  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.
