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 starbur st galaxy Arp 220 at 8.1 GHz (H92 alpha) and 1.4 GHz (H167 alpha and H165 a lpha) and at 84 GHz (H42 alpha), 96 GHz (H40 alpha) and 207 GHz (H31 alpha) 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 upp er limit was obtained. We also present continuum flux measurements at these frequencies as well as at 327 MHz made with the VLA. The continuum spectru m, which has a spectral index alpha similar to -0.6 (S-nu proportional to n u(alpha)) between 5 and 10 GHz, shows a break near 1.5 GHz, a prominent tur nover below 500 MHz, and a flatter spectral index above 50 GHz. We show tha t 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 x 10(7) M., requiring 3 x 10(5) O5 stars with a total Lyman continuum production rate N -Lyc similar to 1.3 x 10(55) photons s(-1). The ratio of the expected to ob served Br alpha and Br gamma fluxes implies a dust extinction A(V) similar to 45 mag. The derived Lyman continuum photon production rate implies a con tinuous star formation rate (SFR) averaged over the lifetime of OB stars of similar to 240 M yr(-1). The Lyman continuum photon Production rate of sim ilar to 3% associated with the high-density H II regions implies a similar SFR at recent epochs (t < 10(5) yr). An alternative model of high-density g as, which cannot be excluded on the basis of the available data, predicts 1 0 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 10(3) M. yr(-1)) and short duration (similar to 10(5) yr). The s imilarity of IR excess, L-IR/L-Ly alpha similar to 24, in Arp 220 to values observed in starburst galaxies shows that most of the high luminosity of A rp 220 is due to the ongoing starburst rather than to a hidden active galac tic 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 functio n 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 fo rmation efficiency (SFE) in Arp 220 is similar to 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.