ABSTRACT We present an analytic toy model for the radiation produced by the interaction between cold streams thought to feed massive haloes at high redshift and their hot CGM. We begin by deriving cosmologically motivated parameters for the streams, as they enter the halo virial radius, Rv, as a function of halo mass and redshift. For $10^{12}\, {\rm M}_⊙$ haloes at z = 2, we find the stream density to be $n_{\rm H,s}∼ (0.1{\!-\!}5)\times 10^{-2}\, {\rm cm}^{-3}$, a factor of δ ∼ (30–300) times denser than the hot CGM, while stream radii are in the range Rs ∼ (0.03−0.50)Rv. As streams accelerate towards the halo centre, they become denser and narrower. The stream–CGM interaction induces Kelvin–Helmholtz instability (KHI), which leads to entrainment of CGM mass by the stream and to stream deceleration by momentum conservation. Assuming the entrainment rates derived by Mandelker et al. (2020) in the absence of gravity can be applied locally at each halocentric radius, we derive equations of motion for the stream in the halo. Using these, we derive the net acceleration, mass growth, and energy dissipation induced by the stream–CGM interaction, as a function of halo mass and redshift, for different CGM density profiles. For the range of model parameters considered, we find that the interaction induces dissipation luminosities Ldiss > 1042 erg s−1 within ≲0.6Rv of haloes with $M_{\rm v}\gt 10^{12}\, {\rm M}_⊙$ at z = 2. The emission scales with halo mass and redshift approximately as $∝ M_{\rm v}\, (1+z)^2$. The magnitude and spatial extent of the emission are consistent with observed Ly α blobs, though better treatment of the UV background and self-shielding is needed to solidify this conclusion.