  Many recent numerical studies have argued that cosmic rays (CRs) from
supernovae (SNe) or active galactic nuclei (AGN) could play a crucial role in
galaxy formation, in particular by establishing a CR-pressure dominated
circum-galactic medium (CGM). But explicit CR-magneto-hydrodynamics (CR-MHD)
remains computationally expensive, and it is not clear whether those results
can be applied to simulations that do not explicitly treat magnetic fields or
resolved ISM phase structure. We therefore present an intentionally
extremely-simplified sub-grid model for CRs, which attempts to capture the key
qualitative behaviors of greatest interest for those interested in simulations
or semi-analytic models including some approximate CR effects on galactic
(>kpc) scales, while imposing negligible computational overhead. The model is
numerically akin to some recently-developed sub-grid models for radiative
feedback, and allows for a simple constant parameterization of the CR
diffusivity and/or streaming speed; it allows for an arbitrary distribution of
sources (proportional to black hole accretion rates or star-particle SNe rates
or gas/galaxy star formation rates), and interpolates between the limits where
CRs escape the galaxies with negligible losses and those where CRs lose most of
their energy catastrophically before escape (relevant in e.g. starburst
galaxies). The numerical equations are solved trivially alongside gravity in
most codes. We compare this to explicit CR-MHD simulations and discuss where
the (many) sub-grid approximations break down, and what drives the major
sources of uncertainty.
