ar X iv : a st ro - p h / 95 05 08 0 v 1 1 7 M ay 1 99 5 Galaxy Tracers and Velocity Bias

This paper examines several methods of tracing galaxies in N-body simulations and the effects of these methods on the derived galaxy statistics. Special attention is paid to the phenomenon of velocity bias, the idea that the velocities of galaxies may be systematically different from that of the mass distribution. Using two simulations with identical initial conditions, one following a single dark matter particle fluid and the other following two particle fluids of dark matter and baryons, both collisionless and collisional methods of tracing galaxies are compared to one another and against a set of idealized criteria. None of the collisionless methods proves satisfactory, including an elaborate scheme developed here to circumvent previously known problems. The main problem is that galactic overdensities are both secularly and impulsively disrupted while orbiting in cluster potentials. With dissipation, the baryonic tracers have much higher density contrasts and much smaller cross sections, allowing them to remain distinct within the cluster potential. The question remains whether the incomplete physical model, especially the expected conversion from a collisional gas to a collisionless stellar fluid, introduces systematic biases. Statistical measures determined from simulations can vary significantly based solely on the galaxy tracing method utilized. The two point correlation function differs most on cluster scales (less than 1 Mpc) with generally good agreement on larger scales (except for one systematically biased method). Pairwise velocity dispersions show less uniformity on all scales addressed here. All tracing methods show a velocity bias to varying degrees, but the predictions are not firm: either the tracing method is not robust or the statistical significance has not been demonstrated. Though theoretical arguments suggest that a mild velocity bias should exist, simulation results are not yet conclusive. Subject headings: cosmology: large-scale structure of universe — galaxies: clustering — galaxies: formation — methods: numerical N-body simulations of large scale structure have sometimes been referred to as ‘experimental cosmology’. Indeed, at the heart of these efforts is the desire to provide stringent tests of various theories of structure development. Much progress has been made in determining which theories produce structure similar to what is observed, but a major obstacle to this progress is the identification of where galaxies would reside in a numerical simulation. Accurate identification of galaxy positions and velocities within the computer models is required in order to provide reliable estimates of important structure measurements such 1 Present address: Princeton University Observatory, Peyton Hall, Princeton, NJ 08544; [email protected] 2 Also Physics Department, University of California at Berkeley; [email protected] 3 [email protected] as the correlation function and the velocity dispersion of galaxies. Tracing galaxies is also essential for following the processes of galaxy, group, and cluster formation. As the results derived may support or reject a cosmogony, the various methods for tracing galaxies must be evaluated carefully. During the last decade, particle simulations became a standard tool for evaluating cosmological theories. Simulations were influential in shifting focus away from the hot dark matter scenario (White, Frenk, & Davis 1983) and toward the cold dark matter (CDM) scenario (Davis et al. 1985). Galaxy redshift surveys are routinely compared against computational realizations of cosmological theories in order to assess the viability of the theories (e.g., Efstathiou, Sutherland, & Maddox 1990, Vogeley et al. 1992, Fisher et al. 1995). Simulations have also played a significant role in the recent attention on the mixed dark matter scenario (Davis, Summers, & Schlegel 1992, Klypin et al. 1993). N-body calculations are now an important method for determining the predictions of a cosmological theory in the non-linear regime. Unfortunately, comparison of a computer model with observations involves several caveats, restrictions, and subtleties of interpretation that limit the range of conclusions that can be made. One of the most important to note is that by no stretch of the imagination does one form ‘galaxies’ in current cosmological simulations: the physical model and dynamic range are inadequate to follow any but the crudest of details of such complex and rich structures. What one hopes to do is find the likely sites of galaxy formation and trace their evolution. It is the statistics of these galaxy tracers that are used to evaluate the theories and thus, it is of paramount importance that the galaxy tracer population be as reliable as possible. The importance of the galaxy tracer population has been illustrated quite vividly. In early simulations of the CDM theory, Melott et al. (1983) found that the correlation function of the mass could replicate the observed correlation function of galaxies. Using more detailed simulations and an algorithm for identifying galaxy tracers, Davis et al. (1985) found that galaxies had to be more correlated than the dark matter to get an acceptable fit to the data. The excess correlation strength was termed ‘biasing’ and their results showed it to be a rather strong effect. Couchman and Carlberg (1992, hereafter CC) also modelled a CDM universe, but, using a different galaxy tracing method, reached a third conclusion. Previously, Carlberg, Couchman, & Thomas (1990) had proposed that the velocity field of galaxies could be systematically lower than that of the dark matter and dubbed this new effect velocity bias in order to differentiate it from the correlation bias. CC found a significant velocity bias such that the data could be consistent with a CDM model where the galaxies were actually slightly less correlated than the dark matter (a mild anti-bias). These claims have sparked a lot of discussion because CDM with large biasing is at odds with several measures of large scale structure such as the APM galaxy distribution (Efstathiou et al. 1990) and the COBE observations (Efstathiou, Bond, & White 1992). From a computational scientist’s point of view, one should be very uncomfortable with such a large impact on one’s conclusions based heavily on a galaxy tracer algorithm.