Directed acyclic graphs (DAGs; e.g., Greenland, et al, 1999) are a part of a formalism of causal inference from the counterfactual interpretation of causality camp. In these graphs the presence of an arrow from variable $A$ to variable $B$ asserts that variable $A$ directly causes (some change in risk of) variable $B$, and the absence of such an arrow asserts that variable $A$ does not directly cause (some change in risk of) variable $B$.
As an example, the statement "tobacco smoke exposure directly causes a change in risk of mesothelioma" is represented by the black arrow from "tobacco smoke exposure" to "mesothelioma" in the not a DAG causal diagram below.
Likewise, the statement "asbestos exposure directly causes a change in risk of mesothelioma" is represented by the black arrow from "asbestos exposure" to "mesothelioma" in the not a DAG causal graph below.
I use the term not a DAG to describe the below causal graph because of the red arrow, which I intend to assert something like "asbestos exposure causes a change in the direct causal effect of tobacco smoke exposure on risk of mesothelioma" (asbestos does physical damage to the cells of the lung that, in addition to directly causing a change in risk of mesothelioma, also renders the cells more susceptible to the carcinogenic harms of tobacco smoke exposure with the result that exposure to both asbestos and tobacco result in an increase in risk that is more than the sum of the two separate risks), and this does not quite fit with the formal meaning of causal arrows in DAGs I described at the start of my question (i.e. because the red arrow does not terminate in a variable).
How does one correctly represent interaction effects within the visual formalism of a DAG?
Greenland, S., Pearl, J., and Robins, J. M. (1999). Causal diagrams for epidemiologic research. Epidemiology, 10(1):37–48.