Starburst in the Ultraluminous Galaxy Arp 220: Constraints from Observations of Radio Recombination Lines and Continuum

We present observations of radio recombination lines (RRL) from the starburst galaxy Arp 220 at 8.1 GHz (H92α) and 1.4 GHz (H167α and H165α) and at 84 GHz (H42α), 96 GHz (H40α) and 207 GHz (H31α) using the Very Large Array and the IRAM 30 m telescope, respectively. RRLs were detected at all the frequencies except 1.4 GHz, where a sensitive upper limit was obtained. We also present continuum flux measurements at these frequencies as well as at 327 MHz made with the VLA. The continuum spectrum, which has a spectral index α ~ -0.6 (S_ν ∝ ν^α) between 5 and 10 GHz, shows a break near 1.5 GHz, a prominent turnover below 500 MHz, and a flatter spectral index above 50 GHz. We show that a model with three components of ionized gas with different densities and area covering factors can consistently explain both RRL and continuum data. The total mass of ionized gas in the three components is 3.2 × 10⁷ M_☉, requiring 3 × 10⁵ O5 stars with a total Lyman continuum production rate N_Lyc ~ 1.3 × 10⁵⁵ photons s^-1. The ratio of the expected to observed Brα and Brγ fluxes implies a dust extinction A_V ~ 45 mag. The derived Lyman continuum photon production rate implies a continuous star formation rate (SFR) averaged over the lifetime of OB stars of ~240 M_☉ yr^-1. The Lyman continuum photon production rate of ~3% associated with the high-density H II regions implies a similar SFR at recent epochs (t < 10⁵ yr). An alternative model of high-density gas, which cannot be excluded on the basis of the available data, predicts 10 times higher SFR at recent epochs. If confirmed, this model implies that star formation in Arp 220 consists of multiple starbursts of very high SFR (few times 10³ M_☉ yr^-1) and short duration (~10⁵ yr). The similarity of IR excess, L_IR/L_Lyα ~ 24, in Arp 220 to values observed in starburst galaxies shows that most of the high luminosity of Arp 220 is due to the ongoing starburst rather than to a hidden active galactic nucleus (AGN). A comparison of the IR excesses in Arp 220, the Galaxy, and M33 indicates that the starburst in Arp 220 has an initial mass function that is similar to that in normal galaxies and has a duration longer than 10⁷ yr. If there was no infall of gas during this period, then the star formation efficiency (SFE) in Arp 220 is ~50%. The high SFR and SFE in Arp 220 is consistent with their known dependences on mass and density of gas in star-forming regions of normal galaxies.