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 Cnα 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. Hnα lines are detected in emission for n=257-278. In addition, we also detect Cnα 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 upper limits 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 2.5×10 −18 s −1 , but the actual value is likely much larger.

In this paper we present the results of the radio light curve and X-ray observations of broad-lined Type Ic SN 2007bg. The light curve shows three distinct phases of spectral and temporal evolution, implying that the SNe shock likely encountered at least 3 different circumstellar medium regimes. We interpret this as the progenitor of SN 2007bg having at least two distinct mass-loss episodes (i.e., phases 1 and 3) during its final stages of evolution, yielding a highly-stratified circumstellar medium. Modelling the phase 1 light curve as a freelyexpanding, synchrotron-emitting shell, self-absorbed by its own radiating electrons, requires a progenitor mass-loss rate ofṀ ≈ 1.9 × 10 −6 (v w /1000 km s −1 ) M ⊙ yr −1 for the last t ∼ 20(v w /1000 km s −1 ) yr before explosion, and a total energy of the radio emitting ejecta of E ≈ 1 × 10 48 erg after 10 days from explosion. This places SN 2007bg among the most energetic Type Ib/c events. We interpret the second phase as a sparser "gap" region between the two winds stages. Phase 3 shows a second absorption turn-on before rising to a peak luminosity 2.6 times higher than in phase 1. Assuming this luminosity jump is due to a circumstellar medium density enhancement from a faster previous mass-loss episode, we estimate that the phase 3 mass-loss rate could be as high asṀ 4.3 × 10 −4 (v w /1000 km s −1 ) M ⊙ yr −1 . The phase 3 wind would have transitioned directly into the phase 1 wind for a wind speed difference of ≈ 2. In summary, the radio light curve provides robust evidence for dramatic global changes in at least some Ic-BL progenitors just prior (∼ 10 − 1000 yr) to explosion. The observed luminosity of this SN is the highest observed for a non-gamma-ray-burst broad-lined Type Ic SN, reaching L 8.46 GHz ≈ 1 × 10 29 erg Hz −1 s −1 , ∼ 567 days after explosion.

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.

We present a study of carbon radio recombination lines towards Cassiopeia A using LO-FAR observations in the frequency range 10-33 MHz. Individual carbon α lines are detected in absorption against the continuum at frequencies as low as 16 MHz. Stacking several Cα 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 Cα lines changes considerably over the 11-33 MHz range with the peak optical depth decreasing from 4 × 10 −3 at 33 MHz to 2 × 10 −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 µm [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 1σ uncertainties in our measurements these are; T e ≈ 68-98 K, n e ≈ 0.02-0.035 cm −3 and T r,100 ≈ 1500-1650 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.

Context. Cassiopeia A is one of the best-studied supernova remnants. Its bright radio and X-ray emission is due to shocked ejecta. Cas A is rather unique in that the unshocked ejecta can also be studied: through emission in the infrared, the radio-active decay of 44 Ti, and the low-frequency free-free absorption caused by cold ionised gas, which is the topic of this paper. Aims. Free-free absorption processes are affected by the mass, geometry, temperature, and ionisation conditions in the absorbing gas. Observations at the lowest radio frequencies can constrain a combination of these properties. Methods. We used Low Frequency Array (LOFAR) Low Band Antenna observations at 30-77 MHz and Very Large Array (VLA) L-band observations at 1-2 GHz to fit for internal absorption as parametrised by the emission measure. We simultaneously fit multiple UV-matched images with a common resolution of 17 (this corresponds to 0.25 pc for a source at the distance of Cas A). The ample frequency coverage allows us separate the relative contributions from the absorbing gas, the unabsorbed front of the shell, and the absorbed back of the shell to the emission spectrum. We explored the effects that a temperature lower than the ∼100-500 K proposed from infrared observations and a high degree of clumping can have on the derived physical properties of the unshocked material, such as its mass and density. We also compiled integrated radio flux density measurements, fit for the absorption processes that occur in the radio band, and considered their effect on the secular decline of the source. Results. We find a mass in the unshocked ejecta of M = 2.95 ± 0.48 M for an assumed gas temperature of T = 100 K. This estimate is reduced for colder gas temperatures and, most significantly, if the ejecta are clumped. We measure the reverse shock to have a radius of 114 ±6 and be centred at 23:23:26, +58:48:54 (J2000). We also find that a decrease in the amount of mass in the unshocked ejecta (as more and more material meets the reverse shock and heats up) cannot account for the observed low-frequency behaviour of the secular decline rate. Conclusions. To reconcile our low-frequency absorption measurements with models that reproduce much of the observed behaviour in Cas A and predict little mass in the unshocked ejecta, the ejecta need to be very clumped or the temperature in the cold gas needs to be low (∼ 10 K). Both of these options are plausible and can together contribute to the high absorption value that we find.Article number, page 16 of 16