Discovery of carbon radio recombination lines in absorption towards Cygnus A

Abstract

INTRODUCTION

Spectral lines resulting from atoms recombining with electrons in diffuse, ionized plasma are potentially important diagnostics to probe the conditions of the emitting and absorbing gas. At low quantum numbers this gives rise to the well-known optical and near-infrared recombination lines. At higher quantum numbers the energy spacing between subsequent quantum levels decreases and a recombination line transition will emit a photon at radio wavelengths. The associated lines for high quantum numbers are therefore called radio recombination lines (RRLs).

RRLs can be used to obtain a wealth of information on the properties of the emitting gas (e.g. Gordon & Sorochenko 2009). Emitting in the radio domain, these lines are unbiased by dust obscuration. At low radio frequencies (<1 GHz) RRLs provide a straightforward method to measure the temperature, density and ionization of the cold neutral medium (CNM; e.g. Payne, Anantharamaiah & Erickson 1989). This information cannot easily be obtained by other means, such as 21 cm neutral hydrogen measurements.

Our own Galaxy is a copious emitter of RRLs, and come in two flavours: (i) classical RRLs and (ii) diffuse RRLs. Classical RRLs are associated with the common H ii regions (Palmer 1967). Here recombination lines from hydrogen, helium and carbon are seen (e.g. Konovalenko & Stepkin 2005). These are predominantly observed at frequencies above ∼1 GHz as they trace the warm (T_e ∼ 10⁴ K), high-density (n_e > 100 cm⁻³) gas.

Diffuse RRLs, however, are associated with the low-density, cold interstellar medium (ISM; e.g. Konovalenko & Sodin 1981; Payne et al. 1989, hereafter PAE89). Here only RRLs from carbon (CRRL) are typically observed as the ionization levels are too low to produce hydrogen and helium lines. Diffuse CRRLs are best observed at radio frequencies below 1 GHz because they arise from stimulated emission and absorption. Whereas the classical RRLs have been studied in great detail, not much is known about the gas associated with diffuse RRLs in our Galaxy.

Low spatial resolution measurements, having beam sizes greater than 2°full width at half-maximum (FWHM), at 330, 76 and 34.5 MHz show that on scales of degrees the CRRL emitting and absorbing gas is widespread along the plane of the inner galaxy (Erickson, McConnell & Anantharamaiah 1995, hereafter EMA95; Kantharia & Anantharamaiah 2001). Similarly, low-frequency CRRLs have also been observed towards a variety of individual sources, such as for example the star-forming region DR 21 and the cold dark cloud L1407 (Golynkin & Konovalenko 1991a,b). Whether this CRRL gas is associated with the outershells of H ii regions, or part of the truly diffuse CNM is not clear from these observations.

Recombination lines allow us to determine the temperature and density of the recombining plasma. At low frequencies these properties are best derived by studying the behaviour of the optical depth and width of the lines as a function of their quantum number (e.g. Dupree 1971; Shaver 1975, 1976a; Salem & Brocklehurst 1979; Walmsley & Watson 1982). So far, such a detailed study has only been possible for the sightline towards Cassiopeia A (Cas A). Here it is found that the CRRLs are associated with low-density (n_e ∼ 0.1 cm⁻³), cold (T_e ∼ 70 K) intervening clouds in the Perseus and Orion spiral arms (e.g. PAE89; Kantharia, Anantharamaiah & Payne 1998). These properties of the intervening gas clouds are not easily deduced from other observations and CRRLs thus have the potential to provide unique information on the conditions of the CNM.

The sightline towards Cas A is special because it shows CRRLs with optical depths that are typically about an order of magnitude brighter than those seen along other directions (e.g. PAE89; EMA95; Asgekar et al. 2013). With the improved capabilities of new low-frequency radio telescopes, in particular their broader frequency coverage and better spatial resolution, it will be possible to study the details of the RRL emitting/absorbing gas along many more sightlines and in more detail.

Here we report on our discovery of low-frequency CRRLs in absorption along the line of sight to Cygnus A (Cyg A) with the Low Frequency Array (LOFAR; van Haarlem et al. 2013). This is an important sightline and well studied at radio wavelengths (e.g. Mebold & Hills 1975; Kassim et al. 1996; Carilli, Dwarakanath & Goss 1998). Cyg A itself is one of the brightest low-frequency radio sources in the sky (e.g. Lazio et al. 2006; McKean et al., in preparation). This powerful FRII radio source is associated with a cD galaxy (PGC 063932) at a redshift z = 0.056 (Owen et al. 1997).

The sightline towards Cyg A cuts through the Milky Way at a galactic longitude l = 76| $_{.}^{\circ}$|19 and latitude b = +5| $_{.}^{\circ}$|76. H i 21 cm line observations show both emission and absorption in the range +30 to −120 km s⁻¹ (e.g. Carilli et al. 1998). The strongest H i absorption features are found around +5 and −85 km s⁻¹. These are associated with the CNM in Orion (+5 km s⁻¹) and the outer spiral arms (−85 km s⁻¹). The H i observations of Cyg A also show absorption from the warm neutral medium (WNM) at velocities of −40 and −70 km s⁻¹ (Mebold & Hills 1975; Carilli et al. 1998).

This paper is structured as follows. Our observations are summarized in Section 2 and the results are presented in Section 3. We discuss these results in Section 4 and present our conclusions in Section 5.

OBSERVATIONS AND REDUCTION

We observed Cyg A with the LOFAR Low Band Antenna (LBA) on 2011 December 27 from 10:00 to 20:30 utc. The observations were taken during the commissioning phase of the array. We obtained complete frequency coverage between 33 and 57 MHz, although a few subbands were corrupted due to issues with the LOFAR offline storage system, see Table 1. The bandwidth was divided in 122 subbands, each 0.1953 MHz wide. The LBA_OUTER configuration was used for the LBA stations and all four linear correlation products were recorded (XX, XY, YX, YY). Each subband was subdivided into 512 frequency channels. The visibility integration time was 2 s. We used nine remote and 22 core stations for this observation, giving baselines between 90 m and 85 km.

As a first step in the data processing, we flagged radio frequency interference (RFI) with the AOFlagger (Offringa et al. 2010). Typically, a few per cent of the data were flagged due to RFI, which is consistent with a study of the LOFAR RFI environment conducted by Offringa et al. (2013). The data were calibrated with the Blackboard Selfcal (bbs) software system (Pandey et al. 2009). We used a high-resolution 10 arcsec clean component model of Cyg A for calibration. This model was obtained from previous LOFAR observations around 70 MHz (McKean et al., in preparation).

Before calibrating, we made a copy of the data set, averaging each subband down from 512 to 1 channel. We then obtained gain solutions for all four correlations with bbs on a 4 s time-scale. We assumed that the source is unpolarized over the observed frequency range. The found gain solutions were then applied to the 512 frequency channel data and a final round of flagging was carried out with the AOFlagger.

Channel cubes were made with casa,¹ imaging and cleaning each channel individually. The first 25 and last 25 channels of each subband were ignored as they are too noisy. Only baselines with a uv-distance shorter than 7 km were selected. We chose Briggs weighting (Briggs 1995) with a robust value of 0.5 to create images with a resolution ranging between 174 × 196 and 267 × 336 arcsec². This low resolution was chosen to speed up the imaging process. LOFAR does currently not support Doppler tracking and as such we have Doppler corrected the data during the imaging process. This introduces a small uncertainty (<1 km s⁻¹) in the derived line widths and velocities, but does not affect our analysis of the data. We then convolved all images from all subbands to a common resolution of 300 × 350 arcsec². At this resolution Cyg A is not resolved.

Our final cubes for each subband image a region with an area of 1 × 1 deg², with Cyg A at the centre. From these cubes we extract spatially integrated on-source spectra from a 15 × 15 arcmin² aperture centred on Cyg A. To estimate the continuum in these on-source spectra we fit a fourth-order polynomial. We then divide the spectra by the fitted continuum (and subtract by 1) to derive the final on-source subband spectra in units of optical depth, i.e. τ_ν = (F_{ν, obs}/F_{ν, cont}) − 1. Here F_{ν, obs} is the observed flux and F_{ν, cont} is the continuum flux. Out of a total of 122 subbands seven were removed due to data corruption. For the remaining 115 subbands spectra were extracted and visually inspected. Subsequently, 10 additional subbands were removed due to strong RFI in the data, leaving 105 subbands for further analysis.

The on-source spectra for each subband were investigated for the presence of RRLs. Their peak optical depth limits, that is the root-mean-square (rms) per 0.4 kHz channel divided by the continuum level, varied from about 3 × 10⁻⁴ at 33 MHz to 8 × 10⁻⁴ at 57 MHz. At these levels RRLs were not detected in the individual subbands.

We proceeded by stacking the on-source spectra. We only included spectra where the expected line position was at least 70 channels away from the edge of the subband to avoid errors due to the bandpass roll-off. Stacking was done in velocity space using a 2 km s⁻¹ channel spacing corresponding to our highest spectroscopic resolution at 57 MHz. The final stacked spectrum is rebinned to 4 km s⁻¹ which corresponds to our lowest spectroscopic resolution at 33 MHz.

Stacked spectra were produced for RRL α transition lines from hydrogen, helium and carbon at redshifts corresponding to (i) the Milky Way foreground (z = 0) and (ii) Cyg A (z = 0.056). In each case about 50 lines were stacked. The noise in units of rms per channel divided by the continuum level is found to decrease from about 4 × 10⁻⁴ for the on-source spectra from individual subbands to about 0.5 × 10⁻⁴ for the final stacked spectra. The decrease in the noise thus roughly scales with the square root of the number of stacked spectra. This is consistent with Gaussian spectral noise in the on-source spectra from individual subbands.

RESULTS

We searched the stacked spectra for RRLs associated with both the Milky Way foreground (z = 0) and with Cyg A (z = 0.056). For the Milky Way foreground stacked spectra we find an absorption feature with a signal-to-noise ratio (SNR) of 5. This absorption feature is found at a velocity of +4 km s⁻¹, relative to the local standard of rest (LSR), if the stack is centred on the carbon α transitions, see Fig. 1. Similarly the absorption feature is found at the expected velocity of −30 and −150 km s⁻¹ when centring on the helium and hydrogen α transitions, respectively, see Fig. 2. We believe that the observed absorption feature is due to carbon and we present our arguments for this in Section 4.1.

Figure 1.

Foreground stacked carbon α spectrum along the line of sight to Cyg A. The data are stacked assuming a redshift z = 0 for the lines and displayed using a resolution of 4 km s⁻¹ per channel. Top-left: stacked spectrum of all 48 carbon α lines in the range 33–57 MHz. Top-right: stacked spectrum of the 21 lowest frequency carbon α lines. Bottom-left: stacked spectrum of 23 carbon α lines in the middle of the observed range. Bottom-right: stacked spectrum of the 27 highest frequency carbon α lines. The black line shows the data and the red line shows the Gaussian fit. The line properties derived from these fits are given in Table 2.

Open in new tabDownload slide

Figure 2.

Foreground stacked hydrogen α and helium α spectra along the line of sight to Cyg A. The data are stacked assuming a redshift z = 0 for the lines and displayed using a resolution of 4 km s⁻¹ per channel. Left: stacked spectrum of all 49 hydrogen α lines in the range 33–57 MHz. The region around −150 km s⁻¹ corresponds to carbon α line absorption and was blanked in all spectra prior to stacking. Right: stacked spectrum of all 48 helium α lines in the range 33–57 MHz. The region around −30 km s⁻¹ corresponds to carbon α line absorption and was blanked in all spectra prior to stacking. For reference we have overplotted, using the blue dashed line, the stacked hydrogen, helium spectra where the carbon α line absorption was not blanked a priori. The upper limits derived from the hydrogen, helium spectra are given in Table 3.

Open in new tabDownload slide

Detected carbon RRLs at |$\boldsymbol {z=0}$|

For carbon α transition RRLs from the Milky Way foreground, a total of 48 on-source subband spectra are stacked. The resulting stacked spectrum, in units of optical depth, is shown in the top left-hand corner of Fig. 1. Henceforth we will refer to this stack as ALL. This carbon α spectrum from the ALL stack shows a RRL absorption feature with a peak optical depth of about 2 × 10⁻⁴. A single Gaussian fit to this feature gives a FWHM line width of 10 km s⁻¹ and a central velocity of +4 km s⁻¹ relative to the LSR, see Table 2.

All of the subband spectra entering the stack were carefully inspected by eye. We then performed a ‘Jacknife minus one’ procedure to investigate whether the observed carbon absorption could have been caused by a rogue feature from any single spectrum. This method consists of leaving out one subband spectrum at a time and recomputing the stack. We did this for all 48 subband spectra, thus creating 47 stacks of 47 subband spectra. For each of these stacks, the absorption line and noise properties are found to be consistent with the full 48 subband stack.

We then split our data into three substacks; LOW, MID and HIGH (Table 2). The LOW substack contains the 21 lowest frequency lines and the HIGH substack contains the 27 highest frequency lines. These two stacks do not overlap, and therefore represent two independent measurements. The MID substack contains 23 lines from the middle portion of the observed frequency range. This stack overlaps with both the LOW and HIGH substack. These three stacks were made to check for (i) variation/changes in the line profile with frequency, and (ii) the possibility of having rogue features from more than one spectrum being responsible for the observed RRL absorption. In all substacks carbon α RRL absorption is detected, see Fig. 1.

Finally, we investigated the off-source spectral properties by excluding the central 15 × 15 arcmin² aperture containing Cyg A from the data, but including the rest of the 1 × 1 deg² field of view. The stacked off-source spectra did not show any spectral features that could have contaminated the above results. We therefore conclude that observed RRL absorption is real and associated with the line-of-sight to Cyg A. The SNR of the integrated optical depth is about 5 for the ALL stack and between 3 and 4 for the substacks.

We also searched for carbon β transition RRLs from the Milky Way foreground but do not detect these. This non-detection is not surprising as the carbon β lines in our Galaxy are typically a factor of about 3 weaker than the α lines (e.g. PAE89; EMA95) and therefore beyond the sensitivity limit of our observation. We set a 3σ upper limit of 1.5 × 10⁻⁴ for the peak optical depth of these lines for a 4 km s⁻¹ channel width.

Upper limits on H and He RRLs at |$\boldsymbol {z=0}$|

Stacked spectra centred on the rest frequency of the hydrogen and helium RRLs for the Milky Way foreground (z = 0) were also produced, see Fig. 2. Prior to stacking the spectra we now first blank the carbon α absorption feature in each spectrum. If this is not done the absorption feature seen in the stacked carbon spectrum shows up at about −150 km s⁻¹ in the stacked hydrogen spectrum and at about −30 km s⁻¹ in the stacked helium spectrum. To illustrate this we show the unblanked hydrogen and helium stacked spectra with the blue dashed line in Fig. 2.

We expect the absorption feature seen in the carbon α stack to also show up in the hydrogen and helium spectra. This is because the RRL rest frequencies for these elements have a constant offset in velocity space. At 45 MHz (n = 526) this corresponds to −22.5 kHz (−150 km s⁻¹) for hydrogen relative to carbon and −4.1 kHz (−27 km s⁻¹) for helium relative to carbon. The relatively small offset in velocity means that in principle the absorption feature could come from any of these three elements. However, as we will discuss below the observed feature is most likely associated with carbon.

The 3σ upper limits on the peak optical depth τ_peak that we obtain from the z = 0 stacked hydrogen and helium spectra are about 1.5 × 10⁻⁴ for a channel width of 4 km s⁻¹, see Table 3.

Upper limits on RRLs at |$\boldsymbol {z=0.056}$|

In the same manner as described above for the Milky Way foreground gas, we also produced stacked hydrogen, helium and carbon RRL spectra in the redshift range 0.046–0.066, i.e. ±3000 km s⁻¹ around the optical emission line redshift 0.056 for Cyg A. The resulting spectra show no sign of RRLs associated with this source. As an example we show the stacked spectra at the redshift z = 0.056 in Fig. 3.

The 3σ upper limits on the peak optical depth τ_peak that we obtain from the z = 0.056 stacked hydrogen, helium and carbon spectra are about 1.3 × 10⁻⁴ for a channel width of 4 km s⁻¹, see Table 3.

DISCUSSION

A carbon origin for the RRL absorption

The foreground RRL absorption feature observed here against Cyg A (l = 76| $_{.}^{\circ}$|19, b = +5| $_{.}^{\circ}$|76) is very narrow and close to zero velocity. A similar RRL feature is seen towards Cas A (l = 111| $_{.}^{\circ}$|74, b = −2| $_{.}^{\circ}$|14) by e.g. PAE89. These authors show that the RRL absorption along the line of sight to Cas A consists of three velocity components at −48, −37 and 0 km s⁻¹. The first two components have an optical depth which is about a factor of 10 larger than the component at zero velocity.

PAE89 show that all three RRL components are carbon RRLs. The −48 and −37 km s⁻¹ components are related to the Perseus spiral arm, whereas the zero velocity component is related to the Orion spiral arm. The similarity between the zero velocity component towards Cyg A and Cas A, in both line width and peak optical depth, indicates that the absorption seen by us against Cyg A is probably coming from carbon RRLs and likely originates from the CNM in the Orion spiral arm of the Milky Way.

If the observed absorption feature were instead due to helium at a velocity of −30 km s⁻¹, then we would expect to not only observe helium but also hydrogen and carbon absorption. This is because (i) hydrogen is much more abundant than helium, and (ii) the high ionization potential of helium implies that hydrogen and carbon would also be ionized.

We believe that it is unlikely that we are observing hydrogen RRL absorption at a velocity of −150 km s⁻¹. This is because the bulk of the H i 21 cm emission, as observed in the Leiden–Argentine–Bonn survey (Kalberla et al. 2005), along the line of sight to Cyg A is found at zero velocity, see Fig. 4 .

Figure 4.

Comparison of the foreground (z = 0) stacked carbon α absorption with the H i emission along the line of sight to Cyg A. The H i emission, from the LAB survey (Kalberla et al. 2005), is given by the black line. The inverted carbon α absorption (this work) is shown by the dashed blue line. For clarity the H i emission has been normalized to 1.0 and the inverted RRL absorption has been normalized to 0.5. Left: H i and RRL in the velocity range ±200 km s⁻¹. The vertical green (CNM) and purple (WNM) lines show the positions of the strongest H i 21 cm components observed in absorption towards Cyg A (Carilli et al. 1998). Right: the central ±60 km s⁻¹ range.

Open in new tabDownload slide

Figure 3.

Stacked hydrogen α, helium α and carbon α spectra for Cyg A. The data are stacked assuming at redshift z = 0.056 for the lines and displayed using a resolution of 4 km s⁻¹ per channel. Left: stacked spectrum of all 55 hydrogen α lines in the range 33–57 MHz. Middle: stacked spectrum of all 50 helium α lines in the range 33–57 MHz. Right: stacked spectrum of all 47 carbon α lines in the range 33–57 MHz. The upper limits derived from these spectra are given in Table 3.

Open in new tabDownload slide

The H i 21 cm emission line profile from Kalberla et al. (2005) is much broader than what we observe for the RRL absorption. This is likely due to the difference in beam size for the two observations. The 21 cm observation has a FWHM beam size of about 40 arcmin which is significantly larger than our RRL observation. It therefore samples a much greater area, having a range of gas velocities that contribute to the broadening of the observed H i 21 cm line profile.

H i absorption observed against Cyg A, by Carilli et al. (1998) and Mebold & Hills (1975), shows much narrower H i absorption line profiles. These authors find several absorbing components in the range +30 to −120 km s⁻¹. The strongest component is found at zero velocity and this component has a width similar to our RRL absorption feature. The H i absorption spectrum shows no significant absorption at either −30 or −150 km s⁻¹. We therefore conclude that the RRL absorption observed by us towards Cyg A is most likely due to carbon.

Comparing the RRL and H i absorption furthermore shows that the RRL absorbing gas is likely associated with the CNM in the Orion arm (Mebold & Hills 1975; Carilli et al. 1998). None of the other H i absorbing components, from either the CNM or WNM, is detected in our RRL spectrum, see Fig. 4. This is not surprising given the low sensitivity of our stacked spectrum. There may be a hint of the outer spiral arm (−85 km s⁻¹) component in the CRRL spectrum, but more sensitive observations are required to confirm this. Higher spatial resolution imaging of our data may in the future also help to investigate the presence of this component. This is because the H i optical depth of the −85 km s⁻¹ component is observed to vary strongly in strength across the radio source (Carilli et al. 1998).

Gas properties from carbon RRLs

Carbon RRLs are not in local thermal equilibrium (LTE). Therefore to obtain physical parameters for the CRRL emitting gas one needs to perform detailed modelling of the transitions (e.g. Dupree 1969; Shaver 1975). The two observables that constrain the properties of the associated gas are the integrated optical depth and the width of the CRRL line.

Here n is the quantum number, T_e is the electron temperature, χ_n = 1.58 × 10⁵/(n²T_e) and EM_C = n_en_{C +}L (cm⁻⁶ pc) is the emission measure for carbon, with L the path length. b_n, β_n are the departure coefficients from LTE and were calculated following Shaver (1975) and Walmsley & Watson (1982) using a modified version of the Brocklehurst & Salem (1977) code that takes the dielectronic-like recombination of carbon into account (Salgado et al., in preparation). These departure coefficients depend on T_e and the electron density n_e.

The current data set only provides a rough constraint on these quantities. Based on a chi-squared minimization, using a fine grid of models with T_e between 10 and 1000 K and n_e between 0.001 and 1.0 cm⁻³, we find that the data are best described by an electron temperature T_e ≈ 110 K, electron density n_e ≈ 0.06 cm⁻³ and EM_C ≈ 0.001 cm⁻⁶ pc. The gas traced by the CRRL absorption is thus found to be consistent with the CNM. However, the large uncertainties and limited frequency coverage of the measurements imply that we can only constrain T_e to be in the range 50–500 K and n_e to be in the range 0.005–0.07 cm⁻³. These ranges for T_e and n_e correspond to a 3σ confidence limit.

The CRRL line width can be broadened by (i) pressure broadening ΔV_P, (ii) radiation broadening ΔV_R and (iii) multiple velocity components along the line of sight (Shaver 1975). Although we observe a weak asymmetry in the CRRL line profile (Fig. 4), also seen in H i absorption (Carilli et al. 1998), the quality of our spectrum is insufficient to determine whether more than one velocity component exists. Hence, we will only consider the line as a single component.

Here c is the speed of light, ν is the frequency, T_{R, 100} is the radiation temperature at 100 MHz and W_ν = Ω/4π is the solid angle of the source on the sky. Whereas pressure broadening depends on T_e and n_e, radiation broadening does not. Extrapolating the 408 MHz (Haslam et al. 1982) and 150 MHz (Landecker & Wielebinski 1970) radio continuum maps of the Milky Way, using a spectral index of 2.6, we find T_{R(MW), 100} ∼ 2700 K for the line of sight to Cyg A. This corresponds to a FWHM velocity broadening of 9.6 km s⁻¹ at 45 MHz (n = 535). This is close to our measured value of 10 km s⁻¹ and we therefore find that the Milky Way radiation field accounts for the bulk of the observed line broadening.

In this case where radiation broadening dominates we cannot obtain further useful constraints on T_e and n_e from pressure broadening. The range in T_e, n_e values allowed for by the optical depth measurements also shows that pressure broadening is not significant and can at most contribute about 5 km s⁻¹ to the FWHM velocity broadening of the line width at 45 MHz. For high SNR data it may be possible to distinguish the pressure contribution to the observed line width. However, with the current data set this is not possible. To explain the observed line widths with pressure broadening alone would require an electron density in excess of 0.1 cm⁻³. This is inconsistent with the upper bound for n_e obtained from the optical depths.

If all of the free electrons are from carbon, then we can estimate the hydrogen density as n_H = n_e/(1.5 × 10^{− 4}) ≈ 400 cm⁻³ and the accompanying gas pressure as p ∼ n_H T_e ∼ 4 × 10⁴ cm⁻³ K. Here we used the gas phase abundance for carbon, i.e. [C/H] = 1.5 × 10⁻⁴. The derived pressure is about an order of magnitude larger than the average pressure of the ISM. Similar high pressures have previously been estimated for the CRRL emitting gas along the line of sight to Cas A (e.g. PAE89; Kantharia et al. 1998). Enforcing pressure equilibrium between the CRRL gas and the average ISM, as advocated by Kantharia et al. (1998), would significantly reduce the allowed range in values for T_e and n_e for the CRRL emitting gas along the line of sight to Cyg A. New observations, covering a wider range in frequency and higher sensitivity, will be needed to further constrain the CRRL emitting gas and investigate its pressure balance.

An upper limit to the ionization rate

We find ζ_H < 4 × 10⁻¹⁶ s⁻¹ for the range of T_e values allowed by our optical depth measurements. Here we have used that τ_{peak, HI} = 0.36 (Carilli et al. 1998), n = 535, Φ₂ = 3.34, ν = 45 MHz, (b_nβ_n)_H = 4.0 (Ponomarev & Sorochenko 1992), T_s = T_e and our 3σ upper limit on |$\tau _{{{\rm peak,H}_{n}}}$| (Table 3). Φ₂ is an integral over gaunt factors (Spitzer 1978), T_s is the H i spin temperature and |$(b_{n}\beta _{n})_{{\rm H}}^{-1}$| are the departure coefficients for hydrogen.

Inserting our measured optical depths (b_nβ_n)_H = 40.0 and (b_nβ_n)_H = 4.0 (Ponomarev & Sorochenko 1992) we again find ζ_H < 4 × 10⁻¹⁶ s⁻¹ for the allowed range of T_e and n_e values. Here we have used the gas phase abundance for carbon. If carbon is not depleted, then the value of this upper limit goes up with a factor of 2 to ζ_H < 8 × 10^{− 16} s⁻¹.

The upper limit for the hydrogen ionization rate derived here from RRLs is consistent with other measurements of the ionization rate for the CNM by cosmic rays in our Galaxy (e.g. Indriolo et al. 2007; Shaw et al. 2008).

Comparison with Cassiopeia A

The most detailed low-frequency CRRL study to date is the one performed for the line of sight towards Cas A (Konovalenko & Sodin 1981; PAE89; Kantharia et al. 1998; Stepkin et al. 2007; Asgekar et al. 2013). This line of sight, at l = 111| $_{.}^{\circ}$|74 and b = −2| $_{.}^{\circ}$|14, shows CRRL emitting gas at a number of velocities that are consistent with individual clouds in the Orion (−5 to +5 km s⁻¹) and Perseus (−50 to −35 km s⁻¹) spiral arms.

The velocity of the CRRL absorption observed by us is consistent with gas in the Orion spiral arm. The Orion arm CRRL component towards Cas A is difficult to measure at low frequencies, because it is blended with the Perseus arm components. Therefore it has not been possible to model this component in detail. At 26 MHz, Stepkin et al. (2007) estimates that the Orion arm component towards Cas A has a peak optical depth τ_peak ≈ 4 × 10⁻⁴, a line width FWHM ≈17 km s⁻¹ and an integrated optical depth of about 0.6 in units of Hz. Upon extrapolating our best-fitting model to 26 MHz we find a similar integrated optical depth for the CRRL emitting gas towards Cyg A.

The Perseus arm CRRL component towards Cas A is about an order of magnitude brighter than the Orion arm component at low frequencies. Therefore it has been measured with considerably better SNR and allows for a more detailed comparison. The best-fitting model for this gas has T_e ≈ 75 K, n_e ≈ 0.02 cm⁻³ and EM_C ≈ 0.01 cm⁻⁶ pc (Kantharia et al. 1998). These parameters, in combination with the low value for the upper limit of the ionization rate (PAE89; Asgekar et al. 2013) and the morphology, velocity structure of the CRRL emission, lead Kantharia et al. (1998) to conclude that the CRRL emitting gas observed towards Cas A is most likely associated with cold, diffuse, atomic clouds.

The measurements by PAE89, Kantharia et al. (1998) and Asgekar et al. (2013) show that from 33 to 57 MHz the CRRLs for the Perseus arm component towards Cas A decrease in line width by a factor of 3–4 and decrease in integrated optical depth by about a factor of 1.5–2, in units of Hz. This is similar to what we observe here and we therefore conclude that the CRRL absorption towards Cyg A also likely originates in similar cold, diffuse, atomic clouds.

Cygnus A

Hydrogen, helium or carbon RRL absorption associated with Cyg A (z = 0.056) itself was searched for in the redshift range 0.046–0.066 and constrained to be less than 1.5 × 10⁻⁴ at the 3σ level for a channel width of 4 km s⁻¹, see Table 3. This non-detection is not surprising as most of the low-frequency radio flux from Cyg A comes from its two giant radio lobes that extend far outside its host galaxy (PGC 063932).

The optical size of the host galaxy is between 15 and 30 arcsec. At the redshift of Cyg A this corresponds to a physical size between 15 and 33 kpc. From a high-resolution LOFAR map at 55 MHz (McKean et al., in preparation) we estimate that between 2 and 10 per cent of the total radio continuum flux at this frequency comes from the optically emitting region. If we now assume that the ISM of the host galaxy is equal to its optical size then we find that our 3σ RRL peak optical depth limit for the radio emission that likely traverses through the ISM of the host galaxy is between 10⁻³ and 10⁻².

The Milky Way is the only galaxy for which RRLs at frequencies below 1 GHz have been detected (e.g. EMA95; Kantharia & Anantharamaiah 2001). At 76 MHz Erickson et al. find an average peak optical depth for carbon RRLs of a few times 10⁻⁴ over large areas in the Milky Way plane. Cyg A does not contain a significant amount of cold gas or star formation (McNamara & Jaffe 1994). Our non-detection of RRLs in this system is therefore not surprising.

Kassim et al. (1996) consider thermal absorption due to Galactic foreground gas, with a radio continuum optical depth τ_74 MHz ∼ 0.3 at 74 MHz, as an explanation for the spectral index asymmetry measured for the two radio lobes of Cyg A. The explanation they favour is that this is due to thermal absorption in foreground, extended H ii region envelopes with n_e ∼ 5 cm⁻³, T_e ∼ 8000 K and EM ∼2500 cm⁻⁶ pc.

Our CRRL measurement traces gas that is cold and mostly neutral. Inserting our values, n_e ∼ 0.06 cm⁻³, T_e ∼ 110 K and EM ∼ 0.001 cm⁻⁶ pc into formula (3.1) from Kassim et al. (1996) gives τ_74 MHz ∼ 3 × 10⁻⁵. We therefore find that the low-density, low-temperature CRRL gas observed here cannot reproduce the required amount of thermal absorption.

CONCLUSIONS

In this paper we have presented high-velocity resolution (∼4 km s⁻¹), low-frequency (∼45 MHz) stacked hydrogen, helium and carbon RRL spectra along the line of sight to Cyg A taken with the LOFAR LBA array during its commissioning phase.

• We have detected, for the first time, Milky Way foreground carbon RRLs in absorption against Cyg A.

• The observed CRRL absorption has a peak optical depth of (2.2 ± 0.5) × 10⁻⁴, a FWHM line width of (10 ± 3) km s⁻¹ and a local standard of rest velocity of (+4 ± 1) km s⁻¹. The velocity of the gas is consistent with the Orion spiral arm in the Milky Way.

• Our measurement allows for a large range in values for T_e (50–500 K) and n_e (0.005–0.07 cm⁻³) of the associated gas. Our best estimate is T_e ∼ 110 K and n_e ∼ 0.06 cm⁻³. These values are consistent with a CNM origin. Comparing to H i 21 cm observations also shows a good match between H i and CRRLs.

• The RRL measurements provide an upper limit on the total ionization rate of hydrogen ζ_H < 4 × 10^{− 16} s⁻¹ for the CRRL emitting gas along the line of sight to Cyg A.

• RRLs from hydrogen, helium and carbon that are associated with Cyg A (z = 0.056) itself are constrained to have peak optical depths less than 1.5 × 10⁻⁴ at the 3σ level for a 4 km s⁻¹ channel.

The optical depths of the CRRL absorption lines observed here along the line of sight to Cyg A are similar to that seen along other sightlines (e.g. EMA95). However, our observations have an order of magnitude higher spatial resolution than these previous low-frequency CRRL absorption studies and show that we can use bright extragalactic radio sources for high-resolution RRL pinhole studies of the ISM. To the best of our knowledge this is the first time that low-frequency carbon RRLs associated with the Milky Way have been detected in absorption against an extragalactic radio source.

Future observations with LOFAR, using wider frequency coverage and higher sensitivity, will allow us to better constrain the properties of the CRRL emitting gas along the line of sight to Cyg A and map its small-scale structure. In particular a deep (∼8 h), high spectral resolution (Δv ∼ 1 km s^{− 1}) observation with the LOFAR High Band Antenna (HBA) array in the frequency range 110–190 MHz will be helpful. Stacking LOFAR spectra from individual subbands shows a decrease in spectral noise that is consistent with Gaussian noise behaviour. This makes it a very promising technique for detecting faint RRLs with LOFAR.

The authors would like to thank the LOFAR observatory staff for their assistance in obtaining and the handling of this large data set.

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.

Support for this work was provided by NASA through Einstein Post-doctoral grant number PF2-130104 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060.

Chiara Ferrari and Giulia Macario acknowledge financial support by the Agence Nationale de la Recherche through grant ANR-09-JCJC-0001-01.

REFERENCES