. The near-side of
the shell is seen in H i absorption against the bright SNR and also against
the 21 cm emission from the far-side part of the shell (i.e. as H i self-
absorption).

####  4.1.1 Cold gas properties derived using 21cm line data

The CGPS H i spectra averaged over an area which matches the GBT beam of 0.66o
at 321 MHz and 0.3o at 750 MHz are shown in Fig. 5 (top-left). A Gaussian
model for the spectrum extracted at 0.3o resolution is also shown in Fig. 5.
The line amplitudes, central velocities and FWHM line widths of the model
components are given in Table 3. The central velocity of the H i self-
absorption feature agrees within 2$\sigma$ with the central velocity of the
750 and 321 MHz CRRLs (see Fig. 5 bottom-left). Thus we conclude that the H i
self-absorption and CRRL forming regions are co-located.

Fig. 5 (top-right) shows the H i line image at the peak velocity ($\sim$ -3.2
km s-1) of the absorption feature. The H i absorption is spread over the GBT
beam as inferred from the lower line temperature compared to the background
emission ($\sim$ 99K; see Table 3). The amplitude of the absorption feature,
however, shows significant variation (see Fig. 5 top-right) which could be due
to a combination of variation in background continuum temperature, amplitude
of the background H i emission and the properties of the cold gas. We conclude
that the self-absorption feature is extended over the GBT beam with which the
RRL observations were made.

We follow the method outlined by Dénes et al. (2018) to constrain the
properties of the cold gas responsible for the H i self-absorption. The spin
temperature, $T_{s}$, of the absorbing gas can be written as (Eq. 4 in Dénes
et al., 2018)

${T_{s}=\frac{T_{ON}-T_{OFF}}{1-e^{-\tau_{HISA}}}+T_{c}+p\;T_{OFF}}$ (1)

where $T_{ON}$ and $T_{OFF}$ are respectively the observed H i spectrum and
that in the absence of absorption (both obtained after continuum subtraction),
$\tau_{HISA}$ is the line optical depth of the absorbing gas, $T_{c}$ is the
brightness temperature of the continuum emission behind the absorbing gas and
$p$ is a parameter used to express the background H i emission as a fraction
of $T_{OFF}$. Eq 1 assumes the line optical depths of the background and
foreground gases producing the H i emission are negligible. The peak optical
depth of the absorbing gas is given by

${\tau_{HISA,peak}=5.2\times 10^{-19}\;\frac{N_{HI}}{T_{s}\;\Delta V}}$ (2)

where $N_{HI}$ is the H i column density of the absorbing gas in units of cm-2
and $\Delta V$ is the FWHM line width of the H i absorption in km s-1.

Gaussian line modeling of the H i spectrum averaged over a 0.3o beam was used
to get $T_{ON}$ and $T_{OFF}$, $\Delta V$ of the absorption component (see
Table 3) and $T_{c}$ is obtained from the CGPS continuum image. Fig 5 (bottom-
right) shows the cold gas $T_{s}$ and $N_{HI}$ that are consistent with the
observed H i self-absorption for $p=0.8$ and 0.9; we assume a large fraction
of $T_{OFF}$ is located behind the absorbing gas. The continuum emission
varies within the GBT beam, so we examine the spectra against different bright
continuum background sources. We also assume that the physical properties of
the cold H i are similar over the beam area. With these assumptions, we
estimate that the physical parameters of the cold H i gas are $T_{s}<55K$ and
$N_{HI}<7\times 10^{20}$ cm-2 for $p=0.9$.

####  4.1.2 Gas properties derived using CRRL data

The carbon line intensity and line width at a given frequency depend on the
electron temperature ($T_{e}$), electron density ($n_{e}$), LOS path length,
background radiation field and the non-LTE parameters characterising the
atomic level population (e.g., Payne et al., 1994; Roshi & Kantharia, 2011;
Salas et al., 2017; Salgado et al., 2017b). Thus observations of multiple CRRL
transitions are required to constrain the physical properties of the gas (Oonk
et al., 2017). We combine our data set with the LOFAR CRRL observations toward
DR4 at 150 MHz (n=350) to estimate the physical properties. The angular
resolution of LOFAR observations is $\sim$ 10′ at this frequency. The details
of the LOFAR observations will be described elsewhere (Oonk et al in prep.).
All three CRRLs observed toward DR4 are shown in Fig. 6. The LOFAR spectra are
obtained by extracting the average line temperature within an aperture equal
to the two GBT beam sizes.

The width of the CRRL is affected by Doppler (thermal and non-thermal),
pressure and radiation broadening. The latter two strongly depend on the
quantum number, electron density and background radiation field (e.g., Payne
et al., 1994; Salas et al., 2017). The line profile due to Doppler broadening
is a Gaussian function while the profiles due to pressure and radiation
broadening are Lorentzian functions. The net line profile is a Voigt profile
that results from the convolution of the Gaussian and Lorentzian profiles. The
FWHM line width of the Voigt profile can be expressed as

${\Delta V\approx 0.53\Delta V_{L}+\sqrt{0.22\Delta V_{L}^{2}+\Delta
V_{D}^{2}},}$ (3)

where $\Delta V_{D}$ and $\Delta V_{L}$ are the FWHM widths of the Gaussian
and Lorentzian profiles respectively. For a given $T_{e}$ and background
temperature $T_{c}$, we can compute the Voigt line width $\Delta V$ as a
function of frequency and determine the $n_{e}$ values that are consistent
with the observed data. An implicit assumption in the modeling is that a
homogeneous gas with one LSR velocity component is present along the
sightline. If multiple line forming regions of similar temperature but with
different LSR velocities are present, then the derived electron density should
be considered as an upper limit.

Careful estimation of the line width is thus crucial to constrain the physical
parameters of the line forming region. We model the line profiles at 750 and
321 MHz with Gaussian functions, as the ‘Lorentzian wings’ are not apparent at
these frequencies. A Voigt profile is necessary to model the 150 MHz line
feature. The spectral baseline removal of the 150 MHz spectrum is critical as
it affects the measured line width. Line parameters obtained after removing a
3rd order polynomial from the 150 MHz spectrum and those obtained without
baseline removal are given in Table 2 (see Fig. 6). The line parameters listed
are the amplitude, central velocity and the FWHM Lorentzian line width. We fix
the value of $\Delta V_{D}$ as the width of the line at 750 MHz for the Voigt
profile modeling as the total contribution from radiation and pressure
broadening at this frequency is only about 0.5% of the observed line width.

The electron densities obtained from the line width modeling are in the range
1.4 $\rightarrow$ 6.5 cm-3 for the assumed electron temperature range 200
$\rightarrow$ 20 K. The temperature range is chosen based on the modeling
results of low-frequency CRRL observations toward other directions in the
Galaxy (eg. Kantharia & Anantharamaiah, 2001). The models used for background
temperature are given in Table 4. The values for $T_{c}$ at 1430.4 MHz and
their uncertainties are obtained from the CGPS image and the spectral index
values, $\alpha$, are taken from Ladouceur & Pineault (2008). The range of the
derived physical parameters includes uncertainties in the line widths and the
variation in $T_{c}$ at different frequencies. We have included the range of
line widths derived from the 150 MHz spectra with and without baseline removal
in the uncertainty of the line width. Two example plots of the expected line
widths as a function of quantum number along with the observed values are
shown in Fig. 7(left).

The LSR velocities of the spectral lines observed toward DR4 are shown in Fig.
5. While the 750 and 321 MHz CRRLs have similar central velocities (within
1$\sigma$), the central velocity of the 150 MHz CRRL is $\sim$ 0.8 km
s-1(4$\sigma$) lower than that of the 750 MHz line. Based on the similarity of
the observed LSR velocities of the H i self-absorption feature and CRRLs at
750 and 321 MHz (see Fig. 5), we assume the cold H i gas and the CRRL region
co-exist. We can therefore assume that the electron temperature of the CRRL
forming region is approximately equal to the kinetic temperature of the cold H
i gas, which is, in turn approximately the same as its spin temperature. For a
representative electron temperature $T_{e}=50$ K, consistent with the upper
limit obtained for $T_{s}$, the estimated electron densities are in the range
2.8 - 4.5 cm-3. For these model parameters, the radiation broadening is in the
range 3.4 to 4.1 km s-1, collisonal transition broadening is in the range 2.5
to 4.1 km s-1 and collisonal ionization broadening is in the range 0.6 to 0.9
km s-1 at 150 MHz. The neutral density of the region from which CRRLs
originate is estimated as $\frac{n_{e}}{\delta A_{c}}$ where $A_{c}=2.9\times
10^{-4}$ is the cosmic abundance of carbon and $\delta=0.48$ is the depletion
factor (Jenkins, 2009). The estimated neutral density is in the range 2 - 3.2
$\times 10^{4}$ cm-3.

####  4.1.3 Gas properties derived using CO data

The 12CO (Dame et al., 2001) and 13CO (Schneider et al., 2006) spectra
averaged over the GBT beam are shown in Fig. 7 (right). The parameters of the
Gaussian line model of the components of interest here are listed in Table 3.
The central velocities of the CO lines overlap with those of the CRRLs (within
2$\sigma$) but have an offset of $\sim$ 1 km s-1 relative to the LSR velocity
of the H i self-absorption feature (see Fig. 5 bottom-left). The 12CO/13CO
integrated line ratios obtained from 0.3o and 0.66o apertures are 12 and 4
respectively. The excitation temperature for 12CO, estimated from the 0.3o
averaged spectrum and by assuming that the 12CO line is optically thick at its
peak, is $\sim$ 5 K. The low values for line ratio and excitation temperature
indicate that the gas volume density is modest.

We use the results presented by Goldsmith et al. (2008) (see also Pineda et
al. 2010; their Table 1 and Fig. 3) from models developed with a large
velocity gradient approximation to get an estimate of the 12CO column density
$N_{CO}$ and H2 density. The modeling also assumes a spherical cloud with
uniform kinetic temperature of 15 K and the levels are subthermally excited
(i.e. not in LTE). The model results were obtained for 12CO/13CO abundance
ratios range between 25 and 65, as this ratio is expected to vary due to
chemical and/or photo effects. Their model results provide $N_{CO}\sim
10^{16}$ cm-2 and $n_{H_{2}}\sim 200$ cm-3. For such low density, diffuse
clouds, the $H_{2}$ column density per K km s-1 of 12CO line emission is 2
$\times 10^{20}$ cm-2/(K km s-1) (Liszt et al., 2010). Using this
relationship, we find the H2 column density of the CO emitting cloud toward
DR4 is $\sim 10^{21}$ cm-2. The range in the above derived quantities is a
factor of 1.5, which is determined from the values estimated using the line
parameters from the 0.3o and 0.66o averaged spectra.

####  4.1.4 Physical picture

The neutral density derived from the CRRL line width is the total hydrogen
density i.e. $n_{H}+2\;n_{H2}$, where $n_{H}$ is the density of the atomic
hydrogen. The total hydrogen density is in the range 2 - 3.2 $\times 10^{4}$
cm-3, which is more than 50 times the density ($n_{H_{2}}\sim$ 200 cm-3)
derived from CO data. The thermal pressure in the CRRL forming region is
$nT_{e}\sim 1-1.6\times 10^{6}$ cm-3 K, where $n$ is the estimated neutral
density of the region. The thermal pressure of the CO emitting gas is $\sim$
3000 cm-3 K, at least 300 times smaller than the CRRL forming region. A likely
scenario is that the CRRL forming region and the cold H i gas reside in a
shocked region at the boundary of, or within the diffuse CO emitting gas. The
SNe which produced the remnant DR4 could be a source of the shock.

###  4.2 DR21

The compact H ii region DR21 is part of a large complex of radio sources
located in the Cygnus X region at a distance of 1.5 kpc (Rygl et al., 2012).
Radio and infrared recombination line observations made toward DR21 have
provided information about the ionization, the spatial and velocity structures
of the ionized gas and the properties of the interface region between the H ii
region and the neutral cloud in its vicinity (Pankonin et al., 1977; Vallée,
1987; Roelfsema et al., 1989; Golynkin & Konovalenko, 1991). Low angular
resolution ($>$ 1${}^{{}^{\prime}}$) observations have detected a change in
the central velocity of the hydrogen RRL from $-$5 to 6 km s-1 over the
frequency range 8.6 to 1.4 GHz (Pankonin et al., 1977). This change in
velocity is interpreted in terms of a simple model involving compact H ii
regions surrounded by an envelope of lower density ionized gas. The H ii
regions are ionized by at least 6 OB stars as inferred from interferometric
RRL observations (Roelfsema et al., 1989). Line emission from many molecular
species, as well as C i and C ii FIR lines have also been observed in this
direction (e.g., Jakob et al., 2007) at central velocities $\sim$ -10 to +20
km s-1. The bright molecular line emissions are concentrated in the velocity
range $\sim$ -10 to 0 km s-1 and $\sim$ +8 to +9 km s-1. These features are
associated with two interacting giant molecular clouds. The negative velocity
cloud is part of the DR21 complex and the +8 to +9 km s-1 velocity cloud is
part of the W75 complex (Dickel et al., 1978; Gottschalk et al., 2012). Cold H
i gas observed as H i self-absorption features was also reported in this
region near the two velocities (Gottschalk et al., 2012).

####  4.2.1 Carbon and Heavy element RRLs

Fig. 6 shows the CRRL spectra observed toward DR21 at 750 and 321 MHz as well
as the LOFAR spectrum at 150 MHz. Three line components are detected near the
expected velocity range of the carbon line in the 750 MHz spectrum. These
components have LSR velocities with respect to the rest frequency of carbon of
-11.5, -2.1 and 8.6 km s-1. Careful examination of the 321 MHz GBT spectrum
indicates that there are line emission features near velocities -2.1 and 8.6
km s-1. Examination of the 150 MHz spectrum clearly shows an absorption line
near -2.1 km s-1, and subtracting a single component Voigt profile fit from
the spectrum shows some excess absorption near 8.6 km s-1 (see Section 4.2.2
for further discussion on Voigt fit to the 150 MHz spectrum). However, no
emission or absorption features are seen in the 321 and 150 MHz spectra near
-11.5 km s-1. It is likely that this line at 750 MHz may be a transition due
to a higher mass element. For the analysis in the subsequent sections, we
consider only two carbon line components at velocities -2.1 and 8.6 km s-1.

We list the parameters of the previous CRRL detections (Pankonin et al., 1977;
Vallée, 1987; Golynkin & Konovalenko, 1991) in Table 5 in order to compare
with those obtained in our observations. A plot of the LSR velocities of the
CRRLs, 12CO, 13CO and CII 158 $\mu$m lines (see Section 4.2.4 and 4.2.6)
observed in the direction of DR21 is shown in Fig. 8(left). CRRLs with
positive ($\sim$ 8.6 km s-1) LSR velocity are observed only at frequencies $<$
1.4 GHz. The uncertainty of the central velocity of the absorption feature
detected at 25 MHz (Golynkin & Konovalenko, 1991) is large (about 8 km s-1)
compared to the errors in the central velocities of other observations; the
absorption feature is likely to coexist with the negative velocity CRRL
component detected in our observations (see also Golynkin & Konovalenko,
1991). The mean value of CRRL emission lines detected at frequencies $>$ 1.4
GHz is -3.0$\pm$0.3 km s-1, consistent (within 3$\sigma$ value) with the -2.1
km s-1 component observed in our observations, which indicates that they may
be associated. CO and CII 158$\mu$m components corresponding to both CRRL
velocity features were detected in the spectra obtained with 0.3o aperture
(see Fig 8 right).

####  4.2.2  Constraints on the gas properties from CRRL width

We follow the method described in Section 4.1.2 for modelling the CRRL line
width as a function of frequency to constrain the gas properties toward DR21.
The parameters of the Gaussian line models obtained from the 750 and 321 MHz
spectra are given in Table 2 (see Fig. 6). The signal-to-noise ratio of the
-2.1 km s-1 component in the 321 MHz spectrum is low, which results in larger
fractional errors in the estimated line parameters than were found in DR4. We
attempt to fit a two component Voigt profile to the 150 MHz spectrum, using
both velocity centroids from the higher frequency data, but the estimated
error in the line parameters is comparable to the derived values. Therefore,
the 150 MHz spectrum is modeled using a single component Voigt profile. The
total contribution to the line width at 750 MHz due to radiation and pressure
broadening is less than 5% of the observed line width at this frequency. The
estimated error of the line width at 750 MHz is 0.1 km s-1, a factor of 2
better than the higher frequency measurements from the literature, and the
angular resolution at this frequency is comparable (within a factor of 2) to
the low frequency CRRL observations. Hence for the Voigt profile fitting we
used $V_{D}=4.1$ km s-1, the observed line width at 750 MHz. We carefully
examined the spectral baseline and subtracted a 3rd order polynomial before
modeling the line profile. The line parameters are given in Table 2. We also
included line parameters that were obtained from the spectrum without any
baseline removal. The line widths for the two cases differ by a factor of 1.7
(see Table 2). Thus the effect of spectral baseline removal on the line width
is substantial for the DR21 direction.

We plot the observed line width of the -2.1 km s-1 CRRL component as a
function of quantum number in Fig. 9(left). Three example models for line
width variation with quantum number are shown in the figure. The line width
for the C$100\alpha$ line observed at an angular resolution of $4.3\arcmin$
(Vallée, 1987) is not consistent with the those of the lower frequency CRRLs.
This difference can be attributed to the different angular resolution between
the observations, as well as changes in the gas probed as a function of
frequency. As seen in Fig. 9(left), for a given $T_{e}=$ 50 K, the electron
densities required to explain the C350$\alpha$ (150 MHz) and the C640$\alpha$
(25 MHz) absorption lines (Golynkin & Konovalenko, 1991) differ by a factor of
75. The situation is similar for other electron temperatures as well. Thus, at
least two line forming regions are needed to explain the observed line widths
as a function of frequency. Below we attempt to separately constrain the
physical parameters of these regions.

We first consider the gas responsible for the 150 MHz absorption line. Fig.
9(right) shows results from the line width modeling along with observed values
at frequencies $<$ 1.4 GHz. We could not find models that are consistent with
the 321 MHz observations for $T_{e}$ ${\mathrel{\mathchoice{\lower
2.9pt\vbox{\halign{$\m@th\displaystyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\textstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\scriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}{\lower
2.9pt\vbox{\halign{$\m@th\scriptscriptstyle\hfil#\hfil$\cr>\crcr\sim\crcr}}}}}$50
K when a 1$\sigma$ range is considered for the observed values. An example
model result that is consistent with all the observed line widths between 750
and 150 MHz requires $T_{e}=$ 20 K, $n_{e}=$ 24 cm-3 (see Fig. 9 right). Since
the signal-to-noise ratio of the -2.1 km s-1 component at 321 MHz
(C$273\alpha$) is low, we include here models that are consistent only with
the 750 and 150 MHz observations. The estimated electron densities from the
line width modeling are in the range 3.5 $\rightarrow$ 24 cm-3 for assumed
electron temperatures in the range 200 $\rightarrow$ 20 K. The range of
neutral densities corresponding to the estimated electron densities is 2.5 -
17.2 $\times 10^{4}$ cm-3. We refer to this gas as the high density CRRL
forming region.

We now consider the gas responsible for the 25 MHz CRRL absorption. The line
width modeling indicates that the electron density of the gas responsible for
the 25 MHz line absorption is in the range 0.008 $\rightarrow$ 0.3 cm-3 for
the assumed range of electron temperature 200 $\rightarrow$ 20 K. Example
model curves are shown in Fig. 9(left). The estimated parameter values are
consistent with the constraints on the gas properties obtained by Golynkin &
Konovalenko (1991). The neutral density of the line forming region obtained
from the estimated electron densities is in the range 58 - 2200 cm-3. We refer
to this gas as the low density CRRL forming region.

####  4.2.3 Gas properties using CRRL amplitude: preliminary results

We take representative values for the gas parameters from the range of
possible values estimated in Section 4.2.2 for the dual line forming regions:
$T_{e}\sim 150$ K, $n_{e}\sim 4.5$ cm-3 and LOS pathlength 7 $\times 10^{-3}$
pc for the high-density region and $T_{e}\sim 50$ K, $n_{e}\sim 0.2$ cm-3 and
LOS pathlength 0.25 pc for the low density region (see Fig. 9 left). These
parameter values are not uniquely determined, which will be attempted as part
of our future modeling work (see Section 5). The higher density region could
be a photo-dissociation region (PDR) located at the H ii region-molecular
cloud interface and the lower density region could be located in the diffuse
interstellar medium along the LOS toward the source. The background continuum
temperature at 750 MHz is $\sim$ 99 K and so the detection of emission lines
from both regions at this frequency indicates that the carbon atom level
population is not in LTE. Therefore, it is essential to have the non-LTE
parameters to compute the expected line intensity from the dual line forming
region model; here we use the results from Walmsley & Watson (1982).

Our modeling shows that the observed CRRL at 150 MHz is dominated by the line
absorption due to the high density region as its electron density is high. The
CRRL from the lower density region is in emission at 150 MHz and is amplified
by stimulated emission due to the background radiation field as its electron
density is low. The relative contributions to line emission from the high and
low density regions at 321 MHz are 10% and 90% and at 750 MHz are 45% and 55%
respectively. The $b_{n}\beta_{n}$ values obtained from Walmsley & Watson
(1982) for the low density region parameters are -7.2, -7.4 and -2.6 for
quantum numbers 206, 273 and 350 respectively. We use the $b_{n}\beta_{n}$
values -5.7, -0.6 and 6.0 for quantum numbers 206, 273 and 350 respectively
for the high density region, which corresponds to $T_{e}=100$ K and $n_{e}=$ 1
cm-3 (Walmsley & Watson, 1982) as departure coefficients for higher
temperatures and densities are not available. We also assumed the
dielectronic-subthermal case discussed by Walmsley & Watson (1982) for the
modeling.

####  4.2.4 H i and CO lines

The H i , 12CO (Dame et al., 2001) and 13CO (Schneider et al., 2010) spectra
toward DR21 averaged over the 0.3o and 0.66o beam are shown in Fig. 8 (right).
The H i line shows a self-absorption feature near (within 1$\sigma$) the -2.1
km s-1 CRRL component but no absorption feature is seen near the 8.6 km s-1
component (see Fig. 8 right). The H i line structure, however, is more complex
than that toward DR4 and so we could not perform a Gaussian decomposition to
extract the line parameters of the absorption feature. The CRRL central
velocities are similar (within 1$\sigma$) to the two features seen in the CO
spectra at -2.1 and 8.6 km s-1. The CO line amplitudes in the 0.66o averaged
spectra are lower by a factor of $\sim$2 compared to those in the 0.3o
averaged spectra, which indicates that the physical properties of the
molecular cloud change over this angular scale. The isotopologue ratio and
excitation temperature (assuming 12CO is optically thick at the line center)
derived from the 0.66 deg averaged spectra are 11 and 7 K respectively. From
the models of Goldsmith et al. (2008), the 12CO column density and H2
densities are 7 $\times 10^{16}$ cm-2 and 275 cm-3 respectively for an assumed
kinetic temperature of 15 K. The estimated H2 column density is 4 $\times
10^{21}$ cm-2 (Liszt et al., 2010).

####  4.2.5 Physical picture

The higher density region responsible for CRRL absorption at 150 MHz has a
neutral density more than 100 times the molecular density inferred from CO
line emission. The LOS extent of the molecular cloud is about 4.5 pc, at least
2 orders of magnitude larger than that of the dense CRRL forming region. The
enhancement in density could be due to shocks resulting from the expansion of
the H ii region DR21. Thus it is likely that the dense CRRL forming region is
a PDR located at the boundary of the DR21 and the associated molecular cloud.
The lower density region responsible for the CRRL absorption at 25 MHz, on the
other hand, has neutral density a factor of $\sim$5 times the CO gas density.
Its LOS extent is 20 times lower than the CO cloud size. Thus the lower
density region could be residing in a denser part of the diffuse CO emitting
cloud. The enhancement in density could be due to shocks resulting from the
interaction of the two giant molecular clouds on this sight line.

####  4.2.6 CII 158 $\mu$m emission

The CII 158 $\mu$m line was detected toward DR21 by SOFIA with an angular
resolution of 0.5o$\times$ 0.2o (see Fig 8 right; Schneider et al., 2020). The
line central velocity of the strongest emission is -2.92 km s-1(see Table 3).
This velocity is 0.8 km s-1 offset from the -2.1 km s-1 CRRL component; about
8 times the uncertainty of the central velocity of the recombination line. The
integrated line temperature of this component is 26.4 K km s-1. We estimate
the expected CII 158 $\mu$m intensity from the dual CRRL forming region using
Eq. 2 of Roshi et al. (2002). The critical densities for electron, hydrogen
atom and hydrogen molecule collisions are assumed to be 10, 3000 and 6000 cm-3
respectively for electron temperatures in the range 50 to 150 K. The total
hydrogen atom densities used for the calculation are estimated from the
derived electron densities for the dual CRRL forming region (see Section
4.2.3). We found that the dual line forming region model can account for 73%
of the observed CII 158 $\mu$m line intensity, with 58 % and 14% contributions
from the high and low density CRRL forming regions respectively.

###  4.3 HB21

HB21 is an evolved, nearby SNR of age 8000-15000 yrs, with an angular extent
of $\sim$ 2.5o$\times$ 2.3o(Kothes et al., 2006). 12CO, H i and radio
continuum observations indicate that the SNR is interacting with the
interstellar material (Tatematsu et al., 1990). The 21 cm line observations
show an HI shell around the SNR expanding at $\sim$ 25 km s-1(Assousa & Erkes,
1973). A giant molecular cloud east of the remnant has been observed and the
CO emission morphology indicates that HB21 is interacting with the molecular
cloud (Tatematsu et al., 1990).

####  4.3.1 Gas properties derived using H i data

The H i spectra averaged over the 0.3o and 0.66o regions are shown in Fig. 10.
The H i line near -5 km s-1 shows a strong emission superposed with a self-
absorption feature. As in the case for DR21 and DR4, the H i profile is
complex and a unique Gaussian decomposition could not be done. We modeled the
self-absorption feature using a single Gaussian emission component and an
absorption component. For the line profile modeling the velocity range was
restricted to -20 to 80 km s-1. The result of the Gaussian line modeling is
shown in Fig. 10 and the H i line parameters are given in Table 3. The
properties of the cold gas responsible for H i self-absorption are constrained
using the method described in Section 4.1.1. Fig 10 shows the H i spin
temperatures and column densities of the cold gas that can produce the
observed self-absorption feature. The H i column densities required to produce
the observed absorption feature are at least 50 % larger than those of the
cold gas observed toward DR4.

####  4.3.2 Constraints from CRRL observations

Our 750 MHz observations did not detect CRRL emission towards HB21. The upper
limit on the line amplitude is 5 mK (see Table 2). Assuming an electron
temperature of 50 K and taking $b_{n}\beta_{n}\sim-3.6$ (Walmsley & Watson,
1982) at 750 MHz, we get an upper limit for the emission measure of 9 $\times
10^{-3}$ pc cm-6. This emission measure is comparable to that of the lower
density CRRL forming region towards DR21.

###  4.4 G34.20+0.0, G34.94+0.0 & G35.17+0.0

CRRL emission is detected towards G34.94+0.0 and tentatively detected toward
G34.20+0.0 at 327 MHz (see Fig. 4). Diffuse CRRL emission and absorption have
been previously detected in the inner galactic plane at frequencies above and
below $\sim$ 100 MHz respectively (Erickson et al., 1995; Kantharia &
Anantharamaiah, 2001; Roshi et al., 2002). The CRRLs detected with the Arecibo
telescope are likely to be from diffuse C ii regions similar to those observed
in earlier carbon line surveys. The line width of the CRRL toward G34.94+0.0
is 18.5 km s-1, much larger (at least a factor of 4) than seen towards DR21
and DR4 at 321 MHz, but closer to the typical line width detected in an
earlier 327 MHz survey of CRRLs (Roshi et al., 2002). The larger line width
could be from contributions to the observed emission from multiple line
forming regions along the LOS with different LSR velocities. Future multi-
frequency observations will be necessary to model the line forming region and
understand its origin.

###  4.5 Hydrogen and Helium RRLs

Hydrogen lines are detected toward almost all observed positions except in the
direction of HB21. We estimate the emission measure (EM) of the H ii regions
responsible for the hydrogen line emission assuming, LTE, electron temperature
of 8000 K and a beam filling factor of unity using the equation

${EM=\frac{\int T_{L}d\nu}{1.92\times 10^{3}\;T_{e}^{1.5}},}$ (4)

where EM is in units of pc cm-6, $T_{e}$ is in K and $\int T_{L}d\nu$ is the
observed integrated line temperature in K kHz. The emission measures obtained
from the 321 and 750 MHz data are 8100 and 1.1 $\times 10^{4}$ pc cm-6
respectively toward DR4. The emission measures estimated toward DR21 are 8500
and 1.5 $\times 10^{4}$ pc cm-6 from the observed lines at the two
frequencies. We attribute the difference in EMs obtained from the two
frequencies to beam dilution effects reflecting clumpiness in the ionized gas.

The emission measure estimated toward G34.94+0.0 is 5500 pc cm-6. We examined
the WISE catalogue (Anderson et al., 2014) to identify H ii regions in this
area. The H ii region G034.940+0.074 (Lockman, 1989) is present within the
Arecibo telescope beam (15${}^{{}^{\prime}}$), but its LSR velocity is 45.6 km
s-1; no strong hydrogen RRL component at 327 MHz was detected at that
velocity. A second H ii region, G034.757-0.669, has LSR velocity 52.1 km s-1,
which agrees with the central velocity of the hydrogen RRL observed toward
G34.94+0.0 at 327 MHz, but is at a separation of 0.7o from the sight line.

The emission measure estimated from the detected hydrogen line toward
G34.20+0.0 is $\sim$ 6000 pc cm-6. There are two H ii regions -
G034.256+00.136, G034.404+00.227 - located respectively at angular distances
of 0.15o and 0.3o from G34.20+0.0, with LSR velocities 53.1 and 60.1 km s-1.
The LSR velocity of G034.404+00.227 is within the 1$\sigma$ uncertainty of the
central velocity of hydrogen line detected toward G34.20+0.0.

Toward G35.17+0.0, we estimate an emission measure of $\sim$ 3000 pc cm-6. The
H ii region G035.063+00.330 (angular distance 0.35o) has LSR velocity 57.2 km
s-1 similar to the central velocity of the detected line toward G35.17+0.0.

We conclude that the Hydrogen RRLs in the Galactic Plane likely arise in the
outer envelopes of H ii regions. (Anantharamaiah, 1986).

A Helium line is detected towards DR21 at 750 MHz. The helium to hydrogen line
ratio is 0.08 (0.02). Earlier observations at frequencies of 1.4 GHz and above
have found that this ratio varies from 0.03 to 0.95 within the DR21 region
(Roelfsema et al., 1989). However these observations were made with an angular
resolution at least a factor of 2 higher than the 750 MHz observations
reported here.

##  5 Summary and future work

Radio recombination lines of carbon are detected toward DR4 and DR21 at 750
and 321 MHz with the GBT. These observations are combined with 150 MHz LOFAR
and other previous CRRL detections to constrain the physical properties of the
line forming regions. Modeling the line width as a function of frequency
indicates that the electron density of the line forming region toward DR4 is
in the range 1.4 $\rightarrow$ 6.5 cm-3. Similar modeling shows that a dual
CRRL forming region with electron densities 3.5 $\rightarrow$ 24 cm-3 and
0.008 $\rightarrow$ 0.3 cm-3 could plausibly explain the observed line width
as a function of frequency toward DR21. The electron densities of the denser
regions in both directions are at least a factor of 10 larger than those
estimated for diffuse C ii regions in the Galactic plane from low ($<$ 1 GHz)
frequency observations (e.g., Kantharia & Anantharamaiah, 2001; Oonk et al.,
2017; Salas et al., 2017). 12CO and 13CO emission and H i self-absorption
lines at similar central velocities to the CRRLs are detected toward DR4 and
DR21. The CII 158 $\mu$m lines observed toward DR21 also have central
velocities similar to those of the CRRLs. The similarity of the central
velocities suggests that these line forming regions are for the most part
associated. The inferred molecular densities from the CO data are at least two
orders of magnitude smaller than that of the denser CRRL forming regions in
both directions. We suggest that the CRRLs and H i self-absorption are formed
in shocked regions at the boundary of or within the cloud producing the CO
emission in the direction of DR4. The shocks, which caused the enhancement of
the density, could be due to SNe blast waves in the case of DR4. The denser
line forming region toward DR21 could be located at the H ii region-molecular
cloud interface and the density enhancement could be due to shocks caused by
the expansion of the H ii region. The lower density CRRL forming region toward
DR21 has a neutral density about 5 times the density of the CO cloud observed
in this direction. This density enhancement could be due to shock caused by
cloud-cloud collision. Our modeling shows that a significant fraction ($\sim$
73%) of the observed CII 158 $\mu$m emission toward DR21 could originate from
the dual CRRL forming region.

We also detect CRRLs toward G34.20+0.0 (tentatively) and G34.94+00 near 327
MHz with the Arecibo telescope. These CRRLs could be from diffuse C ii regions
similar to those detected earlier in the Galactic plane (Anantharamaiah,
1986).

Hydrogen lines were detected in almost all directions except towards HB21, and
at all the observed frequencies. A Helium line was detected toward DR21 at 750
MHz and the observed helium to hydrogen line ratio is 0.08 (0.02).

We plan to expand the GBT observations over a larger area in the Cygnus region
to probe the spatial extent of the CRRL forming region and to better
understand its association with regions producing CO and H i self-absorption
lines. We also plan to make multi-frequency observations toward the Galactic
plane positions where CRRLs were detected with the Arecibo telescope. Our next
step in modeling the line emission is to develop a time dependent
photodissociation model which can self-consistently model the H i CO and
CRRLs. This model will also be able to correctly calculate the level
population of CRRLs at high Rydberg states. The larger data set and temporal
information will help to better constrain the physical properties of the
absorbing clouds. The eventual goal is to derive the molecular formation
rates, thus addressing the wider question of molecular cloud formation.

##  6 Acknowledgements

The Arecibo Observatory is a facility of the NSF operated under cooperative
agreement (#AST-1744119) by the University of Central Florida (UCF) in
alliance with Universidad Ana G. Méndez (UAGM) and Yang Enterprises (YEI),
Inc. The Green Bank Observatory is a major facility funded by the National
Science Foundation operated by Associated Universities, Inc. This publication
makes use of data products from the Wide-field Infrared Survey Explorer, which
is a joint project of the University of California, Los Angeles, and the Jet
Propulsion Laboratory/California Institute of Technology, funded by the
National Aeronautics and Space Administration. This research has made use of
NASA’s Astrophysics Data System. Phil Perillat, Arecibo Observatory, was
crucial in helping us with the observational setup and initial observations.
Basic Research at the Naval Research Laboratory is funded by 6.1 base
programs. We acknowledge the very productive discussion with F. J. Lockman,
Green Bank Observatory, during the course of this work. JBRO acknowledges
financial support from NWO Top LOFAR-CRRL project, project No. 614.001.351.
LOFAR, the Low Frequency Array designed and constructed by ASTRON, has
facilities in several countries, that are owned by various parties (each with
their own funding sources), and that are collectively operated by the
International LOFAR Telescope (ILT) foundation under a joint scientific
policy. The authors would like to thank the LOFAR observatory staff for their
assistance in obtaining and handling of this large data set. Part of this work
was carried out on the Dutch national e-infrastructure with the support of the
SURF Cooperative through grant e-infra 160022 & 160152\. We thank the
anonymous referee whose very helpful comments have significantly improved the
manuscript.

Arecibo Telescope, GBT, LOFAR

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Table 1: Summary of Observations  Source | RA(2000) | DEC(2000) | Date of Obs. | Obs. freq | Beam | Telescope
---|---|---|---|---|---|---
Name | (hh:mm:ss) | (dd:mm:ss) | yyyy-mm-dd | (MHz) | (o) |
DR4 (G78.12+1.92) | 20:21:56 | +40:15:36 | 2012-05-09 | 321,750 | 0.66, 0.3 | GBT
DR21 (G81.68+0.54) | 20:39:01 | +42:19:43 | 2012-05-09, 2012-05-27 | 321,750 | 0.66, 0.3 | GBT
HB21 (G89.00+4.70) | 20:46:05 | +50:39:05 | 2012-05-09 | 750 | 0.66 | GBT
G34.20+0.0 | 18:53:45.1 | +01:07:43 | 2019-06-03, 2020-05-11 | 327 | 0.25 | Arecibo
G34.94+0.0 | 18:55:06.1 | +01:47:14 | 2019-06-02, 2020-05-08 | 327 | 0.25 | Arecibo
|  |  | 2020-06-01, 2020-06-02 |  |  |
G35.17+0.0 | 18:55:31.3 | +01:59:30 | 2019-05-27, 2020-04-26 | 327 | 0.25 | Arecibo
Table 2: Observed RRL parameters  Freq | Atom | n | TLA | VLSR |  $\Delta$V | Note
---|---|---|---|---|---|---
(MHz) |  |  | (K) | km s-1 | (km s-1) |
DR4 (G78.12+1.92)
321 | H | 273 | 0.77(0.05) | 1.4(0.8) | 26.5(1.9) |
| C |  | 0.77(0.09) | -2.8(0.4) | 6.6(0.9) |
750 | H | 206 | 0.46(0.01) | 0.9(0.2) | 25.0(0.5) |
| C |  | 0.24(0.02) | -2.6(0.2) | 5.1(0.5) |
150 | C | 350 | -4.2(0.1) | -1.7(0.1) |  $\Delta V_{L}=$7.4(0.9) | 11Parameters obtained from the spectrum averaged over 0.3o. A 3rd order polynomial baseline was removed from the spectrum. $\Delta V_{D}=$5.1 km s-1
| C |  | -3.8(0.1) | -1.8(0.1) |  $\Delta V_{L}=$8.5(1.0) | 22Parameters obtained from the spectrum averaged over 0.66o. A 3rd order polynomial baseline was removed from the spectrum. $\Delta V_{D}=$5.1 km s-1
| C |  | -4.3(0.2) | -1.7(0.2) |  $\Delta V_{L}=$7.5(1.3) | 33Parameters obtained from the spectrum averaged over 0.3o. $\Delta V_{D}=$5.1 km s-1
| C |  | -3.8(0.1) | -1.8(0.2) |  $\Delta V_{L}=$7.3(1.2) | 44Parameters obtained from the spectrum averaged over 0.66o. $\Delta V_{D}=$5.1 km s-1
DR21 (G81.68+0.54)
321 | H | 273 | 0.76(0.03) | 7.2(0.5) | 28.1(1.3) |
| C |  | 0.63(0.05) | 8.8(0.4) | 7.0(0.9) |
| C |  | 0.22(0.05) | -2.1(1.3) | 9.3(3.2) |
750 | H | 206 | 0.66(0.01) | 6.9(0.1) | 25.3(0.2) |
| He |  | 0.05(0.01) | 7.8(1.0) | 16.2(2.4) |
| C |  | 0.21(0.01) | -2.1(0.1) | 4.1(0.3) |
| C |  | 0.11(0.01) | 8.6(0.3) | 7.4(0.8) |
| S |  | 0.09(0.02) | -2.9(0.2) | 2.4(0.5) | 1010see Section 4.2
150 | C | 350 | -1.1(0.1) | -2.0(0.3) |  $\Delta V_{L}=$17.1(2.1) | 55Parameters obtained from the spectrum averaged over 0.3o. A 3rd order polynomial baseline was removed from the spectrum. $\Delta V_{D}=$4.1 km s-1
| C |  | -1.1(0.1) | -1.6(0.3) |  $\Delta V_{L}=$17.2(1.9) | 66Parameters obtained from the spectrum averaged over 0.66o. A 3rd order polynomial baseline was removed from the spectrum. $\Delta V_{D}=$4.1 km s-1
| C |  | -1.1(0.1) | -2.3(0.3) |  $\Delta V_{L}=$10.2(2.3) | 77Parameters obtained from the spectrum averaged over 0.3o. $\Delta V_{D}=$4.1 km s-1
| C |  | -1.0(0.1) | -1.9(0.3) |  $\Delta V_{L}=$10.6(2.2) | 88Parameters obtained from the spectrum averaged over 0.66o. $\Delta V_{D}=$4.1 km s-1
HB21 (G89.00+4.70)
750 |  | 206 | (0.005) |  |  |
G34.20+0.0
327 | H | 272 | 0.26(0.03) | 62.8(3.6) | 58.6(8.6) | 99Tentative detection
| C |  | 0.25(0.06) | 49.8(2.1) | 11.0(4.9) | 99Tentative detection
G34.94+0.0
327 | H | 272 | 0.43(0.04) | 52.1(1.6) | 32.7(3.7) |
| C |  | 0.24(0.05) | 49.4(2.2) | 18.5(5.1) |
G35.17+0.0
327 | H | 272 | 0.15(0.01) | 56.9(2.7) | 48.5(6.4) | 99Tentative detection
Table 3: H i , CO and CII 158$\mu$m line parameters  Amplitude | Center | Width | Note
---|---|---|---
(K) | (km s-1) | (km s-1) |
DR4 (G78.12+1.92): H i
2.2(1.0) | 48.4(2.4) | 10.9(5.7) | 11Parameters obtained from the spectrum averaged over 0.3o.
99.0(1.2) | -1.2(0.1) | 33.0(0.4) | $T_{OFF}$
-48.0(1.5) | -3.2(0.1) | 6.8(0.3) | $T_{ON}-T_{OFF}$
32.9(1.0) | -33.4(0.4) | 13.6(1.0) |
33.3(1.4) | -47.0(0.3) | 9.5(0.7) |
28.7(2.9) | -62.5(0.3) | 11.3(1.0) |
65.7(0.8) | -78.3(0.5) | 27.2(0.8) |
DR4 (G78.12+1.92): 12CO
2.1(0.1) | -2.0(0.1) | 3.2(0.1) | 11Parameters obtained from the spectrum averaged over 0.3o.
1.3(0.1) | -2.4(0.1) | 2.2(0.1) | 22Parameters obtained from the spectrum averaged over 0.66o.
DR4 (G78.12+1.92): 13CO
0.30(0.01) | -2.05(0.02) | 1.86(0.04) | 11Parameters obtained from the spectrum averaged over 0.3o.
0.28(0.01) | -2.08(0.06) | 2.72(0.12) | 22Parameters obtained from the spectrum averaged over 0.66o.
DR21 (G81.68+0.54):12CO
7.7(0.1) | -2.6(0.1) | 5.0(0.1) | 11Parameters obtained from the spectrum averaged over 0.3o.
4.3(0.2) | 8.2(0.2) | 4.0(0.4) | 11Parameters obtained from the spectrum averaged over 0.3o.
3.7(0.1) | -2.3(0.1) | 5.7(0.2) | 22Parameters obtained from the spectrum averaged over 0.66o.
4.9(0.1) | 8.5(0.1) | 3.9(0.2) | 22Parameters obtained from the spectrum averaged over 0.66o.
DR21 (G81.68+0.54):13CO
1.47(0.01) | -2.75(0.01) | 3.15(0.03) | 11Parameters obtained from the spectrum averaged over 0.3o.
0.43(0.01) | 8.20(0.05) | 3.26(0.11) | 11Parameters obtained from the spectrum averaged over 0.3o.
0.55(0.01) | -2.38(0.03) | 3.47(0.07) | 22Parameters obtained from the spectrum averaged over 0.66o.
0.63(0.01) | 8.66(0.03) | 3.03(0.06) | 22Parameters obtained from the spectrum averaged over 0.66o.
DR21 (G81.68+0.54):CII 158$\mu$m
5.84(0.04) | -2.92(0.02) | 4.52(0.04) | 33Parameters from the spectrum obtained with an angular resolution of 0.5o$\times$ 0.2o.
HB21 (G89.00+4.70): H i
-39.3(4.8) | -4.8(0.2) | 7.0(0.7) | 11Parameters obtained from the spectrum averaged over 0.3o.
108.1(4.9) | -4.9(0.1) | 22.1(0.8) |
Table 4: Continuum parameters used for modeling  Source |  $f_{0}$aaFrequency corresponding to the listed continuum temperature $T_{c}$. The continuum temperature at a frequency $f$ in MHz can be obtained as $T=T_{C}(\frac{f}{f_{0}})^{-\alpha}$ | $T_{C}$ | $\alpha$ | Note
---|---|---|---|---
| (MHz) | (K) |  |
DR4 | 1420.4 | 46(4) | 2.67 (2.63 $\rightarrow$ 2.72) | 11Continuum values obtained with 0.3o beam. The median spectral index from Ladouceur & Pineault (2008) and the interquartile range are listed.
| 1420.4 | 42(4) | 2.67 (2.63 $\rightarrow$ 2.72) | 22Continuum values obtained with 0.66o beam. The median spectral index from Ladouceur & Pineault (2008) and the interquartile range are listed.
DR21 | 150.0 | 2246(10) | 1.94(0.01) | 33Continuum values obtained with 0.3o beam. The spectral index was obtained from 408 and 1420 MHz CGPS measurements.
| 150.0 | 2149(10) | 2.0(0.02) | 44Continuum values obtained with 0.66o beam. The spectral index was obtained from 408 and 1420 MHz CGPS measurements.
HB21 | 1420.4 | 10(4) | 2.38 | 55Continuum values obtained with 0.3o beam. The spectral index was from Kothes et al. (2006).
Table 5: CRRL parameters from previous observations toward DR21  Freq | n | TLA | VLSR |  $\Delta$V | Note
---|---|---|---|---|---
(MHz) |  | (K) | km s-1 | (km s-1) |
1425 | 166 | 0.1(0.02) | -2.9(0.3) | 3.2(0.6) | 11Angular resolution of the observation is 8.5${}^{{}^{\prime}}$(Pankonin et al., 1977).
1652 | 158 | 0.1(0.02) | -3.2(0.4) | 4.2(0.9) | 22Angular resolution of the observation is 7.8${}^{{}^{\prime}}$(Pankonin et al., 1977).
3329 | 125 | 0.017(0.002) | -2.7(0.3) | 4.0(0.5) | 33Angular resolution of the observation is 8.2${}^{{}^{\prime}}$(Vallée, 1987).
6482 | 100 | 0.011(0.002) | -3.0(0.2) | 2.4(0.2) | 44Angular resolution of the observation is 4.3${}^{{}^{\prime}}$(Vallée, 1987).
25 | 640 | -35(15) | 0(8) | 42(12) | 55Equivalent beam width of the observation is 1.7o(Golynkin & Konovalenko, 1991).
Figure 1: Recombination line spectrum along with the fractional channel
weights. The weighted averaged spectrum toward G34.94+0.0 obtained with the
Arecibo telescope at 327 MHz is shown on the top plot and the fractional
channel weights are shown on the bottom plot. The typical variation in weights
across channels in the final averaged spectrum is about 10%.  Figure 2: Top-
left: The 1.4 GHz CGPS continuum image of DR4. Recombination line observations
toward DR4 was made with the GBT. The green and white circles represent the
FWHM beam width at 321 MHz ($\sim$0.66o) and 750 MHz respectively( $\sim$0.3
o). Top-right: Same as top-left figure but toward DR21. Bottom-left: Same as
top-left figure but toward HB21. Bottom-right: The three positions observed
with the Arecibo telescope near 327 MHz are marked on the 22$\mu$m WISE image
of the galactic plane. The white circles represent the FWMH beam width at 327
MHz ($\sim$ 0.25o). Figure 3: Radio recombination line spectra along with
Gaussian line models toward DR4 and DR21. The data toward the two sources were
obtained using the GBT at 750 and 321 MHz.  Figure 4: Radio recombination line
spectra toward G34.2+0.0, G35.17+0.0, G34.94+0.0 and HB21.The data toward the
first three sources were obtained with the Arecibo Telescope at 327 MHz and
those toward HB21 were obtained with the GBT at 750 MHz. The Gaussian line
models (orange solid and dash-dot curves; latter indicates tentative
detection) are over plotted in those spectra where lines were detected.
Figure 5: DR4 compilation. Top-left: H i 21cm spectra averaged over 0.66o and
0.3o beams. Gaussian components of the 0.3o averaged H i spectrum are shown
along with the net Gaussian line model and residual obtained after removing
the line model from the observed spectrum. Top-right: CGPS 21cm image obtained
from the spectral channel data near the peak of the H i self-absorption
velocity of -3.2 km s-1. The angular resolution of the image is $\sim$ 2.5′.
The grey and black circles indicate the GBT beam sizes at 321 MHz and 750 MHz
respectively. The peak amplitude of the background emission near -3.2 km s-1
is 99 K. Thus line amplitudes less than 99 K indicate H i absorption. The H i
absorption is extended over the GBT beam but the absorption amplitude changes
within the beam area. This change could be due to a combination of variations
in physical properties and background continuum. Bottom-left: LSR velocities
of H i , CRRLs and CO lines observed toward DR4. The error bars shown are
$\pm$ 2$\sigma$ values. Bottom-right: The spin temperature and H i column
density of the gas responsible for self-absorption for p=0.8 and 0.9 are shown
by the solid curves (see Section 4.1.1). Figure 6: Carbon recombination line
spectra at 750 (top), 321 (middle) and 150 (bottom) MHz towards DR4 (left) and
DR21 (right). The Gaussian line models (orange curves) for the 750 and 327 MHz
spectra are over plotted. The 150 MHz spectra averaged over 0.3o region are
shown in black solid lines in the bottom panel and the Voigt model fit to
these spectra are shown in orange solid curves. 3rd order polynomials were
subtracted from these spectra. The 150 MHz spectra averaged over 0.66o region
are shown by the dotted and dashed curve. No spectral baselines were
subtracted from the spectra shown in dashed curve while 3rd order polynomials
were subtracted from the spectra shown in dotted curve.

Figure 7: Left: FWHM line widths of CRRLs observed toward DR4 vs principal
quantum number. The observed points along with $\pm$ 1$\sigma$ error bars are
shown for 321 and 750 MHz observations. For 150 MHz, the effect on the line
width due to baseline removal from the spectrum is also included in the error
bar (see text). The solid curves represent the expected line broadening as a
function of quantum number for two different models (see Section 4.1.2), and
also shown are the broadening contributions from Doppler motions (dash dot
dotted), radiation broadening with $\alpha=2.67$ (dashed), collisional
ionizations (dot dashed) and collisional transitions (dotted) relevant for
each model. Right: H i , 12CO and 13CO lines toward DR4. The spectra obtained
by averaging over 0.66o and 0.3o are shown in dashed and solid lines
respectively. The vertical line indicates the LSR velocity of the CRRL
detected at 750 MHz.

Figure 8: Left: The LSR velocities of CRRLs, 12CO, 13CO and CII 158 $\mu$m
lines observed toward DR21. The error bars shown are $\pm$3$\sigma$ values for
all data points except for the C640$\alpha$ line. The error bar for the
C640$\alpha$ line is $\pm 1\sigma$. For the CO and CII 158 $\mu$m lines the
error bars are within the size of the marker. Right: H i 12CO, 13CO and CII
158 $\mu$m spectra toward DR21. The angular resolution and scaling applied to
the spectra are indicated in the legend. The vertical lines indicate the LSR
velocities (-2.1 and 8.6 km s-1) of the CRRLs detected at 750 MHz.

Figure 9: Left: The FWHM line widths of CRRLs observed toward DR21 vs
principal quantum number. The $\pm$ 1$\sigma$ error bars are shown for all
observed data points except for the 150 MHz line width. The error bar of the
150 MHz line width includes the range of values obtained with and without
spectral baseline removal. The solid curves represent the expected line
broadening as a function of quantum number for three different models. It is
evident from the figure that at least two CRRL forming regions with very
different electron densities are required to explain the observed line width
as a function of frequency (see Section 4.2.2). Right: Same as the left figure
but showing observed points at frequencies $<$ 1.4 GHz. The solid curves
represent three different models for the higher density line forming region
(see Section 4.2.2), and also shown are the broadening contributions from
Doppler motions (dash dot dotted), collisional ionizations (dot dashed) and
collisional transitions (dotted) relevant for each model. Radiation broadening
modeled with an $\alpha=1.94$ does not significantly contribute to line
broadening in this region.

Figure 10: Left: H i 21cm spectra toward HB21 along with Gaussian line model
of the line profile. The angular resolution is indicated in the legend. Right:
Constraints on the physical parameters of the cold H i gas in the direction of
HB21 (see Section 4.3).