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Register a new userMapping low frequency carbon radio recombination lines towards Cassiopeia A at 340, 148, 54 and 43 MHz
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Quantitative understanding of the interstellar medium requires knowledge of its physical conditions. Low frequency carbon radio recombination lines (CRRLs) trace cold interstellar gas, and can be used to determine its physical conditions (e.g., electron temperature and density). In this work we present spatially resolved observations of the low frequency ($leq390$ MHz) CRRLs centered around C$268alpha$, C$357alpha$, C$494alpha$ and C$539alpha$ towards Cassiopeia A on scales of $leq1.2$ pc. We compare the spatial distribution of CRRLs with other ISM tracers. This comparison reveals a spatial offset between the peak of the CRRLs and other tracers, which is very characteristic for photodissociation regions and that we take as evidence for CRRLs being preferentially detected from the surfaces of molecular clouds. Using the CRRLs we constrain the gas electron temperature and density. These constraints on the gas conditions suggest variations of less than a factor of two in pressure over $sim1$ pc scales, and an average hydrogen density of $200$-$470$ cm$^{-3}$. From the electron temperature and density maps we also constrain the ionized carbon emission measure, column density and path length. Based on these, the hydrogen column density is larger than $10^{22}$ cm$^{-2}$, with a peak of $sim4times10^{22}$ cm$^{-2}$ towards the South of Cassiopeia A. Towards the southern peak the line of sight length is $sim40$ pc over a $sim2$ pc wide structure, which implies that the gas is a thin surface layer on a large (molecular) cloud that is only partially intersected by Cassiopeia A. These observations highlight the utility of CRRLs as tracers of low density extended HI and CO-dark gas halos around molecular clouds.
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Cassiopeia A was observed using the Low-Band Antennas of the LOw Frequency ARray (LOFAR) with high spectral resolution. This allowed a search for radio recombination lines (RRLs) along the line-of-sight to this source. Five carbon-alpha RRLs were detected in absorption between 40 and 50 MHz with a signal-to-noise ratio of > 5 from two independent LOFAR datasets. The derived line velocities (v_LSR ~ -50 km/s) and integrated optical depths (~ 13 s^-1) of the RRLs in our spectra, extracted over the whole supernova remnant, are consistent within each LOFAR dataset and with those previously reported. For the first time, we are able to extract spectra against the brightest hotspot of the remnant at frequencies below 330 MHz. These spectra show significantly higher (15-80 %) integrated optical depths, indicating that there is small-scale angular structure on the order of ~1 pc in the absorbing gas distribution over the face of the remnant. We also place an upper limit of 3 x 10^-4 on the peak optical depths of hydrogen and helium RRLs. These results demonstrate that LOFAR has the desired spectral stability and sensitivity to study faint recombination lines in the decameter band.
We present a study of carbon radio recombination lines towards Cassiopeia A using LOFAR observations in the frequency range 10-33 MHz. Individual carbon $alpha$ lines are detected in absorption against the continuum at frequencies as low as 16 MHz. Stacking several C$alpha$ lines we obtain detections in the 11-16 MHz range. These are the highest signal-to-noise measurements at these frequencies. The peak optical depth of the C$alpha$ lines changes considerably over the 11-33 MHz range with the peak optical depth decreasing from 4$times10^{-3}$ at 33 MHz to 2$times10^{-3}$ at 11 MHz, while the line width increases from 20 km s$^{-1}$ to 150 km s$^{-1}$. The combined change in peak optical depth and line width results in a roughly constant integrated optical depth. We interpret this as carbon atoms close to local thermodynamic equilibrium. In this work we focus on how the 11-33 MHz carbon radio recombination lines can be used to determine the gas physical conditions. We find that the ratio of the carbon radio recombination lines to that of the 158 $mu$m [CII] fine-structure line is a good thermometer, while the ratio between low frequency carbon radio recombination lines provides a good barometer. By combining the temperature and pressure constraints with those derived from the line width we are able to constrain the gas properties (electron temperature and density) and radiation field intensity. Given the 1$sigma$ uncertainties in our measurements these are; $T_{e}approx68$-$98$ K, $n_{e}approx0.02$-$0.035$ cm$^{-3}$ and $T_{r,100}approx1500$-$1650$ K. Despite challenging RFI and ionospheric conditions, our work demonstrates that observations of carbon radio recombination lines in the 10-33 MHz range can provide insight into the gas conditions.
We use the Low Frequency Array to perform a systematic high spectral resolution investigation of the low-frequency 33-78 MHz spectrum along the line of sight to Cassiopeia A. We complement this with a 304-386 MHz Westerbork Synthesis Radio telescope observation. In this first paper we focus on the carbon radio recombination lines. We detect Cn$alpha$ lines at -47 and -38 km s$^{-1}$ in absorption for quantum numbers n=438-584 and in emission for n=257-278 with high signal to noise. These lines are associated with cold clouds in the Perseus spiral arm component. Hn$alpha$ lines are detected in emission for n=257-278. In addition, we also detect Cn$alpha$ lines at 0 km s$^{-1}$ associated with the Orion arm. We analyze the optical depth of these transitions and their line width. Our models show that the carbon line components in the Perseus arm are best fit with an electron temperature 85 K and an electron density 0.04 cm$^{-3}$ and can be constrained to within 15%. The electron pressure is constrained to within 20%. We argue that much of these carbon radio recombination lines arise in the CO-dark surface layers of molecular clouds where most of the carbon is ionized but hydrogen has made the transition from atomic to molecular. The hydrogen lines are clearly associated with the carbon line emitting clouds, but the low-frequency upperlimits indicate that they likely do not trace the same gas. Combining the hydrogen and carbon results we arrive at a firm lower limit to the cosmic ray ionization rate of 2.5$times$10$^{-18}$ s$^{-1}$, but the actual value is likely much larger.
In the first paper of this series, we study the level population problem of recombining carbon ions. We focus our study on high quantum numbers anticipating observations of Carbon Radio Recombination Lines to be carried out by the LOw Frequency ARray (LOFAR). We solve the level population equation including angular momentum levels with updated collision rates up to high principal quantum numbers. We derive departure coefficients by solving the level population equation in the hydrogenic approximation and including low temperature dielectronic recombination effects. Our results in the hydrogenic approximation agree well with those of previous works. When comparing our results including dielectronic recombination we find differences which we ascribe to updates in the atomic physics (e.g., collision rates) and to the approximate solution method of the statistical equilibrium equations adopted in previous studies. A comparison with observations is discussed in an accompanying article, as radiative transfer effects need to be considered.
In the second paper of the series, we have modeled low frequency carbon radio recombination lines (CRRL) from the interstellar medium. Anticipating the LOw Frequency ARray (LOFAR) survey of Galactic CRRLs, we focus our study on the physical conditions of the diffuse cold neutral medium (CNM). We have used the improved departure coefficients computed in the first paper of the series to calculate line-to-continuum ratios. The results show that the line width and integrated optical depths of CRRL are sensitive probes of the electron density, gas temperature, and the emission measure of the cloud. Furthermore, the ratio of CRRL to the [CII] at 158 $mu$m line is a strong function of the temperature and density of diffuse clouds. Guided by our calculations, we analyze CRRL observations and illustrate their use with data from the literature.
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