look-back time: The amount by which we look into the past when we look at a distant galaxy; a time equal to the distance to the galaxy in light-years.
luminosity (L): The total amount of energy a star radiates in 1 second.
look-back time The time in the past at which the light we now receive from a distant object was emitted. [More Info: Photo Album]
luminosity One of the basic properties used to characterize stars, luminosity is defined as the total energy radiated by a star each second, at all wavelengths.
Long-period variables may vary by as much as 9 magnitudes in the visible, but in the integrated spectrum (most of their radiation is in the infrared) they vary by only 2 or 3 magnitudes. They are usually of spectral type M, R, or N. (sometimes called Red Variables) [H76]
Look-Back Time ...
As distances get larger so does this "look-back time." Our closest stellar neighbor, Alpha Centauri, is so far away that its light travels for 4.3 years before reaching us.
Largely because of this ambiguity, astronomers prefer to work in terms of a quantity known as the look-back time (shown in the last column of Table 25.1), which is simply how long ago an object emitted the radiation we see today.
When dealing with galactic scale distances, it's common to not explicitly talk about the look-back time since it's all in the present epoch relative to the age of the Universe.
Each pair is the result of a galaxy merger with look-back times of four to seven billion years (cosmological redshifts of 0.3-0.8). Beyond this range the emission lines were redshifted out of the wavelength range the survey could detect.
The number of quasars drops off for very large redshifts (redshifts greater than about 50% of the speed of light). The Hubble Law says that these are for large look-back times. This observation is taken to mean that the universe was not old enough to produce quasars at those large redshifts.
He presents a figure that nicely connects look-back time and the stellar evolution timescale (and shows why such work indirectly constrains H0, connecting a redshift-scaled time to the absolute timescales of stellar lifetimes), which I have gleefully cribbed below (courtesy of the AAS).
See also: What is the meaning of Galaxies, Earth, Star, Telescope, Sun?