We present near-infrared spectroscopy and narrow-band imaging at the wavelength of redshifted H \alpha for a sample of 30 high-redshift , far-infrared luminous galaxies .
This sample is selected from surveys in the sub-millimeter , millimeter and radio wavebands and has complete redshift coverage with a median redshift of z \sim 2.4 .
We use our data to measure the H \alpha properties of these systems and to gauge the prevalence of active galactic nuclei ( AGN ) in these galaxies through their [ N ii ] /H \alpha ratios and H \alpha line widths .
Removing obvious AGN , we find that the predicted H \alpha star formation rates in this diverse population are suppressed ( by a factor of \sim 10 ) compared to those derived from their far-infrared luminosities .
Using the AGN indicators provided by our near-infrared spectra , we estimate that AGN are present in at least 40 % of the galaxies in our sample .
To further investigate this , we construct a composite rest-frame spectrum for both the entire sample and for those galaxies which individually show no signs of nuclear activity .
We find [ N ii ] /H \alpha ratios for both composite spectra which suggest that the energy output of the galaxies is star-formation- rather than AGN-dominated .
However , we also find that the H \alpha line in the composite non-AGN spectrum is best fit with an underlying broad-line component with a narrow/broad flux ratio of 0.45 \pm 0.20 .
The median H \alpha line width for our sample ( removing obvious AGN ) is 400 \pm 70 km s ^ { -1 } ( FWHM ) , and the typical spatial extent of the H \alpha emission in our narrow-band observations is \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle < $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 4 –8 kpc , which indicates a dynamical mass of 1–2 \times 10 ^ { 11 } M _ { \odot } with corresponding dynamical times of 10–20 Myr .
Using both high-resolution imaging and spectroscopically identified velocity offsets , we find that seven of the far-infrared luminous galaxies have companions , suggesting that they are undergoing interactions/mergers and from their relative velocities we can determine a dynamical mass of 1.5 \pm 0.9 \times 10 ^ { 11 } M _ { \odot } .
These measurements are comparable to millimeter CO estimates for the dynamical masses of these systems on similar scales , and larger than recent estimates of the dynamical masses of UV-selected galaxies at similar redshifts derived in an identical manner .
Using the [ N ii ] /H \alpha index to predict abundances , we investigate the Luminosity–Metallicity relation for these galaxies and find that many have metallicities consistent with UV-selected high-redshift galaxies and slightly lower than local luminous infrared and elliptical galaxies ( although we caution that our metallicity estimates have possible systematic uncertainties ) .
We also compared our H \alpha and far-infrared luminosities with deep Chandra observations of a subset of our survey fields and use these data to further assess their AGN content .
We conclude that these high-redshift , far-infrared luminous galaxies represent a population of massive , metal-rich , merging systems with high instantaneous star formation rates , strong dust obscuration and actively-fueled AGN which are likely to be the progenitors of massive local elliptical galaxies .