We review the use of emission-lines for understanding galaxy evolution, focusing on excitation source, metallicity, ionization parameter, ISM pressure and electron density. We show that the UV, optical and infrared contain complementary diagnostics that can probe the conditions within different nebular ionization zones. In anticipation of upcoming telescope facilities, we provide new self-consistent emission-line diagnostic calibrations for complete spectral coverage from the UV to the infrared. These diagnostics can be used in concert to understand how fundamental galaxy properties have changed across cosmic time. We describe new 2D and 3D emission-line diagnostics to separate the contributions from star formation, AGN and shocks using integral field spectroscopy. We discuss the physics, benefits, and caveats of emissionline diagnostics, including the effect of theoretical model uncertainties, diffuse ionized gas, and sample selection bias. Accounting for complex density gradients and temperature profiles is critical for reliably estimating the fundamental properties of H ii regions and galaxies. Diffuse ionized gas can raise metallicity estimates, flatten metallicity gradients, and introduce scatter in ionization parameter measurements. We summarize with a discussion of the challenges and major opportunities for emission-line diagnostics in the coming years.

Recently, Nicholls et al., inspired by in situ observations of solar system astrophysical plasmas, suggested that the electrons in H ii regions are characterized by a κ-distribution of energies rather than a simple Maxwell-Boltzmann distribution. Here, we have collected together new atomic data within a modified photoionization code to explore the effects of both the new atomic data and the κ-distribution on the strong-line techniques used to determine chemical abundances in H ii regions. By comparing the recombination temperatures (T rec ) with the forbidden line temperatures (T FL ), we conclude that κ ∼ 20. While representing only a mild deviation from equilibrium, this result is sufficient to strongly influence abundances determined using methods that depend on measurements of the electron temperature from forbidden lines. We present a number of new emission line ratio diagnostics that cleanly separate the two parameters determining the optical spectrum of H ii regions-the ionization parameter q or U and the chemical abundance, 12+log(O/H). An automated code to extract these parameters is presented. Using the homogeneous data set from van Zee et al., we find self-consistent results between all of these different diagnostics. The systematic errors between different line ratio diagnostics are much smaller than those found in the earlier strong-line work. Overall, the effect of the κ-distribution on the strong-line abundances derived solely on the basis of theoretical models is rather small.

The measurement of electron temperatures and metallicities in H ii regions and Planetary Nebulae (PNe) has-for several decades-presented a problem: results obtained using different techniques disagree. What is worse, they disagree consistently. There have been numerous attempts to explain these discrepancies, but none has provided a satisfactory solution to the problem. In this paper, we explore the possibility that electrons in H ii regions and PNe depart from a M-B equilibrium energy distribution. We adopt a "κ-distribution" for the electron energies. Such distributions are widely found in solar system plasmas, where they can be directly measured. This simple assumption is able to explain the temperature and metallicity discrepancies in H ii regions and PNe arising from the different measurement techniques. We find that the energy distribution does not need to depart dramatically from an equilibrium distribution. From an examination of data from H ii regions and PNe it appears that κ 10 is sufficient to encompass nearly all objects. We argue that the kappadistribution offers an important new insight into the physics of gaseous nebulae, both in the Milky Way and elsewhere, and one that promises significantly more accurate estimates of temperature and metallicity in these regions.