3.1. The evolution of close galaxy pairs
One of the most promising measures of galaxy merger rate is the evolution in the population of close galaxy pairs. Most close (often defined as being separated by < 20 kpc), bound galaxy pairs with roughly equal masses will merge within 1 Gyr owing to strong dynamical friction (e.g., [Patton et al. (2000)]). Thus, if it can be measured, the fraction of galaxies in physical close pairs is an excellent proxy for merger rate.
Accordingly, there have been a large number of studies which have attempted to measure close pair fraction evolution (a few examples are [Zepf & Koo (1989)], [Carlberg, Pritchet, & Infante (1994)], [Le Fèvre et al. (2000)]; see [Patton et al. (2000)] for an extensive discussion of the background to this subject). In Fig. 3, I show the fraction of MB - 5 log10 h - 19.5 galaxies in close |proj| < 20h-1 kpc pairs from [Patton et al. (2000)], [Le Fèvre et al. (2000)], and [Patton et al. (2002)]. [Patton et al. (2000)], and [Patton et al. (2002)] explore the fraction of galaxies in close pairs with velocity differences < 500 km s-1, whereas [Le Fèvre et al. (2000)] study projected galaxy pairs, and correct them for projection in a statistical way. Both studies, and indeed most other studies, paint a broadly consistent picture that the frequency of galaxy interactions was much higher in the past than at the present, and that the average ~ L* galaxy has suffered 0.1-1 major interaction between z ~ 1 and the present day. Small number statistics, coupled with differences in assumptions about how to transform pair fractions into merger rate, lead to a wide dispersion in the importance of major merging since z ~ 1.
Figure 3. The evolution of the close pair fraction. Data points show measurements of the fraction of galaxies with 1 or more neighbors within a projected distance of 20h-1kpc, corrected for projection (open points; [Le Fèvre et al. (2000)]), and within a projected distance of 20h-1kpc and a velocity separation of < 500 km s-1 (solid points; [Patton et al. (2000), Patton et al. (2002)]). The lines show the evolution of approximately equivalent measurements from the van Kampen et al. (in prep.) mock COMBO-17 catalogs: projection-corrected fraction (dotted line), the fraction of galaxies with 1 neighbor within 20h-1kpc and with velocity difference < 300 km s-1 (dashed line), and the real fraction of galaxies with 1 neighbor within 20h-1 kpc in real space.
Yet, there are significant obstacles to the interpretation of these, and indeed future, insights into galaxy major merger rate evolution. Technical issues, such as contamination from foreground or background galaxies, redshift incompleteness, and the construction of equivalent samples across the whole redshift range of interest must be thought about carefully (see, e.g., [Patton et al. (2000), Patton et al. (2002)]). Yet, it is also vitally important to build one's intuition as to how the measured quantities relate to the true quantities of interest. Work towards this goal is relatively immature, and must be an important focus of researchers in this important field in the years to come.
As a crude example of this, I carry out the simple thought experiment where we compare the pair fraction derived from projection-corrected projected pair statistics (dotted line in Fig. 3), the pair fraction derived if one used spectroscopy to keep only those galaxies with |v| < 300 km s-1 (dashed line), and the true fraction of galaxies with real space physical separation of < 20h-1 kpc (solid line). I use a mock COMBO-17 catalog under development by van Kampen et al. (in prep.; see [van Kampen, Jimenez, & Peacock (1999)] for a description of this semi-numerical technique) to explore this issue; this model is used with their kind permission. It is important to note that this simulation is still under development; the match between the observations and models at z 0.5 is mildly encouraging, although the generally flat evolution of pair fraction may not be a robust prediction of this model. Nonetheless, this model can be used to great effect to gain some insight into sources of bias and uncertainty.
The catalog is tailored to match the broad characteristics of the COMBO-17 survey to the largest extent possible (see [Wolf et al. (2003)] for a description of COMBO-17): it has 3 × 1/4 square degree fields, limited to mR < 24 and with photometric redshift accuracy mimicking COMBO-17's as closely as possible. Primary galaxies with mR < 23, 0.2 z 1.0 and MV - 19 are chosen; satellite galaxies are constrained only to have mR < 24 and |mR| < 1mag (i.e., to have a small luminosity difference). The dotted and dashed lines show the pair fraction recovered by approximately reproducing the methodologies of Le Fèvre et al. (2000; dotted line)] and Patton et al. (2000, 2002; dashed line)]. It is clear that statistical field subtraction, adopted by [Le Fèvre et al. (2000)] and others, may be rather robust, in terms of recovering the trends that one sees with the spectroscopic+imaging data. The solid line shows the fraction of galaxies actually separated by 20h-1kpc. It is clear that, at least in this simulation, many galaxies with projected close separation and small velocity difference are members of the primary galaxy's group which happen to lie close to the line of sight to the primary galaxy but are 20 kpc from the primary. In [Le Fèvre et al. (2000)], [Patton et al. (2002)], and other studies, this was often corrected for by multiplying the observed fraction by 0.5(1 + z) following the analysis of [Yee & Ellingson (1995)]; the data showed in Fig. 3 was corrected in this way. Our analysis of these preliminary COMBO-17 mock catalogs suggest that these corrections are uncertain, and that our current understanding of galaxy merger rate from close pairs may be biased. It is important to remember that the simulations discussed here are preliminary; the relationship between `observed' and true close pair fractions may well be different from the trends predicted by the model. Yet, it is nonetheless clear that further modeling work is required before one can state with confidence that one understands the implications of close pair measurements.