The baryonic Tully-Fisher Relation predicted by cold dark matter cosmogony

Abstract

Providing a theoretical basis for the baryonic Tully-Fisher Relation (BTFR; baryonic mass vs rotational velocity in spiral galaxies) in the LCDM paradigm has proved problematic. Simple calculations suggest too low a slope and too high a scatter, and recent semi-analytic models and numerical galaxy simulations typically fail to reproduce some aspects of the relation. Furthermore, the assumptions underlying one model are often inconsistent with those behind another. This paper aims to develop a rigorous prediction for the BTFR in the context of LCDM, using only a priori expected effects and relations, a minimum of theoretical assumptions, and no free parameters. The robustness of the relation to changes in key galactic parameters will be explored. I adopt a modular approach, taking each of the stand alone galaxy relations necessary for constructing the BTFR from up-to-date numerical simulations of dark halos. These relations -- and their expected scatter -- are used to describe model spirals with a range of masses, resulting in a band in the space of the BTFR that represents the current best guess for the LCDM prediction. Consistent treatment of expected LCDM effects goes a large way towards reconciling the naive slope-3 LCDM prediction with the data, especially in the range 10^9 M_sun < M_bar < 10^11 M_sun. The theoretical BTFR becomes significantly curved at M_bar > 10^11 M_sun, but this is difficult to test observationally due to the scarcity of extremely high mass spirals. Low mass gas-rich galaxies have systematically lower rotational velocity than the LCDM prediction, although the relation used to describe baryon mass fractions must be extrapolated in this regime. The fact that the BTFR slope derived here is significantly greater than in early predictions is a direct consequence of a corresponding increase in the expected sensitivity of baryon mass fraction to total halo mass.